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Transcript
Intermediate Macroeconomics Dirk Krueger1 December 21, 2001 1 I would like to thank Charles Jones, Felix Kubler, Beatrix Pall and Tom Sargent for stimulating discussions about teaching modern macro. All remaining errors are mine. ii Contents 1 Introduction 1.1 The Scope of Macroeconomics . . . . . . . . . 1.2 US Macroeconomic Data: A Helicopter Tour 1.2.1 Real GDP . . . . . . . . . . . . . . . . 1.2.2 Digression: The Rest of the Course . . 1.2.3 Other Macroeconomic Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 2 3 6 2 National Income and Product Accounting (NIPA) 2.1 Gross Domestic Product (GDP) . . . . . . . . . . . . 2.1.1 Computing GDP through Production . . . . 2.1.2 Computing GDP through Spending . . . . . 2.1.3 Computing GDP through Income . . . . . . . 2.2 Price Indices . . . . . . . . . . . . . . . . . . . . . . 2.3 From Nominal to Real GDP . . . . . . . . . . . . . . 2.4 Measuring In‡ation . . . . . . . . . . . . . . . . . . . 2.5 Measuring Unemployment . . . . . . . . . . . . . . . 2.6 Measuring Transactions with the Rest of the World . 2.7 Appendix A: More on Growth Rates . . . . . . . . . 2.8 Appendix B: Chain-Weighted GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 11 12 13 16 19 20 21 22 23 25 27 3 Economic Growth 3.1 Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . . . 3.1.1 Discrete vs. Continuous Time . . . . . . . . . . . . . . . . 3.1.2 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Some Useful Facts about Logs . . . . . . . . . . . . . . . 3.1.4 Growth Rates (once again) . . . . . . . . . . . . . . . . . 3.1.5 Growth Rates of Functions . . . . . . . . . . . . . . . . . 3.1.6 Simple Di¤erential Equations and Constant Growth Rates 3.2 Growth and Development Facts . . . . . . . . . . . . . . . . . . . 3.3 The Solow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Setup of the Basic Model and Model Assumptions . . . . 3.3.3 Analysis of the Model . . . . . . . . . . . . . . . . . . . . 3.3.4 Introducing Growth . . . . . . . . . . . . . . . . . . . . . 33 33 33 33 34 35 35 36 37 43 43 44 46 50 iii . . . . . . . . . . . . . . . CONTENTS iv . . . . . . . . . . . . . . 55 65 68 73 76 76 77 80 81 82 82 84 86 88 4 Business Cycle Fluctuations 4.1 Potential GDP and Aggregate Demand . . . . . . . . . . . . . . 4.2 The IS-LM Framework . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 The Balance of Income and Spending: Keynesian Cross and Multiplier . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Investment, the Interest Rate and the IS Curve . . . . . . 4.2.3 The Demand for Money and the LM-Curve . . . . . . . . 4.2.4 Combination of IS-Curve and LM-Curve: Short-Run Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Monetary and Fiscal Policy in the IS-LM Framework . . . 4.3 The Aggregate Demand Curve . . . . . . . . . . . . . . . . . . . 4.4 Unemployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Concepts and Facts . . . . . . . . . . . . . . . . . . . . . 4.4.2 Some Theory and the Natural Rate of Unemployment . . 4.4.3 Unemployment and the Business Cycle . . . . . . . . . . . 4.5 The Price Adjustment Process . . . . . . . . . . . . . . . . . . . 4.5.1 Aggregate Demand, Potential GDP and the Price Adjustment Process . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Fiscal Policy . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Stabilization Policy . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Aggregate Demand Shocks and Their Stabilization . . . . 4.6.2 Price Shocks and Their Stabilization . . . . . . . . . . . . 4.7 Real Business Cycle Theory . . . . . . . . . . . . . . . . . . . . . 89 89 93 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.3.5 Analysis of the Extended Model . . . . . . . 3.3.6 Evaluation of the Solow Model . . . . . . . . The Convergence Discussion . . . . . . . . . . . . . . Growth Accounting and the Productivity Slowdown Ideas as Engine of Growth . . . . . . . . . . . . . . . 3.6.1 Technology . . . . . . . . . . . . . . . . . . . 3.6.2 Ideas . . . . . . . . . . . . . . . . . . . . . . . 3.6.3 Data on Ideas . . . . . . . . . . . . . . . . . . Infrastructure . . . . . . . . . . . . . . . . . . . . . . 3.7.1 Cost of Investment . . . . . . . . . . . . . . . 3.7.2 Bene…ts of Investment . . . . . . . . . . . . . Endogenous Growth Models . . . . . . . . . . . . . . Neutrality of Money . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 106 110 117 119 123 124 125 128 131 132 138 138 141 141 142 145 148 5 Microeconomic Foundations of Macroeconomics 151 5.1 Consumption Demand . . . . . . . . . . . . . . . . . . . . . . . . 151 5.1.1 Data on Consumption . . . . . . . . . . . . . . . . . . . . 151 5.1.2 The Keynesian Aggregate Consumption Function and the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 5.1.3 The Life Cycle/Permanent Income Model of Consumption 156 CONTENTS 5.2 v Investment Demand . . . . . . . . . . . . . . . . . . . . . . . . . 170 5.2.1 Facts about Investment . . . . . . . . . . . . . . . . . . . 170 5.2.2 The Theory of Investment . . . . . . . . . . . . . . . . . . 173 6 Trade, Exchange Rates & International Financial Markets 6.1 Terms of Trade, the Nominal and the Real Exchange Rate . . 6.2 E¤ects of the Real Exchange Rate on the Trade Balance . . . 6.3 Determinants of the Real Exchange Rate . . . . . . . . . . . . 6.3.1 Purchasing Power Parity . . . . . . . . . . . . . . . . . 6.3.2 Real Exchange Rates and Interest Rates . . . . . . . . 6.4 The International Financial System . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 179 183 184 184 186 187 7 Fiscal and Monetary Policy in Practice 7.1 Fiscal Policy . . . . . . . . . . . . . . . 7.1.1 Data on Fiscal Policy . . . . . . 7.1.2 A Few Theoretical Remarks . . . 7.2 Monetary Policy . . . . . . . . . . . . . . . . . . . . . 189 189 189 195 199 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi CONTENTS Chapter 1 Introduction 1.1 The Scope of Macroeconomics Macroeconomics wants to explain the evolution of the main economic aggregates over time. We are interested in why total production (real GDP) grows over time on average and why it shows sizeable ‡uctuations around its long-run growth trend. We want to understand what causes unemployment and in‡ation, how interest rates behave and what causes a trade de…cit. In contrast to microeconomics, where the object of interest is a single …rm or household, in macroeconomics we study the whole economy. Our reasoning, however, will be based on the insights that microeconomic theory provides (therefore the prerequisite requirements for this course). Why should we care about macroeconomics. I could think of three good reasons 1. It a¤ects us on a day-to-day basis: A rise in the interest rate makes loans for cars more expensive, raises the interest rate that you pay on a mortgage and (usually) has a negative e¤ect on stock prices. A decline in production leads to people being laid o¤ -and that could be a member of your family. High in‡ation wipes out part of the value of your savings. The list goes on and on.... 2. A good understanding of macroeconomics is essential for policy makers. Politicians can change …scal policy (how much the government spends and how much it taxes you) and central bankers (Alan Greenspan and his Federal Reserve Board) can change monetary policy (how much currency to issue and how high to set the Federal Funds Rate -an important interest rate). As we will see later …scal and monetary policy can have good and bad e¤ects on the economy. It is crucial that policy makers and central bankers understand macroeconomic data and macroeconomic theory to make an informed decision about when and to what extent to change monetary and …scal policy. 1 CHAPTER 1. INTRODUCTION 2 3. A good understanding is important for us as good citizens because it helps us to understand and critic what politicians, central bankers and the press tell us about the economy and what should be done to improve it. But let’s …rst look at some data to see what it is that we’re talking about, or, to speak with Sherlock Holmes Data! Data! Data! I can’t make bricks without clay. 1.2 1.2.1 US Macroeconomic Data: A Helicopter Tour Real GDP When economists say that the US economy grew 2% last year they usually mean: real Gross Domestic Product (GDP) was 2% higher in 2000 than in 1999. Let us …rst de…ne what nominal GDP is. De…nition 1 Nominal GDP is the total value of goods and services produced in an economy during a particular time period. Note that when talking about GDP we have to specify the GDP of what economy (e.g. the US) for what time period (e.g. a year, say 2000) we mean. Nominal GDP is measured in dollars. Since prices tend to increase over time (ask your parents how much college tuition cost 30 years ago), so will nominal GDP. To measure the economic activity of a country we are really interested in how many real goods and services were produced in the economy. This is measured by real GDP. Real GDP = Nominal GDP Price Level We will discuss how to compute the “Price Level” in the next section. Finally, a growth rate of a variable is computed as follows. Let Yt denote real GDP in period t (i.e. Y2000 is real GDP for the year 2000). Then the growth rate of real GDP from period t ¡ 1 to period t is computed as gY (t ¡ 1; t) = Yt ¡ Yt¡1 Yt¡1 As an example, suppose real GDP in 1988 equals $ 585 and $ 605 in 1989, then the growth rate of real GDP between 1988 and 1989 would equal gy (1988; 1989) = $605 ¡ $585 = 0:034 = 3:4% $585 This is the number that people mean when they say that the economy grew by 3:4% in 1989. 1.2. US MACROECONOMIC DATA: A HELICOPTER TOUR 3 Let’s look at some data for real GDP. The solid line in Figure 1 shows the evolution of real GDP for the US economy from 1967 to 2001.1 We have two principal observations 1. Real GDP grows over time. If GDP would have grown at 2.75%, then the graph of real GDP would have looked like the dotted line. The dotted line is called “Trend”, because it shows how real GDP evolved on average. 2. Actual real GDP exhibits -occasionally sizeable- deviations from its long term growth trend. These ‡uctuations are called business cycles. Figure 2 shows these ‡uctuations in more detail. The dotted line at 0 corresponds to the trend. When the solid line takes the value -0.061 as in 1983, this means that actual real GDP was 6.1% below the trend. Periods in which real GDP actually declines are called recessions, and, if these declines are extremely severe, depressions.2 From 1967 until 2001 the US experienced 5 recessions.3 Note that, although recessions are recurrent events, the exact timing of a recession is extremely hard to forecast. 1.2.2 Digression: The Rest of the Course At this stage let’s have a short preview of the course. The two main sections, Sections 3 and 4 deal exactly with the two observations we made about Figure 1: In Section 3 we will study why, on average, the economy grows over time. This area of study is called growth theory and we will discuss the neoclassical growth model. As a sneak preview, the economy grows over time because: 1 The data have quarterly frequency, i.e. there one observation for real GDP for each quarter. The …rst observation is the GDP for the …rst three months of 1967, the last observation is the GDP for April to June 2001. The data are then converted to yearly numbers (basically by multiplying them by 4). If you are interested in the actual data, on the WWW go to http://www.economagic.com/em-cgi/data.exe/fedstl/gdp96+1#DataWhat is actually plotted is the natural logarithm of real GDP, for the following reason. If GDP grows at a constant rate g; then the log of GDP is a straight line with slope g: By plotting the log of GDP we can draw the long-term growth trend as a straight line (rather than an exponential function). This technique is used quite often by economists. Hall and Taylor plot GDP instead of log GDP, but use a logarithmic scale on the y-axis on p. 6 (observe that the distance between 3500 and 4000 is bigger than between 6000 and 6500 on the y-axis; this is what a log-scale does). Both tricks are equivalent. 2 The US economy as well as other economies in the world experienced a depression, the so-called great depression, from 1929 to 1932. 3 One de…nition of a recession is “a decline in two subsequent quarters of real GDP”. If you are interested in more detailed information about the timing and length of expansions and recessions, visit the webpage of the National Bureau of Economic Research (NBER) at http://www.nber.org/cycles.html. Note that, according to the o¢cial de…nition of a recession, the U.S. economy is not currently in a recession, as real GDP growth has not been negative in the …rst two quarters of 2001. CHAPTER 1. INTRODUCTION 4 Real GDP in the United States 1967-2001 9.2 Log of real GDP 9 8.8 Trend 8.6 GDP 8.4 8.2 8 1970 1975 1980 1985 Year 1990 1995 Figure 1.1: 1. the population grows. A higher population means that a bigger labor force is available for the production of goods and services. 2. more capital is accumulated. Over time, more and more machines and other equipment are used in the production process 3. there is technological progress (e.g. the development of faster and faster computer chips) makes capital and labor more productive in the production process. In Section 4 we will study why there are business cycles, i.e. why the economy ‡uctuates around its long-term growth trend. In contrast to growth theory, where the level of agreement between economists is fairly high, in business cycle theory there is substantial disagreement about why business cycles exist and what the government can do about them. Again a brief sneak preview: 2000 Percentage Deviation of Real GDP from Trend 1.2. US MACROECONOMIC DATA: A HELICOPTER TOUR 5 Expansions and Recessions 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 1970-71 recession 1974-75 recession 1970 1975 1990-91 recession 1980-82 back-to-back recessions 1980 1985 1990 1995 Year Figure 1.2: 1. in this course we mostly will follow Hall and Taylor (and many others) and assume that in the short run wages and/or prices are “sticky”, i.e. not ‡exible to adjust immediately to shocks hitting the economy. Potential shocks could come from the private sector of the economy (a certain drop of households’ willingness to buy cars), from world markets (remember the oil price shocks in 1973 and 1980) or from changes in monetary and …scal policy. The results are business cycles. 2. an alternative view holds that business cycles originate from “technology shocks” (e.g. in certain years we have bad weather and that makes production, in particular agricultural production, more di¢cult). Prices and wages are fully ‡exible even in the short run. People respond optimally and work more when the conditions are such that they are productive (in years of good technology shocks) and less when they are not so productive. 2000 CHAPTER 1. INTRODUCTION 6 Hence in good years workers supply a lot of labor and production (real GDP) is high, in years with bad technology workers supply little labor and real GDP is low. This view has become known as “Real Business Cycle Theory” (“Real” because the shocks underlying business cycles are technology shocks).4 The dispute between these two schools is not only theoretical. Based on theory, economists from both camps have di¤erent views about economic policy. In RBC-theory business cycles arise because households react optimally to technology shocks. Hence there is no role for government policy to improve matters. If business cycles come about because prices and wages can’t adjust in the short run (as in the …rst view), there may be a role for an active monetary and …scal policy to reduce the economic ‡uctuations. Common among both schools is that they both use models -abstract simple descriptions of the economy, either with equations or graphs- to explain business cycles and to argue for or against a certain policy. We will follow this methodological approach. 1.2.3 Other Macroeconomic Aggregates Why are business cycles bad? Because if real production declines, workers get laid o¤ and the unemployment rate increases. We should expect that the unemployment rate follows the path of real output rather closely. Let us …rst de…ne the unemployment rate. De…nition 2 The labor force is the number of people, 16 or older, that are either employed or unemployed but actively looking for a job. The unemployment rate is given by Unemployment Rate = number of unemployed people labor force In Figure 3 we plot the unemployment rate for the US from 1967 to 2001.5 We see that in recessions the unemployment rate increases, whereas in expansion it decreases. A variable that shows such a behavior is called “countercyclical”: it is high when real GDP is low (relative to trend) and it is low when real GDP is high. Also note that currently unemployment is at its lowest level since 1970. Another important macroeconomic variable is the in‡ation rate. It measures the growth rate of the price of a particular basket of goods and services.6 4 The founders of RBC-theory are Finn Kydland from Carnegie Mellon University and Ed Prescott from the University of Minnesota -incidentally my Ph.D. thesis advisor. 5 The unemployment rate is measured by the Bureau of Labor Statistics (BLS). Go to their homepage at http://stats.bls.gov/top20.html if you want to have a look at the original data. 6 There are several measures of the in‡ation rate. They are distinguished by what goods and services are included in the basket of goods whose price is measured. The two most important indexes for in‡ation are the Consumer Price Index (CPI) and the GDP de‡ator. Both will be discussed in the next section. 1.2. US MACROECONOMIC DATA: A HELICOPTER TOUR Unemployment Rate for the US 1967-2001 12 1980-82 back-to-back recessions 11 1974-75 recession 10 Unemployment Rate 7 9 1990-91 recession 8 7 1970-71 recession 6 5 4 3 2 1970 1975 1980 1985 Year 1990 1995 Figure 1.3: Let Pt be the price level in period t: Then the in‡ation rate between periods t ¡ 1 and t is given by ¼t = gP (t ¡ 1; t) = Pt ¡ Pt¡1 Pt¡1 Figure 4 shows the in‡ation rate for the US economy from 1967 to 2001. We see that in‡ation rates were higher and more volatile in the 70’s and early 80’s than in the 90’s. Combining …gure 2 and 4 it is not apparent whether the in‡ation rate is procyclical or countercyclical. Interest Rates are important macroeconomic variables because they determine how costly it is to take out a loan to buy a car, a house, stocks, or, for …rms, to …nance new equipment. How are interest rates computed. Suppose in 2000 CHAPTER 1. INTRODUCTION 8 Inflation Rate for the US 1967-2001 16 14 Inflation Rate 12 10 8 6 4 2 0 1970 1975 1980 1985 Year 1990 1995 Figure 1.4: period t ¡ 1 you borrow the amount $Bt¡1 . The loan speci…es that in period t you have to repay $Bt : In general $Bt will be bigger than Bt¡1 (since you have to repay Bt¡1 ; the so-called principal, and the interest on the loan): The nominal interest rate on the loan from period t ¡ 1 to period t, it ; is computed as Bt ¡ Bt¡1 it = Bt¡1 This is called a nominal interest rate because it does not take into account in‡ation. The real interest rate rt is de…ned as the di¤erence between the nominal interest rate and the in‡ation rate: rt = it ¡ ¼t Note that nominal interest rates historically tend to rise with in‡ation: lenders demand a higher nominal interest rate in times of high in‡ation as compensation 2000 1.2. US MACROECONOMIC DATA: A HELICOPTER TOUR 9 for the loss of purchasing power of their money, due to high in‡ation. Example: In the year 2000 you borrow $15; 000 to buy a new car and the bank asks you to repay $16; 500 exactly one year later. Then the yearly nominal interest rate from 2000 to 2001 is i2001 = $16; 500 ¡ $15; 000 = 0:1 = 10% $15; 000 Now suppose the in‡ation rate is 3% in 2001. Then the real interest rate equals 10% ¡ 3% = 7% Note that whenever stating an interest rate, it is crucial to state the length of the period with respect to which it applies, i.e. whether it is a yearly, a quarterly, a monthly or a daily interest rate. In Figure 5 the nominal interest rate for the US economy from 1967 to 2001 is plotted.7 Comparing Figure 2 and Figure 5 indicates that interest rates tend to be procyclical: they increase during expansions and fall during recessions. Now we have a rough idea about how the most important macroeconomic variables evolved over the last 30 years. Now we turn to a discussion how these variables are actually measured in the data. 7 There are many di¤erent interest rates. rate that banks charge each other for loans So this is a daily interest rate. This daily yearly interest rate by “multiplying” the daily http://www.stls.frb.org/fred/data/irates.html. The Federal Funds rate is the interest from one evening to the next morning. interest rate has been converted into a rate by 365. For the original data go to CHAPTER 1. INTRODUCTION 10 Federal Funds Interest Rate 1967-2001 20 Nominal Interest Rate in % 18 16 14 12 10 8 6 4 2 0 1970 1975 1980 1985 Year Figure 1.5: 1990 1995 2000 Chapter 2 National Income and Product Accounting (NIPA) In this section we look in detail at how the macroeconomic aggregates whose behavior over the last thirty years we studied in the last section are de…ned and measured in the data. We will start with gross domestic product (GDP). 2.1 Gross Domestic Product (GDP) We de…ned nominal and real GDP in the last section. Now will we discuss how we measure these entities in the data. Nominal GDP can be measured in three di¤erent ways which all lead to the same result:1 1. We can measure nominal GDP by adding together the value of production in all di¤erent industries in the economy. 2. We can measure nominal GDP by adding together the spending on goods and services of the di¤erent sectors of the economy (households, …rms, the government and foreigners). 3. We can measure nominal GDP by adding together all the income that is generated from the production process: wages, salaries and pro…ts. In fact, the Bureau of Economic Analysis (BEA), the US government agency that is responsible for measuring GDP, does calculate GDP in these three different ways and makes sure that the three numbers they get coincide (as they should according to accounting principles). 1 The fact that the total value of production always equals the total value of spending and always equals the total income is called an identity, it is inevitably true as a consequence of accounting principles. 11 12CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) 2.1.1 Computing GDP through Production We want to calculate nominal GDP by adding together the value of production for all di¤erent industries in the economy, agriculture, mining, construction, manufacturing etc. Can we just add together all those industries’ sales? Consider the following example: US steel produces a ton of steel and sells it to GM for $1500. GM then uses this steel to build a car that it sells for $10,000. Assume for the moment that a car can be produced only with steel and labor. Should the contribution to GDP be the whole $11,500, the sum of total sales? No, since the steel has been counted double; once when it was sold from US Steel to GM and once when it, as a part of the car, was sold by GM. But it was only produced once, so we should only count it once. This is achieved by the concept of value added. It basically measures how much a …rm, in its production process, added to the value of the intermediate goods it purchased from its suppliers. Roughly, value added of a …rm equals its revenues from sales minus the purchases of intermediate goods -goods that the …rm bought from other …rms and used to produce its own products. For the example then, the contribution should be only $1500 (from the sale of steel to GM, the value added of US Steel) plus $8500 (the value added of GM, equal to the total sale of $10,000 minus the purchase of the intermediate good steel for $1,500). So when we measure nominal GDP through production, we sum up the value added of all industries in the economy, because the value added (and not the sales) are the correct contributions of the industries to production. Table 1 shows the contribution of di¤erent industries to nominal GDP for 1999. The numbers in column 2 are in billions of dollars.2 Table 1 Industries Total Nom. GDP Agriculture, Forestry, Fishing Mining Construction Manufacturing Transportation, Publ. Utilities Wholesale Trade Retail Trade Finance, Insurance, Real Estate Services Government Statistical Discrepancy Value Added 9,299.2 125.4 111.8 416.4 1,500.8 779,6 643.3 856.4 1,792.1 1,986.9 1,158.4 -71.9 in % of Tot. Nom. GDP 100.0% 1.3% 1.2% 4.5% 16.1% 8.4% 6.9% 9.2% 19.3% 21.4% 12.5% -0.8% Note that total nominal GDP in 1999 was $US 9,299.2 billion, or $US 9,299,200,000,000. To make this number a little less intimidating, economists 2 All data in this section come from the Economic Report of the President (2001). 2.1. GROSS DOMESTIC PRODUCT (GDP) 13 often report GDP per capita. On average in 1999 the population of the US was 275,372,000. Hence GDP per capita in 1999 amounted to $33,769.59. In 1999 every person in the US, from the newborns to the old, produced on average about $34,000 worth of goods and services. 2.1.2 Computing GDP through Spending Nominal GDP can also be computed by summing up the total spending on goods and services by the di¤erent sectors of the economy. Formally, let C I G X M Y = = = = = = Consumption (Gross) Investment Government Purchases Exports Imports Nominal GDP Then Y = C + I + G + (X ¡ M ) Let us turn to a brief description of the components of GDP: ² Consumption (C) is de…ned as spending of households on all goods, such as durable goods (cars, TV’s, Furniture), nondurable goods (food, clothing, gasoline) and services (massages, …nancial services, education, health care). The only form of household spending that is not included in consumption is spending on new houses.3 Spending on new houses is included in …xed investment, to which we turn next. ² Gross Investment (I) is de…ned as the sum of all spending of …rms on plant, equipment and inventories, and the spending of households on new houses. It is broken down into three categories: residential …xed investment (the spending of households on the construction of new houses), nonresidential …xed investment (the spending of …rms on buildings and equipment for business use) and inventory investment (the change in inventories of …rms). To make the concept of investment clearer, we have to take a little digression about stocks and ‡ows. A stock is a quantity measured at a given point in time. A ‡ow is a quantity measured per unit of time. As an example consider …lling a bathtub with water. The amount of water in the tub is a stock -we say that the bathtub contains 3 What about purchases of old houses? Note that no production has occured (since the house was already built before). Hence this transaction does not enter this years’ GDP. Of course, when the then new house was …rst bought by its …rst owner it entered GDP in the particular year. 14CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) 50 gallon of water. The amount of water ‡owing out of the faucet is a ‡ow -we say that 2 gallon of water per minute ‡ow into the tub. Note that we measure the stock by gallon, the ‡ow by gallon per minute. Often stocks and ‡ows are related. In our example the stock of water in the tub equals the accumulated ‡ow of water out of the faucet. The same is true with investment and the capital stock. The capital stock of an economy is the typical economic example of a stock, whereas investment, like GDP and its other components consumption, government purchases etc. are ‡ow variables.4 The capital stock is the total amount of physical capital in the economy, including all buildings and equipment. Part of the capital stock wears out every period in the production process, a process called depreciation (which is again a ‡ow variable). We have the following relationship between the capital stock, gross investment and depreciation: Capital Stock at end of this period = Capital Stock at end of last period +Gross Investment in this period ¡Depreciation in this period We de…ne net investment as Net Investment = Gross Investment ¡ Depreciation and therefore Net Investment = Capital Stock at end of this period ¡Capital Stock at end of last period Note that what enters nominal GDP is gross, not net investment, but that net investment in this period equals the change of the capital stock from the end of last to this period. What residential and nonresidential …xed investment are and why they are included in nominal GDP is rather obvious. So let’s spend some time to understand inventory investment. Suppose in 1999 Ford produces a car that you purchase in 1999. Then your spending on the car enters GDP as consumption under C: But now suppose Ford produces the car and puts it in its stock for sale in 2000. Since the car is not sold yet, it doesn’t enter GDP as consumption in 1999. But Ford’s production activity is the same, no matter whether the car was sold or not in 1999, so the contribution to GDP should be the same. The key is inventory investment: By producing now and putting the car in its stock, Ford increased its inventory by one car, and the statisticians count this as investment in inventories. By the same token as before Inventory Investment = Stock of Inventories at end of this year ¡Stock of Inventories at the end of last year 4 Remember the de…nition of nominal GDP: it is the total value of goods and services produced in an economy during a particular time period, i.e measured in units per time period. 2.1. GROSS DOMESTIC PRODUCT (GDP) 15 Sometimes the variable …nal sales is reported in the news. (Nominal) …nal sales equal nominal GDP minus inventory investment. ² Government spending (G) is the sum of federal, state and local government purchases of goods and services. Note that government spending does not equal total government outlays: transfer payments to households (such as welfare, social security or unemployment bene…t payments) or interest payments on public debt are part of government outlays, but not included in government spending G: ² As an open economy, the US trades goods and services with the rest of the world. Exports (E) are deliveries of US goods and services to the rest of the world, imports (M) are deliveries of goods and services from other countries of the world to the US. Why are imports subtracted from exports when computing GDP. Suppose Boeing buys 4 jet engines from the British company Rolls Royce, puts them into a Boeing 747 and sells the aircraft to the French airline Air France. What has been produced in the US was the plane, excluding the engines. So we count the plane as exports out of the US, the engines as import into the US and the net contribution to GDP is (X ¡M ), that is, exports minus imports. The quantity (X ¡M ) is also referred to as net exports or the trade balance. We say that a country (such as Germany) has a trade surplus if exports exceed imports, i.e. if X ¡ M > 0. A country has a trade de…cit if X ¡ M < 0; which was the case for the US in recent years. In Table 2 you can see the composition of nominal GDP for 1997, broken down to the di¤erent spending categories discussed above. Again the numbers are in billion US dollars. Table 2 Total Nom. GDP Consumption Durable Goods Nondurable Goods Services Gross Investment Nonresidential Residential Changes in Inventory Government Purchases Federal Government State and Local Government Net Exports Exports Imports Final Sales in billion $ 9,299.2 6,268.7 761.3 1,845.5 3,661.9 1,650.1 1,203.1 403.8 43.3 1,634.4 586.6 1,065.8 -254.0 990.2 1,244.2 9,255.9 in % of Tot. Nom. GDP 100.0% 67.4% 8.2% 19.8% 39.3% 17.7% 12.9% 4.3% 0.5% 17.6% 6.3% 11.5% -2.7% 10.6% 13.4% 99.5% 16CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) 2.1.3 Computing GDP through Income The production of goods and services generates income, either in the form of wages and salaries for workers, or in the form of pro…ts for individuals running a business. This fact provides a third way of computing nominal GDP. The broadest measure of the total incomes of all Americans is called national income. It is closely related, but not equal to nominal GDP. Remember that US GDP is the value of goods and services produced in the US. Some people in this country are not Americans, so, although they contribute to US GDP, their income is not part of national income. On the other hand there are Americans who produce goods and services abroad, so they don’t contribute to US GDP, but their income is part of national income. When we add to GDP factor income from the rest of the world (income of Americans not earned in America) and subtract factor income to the rest of the world (income of Non-Americans earned in the US, like my salary) we arrive at Gross National Product (GNP). GNP is the value of all goods and services produced by Americans, whereas GDP is the value of all goods and services produced in America. There are other parts of GNP that are not part of national income. First we have to subtract depreciation, Since depreciation of capital is a cost of producing the output of the economy, subtracting depreciation shows the net result of economic activity. GNP minus depreciation equals Net National Product (NNP). From NNP we subtract sales and excise taxes to obtain national income.5 This is due to the fact that NNP is measured in terms of the prices that …rms receive for their products, but only that part of these prices which does not go to the government becomes income of households. So the connection between GDP and national income is given by (in brackets the numbers for the US in 1999, in billion $US). Gross Domestic Product (9,299.2) +Factor Income from abroad (305.9) ¡Factor Income to abroad (316.9) = Gross National Product (9,288.2) ¡Depreciation (1,161.0) = Net National Product (8,127.1) ¡Sales and Excise Taxes (718.1) ¡Other Adjustments6 (-3.8) = National Income (7,469.7) National Income is divided into …ve components, depending on the way the income is earned: 5 Other minor corrections of NNP to obtain national income are the following. To NNP we add net subsidies of the government to government businesses, and we substract business transfers (gifts of businesses) and statistical discrepancy. These adjustments are of minor importance. 2.1. GROSS DOMESTIC PRODUCT (GDP) 17 1. Compensation of Employees: wages, salaries and fringe bene…ts earned by workers 2. Proprietors’ Income: income of noncorporate business, such as small farms and law partnerships 3. Rental Income: income that landlords receive from renting, including the “imputed” rent that homeowners pay themselves, less expenses on the house, such as depreciation 4. Corporate Pro…ts: income of corporations after payments to their workers and creditors 5. Net interest: interest paid by domestic businesses plus interest earned from foreigners Commonly the …rst component is called labor income, components 2 to 5 together are called capital income.7 The labor share is de…ned as the fraction of national income that goes to labor income, the capital share is de…ned as the fraction of national income that goes to capital income. Formally Labor Share = Capital Share = Labor Income National Income Capital Income National Income Obviously, since national income equals labor income plus capital income, the labor share and the capital share sum to 1. In Table 3 you can …nd national income and its component for the US in 1999 Table 3 National Income Compensation of Employees Proprietors’ Income Rental Income Corporate Pro…ts Net Interest Billion $US 7,469.7 5,299.8 663.5 143.4 856.0 507.1 % of National Income 100.0% 71.0% 8.9% 1.9% 11.5% 6.8% We see that for 1999 the labor share equals 71% and the capital share equals 29%. Finally, let us relate national income to two other, commonly used income concepts that may coincide more with your common understanding about what the income of a household (or in our case the income of all households) is. A series of adjustments takes us from national income to personal income, the 7 There is some ambiguity about counting proprietors’ income as capital income, since arguably the labor of the farmer is one of the most important inputs to the farms’ production of agricultural products. 18CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) income that households and noncorporate businesses receive. First we have to reduce national income by that fraction of corporate pro…ts that are not paid out in the form of dividends. This entity is called retained earnings. Second we have to subtract contributions for social insurance (the amount paid to the government for social security and medicare). Third, we want to include interest payments that households receive, rather than interest payments that businesses pay. This is accomplished by reducing national income by net interest paid by businesses and adding personal interest income. Finally we add to national income transfers from the government and businesses to households, such as social security bene…ts and pensions paid by …rms to their retired employees. The relation between national income and personal income is then given by (in brackets again the numbers for 1999 in billion $US) National Income (7,469.7) ¡Retained Earnings (485.7) ¡Contributions for Social Insurance (662.1) ¡Net Interest (507.1) +Personal Interest Income (963.7) +Government and Business Transfers (1,016.2) = Personal Income (7,789.6) Finally, we arrive at Disposable Personal Income (the income that households and noncorporate businesses can spend, after having satis…ed their tax obligations) by subtracting from personal income personal tax and nontax payments (such as parking tickets) to the government: Personal Income (7,789.6) ¡Personal Tax and Nontax Payments (1,152.0) = Disposable Personal Income (6,637.6) This concludes the discussion of how nominal GDP is measured. As you see from the numbers for 1999 (and as you will see in the problem sets) all three methods indeed lead to the same result. One last, but very important fact follows from the equivalence of GDP measured by spending and measured by income. For simplicity let us consider an economy without government and international trade.8 Saving (S) is de…ned as income minus consumption, or S =Y ¡C But from the spending side of GDP we know that Y =C +I 8 Hall and Taylor show the argument that will follow for the general case with government and international trade. The reader is refered to the book for details. 2.2. PRICE INDICES 19 (remember that we assumed that G = X = M = 0). Substituting for Y in the …rst equation we get S = Y ¡C = C+I ¡C = I Hence saving equals investment. This is again an accounting identity, it is always true. Note that this identity of saving and investment also holds for the general case with government and foreign trade, with saving and investment rede…ned to account for the presence of the government and other countries. It is a crucial identity that we will use over and over again in growth theory and business cycle theory. 2.2 Price Indices To compute real GDP we divide nominal GDP by the “Price Level”. To compute the in‡ation rate we need price levels in two di¤erent periods. In this section we discuss how we measure the “Price Level”. In general economists measure the price level by a price index. A price index is a ratio between the price of a particular basket of goods in period t and the price of the same basket in a base period, say period 0: There are two important questions involved in constructing a price index: a) what period to chose as base period b) what basket of goods to chose. Let’s consider a very simple economy in which people just produce and buy two goods, say hamburgers and coke. We denote by ht the amount of hamburgers consumed (and produced) in period t; and by ct the amount of coke consumed in period t: Also let Pht be the price of one hamburger in period t and pct the price of one bottle of coke in period t: Let (h0 ; c0 ; ph0 ; pc0 ) denote the same variables at period 0: Now let’s ask ourselves how one would measure the price level in period t as compared to period 0; which we will take as our base period? One option is to compare how expensive the basket of goods consumed in period 0 are in period t: The result is Lt = pht h0 + pct c0 ph0 h0 + pc0 c0 Such a price index is called a Laspeyres price index. If, on the other hand, we take as our basket the goods purchased in period t; then we have P at = pht ht + pct ct ph0 ht + pc0 ct Such a price index is called a Paasche price index. It turns out that all price indices actually used in practice to compute real GDP or the in‡ation rate are either Laspeyres or Paasche price indices. Before turning to this point, a brief 20CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) comment about these indices. Unfortunately both have their problems.9 The problem with the Laspeyres price index is that it tends to overstate in‡ation by assuming that households buy the same basket of goods in period t as in period 0: But as prices change from period 0 to period t; consumers tend to substitute goods that have become relatively more expensive from period 0 to period t with goods that have become relatively less expensive. By holding the basket of goods …xed at the basket bought in period 0; the Laspeyres price index ignores this substitution e¤ect, which tends to lead to an overstatement of in‡ation. Now let’s look at the Paasche price index. Consider the following scenario: suppose a virus is detected in all coke bottles in the country at period t; so that at period t no coke is produced (and the price of the few bottles in the stores from last year sky-rockets). And suppose that the price for hamburgers stays constant between period 0 and t: What would the Paasche index say about the price level in period as opposed to period 0: Since the Paasche index uses the basket of goods in period t; and since no coke is produced in period t; the price change for coke does not have any e¤ect, and the Paasche index would be at P at = 1 (under the assumption that hamburger prices have remained constant). But would we really think that the situation just described is one in which prices have remained constant, as the Paasche index indicates. In general, because of this problem the Paasche index tends to understate in‡ation. But now let’s leave the general theory of price indices and talk about real GDP and in‡ation 2.3 From Nominal to Real GDP Real GDP is the meant to measure the total production of goods and services in physical units. But how does one add 10 cars, twelve haircuts and a cruise missile together to one number? What statisticians do in practice to determine real GDP is the following: they pick a base year, say 1996. The contribution of computers to real GDP in 2000 is then computed as follows: take the dollar amount spent on computers in 2000 and divide by the price of computers in 2000 relative to 1996 (i.e. divide by the price in 2000 and multiply by the price in 1996). The result the total value of computers sold in 2000 in prices of 1996. Summing up all goods and commodities, evaluated at their 1996 prices, yields real GDP. Note that for the base year nominal and real GDP always coincide. The ratio between nominal and real GDP turns out to be a price index, the so-called GDP-de‡ator: GDP de‡ator = Nominal GDP Real GDP 9 In fact, the problem of how to construct an ideal price index is a deep methological problem, know as the index number problem. It has not been, and in fact can’t be fully resolved. Also it is hard to say which of the two indices discussed is superior. 2.4. MEASURING INFLATION 21 To see why this is, suppose again that our economy produces only hamburgers and coke. Nominal GDP in 2000 would be given by Nominal GDP = h2000 ph2000 + c2000 pc2000 Real GDP would be given by (assuming 1996 is the base year) Real GDP = h2000 ph1996 + c2000 pc1996 From the previous formula we get GDP de‡ator = h2000 ph2000 + c2000 pc2000 h2000 ph1996 + c2000 pc1996 This should look familiar to you; in fact the GDP de‡ator is a Paasche price index; compare this formula to the one for a Paasche price index in the previous section. 2.4 Measuring In‡ation Remember that the in‡ation rate from period t ¡ 1 to period t was de…ned as ¼t = Pt ¡ Pt¡1 Pt¡1 where Pt is the price level in period t: One possibility to compute the in‡ation rate is to take as the price level the GDP de‡ator from the previous section. The basket of goods on which the in‡ation rate is then based corresponds to the current composition of GDP. More often an in‡ation rate is reported that uses a di¤erent basket of goods and services.10 Mostly when the in‡ation rate is reported in the news, it is based on the Consumer Price Index (CPI), which the Bureau of Labor Statistics determines every month. The news release of this monthly number is followed with wide interest for the following reasons. The Federal Reserve Bank, who is responsible for monetary policy, bases its decision on the development of the in‡ation rate, as its major objective is to achieve “price stability”. A higher than expected in‡ation rate causes the FED to increase interest rates, which usually a¤ect the stock market adversely. Knowing this in advance, the stock market tends to react negatively to higher than expected in‡ation and positively to lower than expected in‡ation. It is also important because many contracts include socalled COLA’s, cost-of-living adjustments that specify that payments increase proportionally to the CPI. This is the case for social security bene…ts, for example. So the CPI is likely the most-watched macroeconomic variable. How is it computed? 10 When we are concerned about how the purchasing power of a typical household has changed over time, a basket of goods that includes cruise missiles, oil platforms and the like (as for the GDP de‡ator) may not be very informative. 22CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) Basically, the BLS determines a basket of goods and services that a typical American household buys in a typical month of the base year. This basket includes 4 loafs of bread, a case of beer, 1/60 of a car, 4 haircuts and so forth. The BLS then determines how much this basket cost in a typical month of the base year, and how much it cost in a typical month this year. The CPI for this month equals the ratio between the price of the basket in this year and the price in the base year. Again suppose that the BLS decided that the correct basket was composed only of hamburgers and coke (and the base year is 1996), then the CPI for 2000 is given by CPI = h1996 ph2000 + c1996 pc2000 h1996 ph1996 + c1996 pc1996 Again note that this is exactly a Laspeyres price index from the previous section. The in‡ation rate is then computed using as price level in period t; Pt the CPI for period t: There is a recent political discussion about whether the CPI overstates in‡ation. One problem that we already discussed in the previous section is that people may substitute away from goods that have become relatively more expensive. A second problem is the introduction of new goods. Since new goods are not included in the base year basket, they have no e¤ect on the CPI. Arguably, however, the introduction of new goods makes consumers better o¤. A third problem is unmeasured changes in quality. Suppose a good gets better without this improvement being re‡ected in the price (maybe because the improvement is hard to measure), then the CPI remains unchanged although it should have fallen. This problem is not only academic. Because of the COLA’s, government outlays depend signi…cantly on how in‡ation is measured. Suppose the CPI overstates true in‡ation by one percentage point (this is the magnitude that some economists believe is realistic), then the government in 1997 paid about $10 billion too much for social security bene…ts, quite a signi…cant number. 2.5 Measuring Unemployment Remember our de…nition of the unemployment rate as the ratio between the number of unemployed people and the labor force. In practice about 100,000 adults in each month are interviewed and asked about whether they are employed, and, if not, are asked if they are actively looking for a job (i.e. if they are in the labor force).11 . The number of people that are unemployed and the number of people in the labor force are counted and the ratio computed, which gives the unemployment rate for that month. 11 Asking everybody in the US would be quite expensive, and a sample of 100,000 gives a quite accurate description of the entire population. 2.6. MEASURING TRANSACTIONS WITH THE REST OF THE WORLD23 2.6 Measuring Transactions with the Rest of the World We already de…ned what the trade balance is: it is the total value of exports minus the total value of imports of the US with all its trading partners. A closely related concept is the current account balance. The current account balance equals the trade balance plus net unilateral transfers Current Account Balance = Trade Balance + Net Unilateral Transfers Unilateral transfers that the US pays to countries abroad include aid to poor countries, interest payments to foreigners for US government debt, and grants to foreign researchers or institutions. Net unilateral transfers equal transfers of the sort just described received by the US, minus transfers paid out by the US. Usually net unilateral transfers are negative for the US, but small in size (they amounted to about 0.5% of GDP in 1999). So for all practical purposes we can use the trade balance and the current account balance interchangeably. We say that the US has a current account de…cit if the current account balance is negative and a current account surplus if the current account balance is positive. Note that the current account balance is a ‡ow (since exports and imports are ‡ows). The current account balance keeps track of import and export ‡ows between countries. The capital account balance keeps track of borrowing and lending of the US with abroad. It equals to the change of the net wealth position of the US. The US owes money to foreign countries, in the form of government debt held by foreigners, loans that foreign banks made to US companies and in the form of shares that foreigners hold in US companies. Foreign countries owe money to the US for exactly the same reason The net wealth position of the US is the di¤erence between what the US is owed and what it owes to foreign countries. Note that the net wealth position is a stock, but that the capital account balance, as the change in the net wealth position, is a ‡ow: Capital Account Balance this year = Net wealth position at end of this year ¡Net wealth postion at end of last year Compare this to the relationship between the capital stock and investment from above: it is exactly the same principle. Note that a negative capital account balance means that the net wealth position of the US has decreased: in net terms, capital has ‡own out of the US. The reverse is true if the capital account balance is positive: capital ‡ew into the US. The current account and the capital account balance are intimately related: they are always equal to each other. This is another example of an accounting identity. Current Account Balance this year = Capital Account Balance this year 24CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) The reason for this is simple: if the US imports more than it exports, it has to borrow from the rest of the world to pay for the imports. But this change in the net asset position is exactly what the capital account balance captures. In the next …gure we plot the trade balance for the US for the last 30 years. Trade Balance for the US 1967-2001 (in Constant Prices) 0 -50 Trade Balance -100 -150 -200 -250 -300 -350 -400 1970 1975 1980 1985 Year 1990 1995 Figure 2.1: One can see that the trade balance was mostly negative during this period, and has been particularly negative during the expansion of the 90’s. One consequence of this …gure and the accounting identity is that the net wealth position of the US has declined over the years. Since 1989 the US, traditionally a net lender to the world, has become a net borrower: the net wealth position of the US has become negative in 1989. A last variable that is of strong importance when discussing international trade are exchange rates. The exchange rate of the dollar with the yen measures how many yen somebody has to pay to buy one dollar (currently about 119). The exchange rate of the dollar with the Euro measures how many euro somebody has to spend in order to buy 1 dollar (currently about 1.1). The exchange 2000 2.7. APPENDIX A: MORE ON GROWTH RATES 25 rates are important for the following reasons: suppose the exchange rate of the dollar with the yen increases (i.e. dollar become more expensive to buy for Japanese households). That means it becomes more expensive for Japanese to buy American products. Reversely if the exchange rate declines. Hence there tends to be a close relation between exchange rates and imports and exports (and hence the trade balance). A strong dollar (Euro are cheap, dollars expensive) tends to increase the trade de…cit, a weak dollar tends to decrease it. 2.7 Appendix A: More on Growth Rates Remember that the growth rate of a variable Y (say nominal GDP) from period t ¡ 1 to t is given by gY (t ¡ 1; t) = Yt ¡ Yt¡1 Yt¡1 (2.1) Similarly the growth rate between period t ¡ 5 and period t is given by gY (t ¡ 5; t) = Yt ¡ Yt¡5 Yt¡5 Now suppose that GDP equals $1000 in 1992. From 1992 to 1993 it grows at a growth rate of 2%. From 1993 to 1994 it grows at a rate of 4%, from 1994 to 1995 at 7%, from 1995 to 1996 at 1% and from 1996 to 1997 at 3%. How do we …gure out how big GDP was in 1997? We can use the formula in (2:1): Note that Yt ¡ Yt¡1 Yt¡1 = Yt ¡ Yt¡1 = Yt = Yt gY (t ¡ 1; t) = gY (t ¡ 1; t) ¤ Yt¡1 gY (t ¡ 1; t) ¤ Yt¡1 + Yt¡1 (1 + gY (t ¡ 1; t))Yt¡1 Hence GDP in period t equals GDP in period t ¡ 1; multiplied by 1 plus the growth rate. For the example: Y1993 Y1994 Y1995 Y1996 Y1997 = = = = = = (1 + gY (1992; 1993)) ¤ Y1992 (1 + 0:02) ¤ $1000 = $1020 (1 + 0:04) ¤ $1020 = $1060:80 (1 + 0:07) ¤ $1060:80 = $1135:06 (1 + 0:01) ¤ $1135:06 = $1146:41 (1 + 0:03) ¤ $1146:41 = $1180:80 and the growth rate from 1992 to 1997 is given by gY (1992; 1997) = $1180:80 ¡ $1000 = 18:08% $1000 26CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) Particularly interesting is the case where a variable grows at a constant rate, say g, over time. Suppose at period 0 GDP equals some number Y0 and GDP grows at a constant rate of g% a year. Then in period t GDP equals Yt = (1 + g)t Y0 (2.2) For example, if Jesus would have put 1 dollar in the bank at year 0AC and the bank would have paid a constant interest rate of, say, 1.5%, then in 1999 he would have had a fortune of Y1999 = (1:015)1999 ¤ $1 = $8; 425; 941; 823 which is almost the US GDP for this year. Sometime it is interesting to do the reverse calculation. Suppose you know GDP at time 0 and at time t and want to know at what constant rate GDP must have grown to reach Yt ; starting from Y0 in t years. We can use the formula (2:2) to solve for g = (1 + g)t Y0 Yt (1 + g)t = Y0 µ ¶ 1t Yt (1 + g) = Y0 µ ¶ 1t Yt ¡1 g = Y0 Yt As an example: Suppose we know that in the year 1900 a country has GDP of $1,000 and in 1999 it has GDP of $15,000. Suppose we assume that the GDP of this country has grown over these years at a constant rate g: How big must this growth rate be? If we take 1900 as period 0; then 1999 is period t = 99: We apply the formula to get g = µ µ Yt Y0 ¶ 1t ¡1 ¶1 $15; 000 99 ¡1 $1; 000 = 0:028 = 2:8% = Finally, we might be interested in the following question: Suppose we know the GDP of a country in period 0 and its growth rate g and we want to know how many time periods it takes for GDP in this country to double (to triple and so forth). Again we can use the formula, but this time we solve for t : Yt (1 + g)t = (1 + g)t Y0 Yt = Y0 (2.3) 2.8. APPENDIX B: CHAIN-WEIGHTED GDP 27 Now we need a little mathematical fact about logarithms: if a and b are arbitrary positive numbers, then ¡ ¢ log ab = b ¤ log(a) Using this fact and taking (natural) logarithms on both sides of equation (2:3) yields µ ¶ ¢ ¡ Yt log (1 + g)t = log Y0 µ ¶ Yt t ¤ log(1 + g) = log Y0 ³ ´ log YY0t t = log(1 + g) Now suppose we want to …nd the number of years it takes for GDP to double, i.e. the t such that Yt = 2 ¤ Y0 or YY0t = 2: We get t= log(2) log(1 + g) So once we know the growth rate of our country, we can answer our question. For example with a growth rate of g = 1% it takes about 70 years, with a growth rate of g = 2% it takes about 35 years, with a growth rate of g = 5% it takes about 14 years and so forth. 2.8 Appendix B: Chain-Weighted GDP In this appendix we discuss a recent development in the computation of real GDP and the GDP de‡ator. The Bureau of Labor Statistics used to compute real GDP and the GDP de‡ator in exactly the fashion described in the main text. In 1996 it also introduced the Fisher indices to compute real GDP (it still reports two measures of real GDP, the old and the revised numbers). What is the problem with the old method? With the old method one would pick a base year, say 1992. The contribution of computers to real GDP in 1999 is them computed as follows: take the dollar amount spent on computers in 1999 and divide by the price of computers in 1999 relative to 1992 (i.e. divide by the price in 1999 and multiply by the price in 1992). The result the total value of computers sold in 1999 in prices of 1992. Summing up all goods and commodities, evaluated at their 1992 prices, yields real GDP. Note that for the base year nominal and real GDP always coincide. The problem is that goods whose prices have fallen a lot between this year and the base year (like computers) receive more and more weight in computing real GDP. I will use the same example as Hall and Taylor (p. 33), but will deviate once I describe the reforms the BEA has undertaken. Suppose a country produces only two goods, computers and hamburgers. The next table describes the spending on both goods as well as their prices 28CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) Table 4 Year 1992 1994 1996 1998 Spending in Current $ Computers (1) Hamburgers (2) 100 106 105 98 103 104 99 100 Prices in Current $ Computers (3) Hamburgers (4) 1.00 1.00 0.80 1.05 0.60 1.10 0.40 1.15 This is how real GDP and the GDP de‡ator are computed using the old method. The …rst step is to determine real quantities for the years 1994, 1996 and 1998 (again, this is equivalent to valuing 1994, 1996 and 1998 quantities in 1992 prices). Note that, since we have chosen 1992 as our base year, in 1992 nominal and real quantities coincide (as we have normalized all prices in 1992 to 1). This is done by dividing the spending numbers for computers in column (1) by the current prices for computers in column (3), and likewise for hamburgers by dividing the numbers in column (2) by current prices in column (4). The results are found in the …rst two columns of the next table. Table 5 Year 1992 1993 1994 1995 Real Quantities Computers (5) Hamburgers (6) 100.0 106.0 131.3 93.3 171.7 94.5 247.5 87.0 Real GDP (7)=(5) + (6) 206.0 224.6 266.2 334.5 GDP De‡ator ((1)+(2))/(7) 1.000 0.904 0.778 0.595 Next we determine real GDP by summing up all real quantities, in this case only computers and hamburgers. This is done by summing the …rst two columns and yields the third column. Finally we compute the GDP de‡ator by diving nominal GDP by real GDP in the di¤erent years. Nominal GDP is given by the sum of columns (1) and (2), real GDP is given by the column labeled (7). It yields the last column of Table 5. The problem with the old method is evident: although in 1998 people spent more on hamburgers than computers, the weight that computers receive in real GDP is about three times that for hamburgers. Also, the choice of the base year is quite important, and changes in the base year (which are done about every 5 to 7 years) can lead to serious revisions of growth rates of real GDP and the GDP de‡ator. The BEA reform addressed both problems. The …rst change was to introduce chain-weighted indices. Instead of computing variables in comparison to a …xed base year, variables computed in 1993 are based on 1992, variables in 1994 are based on 1993 and so forth. Before they were all based on the base year, 1992. Growth rates between 1992 and 1995 are then found by “chaining” the growth rates for single years together (as described in the previous appendix). The 2.8. APPENDIX B: CHAIN-WEIGHTED GDP 29 second change was to allow weights for real GDP to take into account relative price changes. I will now describe how the new method computes real GDP and the de‡ator mechanically.12 We …rst have to introduce two quantity indices (which are very similar to the price indices discussed before). Let pct ct pht ht = = = = Price of a computer in period t Number of computers bought in period t Price of hamburgers in period t Number of hamburgers bought in period t Let (pc0 ; c0 ; ph0 ; h0 ) be the corresponding value for period 0: We de…ne the Laspeyres quantity index as LQt = ht ph0 + ct pc0 h0 ph0 + c0 pc0 Note that here we keep prices …xed at period 0 prices and vary the quantities, whereas with the Laspeyres price index we kept quantities …xed at period 0 quantities and varied the prices. Similarly we de…ne the Paasche Quantity index as P aQt = ht pht + ct pct h0 pht + c0 pct The new measure for real GDP, in, say 1993, is the real GDP in 1992 times the square-root of the product of Laspeyres and Paasche quantity index between 1992 and 1993. Formally p real GDP in 1993 = real GDP in 1992 ¤ LQ1993 ¤ P aQ1993 where period 0 corresponds to 1992. Let us compute real GDP for 1993, using this new method. The only thing we need are the ingredients for our quantity indices and last periods GDP. We have prices already given in columns (3) and (4), and quantities in (5) and (6), as well as 1992 real GDP from summing (1) and (2) for 1992. Nothing more is required. The Laspeyres quantity index is LQ1993 = = = h1993 ph1992 + c1993 pc1992 h1992 ph1992 + c1992 pc1992 93:3 ¤ 1 + 131:3 ¤ 1 106 ¤ 1 + 100 ¤ 1 224:6 = 1:090 206 12 This discussion is somewhat technical and di¤ers from Hall and Taylor. For further reference, the original article from the BEA describing the procedure is by Steven Landefeld and Robert Parker and can by found in the Survey of Current Business, May 1997, pp 58-68. 30CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) The Paasche quantity index is LQ1993 = = = h1993 ph1993 + c1993 pc1993 h1992 ph1993 + c1992 pc1993 93:3 ¤ 1:05 + 131:3 ¤ 0:8 106 ¤ 1:05 + 100 ¤ 0:8 203 = 1:061 191:3 Hence real GDP in 1993 equals p real GDP in 1993 = real GDP in 1992 ¤ LQ1993 ¤ P aQ1993 p = 206 ¤ 1:090 ¤ 1:061 = 221:5 The GDP de‡ator is computed as before by dividing nominal by real GDP. Let us do one more year, since it shows the “chain” character of the new method. For 1994 we now take 1993 as period 0: Again we have all the ingredients ready, since we just computed real GDP for 1993. In particular p real GDP in 1994 = real GDP in 1993 LQ1994 ¤ P aQ1994 and we compute the Laspeyres quantity index as LQ1994 = = = h1994 ph1993 + c1994 pc1993 h1993 ph1993 + c1993 pc1993 94:5 ¤ 1:05 + 171:7 ¤ 0:8 93:3 ¤ 1:05 + 131:3 ¤ 0:8 236:6 = 1:166 203 and the Paasche quantity index as LQ1994 = = = h1994 ph1994 + c1994 pc1994 h1993 ph1994 + c1993 pc1994 94:5 ¤ 1:1 + 171:7 ¤ 0:6 93:3 ¤ 1:1 + 131:3 ¤ 0:6 207 = 1:141 181:4 We get p real GDP in 1994 = real GDP in 1993 LQ1994 ¤ P aQ1994 p = 221:5 ¤ 1:166 ¤ 1:141 = 255:5 The …nal results of this exercise are given in Table 6 2.8. APPENDIX B: CHAIN-WEIGHTED GDP 31 Table 6 Year 1992 1993 1994 1995 Real GDP 206.0 221.5 255.5 294.2 GDP De‡. 1.000 0.916 0.810 0.676 Gr.R. GDP In‡. R. Gr.R. GDP (old) In‡. R. (old) 7.5% 15.3% 15.1% -8.4% -11.6% -16.5% 9.0% 18.5% 25.7% -9.6% -13.9% -23.5% Let us get some feeling for the results. The whole objective of computing real GDP and the GDP de‡ator was to decompose nominal GDP into a price component and a quantity component since we are interested about how real economic activity in an economy evolves over time. The old method of computing GDP gives too much weight to commodities whose prices have fallen rapidly, in our example computers. Hence the old method overstates by how much the real component of GDP increased and understates by how much the price component increased (in this example it overstates by how much it declined). Comparing growth rates of real GDP for both methods and in‡ation rates for both methods we see that the new methods shows lower growth rates of real GDP and higher in‡ation rates.13 This is exactly the problem of the old method: it understates the importance of the price decline in computers. Finally, the di¤erence between both methods can be sizeable, not only in our cooked-up example. Growth of real GDP, using these two methods, seem to di¤er by as much as 0.5 to 1% yearly. Given that policies are based on real GDP growth numbers this is not to be underestimated in its importance. 13 Note that, as discussed before, the GDP de‡ator, computed using the old method, is a Paasche price index, and that, as discussed in the main text, Paasche price indices tend to understate in‡ation. 32CHAPTER 2. NATIONAL INCOME AND PRODUCT ACCOUNTING (NIPA) Chapter 3 Economic Growth 3.1 3.1.1 Mathematical Preliminaries Discrete vs. Continuous Time So far in this course we have dealt with time as a discrete variable. Time could take the values t = 0; t = 1; t = 1995 and so on, but no values in between. For the purposes of growth theory it is often convenient to think of time as a continuous variable, so that t = 0:3; t = 1995:25 etc are possible. When time is continuous, we write our economic variables of interest, like GDP, population, in‡ation rate, as functions of time. Let us look at an example. Suppose that the population in a particular country is a function of time: N(t) gives the population of a particular country at date t; where t can take any value (not just integer values). So N (1995) is the population of the country on January 1, 1995, N (1995:5) is the population on July 1, 1995 and so on. 3.1.2 Derivatives The derivative of a function N; denoted by N 0 or dN dt measures by how much the population changes when the date changes by a very small bit (an instantaneous change). If the independent variable of a function N is time (as in our example), then it has become customary to denote the derivative of the function N by N_ . _ Hence N 0 ; dN dt and N all denote the same thing, namely the derivative of the function N with respect to time. Note that when the population increases over dN time, then dN dt > 0 and when it decreases, then dt < 0: The derivative of a function with respect to time expresses the instantaneous change of the function. It is closely related to the change of the function over a discrete time span. Let N (1996) be the population of our country on January 1, 1996 and N(1997) be the population on January 1, 1997. Then N (1997) ¡ N(1996) is the change in the population in the time interval between January 1, 1996 and January 1, 1997. Here the time interval is one year. If we let the time interval get shorter and shorter, the change of the variable during that 33 CHAPTER 3. ECONOMIC GROWTH 34 time interval approaches the derivative of the function. Formally, let ¢t denote the length of the time interval, then the derivative of N with respect to time t is de…ned as N (t) ¡ N(t ¡ ¢t) dN (t) ´ N 0 (t) ´ N_ (t) = lim ¢t!0 dt ¢t There are a few basic rules to take derivatives: 1. If N (t) = tn with n a positive integer, then N_ (t) = ntn¡1 2. If N (t) = ex ; then N_ (t) = ex 3. If N (t) = log(t); then 1 _ N(t) = t 4. If N (t) = g(h(t)); with g; h functions, then _ N_ (t) = g 0 (h(t)) ¤ h(t) Note that whenever we use the log in this course, we mean the log with basis e; or the natural logarithm (Sometime the symbol ln is used for the natural log, but we will always use log to denote the natural logarithm). Examples If N (t) = t5 then N_ (t) = 5t4 6x2 3 If N (t) = log(2x3 ) then N_ (t) = 3 = 2x x Also note that a very important consequence of the forth rule (the so-called chain rule) is the following. Suppose we want to …nd the time derivative of log (N (t)) : Then we use as our function g the log; and as our function h the function N to get ³ ´ d log(N(t)) _ 1 N(t) _ log(N_ (t)) ´ = ¤ N(t) = dt N (t) N(t) 3.1.3 Some Useful Facts about Logs Here are some rules for the natural logarithm log(x ¤ y) µ ¶ x log y log(xa ) log(ex ) elog(x) = log(x) + log(y) = log(x) ¡ log(y) = a ¤ log(x) = x = x 3.1. MATHEMATICAL PRELIMINARIES 3.1.4 35 Growth Rates (once again) Remember how growth rates were de…ned in the case where time is discrete gN (t ¡ 1; t) = Nt ¡ Nt¡1 Nt¡1 In continuous time growth rates are de…ned analogously. Noting that, as the time interval between t¡1 and t converges to 0; the di¤erence Nt ¡Nt¡1 (divided _ by the time interval) converges to N(t) and Nt¡1 gets closer and closer to Nt : This motivates the fact that in continuous time we de…ne the growth rate of a variable N at time t as gN (t) = N_ (t) N (t) ; i.e. we can compute the growth Note the important fact that gN (t) = d log(N(t)) dt rate of a variable by taking the time derivative of the log of this variable. This fact turns out to be very useful. 3.1.5 Growth Rates of Functions The preceding fact, plus the rules for logarithms, can be used to compute growth rates of functions. Suppose we have a variable k(t) that is de…ned to be the ratio of two other variables K(t) and L(t); i.e. k(t) = K(t) L(t) In our application we will denote by k(t) as capital per worker, by K(t) the aggregate capital stock and by L(t) the number of workers at time t: Suppose we know the growth rate of K(t) and L(t) and want to …nd the growth rate of k(t): We do the following. First we take logs on both sides (and use the rules for logs) log(k(t)) = log(K(t)) ¡ log(L(t)) Now we di¤erentiate both sides with respect to time to get d log(K(t)) d log(L(t)) ¡ dt dt _ _ K(t) L(t) = ¡ k(t) K(t) L(t) gk (t) = gK (t) ¡ gL (t) d log((k(t)) dt _ k(t) = Hence the growth rate of the ratio K(t) L(t) equals the di¤erence of the growth rates. Also, if we want the ratio to remain constant over time (i.e. gk (t) = 0), this requires that both K(t) and L(t) must grow at the same rate, i.e. gK (t) = gL (t): CHAPTER 3. ECONOMIC GROWTH 36 Suppose that total output at period t; Y (t) depends on the total capital stock K(t) and total number of workers L(t) used in the production process in the following form Y (t) = K(t)® L(t)1¡® with ® a …xed constant between 0 and 1: This particular relationship between output and capital and labor input is called Cobb-Douglas production function and we will use it extensively later. Suppose we know the growth rates of capital K(t) and labor L(t) and we want to …nd the growth rate of output. Again we can use the trick of …rst taking logs and then di¤erentiate with respect to time. log(Y (t)) d log(Y (t)) dt Y_ (t) Y (t) gY (t) = ® ¤ log(K(t)) + (1 ¡ ®) ¤ log(L(t)) d log(K(t)) d log(L(t)) = ®¤ + (1 ¡ ®) ¤ dt dt _ _ K(t) L(t) = ®¤ + (1 ¡ ®) ¤ K(t) L(t) = ® ¤ gK (t) + (1 ¡ ®) ¤ gL (t) Hence the growth rate of output equals the weighted sum of the growth rates of inputs, with the weight being equal to the (share) parameter ® in the production function. 3.1.6 Simple Di¤erential Equations and Constant Growth Rates Suppose a variable,1 say output Y grows at a constant rate gY (t) from date 0 to date T and suppose we know output at period 0; Y (0): What is output at period T ? In discrete time the answer was YT = (1 + g)T Y0 Now we want to derive a similar formula for continuous time. We start with the de…nition of a growth rate in continuous time (and use the fact that this growth rate is constant from t = 0 to t = T ) g= Y_ (t) Y (t) Integrating both sides with respect to time t; from 0 to T; yields2 1 This section assumes familiarity with the theory of integration. Readers without this knowledge may skip to the …nal formulas. 2 Keep Y_ (t) Y (t) in mind that the time derivative of log(Y (t)) equals equals log(Y (t)): Y_ (t) ; Y (t) so the anti-derivative of 3.2. GROWTH AND DEVELOPMENT FACTS Z T Y_ (t) dt 0 Y (t) = log(Y (T )) ¡ log(Y (0)) µ ¶ Y (T ) = log Y (0) Y (T ) = Y (0) gdt = 0 gT gT egT Z 37 T Y (T ) = egT ¤ Y (0) (3.1) Hence if output at time 0 equals Y (0) and grows at constant rate g; then at time T output equals egT Y (0): Note that with formula (3.1) we can ask exactly the same questions (and use exactly the same manipulations) in continuous time as in Appendix 1 of Chapter 2 with discrete time. We should note two things: …rst, by taking logs in the formula we get log(Y (T )) = log(Y (0)) + gT Hence if output (or any other variable) grows at a constant rate g; then plotting the log of output gives a straight line with intercept log(Y (0)) and slope g: Therefore economists often plot the log of a variable (rather than the variable itself), because this way it is easy to see whether (and at what rate) the variable grows over time. See Figures 7 and 8 for the e¤ect. Second, the formulas for discrete and continuous time yield roughly the same result (you should work out some examples with your pocket calculator). The two formulas would in fact be identical if eg = (1 + g): That this equality is approximately true can be seen from the Taylor series expansion of eg around g=0 eg = e0 + (g ¡ 0)e0 + = 1+g+ (g ¡ 0)2 0 (g ¡ 0)3 0 e + e +::: 2 6 g2 g3 + + ::: 2 6 ¼ 1+g if g is not too large 3.2 Growth and Development Facts The economist Niclas Kaldor pointed out the following stylized growth facts (empirical regularities of the growth process) for the US and for most other industrialized countries (look back at the …gures in the last section): 1. Output (real GDP) per worker y = YL and capital per worker k = over time at relatively constant and positive rate. K L grow CHAPTER 3. ECONOMIC GROWTH 38 Exponentially Growing Variable 1600 1400 1200 Y(t) 1000 800 600 400 200 0 0 0.5 1 1.5 2 2.5 Time 3 3.5 4 4.5 Figure 3.1: 2. They grow at similar rates, so that the ratio between capital and output, K Y is relatively constant over time 3. The real return to capital r (and the real interest rate r ¡ ±) is relatively constant over time 4. The capital and labor shares are roughly constant over time. The capital share ® is the fraction of GDP that is devoted to interest payments on capital, ® = rK Y : The labor share 1 ¡ ® is the fraction of GDP that is devoted to the payments to labor inputs; i.e. to wages and salaries and other compensations: 1 ¡ ® = wL Y : Here w is the real wage. These stylized facts motivated the development of the neoclassical growth model, the so-called Solow model, to be discussed below. The Solow model has spectacular success in explaining the stylized growth facts by Kaldor. Note that the growth facts pertain to data for a single country over a (long) period of time. Such a data set is called a time series. 5 3.2. GROWTH AND DEVELOPMENT FACTS 39 Exponentially Growing Variable, Log Scale 8 7 log(Y(t)) 6 5 4 3 2 0 0.5 1 1.5 2 2.5 Time 3 3.5 4 4.5 Figure 3.2: In addition to the growth facts we will be concerned with how income (per worker) levels and growth rates vary across countries in di¤erent stages of their development process. The true test of the Solow model is to what extent it can explain di¤erences in income levels and growth rates across countries, the so called development facts. As we will see, the verdict here is mixed. Now we summarize the most important facts from the Summers and Heston’s panel data set. This data set follows about 100 countries for 30 years and has data on income (production) levels and growth rates as well as population and labor force data. In what follows we focus on the variable income per worker. This is due to two considerations: a) our theory (the Solow model) will make predictions about exactly this variable b) although other variables are also important determinants for the standard of living in a country, income per worker (or income per capita) may be the most important variable (for the economist anyway) and other determinants of well-being tend to be highly positively correlated with income per worker. 5 40 CHAPTER 3. ECONOMIC GROWTH Before looking at the data we have to think about an important measurement issue. Income is measured as GDP, and GDP of a particular country is measured in the currency of that particular country. In order to compare income between countries we have to convert the income measures into a common unit. One option would be exchange rates. These, however, tend to be rather volatile and reactive to events on world …nancial markets. Economists that study growth and development tend to use a di¤erent procedure to measure the value of currencies against each other. They ask how many dollars it costs to buy a middle class car in the US, and how many yen the same type of car costs in Japan. Suppose the numbers are $15,000 and 2,000,000 yen. Then the exchange rate, based on cars would be $0.75 per 100 Yen. By extending this procedure to a lot of di¤erent products and taking a weighted average one constructs an exchange rate that measures the relative purchasing power of two currencies. This exchange rate is called the PPP-based exchange rate, where PPP stands for Purchasing Power Parity. All income numbers used by Summers and Heston (and used in these notes) are converted to $US via PPP-based exchange rates. Here are the most important facts from the Summers and Heston data set: 1. Enormous variation of per capita income across countries: the poorest countries have about 5% of per capita GDP of US per capita GDP. This fact is about dispersion in income levels. When we look at Figure 9, we see that out of the 104 countries in the data set, 37 in 1990 and 38 in 1960 had per worker incomes of less than 10% of the US level. The richest countries in 1990, in terms of per worker income, are Luxembourg, the US, Canada and Switzerland with over $30,000, the poorest countries, without exceptions, are in Africa. Mali, Uganda, Chad, Central African Republic, Burundi, Burkina Faso all have income per worker of less than $1000. Jones’ Figure 1.2. shows that not only are most countries extremely poor compared to the US, but most of the world’s population is poor relative to the US. 2. Enormous variation in growth rates of per worker income. This is a fact about changes of levels in per capita income. Figure 10 shows the distribution of average yearly growth rates from 1960 to 1990. The majority of countries grew at average rates of between 1% and 3% (these are growth rates for real GDP per worker ). Note that some countries posted average growth rates in excess of 6% (Singapore, Hong Kong, Japan, Taiwan, South Korea) whereas other countries actually shrunk, i.e. had negative growth rates (Venezuela, Nicaragua, Guyana, Zambia, Benin, Ghana, Mauretania, Madagascar, Mozambique, Malawi, Uganda, Mali). We will sometimes call the …rst group growth miracles, the second group growth disasters. Note that not only did the disasters’ relative position worsen, but that these countries experienced absolute declines in living standards. The US, in terms of its growth experience in the last 30 years, was in the middle of the pack with a growth rate of real per worker GDP of 1.4% between 1960 and 1990. 3.2. GROWTH AND DEVELOPMENT FACTS 41 Distribution of Relative Per Worker Income 40 1960 1990 35 Number of Countries 30 25 20 15 10 5 0 0 0.2 0.4 0.6 0.8 1 Income Per Worker Relative to US 1.2 Figure 3.3: 3. Growth rate determine economic fate of a country over longer periods of time. How long does it take for a country to double its per capita GDP if it grows at average rate of g% per year. A good rule of thumb: 70=g years (this rule of thumb is due to Nobel Price winner Robert E. Lucas (1988)). Growth rates are not constant over time for a given country. This can easily be demonstrated for the US. GDP per worker in 1990 was $36,810. If GDP would always have grown at 1.4% , then for the US GDP per worker would have been about $9,000 in 1900, $2,300 in 1800, $570 in 1700, $140 in 1600, $35 in 1500 and so forth. Economic historians (and common sense) tells us that nobody can survive on $35 per year (estimates are that about $300 are necessary as minimum income level for survival). This indicates that the US (or any other country) cannot have experienced sustained positive growth for the last millennium or so. In fact, prior to the era of modern economic growth, which started in England in the late 18-th century, per worker income levels have been 1.4 CHAPTER 3. ECONOMIC GROWTH 42 Distribution of Average Growth Rates (Real GDP) Between 1960 and 1990 25 Number of Countries 20 15 10 5 0 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 Average Growth Rate 0.04 0.05 Figure 3.4: almost constant at subsistence levels. This can be seen from Figure 11, which compiles data from various historical sources. The start of modern economic growth is sometimes referred to as the Industrial Revolution. It is the single most signi…cant economic event in history and has, like no other event, changed the economic circumstances in which we live. Hence modern economic growth is a quite recent phenomenon, and so far has occurred only in Western Europe and its o¤springs (US, Canada, Australia and New Zealand) as well as recently in East Asia. 4. Countries change their relative position in the (international) income distribution. Growth disasters fall, growth miracles rise, in the relative crosscountry income distribution. A classical example of a growth disaster is Argentina. At the turn of the century Argentina had a per-worker income that was comparable to that in the US. In 1990 the per-worker income of Argentina was only on a level of one third of the US, due to a healthy growth experience of the US and a disastrous growth performance of Ar- 0.06 3.3. THE SOLOW MODEL 43 GDP pe r Capita (in 1985 US $): W e ste rn Europe a nd its Offsprings 16000 14000 12000 10000 GDP per Capita 8000 6000 4000 2000 89 73 19 50 19 13 19 70 19 20 18 10 18 00 16 14 0 00 10 50 0 0 Tim e Figure 3.5: gentina. Countries that dramatically moved up in the relative income distribution include Italy, Spain, Hong Kong, Japan, Taiwan and South Korea, countries that moved down are New Zealand, Venezuela, Iran, Nicaragua, Peru and Trinidad&Tobago. In the next sections we have two tasks: to construct a model, the Solow model, that a) can successfully explain the stylized growth facts b) investigate to which extent the Solow model can explain the development facts. 3.3 The Solow Model We look for a model that explains the stylized growth facts from above. In 1956 Robert Solow from MIT developed such a model, the Solow growth model in his paper “A Contribution to the Theory of Economic Growth”. This brought him the Nobel Price in 1987. 3.3.1 Models Before discussing the Solow model, let’s brie‡y make clear what a successful model is. What is a model? It is a mathematical description of the economy. Why do we need a model? The world is too complex to describe it in every detail. A model abstracts from details to describe clearly the main forces driving the economy. What makes a model successful? When it is simple but e¤ective in describing and predicting how the (economic) world works. Note: A model CHAPTER 3. ECONOMIC GROWTH 44 relies on simplifying assumptions. These assumptions drive the conclusions of the model. When analyzing a model it is therefore crucial to clearly spell out the assumptions underlying the model. 3.3.2 Setup of the Basic Model and Model Assumptions The basic assumptions of the Solow model are that there is a single good produced in our economy and that there is no international trade, i.e. the Solow model is a model of a closed economy Also there is no government. It is also assumed that all factors of production (labor, capital) are fully employed in the production process. The model consists of two basic equations, the neoclassical aggregate production function and a capital accumulation equation. 1. neoclassical aggregate production function Y (t) = F (K(t); L(t)) where Y (t) is total output produced in our economy at date t: Output is produced using the two inputs capital K(t) and labor services L(t): Assumptions on F : ² Constant returns to scale: doubling both inputs will result in doubled output. Mathematically: for all constants c > 0 F (cK(t); cL(t)) = cF (K(t); L(t)) ² Positive, but decreasing marginal products: holding one input …xed, by increasing the other input we increase output, but at decreasing rate. Mathematically @F @K @F @L @2 F <0 @K 2 @2F > 0; <0 @L2 > 0; An important example for F is the Cobb-Douglas production function Y (t) = F (K(t); L(t)) = K(t)® L(t)1¡® (3.2) where ® is a …xed parameter between 0 and 1: You should verify that the Cobb-Douglas production function satis…es the two assumptions made on F above. Our stylized growth facts dealt with output per (t) and capital per worker k(t) = K(t) worker y(t) = YL(t) L(t) . Dividing both sides of equation (3:2) by the number of workers L(t) yields µ ¶a µ ¶1¡® K(t)® L(t)1¡® K(t)® L(t)1¡® K(t) L(t) = y(t) = = = k(t)® L(t) L(t)® L(t)1¡® L(t) L(t) 3.3. THE SOLOW MODEL 45 The fact that we can write output per worker as a function of capital per worker alone is due to the …rst assumption. The fact that there are decreasing returns to capital per worker (an increase in capital per worker increases output per worker at a decreasing rate) is due to the second assumption. In summary, the aggregate production function, written in per-worker terms for the Cobb-Douglas case, is given by y(t) = k(t)® (3.3) 2. capital accumulation equation _ K(t) = sY (t) ¡ ±K(t) (3.4) _ The change of the capital stock in period t, K(t) is given by the total amount of investment in period t; sY (t) minus the depreciation of the old capital stock ±K(t): Here s is the fraction of total output (income) in period t that is saved, i.e. not consumed. If s = 0:2; then 20% of the total output in period t is saved by the households in the economy. Similarly ± is the fraction of the capital stock at period t that wears out in the production process. The important assumptions implicit in equation (3:4) are ² Households save a constant fraction s of output (income), regardless of the level of output. This is a strong assumption about the behavior of households (and much theoretical work has been done to relax this assumption). s is an important parameter of the model. Note that the fact that total saving of households sY (t) equals total investment is not an assumption, but follows from the accounting identity that saving equals investment. ² A constant fraction ± of capital depreciates in each period. Rather than a behavioral assumption (as the …rst one), this is an assumption about technology: the production process is such that a constant fraction of capital wears out in each period. Since equation (3:3) is in per-worker terms, we look for a representation of equation (3:4) in per-worker terms. The last assumptions that we make is that the labor force participation rate is constant and that the populations grows exponentially at a growth rate of n: Then the number of workers grows at rate n; i.e. L(t) = ent L(0) (3.5) Note that it follows from equation (3:5) that (remember that a dot over a variable denotes the derivative of that variable with respect to time) _ L(t) nent L(0) = nt =n L(t) e L(0) (3.6) CHAPTER 3. ECONOMIC GROWTH 46 Now we can divide both sides of equation (3:4) by L(t) to obtain _ K(t) = sy(t) ¡ ±k(t) L(t) (3.7) The right hand side of equation (3:7) is already in per-worker form, but the left hand side requires more work. But _ _ _ K(t) K(t) K(t) K(t) = = k(t) (3.8) L(t) K(t) L(t) K(t) Remember that _ _ _ _ K(t) L(t) K(t) k(t) = ¡ = ¡n k(t) K(t) L(t) K(t) Hence _ _ k(t) K(t) = +n K(t) k(t) Combining equations (3:8) and (3:9) we get à ! _ _ _ K(t) K(t) k(t) _ + nk(t) = k(t) = + n k(t) = k(t) L(t) K(t) k(t) (3.9) (3.10) Finally, we use (3:10) in (3:7) to obtain _ + nk(t) = sy(t) ¡ ±k(t) k(t) or _ k(t) = sy(t) ¡ (± + n)k(t) (3.11) This is the capital accumulation equation in per-worker terms 3.3.3 Analysis of the Model The Solow growth model characterizes output per capita and capital per capita by the two basic equations y(t) = k(t)® _ k(t) = sy(t) ¡ (± + n)k(t) (3.12) Substituting the …rst into the second we obtain a di¤erential equation in k; the per-worker capital stock: _ k(t) = sk(t)® ¡ (± + n)k(t) (3.13) We will proceed by analyzing this di¤erential equation. Note that once we know the behavior of k(t) over time, then from (3:12) we know the behavior of y(t): Together with the knowledge of the initial number of workers L(0) and with help of equation (3:5) we know the behavior of K(t) = k(t)L(t) and Y (t) = y(t)L(t): Note that the values of these variables depend on the parameters s; ± and n: We will demonstrate this below with some numerical examples. But now let us proceed with the analysis of (3:13): 3.3. THE SOLOW MODEL 47 Graphical Analysis Our di¤erential equation (3:13) describes how the capital stock per worker in our model evolves over time. For example, we can analyze what happens with the capital stock if we start at an arbitrary initial level k(0): We can also analyze how capital per worker and hence output per worker di¤er in two economies that di¤er in their savings or population rates. _ Remember that k(t) is the change in per-worker capital stock. This change at period t is given by the di¤erence between investment (=saving) per worker sy(t) = sk(t)® and e¤ective depreciation (± + n)k(t):3 In Figure 12 we draw graphs of sy(t) = sk(t)® and (± + n)k(t) as functions of k(t): As a function of k(t); the graph of (± + n)k(t) is a straight line with slope (± + n) that starts at 0: The graph of sk(t)® also starts at 0; and is very steep for small values of k(t) and very ‡at for large values of k(t): This is a consequence of our assumptions on the production function. Remember that the derivative of a function gives the slope of the function. The derivative of sk(t)® with respect to k(t) is given by ®s k(t)1¡® As long as 0 < ® < 1 this derivative approaches in…nity as k(t) approaches 0 and it approaches 0 as k(t) gets larger and larger. _ The change in k(t); k(t) is given by the di¤erence between the two graphs, sk(t)® and (± + n)k(t): Suppose our economy starts at k(0): Since at k(0) we _ is positive and the capital stock per have that sk(t)® exceeds (± + n)k(t); k(t) worker increases. This is indicated by the arrows on the x-axis. In fact, the process of increasing k(t) continues as long as sk(t)® is bigger than(± + n)k(t): Over time, the capital stock per worker converges to k¤ ; the capital stock at _ = 0; i.e. which sk(t)® = (± + n)k(t): At k¤ we have the situation in which k(t) the capital stock per worker does not change anymore. Such a point at which _ k(t) = 0 is called a steady state: once the economy reaches this point, it stays there forever. Given the properties of the production function there is a unique positive steady state capital stock per worker in the Solow model and from any positive initial capital stock k(0) the economy converges to this steady state over time (we demonstrated this for k(0) < k¤ ; you should convince yourself that this also happens if k(0) > k¤ ). Therefore this steady state is called (locally) stable: starting close to k¤ brings the economy to k¤ over time. We make several other observations: …rst, there is another (trivial) steady state k¤ = 0: If the economy starts with k(0) = 0; it stays there forever. Second, once we have determined the behavior of k(t); since y(t) = k(t)® we know the behavior of output per worker, and also the behavior of consumption per worker c(t) = (1 ¡ s)k(t)® over time. The behavior of total consumption, output and the capital stock follows from the fact that the number of workers grow at constant rate n: 3 Note that k is per-worker capital. As population increases at rate n; this reduces capital per worker (for a given capital stock). This e¤ect acts in exactly the same fashion as physical depreciation. CHAPTER 3. ECONOMIC GROWTH 48 (n+δ)k(t) sy(t) k(0) k* k(t) Figure 3.6: Steady State Analysis We can solve for the steady state analytically. Remember that a steady state is _ = 0: We a situation in which per capita capital is constant over time, i.e. k(t) ¤ ¤ denote steady state capital per worker by k : Obviously k solves the equation 0 = s (k¤ )® ¡ (n + ±)k¤ or ¤ k = µ s n+± 1 ¶ 1¡® The steady state output per worker is then given by ® µ ¶ 1¡® s ¤ y = n+± (3.14) 3.3. THE SOLOW MODEL 49 Hence the steady state of an economy depends positively on the saving rate s and negatively on the population growth rate n of the economy (and on the technological parameters ±; ®). An increase in the saving rate and a decrease in the population growth rate increases per worker capital and output. This type of analysis -how does the steady state change with a change in model parametersis called comparative statics. (n+δ)k(t) s’y(t) sy(t) k(0)=k* k’* k(t) Figure 3.7: Let us now demonstrate the dynamic response of the economy to a change in the saving rate from s to s0 : Suppose the economy initially is in the steady state with the old saving rate, i.e. k(0) = k¤ : Now (for some model-exogenous reason) the households in our economy start saving more, so that the saving rate increases from s to s0 : As shown in Figure 13, such a change does not a¤ect the (n + ±)k(t) line, but it tilts the sk(t)® line outwards around zero to s0 k(t)® = s0 y(t): For the old steady state capital stock k(0) = k¤ ; now with the _ > 0 and new saving rate s0 we have that s0 k(0)® > (n + ±)k(0): Hence k(0) CHAPTER 3. ECONOMIC GROWTH 50 the capital stock per worker starts growing. It continues to grow until it hits the new steady state k0¤ > k¤ ; where it stays forever, unless new changes in the saving rate or the depreciation rate happen. The process of the economy moving from one steady state to the new steady state is called transition path or transition dynamics. The same analysis can be done with a change in the population growth rate, which is left as an exercise. Evaluating the Basic Model The simple Solow model gives a simple answer to the question why some countries have such a high level of output per worker and other have such a low level of output per worker (i.e. why some countries are so rich whereas others are so poor). Assuming that all countries have reached their respective steady states, the Solow model predicts that countries with high saving (investment) rates s and low population growth rates n have high per-worker output. We can use the Summers-Heston data set to see whether this prediction of the model can be found in the data. This is a …rst test of the model. In Figure 14 we plot GDP per worker in 1990 against the average investment rate (the fraction of GDP used for investment, equal to the saving rate s in our model) between 1980-90. Each dot is one country (try to guess where the US -or your country of birth- is located in this plot and then look at Jones’ Figure 2.6 if you want). We see the positive correlation between GDP per worker and the investment rate: countries with higher investment rates in the data tend to have higher GDP per worker, as predicted by the Solow model. This can be viewed as a …rst success of the Solow model. Figure 15 plots GDP per worker in 1990 against the average population growth rate between 1980-90. Again each dot represents one country. As predicted by the Solow model there is a negative correlation between population growth rates and per worker GDP. Again the data support this prediction of the Solow model. 3.3.4 Introducing Growth We wrote down the Solow growth model to explain the stylized facts of Kaldor, in particular the facts that income and capital per worker grow at equal constant and positive rates. So what about growth in the simple Solow model? We saw that in the model capital and output per capita converged to their steady state levels and then stayed there forever (remember that a steady state was de…ned as a situation in which the per worker capital stock does not change anymore). Hence in this version of the model there is no long-run growth of capital per worker or output per worker. Output and the capital stock grow, but only at the rate of population growth n: Fortunately this failure of the model is easy 3.3. THE SOLOW MODEL 51 GDP per Worker 1990 as Function of Investment Rate 4.5 GDP per Worker 1990 in $10,000 4 3.5 3 2.5 2 1.5 1 0.5 0 -0.5 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Average Investment Share of Output 1980-90 Figure 3.8: to correct as we will see in a second. But …rst let’s look at growth along the transition path to the steady state. Dividing both sides of (3:13) by k(t) we get gk (t) ´ _ k(t) = sk(t)®¡1 ¡ (n + ±) k(t) (3.15) Since ® < 1; ® ¡ 1 < 0 and therefore the bigger the per worker capital stock k(t); the smaller is the growth rate of the per worker capital stock gk (t): At the steady state k¤ the growth rate is zero (you should verify this by plugging the formula for k¤ into (3:15) for k(t)). If the economy starts at k(0) < k¤ ; the growth rate of k is positive. Over time capital per worker gets bigger and bigger and the growth rate declines (but is still positive). Eventually k reaches the steady state k¤ and growth stops as the growth rate falls to zero. Hence there is growth along the transition path in the simple Solow model, but no 0.45 CHAPTER 3. ECONOMIC GROWTH 52 GDP per Worker 1990 as Function of Population Growth Rate 4.5 4 GDP per Worker 1990 in $10,000 3.5 3 2.5 2 1.5 1 0.5 0 -0.5 0 0.01 0.02 0.03 0.04 Average Population Growth Rate 1980-90 Figure 3.9: sustained growth over time. The behavior of output per worker parallels that of k; as y(t) = k(t)® : On the other hand, if the economy starts at k(0) > k¤ ; then the growth rate is negative and the capital stock per worker declines to k¤ over time. The growth rate becomes less and less negative and …nally arrives at 0 in the steady state. This discussion is neatly summarized in Figure 16, where on the x-axis we have k(t) and we plot the curve sk(t)®¡1 and the line n+±: The vertical distance _ _ k(t) k(t) : We see that k(t) > 0 between the two lines represents the growth rate k(t) whenever k(t) < k¤ and _ k(t) k(t) < 0 whenever k(t) > k¤ Now let us return to the question of how to generate sustained growth in the Solow model. The answer that Solow gave was to introduce technological progress in the aggregate production function. Aggregate output is now given 0.05 3.3. THE SOLOW MODEL 53 α-1 sk(t) (n+δ) k(0) k* k(t) Figure 3.10: by Y (t) = K(t)® (A(t)L(t))1¡® where A(t) is the level of technology at date t: The capital accumulation equation remains unchanged. When the level of technology multiplies labor input L(t) as above, technological progress is said to be labor-augmenting (or Harrod neutral): a higher level of technology A(t) makes a given number of workers more productive in that the same number of workers can now produce more output. For concreteness we interpret A(t) to be the stock of ideas or knowledge that an economy at time t has access to. We assume that the level of technology grows at a constant rate g > 0 over time, i.e. _ A(t) =g A(t) CHAPTER 3. ECONOMIC GROWTH 54 This is a crucial (maybe the most crucial) assumption of the model. Note that we do not explain why the level of technology grows over time, that is we take growth of technology as exogenously given, as manna from heaven, so to speak. Therefore the Solow model is often referred to as an exogenous growth model. In later sections we will look at the so-called endogenous growth theory, at models that try to explain why we have technological progress. Now let’s proceed with the analysis of the Solow model with technological progress. Because of technological progress it is clear that the economy will not any longer have a steady state in which output and capital per worker are constant. But it turns out that it possesses a very similar property. By a balanced growth path we de…ne a situation in which output, capital and consumption per worker grow at constant rates (which need not be the same). Note that a steady state is just a special case of a balanced growth path in which all variables grow at constant rate 0: We …rst want to …nd out at what growth rate output per worker and capital per worker grow in a balanced growth path. Remember that the capital accumulation equation is given by _ K(t) = sY (t) ¡ ±K(t) Dividing both sides by K(t) yields gK (t) ´ _ Y (t) K(t) =s ¡± K(t) K(t) Remember that gk (t) ´ _ _ K(t) k(t) = ¡n k(t) K(t) Hence gk (t) ´ _ Y (t) k(t) =s ¡ (n + ±) k(t) K(t) In a balanced growth path by de…nition gk (t) is constant. From the equation Y (t) above this requires that K(t) is constant over time, i.e. that output Y (t) and the capital stock K(t) must grow at the same rate. It then follows that output per worker y(t) and capital per worker k(t) must grow at the same rate in a balanced growth path, i.e. gk = gy .4 The next question is at what common rate do y and k grow? Dividing the aggregate production function by the labor force L(t) we get y(t) = = K(t)® (A(t)L(t))1¡® Y (t) = L(t) L(t) K(t)® (A(t)L(t))1¡® L(t)® L(t)1¡® = k(t)® A(t)1¡® 4 This follows from the fact that g = g ¡n and g = g ¡n: From g y k K Y K = gY then gk = gy immediately follows. 3.3. THE SOLOW MODEL 55 In order to get growth rates we take logs and then di¤erentiate with respect to time d log(k(t)) d log(A(t)) d log(y(t)) = ® + (1 ¡ ®) dt dt dt gy (t) = ®gk (t) + (1 ¡ ®)gA (t) Now we use the result that k and y grow at the same rate in a balanced growth path and that A grows at constant rate g by assumption. We then have gy (1 ¡ ®)gk gk = gk = ®gk + (1 ¡ ®)gA = (1 ¡ ®)g = gy = g Hence along a balanced growth path capital per worker and output per worker (and consumption per worker) all grow at the same rate g; the growth rate of technological progress. Also, if there is no technological progress, then g = 0 and there is no sustained growth in the economy (and we are back in the simple Solow model). Therefore the engine of growth in per capita output in this model is technological progress. 3.3.5 Analysis of the Extended Model The previous discussion indicates that along a balanced growth path our variables of interest, y(t) and k(t) grow at constant rate g; the rate of technological progress. To analyze the new model graphically it is convenient to work with variables that are constant in the long run. Since y(t) and k(t) and A(t) grow at the same rate g; we de…ne new variables y~(t) = ~ k(t) = Y (t) y(t) = A(t) A(t)L(t) K(t) k(t) = A(t) A(t)L(t) Note that in a balanced growth path y~ and k~ are constant. We will call k~ the technology-adjusted per worker capital stock and y~ the technology-adjusted output per worker. It turns out that once we look at the variables y~ and k~ the analysis from the previous section goes through almost unchanged. First look at the aggregate production function y~(t) ´ = Y (t) A(t)L(t) K(t)® (A(t)L(t))1¡® A(t)L(t) K(t)® (A(t)L(t))1¡® (A(t)L(t))® (A(t)L(t))1¡® ~ ® = k(t) = CHAPTER 3. ECONOMIC GROWTH 56 which is exactly the same as before, once we made the change in variables. Now let’s look at the capital accumulation equation _ K(t) = sY (t) ¡ ±K(t) Dividing both sides by A(t)L(t) we obtain _ K(t) A(t)L(t) _ K(t) A(t)L(t) = sY (t) K(t) ¡± A(t)L(t) A(t)L(t) ~ = s~ y(t) ¡ ± k(t) The right hand side of this equation is already in a form that we like, the left hand side requires more work, basically the same work as in the last section: _ _ _ K(t) K(t) K(t) K(t) ~ = = k(t) A(t)L(t) K(t) A(t)L(t) K(t) (3.16) Also gk~ (t) ´ = Hence _ K(t) K(t) = : ~ k(t) ~ k(t) : ~ k(t) = gK (t) ¡ gA (t) ¡ gL (t) ~ k(t) _ K(t) ¡g¡n K(t) + g + n: Substituting into equation (3:16) we get 0 1 : : ~ _ B k(t) C K(t) ~ = k(t) ~ C k(t) ~ =B + g + n + (g + n)k(t) A ~ A(t)L(t) @ k(t) and hence the capital accumulation equation becomes : ~ ~ = s~ y(t) ¡ (n + g + ±)k(t) k(t) Summarizing, with our new variables k~ and y~ our two equations of the Solow model become ~ ® y~(t) = k(t) : ~ k(t) ~ = s~ y (t) ¡ (n + g + ±)k(t) 3.3. THE SOLOW MODEL 57 ~ which can be combined to the di¤erential equation in k(t): : ~ ~ ® ¡ (n + g + ±)k(t) ~ k(t) = sk(t) (3.17) Note how similar equation (3:17) is to equation (3:13) once we make our change of variables. In particular, we can analyze (3:17) graphically in exactly the same way as we did with (3:13): Graphical Analysis We can draw the Solow diagram for the model with technological progress. ~ In Figure 17 we let k(t) be the variable on the x-axis and we plot the curves ~ on the y-axis. The …rst curve looks exactly as before, ~ ® and (n + g + ±)k(t) sk(t) the other is again a straight line, but now with slope (n + g + ±) instead with ~ ® and (n + g + ±)k(t) ~ gives the change in (n + ±): The di¤erence between sk(t) : ~ : the technology adjusted capital stock per worker k(t) ~ ~ ~ ® exSuppose our economy starts at k(0): Since at k(0) we have that sk(t) : ~ ~ is positive and the technology-adjusted capital stock per ceeds (±+n)k(t); k(t) worker increases. This is indicated by the arrows on the x-axis. In fact, the pro~ ~ continues as long as sk(t) ~ ® is bigger than (± + n + g)k(t): cess of increasing k(t) ¤ ~ Over time, the capital stock per worker converges to k ; the capital stock at : ® ¤ ~ ~ ~ ~ which sk(t) = (± +n)k(t)s: At k we have the situation in which k(t) = 0; i.e. the technology adjusted capital stock per worker does not change anymore. As ~ before there is only one such k~¤ and from all positive starting values of k(0) we always go to k~¤ : Hence in the long run in our economy converges to the balanced ~ grow path in which capital per worker k(t) = k(t)A(t) and output per worker y(t) = y~(t)A(t) grow at the constant rate g: Total output Y (t) = y(t)L(t) and the capital stock K(t) = k(t)L(t) grow at rates g + n: Balanced Growth Path Analysis As before we can solve for the balanced growth path analytically. We know that : ¤ ~ ~ at k we have k(t) = 0; i.e. k~¤ solves ® 0 = sk~¤ ¡ (n + g + ±)k~¤ CHAPTER 3. ECONOMIC GROWTH 58 ~ (n+g+δ) k(t) ~ α sk(t) . ~ k(0) ~ k(0) ~ k* ~ k(t) Figure 3.11: Hence k~¤ = µ s n+g+± 1 ¶ 1¡® µ s n+g+± ® ¶ 1¡® and therefore ¤ y~ = 3.3. THE SOLOW MODEL 59 It follows that along a balanced growth path k(t) = A(t) µ µ s n+g+± 1 ¶ 1¡® ® ¶ 1¡® s y(t) = A(t) n+g+± 1 µ ¶ 1¡® s K(t) = L(t)A(t) n+g+± ® µ ¶ 1¡® s Y (t) = L(t)A(t) n+g+± We can now do comparative statics as before. Suppose that in period t = T all of a sudden the saving (investment) rate s in our economy increases to s0 . The economic intuition of what happens is simple: people save more and hence there are more funds for investment into capital. Therefore the capital stock per worker will increase over time, hence output per worker will increase over time. Let’s look at what exactly happens a bit more carefully. From the formulas above we note the following: …rst of all, since the growth rate of the economy is given by g; the rate of technological progress, the growth rate of the economy is not a¤ected by the increase of the saving rate. From the formulas above, however, we see that y~¤ increases to y~¤0 . Hence the levels of output and capital per worker, y(t) and k(t); are higher in the new balanced growth path, and so are the levels of total output and capital, Y (t) and K(t): We will see this graphically from several …gures. In Figure 18 we show how a change in the saving rate from s to s0 a¤ects the technology adjusted capital stock per worker k~ over time. The story is exactly the same as in Figure 13 for the simple Solow model. Suppose the economy initially is in the steady state with the old saving rate, ~ ) = k~¤ : Now (for some model-exogenous reason) the households in our i.e. k(T economy start saving more, so that the saving rate increases from s to s0 : As ~ line, but shown in Figure 18, such a change does not a¤ect the (n + g + ±)k(t) ~ ® = s0 y~(t): For the old ~ ® line outwards around zero to s0 k(t) it tilts the sk(t) ~ ) = k~¤ ; now with the new saving rate s0 we have steady state capital stock k(T : 0~ ® ~ ~ that s k(T ) > (n + g + ±)k(T ): Hence k(T ) > 0 and the technology-adjusted capital stock per worker starts growing. It continues to grow until it hits the new steady state k~0¤ > k~¤ ; where it stays forever. What happens to economic growth over time? We already concluded that in the long run an increase in the saving rate has no e¤ect on the growth rate of this economy. But what along CHAPTER 3. ECONOMIC GROWTH 60 ~ (n+g+δ) k(t) ~ α s’k(t) . ~ k(T) ~ k* ~ α sk(t) ~ k*’ ~ k(t) Figure 3.12: the transition path? Recall our basic equation for the extended Solow model : ~ ~ ® ¡ (n + g + ±)k(t) ~ k(t) = sk(t) ~ ) = k~¤ Along the initial balanced growth path, for k(T : ~ )=0 ~ )® ¡ (n + g + ±)k(T ~ k(T ) = sk(T 3.3. THE SOLOW MODEL 61 ~ ) = k~¤ we have But now the saving rate increases from s to s0 > s; so at k(T : ~ )>0 ~ )® ¡ (n + g + ±)k(T ~ ) = s0 k(T k(T ~ Hence the growth rate of k; : ~ k(t) ~ k(t) is positive. Along the entire transition path : ~ ® curve lies above the (n + g + ±)k(t) ~ line. ~ remains positive, as the s0 k(t) k(t) ~ increases The di¤erence between these two lines gets smaller and smaller as k(t) : ~ to the new steady state. Therefore k(t) gets smaller and smaller (but remains ~ increases along the transition path. Therefore the growth rate positive) and k(t) of k~ behaves as follows: it is equal to zero before time T (as we are in a balanced growth path), then at time T; jumps up to a positive number, and then over time declines (but remains positive) to the old, zero growth rate. Figure 19 shows this discussion graphically. Remember that we chose the ~variables only for convenience. What we are really interested in is the behavior of capital per worker and output per worker. Let us …rst look at the growth rates of these variables as the saving rate changes y K k Y =A =A : Therefore and y~ = AL from s to s0 : Remember that k~ = AL ~ k(t) = k(t)A(t) Taking logs and di¤erentiate with respect to time we …nd the growth rate of capital per worker as : ~ _k(t) k(t) = +g ~ k(t) k(t) Therefore the growth rate of capital per worker reacts to an increase in the saving rate in exactly the same way as the growth rate of k~ (just shifted upwards by g): before time T capital per worker grows at rate g; at time T the growth rate jumps above g and comes back to g over time. We show this in Figure 20. It is equally straightforward to determine the behavior of the growth rate of output per capita over time. The production function is given by ~ ® y~(t) = k(t) and therefore : y~(t) =® y~(t) : ~ k(t) ~ k(t) CHAPTER 3. ECONOMIC GROWTH 62 . ~ ~ k(t)/ k(t) 0 T time t Figure 3.13: Also, since y(t) = y~(t)A(t) we have y(t) _ y(t) : y~(t) y~(t) = = : y~(t) +g y~(t) y(t) _ ¡g y(t) and hence y(t) _ =® y(t) : ~ k(t) +g ~ k(t) 3.3. THE SOLOW MODEL 63 . k(t)/k(t) g T time t Figure 3.14: Therefore the growth rate of output also behaves similar to the growth rate ~ Before time T output per worker grows at constant rate g as we are in of k: the balanced growth path. At time T; the growth rate jumps up (but only by ~ and then comes back to its balanced a fraction ® than the jump for k or k) growth path level of g: We demonstrate this in Figure 21. So far we only talked about growth rates. But what happens to the level of per capita output? We know that in the old balanced growth path and in the new balanced growth path the level of per capita income grows at constant rate g: Along the transition path the growth rate is higher than g, i.e. output per worker temporarily grows at a faster pace. In Figure 22 we draw the behavior of the level of output per capita. Instead of y we plot log(y) (remember why it is easier to plot the log of a variable that grows at a constant rate over time). Note that the picture makes clear that there are no long run e¤ects on the CHAPTER 3. ECONOMIC GROWTH 64 . y(t)/y(t) g T time t Figure 3.15: growth rate of output per capita from an increase in the saving (investment) rate: in the long run output grows at rate g and only increases in the rate of technological progress a¤ect the long-term growth rate of output per capita. Therefore any policy that helps to raise the saving rate s is unsuccessful in increasing long term growth rates of real per worker GDP (if, of course, we believe in the Solow model). On the other hand, an increase in the saving rate has a level e¤ect: it permanently increases the “plateau” on which output per capita grows, as shown in Figure 22. This ends our discussion of how a change in the saving rate a¤ects growth rates and level of output (and income) per capita in the extended Solow model. The same techniques and graphs can be applied when analyzing changes in the population growth rate n, the depreciation rate ± or the rate of technological progress g. 3.3. THE SOLOW MODEL 65 log(y) level effect slope g slope g T time t Figure 3.16: 3.3.6 Evaluation of the Solow Model So is the extended Solow model a success? Let us start with the growth facts. In the Solow model, in the long run (along a balanced growth path) output per worker and capital per worker grow at the same positive rate g; the rate of technological progress. Hence the ratio between the aggregate capital stock and output K Y is constant. Therefore the …rst two stylized facts can be explained by the Solow model. However, they are only explained when we introduce technological progress at rate g > 0: Why this progress happens is left unexplained. In the next sections we will look at models that explicitly try to explain technological progress. What about the other two stylized growth facts, the facts that the real interest rate and the capital and labor shares are constant over time? It turns out that the Solow model has the property that the real interest rate and the capital and labor share are constant along a balanced growth path. To see this CHAPTER 3. ECONOMIC GROWTH 66 we have to take a little detour. So far we didn’t talk about who produces the output in our economy. So let us introduce …rms. Firms produce output by hiring L(t) numbers of workers, which are paid a wage w(t) and by renting capital K(t) from households who own the capital stock. Per unit of capital the …rms have to pay rent r(t): The real interest rate equals r(t) ¡ ±: households receive rent r(t) for one unit of capital, but a fraction ± of the capital that they lend to …rms they don’t get back because it wears out in the production process. Therefore the e¤ective return on lending out capital (which is the real interest rate) equals r(t) ¡ ± We assume that …rms are price takers, hence take the price for output p(t) and the prices for their inputs, w(t) and r(t); as given. We normalize5 the price of output to p(t) = 1: A …rm then solves the problem to maximize their pro…ts, which are given by the di¤erence between the sales of their output and the payments for their inputs. They do so by choosing how many workers L(t) to hire and how much capital K(t) to rent. max K(t)® (A(t)L(t))1¡® ¡ w(t)L(t) ¡ r(t)K(t) K(t);L(t) Remember from calculus that we maximize a function by taking …rst order conditions and setting them to 0: Taking …rst order conditions with respect to K(t) yields ®K(t)®¡1 (A(t)L(t))1¡® = r(t) or ® µ K(t) A(t)L(t) ~ = But remember our variable k(t) ¶®¡1 K(t) A(t)L(t) : = r(t) Hence ~ ®¡1 r(t) = ®k(t) Along the balanced growth path k~ is constant, and it follows that the rental price for capital, r(t) is constant along the balanced growth path in the Solow model. From this it follows that the real interest rate is constant along the balanced growth path. What about the capital share? Total income in this 1¡® : Per unit of capital, the amount r(t) economy is Y (t) = K(t)® (A(t)L(t)) is earned as capital income (rent). Hence total capital income equals r(t)K(t) and the capital share (the fraction of income that goes to capital) equals r(t)K(t) Y (t) = ®K(t)®¡1 (A(t)L(t))1¡® K(t) K(t)® (A(t)L(t))1¡® ®K(t)® (A(t)L(t))1¡® = K(t)® (A(t)L(t))1¡® = ® 5 As in microeconomics, as long as there is no money in the economy we can pick one good to be the numeraire and normalize its price to 1: In the presence of money, money is usually taken to be the numeraire, and the degree of freedom to normalize another price to 1 is gone. 3.3. THE SOLOW MODEL 67 Hence the capital share in the Solow model equals ® (and therefore the labor share equals 1 ¡ ®): So ® is not only a technical parameter in the production function, but turns out to be equal to the capital share. Note that this is true not only along a balanced growth path, but is true at all times in the Solow model.6 This motivates economists to pick values for ® of around 13 in numerical exercises. Finally it is easy to show that along the balanced growth path wages also grow at rate g; the rate of technological progress (by looking at the …rst order condition of the …rm with respect to L(t)). We conclude that the extended Solow model is successful in explaining all four stylized growth facts of Kaldor. What about the development facts from the Summers-Heston data set? 1. Enormous di¤erences in income levels across countries: the Solow model can explain di¤erences in levels by pointing to di¤erences in population growth rates and di¤erences in saving (investment) rates. But can it explain the magnitude of these di¤erences? We will come back to this point, but the verdict here will be negative 2. Enormous variation in growth rates per worker. There are two answers the Solow model can give. According to the model, two countries can permanently grow at di¤erent rates only if they have di¤erences in the rate of technological progress g (otherwise they eventually grow at the same rate). Given that technology, at least most of it, is based on knowledge that freely moves across countries this would be a rather unsatisfactory answer. The Solow model can do better than this, by appealing to transition dynamics. Remember that along the transition to a balanced growth path the growth rate changes over time. So di¤erences in growth rates across countries could be due to the fact that some countries are closer to the balanced growth path than others (but eventually they will all grow at the same rate). Germany and Japan, for example, lost most of their capital stock during World War II. So by starting far below the balanced growth path these countries are predicted by the model to grow faster than countries that did not have their productive capacity destroyed during WWII. 3. Transition dynamics can also explain why the growth rate of a country is not constant over time. 4. Changes in the relative position of a country can be explained by the Solow model by appealing to the same features as in point 1: Countries whose population growth rate declines or saving rates move up, relative to other countries, should move up in the international income distribution. 6 It is a consequence of the assumption of price taking behavior and a constant returns to scale production function of Cobb-Douglas type. Also remember from your micro class that with constant returns to scale all …rms earn zero pro…ts and the number of …rms operating is undetermined -and we might as well assume that there is a single …rm producing all the output. 68 CHAPTER 3. ECONOMIC GROWTH So in principle the Solow model can capture most of the stylized facts that we set out in the beginning, at least qualitatively. It does so, however, by appealing to technological progress that is left unexplained in the model. After taking some further looks at the data we will pick this point up again. 3.4 The Convergence Discussion We have seen that one of the most puzzling, and probably the most troublesome facts coming from the Summers-Heston cross country data set is the enormous disparity in incomes per worker across countries. Development economists (and not only those) naturally ask the question of whether these di¤erences are permanent or whether we should expect that eventually the poor countries catch up to the rich countries, a phenomenon that economists term “convergence”. Among others, economic historians Aleksander Gerschenkron (1952) and Moses Abramovitz (1986) have advanced the hypothesis that poor countries should grow faster, under the appropriate assumptions, than rich countries. We term this hypothesis the “convergence hypothesis”. Note that the question of convergence is intimately related to the observation of variation of growth rates across countries: a country can only catch up to another (group of) country if it grows at a faster pace. So convergence requires poorer countries to grow faster than richer countries. In this section we ask two questions: a) do we see convergence in the data b) what does the Solow model have to say about convergence. The main prediction of the convergence hypothesis is that poor countries grow faster than rich countries. We can test the convergence hypothesis by looking at whether this prediction is born out in the data. This is typically done by looking at a plot of the following sort: on the x-axis we have a variable that indicates how rich a country initially is, typically the level of GDP per worker or GDP per capita for the …rst year for which we have data. On the y-axis we have the growth rate of a country from the initial to the …nal period. Plotting lots of di¤erent countries we would expect a negative correlation between the initial level of GDP per worker and the growth rate if the convergence hypothesis is true: rich countries grow slower than poor countries, according to the convergence hypothesis. Let look at such plots. In Figure 23 we use data for a long time horizon for 16 now industrialized countries. Clearly the level of GDP per capita in 1885 is negatively correlated with the growth rate of GDP per capita over the last 100 years across countries. So this …gure lends support to the convergence hypothesis. We get the same qualitative picture when we use more recent data for 22 industrialized countries: the level of GDP per worker in 1960 is negatively correlated with the growth rate between 1960 and 1990 across this group of countries, as Figure 24 shows. This result, however, may be due to the way we selected countries: the very fact that these countries are now industrialized countries means that they must 3.4. THE CONVERGENCE DISCUSSION 69 Growth Rate of Per Capita GDP, 1885-1994 Growth Rate Versus Initial Per Capita GDP 3 JPN 2.5 NOR FIN ITL 2 CAN DNK GER SWE AUT FRA USA BEL 1.5 NLD GBR AUS NZL 1 0 1000 2000 3000 4000 5000 Per Capita GDP, 1885 Figure 3.17: have caught up with the leading country (otherwise they wouldn’t be called industrialized countries). When we do the same plot for the whole sample of 104 countries (not just industrialized countries) Figure 25 doesn’t seem to support the convergence hypothesis: for the whole sample initial levels of GDP per worker are pretty much uncorrelated with consequent growth rates. In particular, it doesn’t seem to be the case that most of the very poor countries, in particular in Africa, are catching up with the rest of the world, at least not until 1990 (or until 2000 for that matter). What does the Solow growth model have to say about convergence. Let us distinguish two situations CHAPTER 3. ECONOMIC GROWTH 70 Growth Rate of Per Capita GDP, 1960-1990 Growth Rate Versus Initial Per Capita GDP JPN 5 POR 4 GRC ESP 3 ITL IRL TUR AUT 2 FRA BEL FIN NOR GER GBR DNK NLD SWE CAN CHE AUS USA 1 NZL 0 0 0.5 1 1.5 2 2.5 Per Worker GDP, 1960 Figure 3.18: 1. Suppose all countries have the same savings rates s; same population growth rates n and the same growth rate of technological progress (because there is free transfer of knowledge across borders). That is, all countries have the same balanced growth path. Then the Solow model predicts two things: a) eventually all countries reach the balanced growth path, all countries will have the same growth rate and the same level of per worker GDP b) countries that start with capital per worker further below the balanced growth path (i.e. are initially poorer) grow faster along the transition path than do countries that are initially richer. Remember Figures 16 and 17. So the Solow model predicts convergence among countries with similar saving rates, depreciation rates and population growth rates, convergence to the same balanced growth path. Such convergence is also called absolute convergence, because eventually these countries will have the same level of income per capita. Figures 23 and 24 show convergence 4 x 10 3.4. THE CONVERGENCE DISCUSSION 71 Growth Rate of Per Capita GDP, 1960-1990 Growth Rate Versus Initial Per Capita GDP 6 4 2 0 -2 KOR HKG OAN SGP JPN SYC CYP LSO THA PRT GRC ESP MYS ITA IDN JOR SYR TUR IRL EGY ISRAUTFINFRABEL YUG ECU CHN BOL PRY BRA GER LUX NAM CAN GIN COL DZA NOR NLD CMR TUNGAB ISL PNG MUS MEX GBR BGDCSK PAN CHE DNK ZAF FJI AUS DOM HND LKA SWE NGA GTM CIV CRI PHL COM GNB SLV CHL MAR URY COGJAM IND CIV NZL SEN CAF ZMBZWE IRN PER TTO KEN BEN GMB TGO GHA MOZ TCD VEN RWANIC MLI MRT UGA CAF MDG MLI MWI BFA BDI LSO BFA GUY MOZ PAK USA -4 0 0.5 1 1.5 2 2.5 Per Worker GDP, 1960 Figure 3.19: among industrialized countries. To the extent that the industrialized countries in Figures 23 and 24 have similar characteristics (similar s; n; ±; ®; g) this is exactly what the Solow model would predict. 2. So does Figure 25 constitute the big failure of the Solow model? After all, for the big sample of countries it didn’t seem to be the case that poor countries grow faster than rich countries. But isn’t that what the Solow model predicts? Not exactly: the Solow model predicts that countries that are further away from their balanced growth path grow faster than countries that are closer to their balanced growth path (always assuming that the rate of technological progress is the same across countries). This is called conditional convergence. The “conditional” means that we have to look at the individual countries’ steady states to determine how fast a country should grow. So the fact that poor African countries grow slowly 4 x 10 72 CHAPTER 3. ECONOMIC GROWTH even though they are poor may be, according to the conditional convergence hypothesis, due to the fact that they have a low balanced growth path and are already close to it, whereas some richer countries grow fast since they have a high balanced growth path and are still far from reaching it. To test the conditional convergence hypothesis economists basically do the following: they compute the steady state output per worker7 that a country should possess in a given initial period, say 1960, given n; s; ±; ® measured for this country’s data. Then they measure the actual GDP per worker in this period and build the di¤erence. This di¤erence indicates how far away this particular country is away from its balanced growth path. This variable, the di¤erence between hypothetical steady state and actual GDP per worker is then plotted against the growth rate of GDP per worker. If the hypothesis of conditional convergence were true, these two variables should be negatively correlated across countries: countries that are further away from their balanced growth path should grow faster. Jones’ Figure 3.8 provides such a plot. In contrast to Figure 25 (or his Figure 3.6) we see that, once we condition on country-speci…c balanced growth paths, poor (relative to their BGP) countries tend to grow faster than rich countries. So again, the Solow model is quite successful. A few words of caution about the success of the Solow model. Most of the arguments presented in this section rely on transition dynamics: countries are not in the balanced growth path and hence can grow at rates di¤erent from g; the rate of technological progress. There are obvious and frequent reasons why countries may be thrown out of their balanced growth paths: wars, famines, political instability, you name it. The Solow model is obviously silent about why these events come about. Also, the model doesn’t answer the important question of what it is about special countries that makes them have low saving rates, low population growth rates and hence lower balanced growth paths. It also does not speak to the question where technological progress, the source of growth in the model, comes from. Finally, so far it only provides qualitatively the right answers. But if we take reasonable numbers for s; n; ±; ® in di¤erent countries, does the model provide reasonable numbers for the size of dispersion in per worker output across the world. In other words: are the s; n; ±; ® in the data really so much di¤erent for the US and Ethiopia as to give rise to 40 times higher output per worker in the US as in Ethiopia?8 7 Which is proportional to the balanced growth path output per worker (just multiply it by the constant A(1960)): 8 The answer to this question is highly disputed, but I doubt it. For those interested I have further references on this issue. 3.5. GROWTH ACCOUNTING AND THE PRODUCTIVITY SLOWDOWN73 3.5 Growth Accounting and the Productivity Slowdown The aggregate production function posits that the output Y (t) of an economy is produced by the two factors of production: capital K(t); labor L(t); in combination with the available technology A(t): We can follows Solow (1957) and perform some simple accounting to break down the growth rate of output into the growth rate of capital input, the growth rate of labor input and the growth rate of technological progress. We rewrite the aggregate production function as Y (t) = B(t)K(t)® L(t)1¡® The factor B(t) captures the level of technology and equals A(t)1¡® from before. B(t) is called total factor productivity, and a production function in which technological progress enters the way as shown is said to have Hicks-neutral technological progress.9 Doing our usual trick of …rst taking logs with respect to time and then di¤erentiating with respect to time we get gY (t) = gB (t) + ®gK (t) + (1 ¡ ®)gL (t) or, if we work with A(t) instead of B(t) gY (t) = (1 ¡ ®)gA (t) + ®gK (t) + (1 ¡ ®)gL (t) The growth rate of B(t); gB (t) is called total factor productivity (TFP) growth or multifactor productivity growth. We can use these formulas to perform our basic accounting exercise for a particular country: …rst we have to take a stand on what ® is. Since it turns out to be the capital share, an ® = 13 is quite popular among economists. Next we measure the growth rate of real GDP, gY the growth rate of the aggregate capital stock gK and the growth rate of labor input gL from the data.10 We then use the formula above to compute gB as the residual gB (t) = gY (t) ¡ ®gK (t) ¡ (1 ¡ ®)gL (t) Computed this way, gB is also called the Solow residual, it is that part of output growth that cannot be explained by the growth in inputs capital and labor.11 9 There are several reasons of why we make the change from A(t); multiplying labor, to B(t); multiplying K(t)® L(t)1¡® : First, the growth rate of B is a widely used productivity measure by economists. Second, Solow did it this way (which shows that economists cannot be consistent with their notation). Third, in the Cobb-Douglas case both ways are equivalent, but for more general production functions this is not true anymore. 10 Labor input is usually measured by the total number of manhours worked in the economy in a given period. This is a more precise measure of labor input than the number of workers as the number of hours a worker works per year may change over time. 11 In some sense it measures our ignorance in explaining growth. In the light of our previous discussion, the Solow residual may (should!) measure technological progress. CHAPTER 3. ECONOMIC GROWTH 74 Before actually carrying out the accounting exercise one word of caution is in order. We will only measure TFP growth correctly if we measure the growth in output and in labor and capital inputs correctly. Measuring gY and gL is relatively straightforward, but measuring the growth rate of the capital stock may be tricky. An example: suppose the capital stock of an economy consists only of 10 486-processor computers and now the economy invests in a new Pentium 2, which is double as fast as the 486’ers. Did the capital stock go up by 10% (as the number of computers went up by 10%) or did it go up by 20% (as the computing power went up by 20%)? In practice a lot of assumptions and simpli…cations are needed when measuring the growth rate of the capital stock and this variable is probably one of the most poorly measured economic variables. The consequences of this problem for measuring TFP growth are enormous: suppose we measure gK as 3% but it was in fact 6%: Then we attribute ® ¤ (6% ¡ 3%) = 1% of output growth to productivity growth when it was in fact due to growth in capital input. Computing productivity as a residual leads to mismeasurement of productivity whenever inputs or output are not measured correctly. But now let’s go ahead and perform the accounting exercise for US data from 1960 to 1990. In Table 7 we report averages of growth rates for output and factor inputs for several subperiods. We assume that ® = 13 : In parenthesis is the percent that capital, labor and TFP growth contribute to GDP growth Table 7 Period 1960 ¡ 90 1960 ¡ 70 1970 ¡ 80 1980 ¡ 90 GDP gY 3:1 4:0 2:7 2:6 Capital ®gK 0:9 (28%) 0:8 (20%) 0:9 (35%) 0:9 (34%) Labor (1 ¡ ®)gL 1:2 (38%) 1:2 (30%) 1:5 (56%) 0:7 (26%) TFP (gB ) 1:1 (34%) 1:9 (50%) 0:2 (8%) 1:1 (41%) GDP p. worker gy 1:4 2:2 0:4 1:5 We see that real GDP grew strongest in the 60’s, at 4% a year, and at about 2 12 % since then. Approximately 1 percentage point of this growth is due to accumulation of physical capital. Between 0:7 and 1:5 percentage points is due to growth of labor input. We see the dramatic decline of total factor productivity in the 70’s: from 1:9% in the 60’s to just about 0: This productivity slowdown is one of the most studied and least understood phenomena of recent economic history; it is an international phenomenon in that a lot of countries experienced a productivity slowdown at approximately the same time. The 80’s showed somewhat of a recovery of TFP growth to 1:1%; and the latest numbers indicate that for the last four years TFP growth was again at the speed of the 60’s. Remember that GDP per worker is de…ned as y = YL : Sometimes this variable is also referred to as labor productivity, as the ratio of output to labor input. 3.5. GROWTH ACCOUNTING AND THE PRODUCTIVITY SLOWDOWN75 We immediately have that gy = gY ¡ gL ; hence from the formulas above gy gy = gB + ®gk = (1 ¡ ®)gA + ®gk and we see the direct impact of TFP growth on per worker income growth (or labor productivity). As predicted by this equation, the productivity slowdown of the 70’s led to a sharp decline of income per worker in that period, with the growth rate of per worker income recovering in the 80’s (and even more so in the late 90’s). What are possible reasons for the productivity slowdown? As mentioned it is still somewhat of a puzzle. Here are some explanations 1. Sharp increases in the price of oil which made companies use inferior technology that didn’t require oil. Problem: oil prices (adjusted for in‡ation) are lower in the late 80’s than in the 60’s. 2. Structural changes: as the economy produced more and more services and less and less manufacturing goods the high productivity sectors (manufacturing) become less important than the low productivity sectors (services). 3. Slowdown in resources spent on R&D in the late 60’s. 4. TFP was abnormally high in the 50’s and 60’s since all the new technologies developed for the war became available for private business sector use. So the 70’s and 80’s are the “normal” situation. 5. Information technology (IT) revolution in the 70’s. Computers swept into business o¢ces and for the last 10 to 15 years a lot of time was spent learning how to use them (instead of producing output). Hence the productivity slowdown. Once the new technology is …gured out, TFP should boom again. Probably the truth is that all these factors contributed to the slowdown, although I personally …nd the last explanation very intriguing, in particular given that TFP has been extraordinarily high in the last …ve years, possibly showing the e¤ects of investment in IT started in the 70’s and 80’s. We can use the same framework for the analysis of the growth process in other countries. In particular, what determinants are responsible for the growth miracles in East Asia, the Singapores, Japans, Koreas, Hong Kongs and Taiwans? There exists a somewhat heated discussion about this issue, with one group of economists attributing most of the fantastically high growth rates from the 60’s to the mid 90’s to TFP growth, whereas others attribute most of it to the fast accumulation of physical (and human) capital. In Table 8 we show results from growth accounting for the Asian growth miracles, and, as a comparison, data for some industrialized and some Latin American countries. The calculations are done with country-speci…c ®’s, where the ® for a particular country is matched to that country’s average capital share during the relevant time period. CHAPTER 3. ECONOMIC GROWTH 76 Table 8 Country Germany Italy UK Argentina Brazil Chile Mexico Japan Hong Kong Singapore South Korea Taiwan Time Per. 1960 - 90 1960 - 90 1960 - 90 1940 - 80 1940 - 80 1940 - 80 1940 - 80 1960 - 90 1966 - 90 1966 - 90 1966 - 90 1966 - 90 GDP gY 3:2 4:1 2:5 3:6 6:4 3:8 6:3 6:8 7:3 8:5 10:3 9:1 Cap. Sh. ® 0:4 0:38 0:39 0:54 0:45 0:52 0:63 0:42 0:37 0:53 0:32 0:29 Cap. ®gK 1:9(59%) 2:0(49%) 1:3(52%) 1:6(43%) 3:3(51%) 1:3(34%) 2:6(41%) 3:9(57%) 3:1(42%) 6:2(73%) 4:8(46%) 3:7(40%) Labor (1 ¡ ®)gL ¡0:3(¡8%) 0:1(3%) ¡0:1(¡4%) 1:0(26%) 1:3(20%) 1:0(26%) 1:5(23%) 1:0(14%) 2:0(28%) 2:7(31%) 4:4(42%) 3:6(40%) Although there is always the issue of mismeasurement (which is very important in these exercises) it does not appear to be the case that the bulk of East Asia’s growth miracle is due to particularly strong TFP growth. Fast capital accumulation (a high growth rate of the capital stock) seems to be at least as important. 3.6 Ideas as Engine of Growth We saw that the Solow model was very successful in explaining Kaldor’s growth facts and fairly successful in explaining the stylized development facts that we found from the Summers-Heston cross country data set. However, I stressed several time that the source of growth in the Solow model is technological progress and that this technological progress is an assumption of the model. Why there _ A(t) = gA > 0) is not explained within the is positive technological progress (i.e. A(t) model. In this section we will informally discuss the main ingredients of growth models that eliminate this shortcoming by explicitly explaining why technology grows at a constant positive rate. In the second part of this section we will brie‡y describe how we can measure technological progress directly from the data.12 3.6.1 Technology Let us …rst de…ne precisely what we mean by technology. Technology is the way inputs to the production process (in our case labor and capital) are transformed 12 Note that we tried to measure technological progress in the last section. There technological progress or TFP was not measured directly, it was de…ned as the residual of output growth and growth of inputs labor and capital. TFP (gB ) 1:6(49%) 2:0(48%) 1:3(52%) 1:1(31%) 1:9(29%) 1:5(40%) 2:3(36%) 0:2(29%) 2:2(30%) ¡0:4(¡4%) 1:2(12%) 1:8(20%) 3.6. IDEAS AS ENGINE OF GROWTH 77 into output. In our example without technological progress we had Y (t) = K(t)® L(t)1¡® In this case technology is completely described by the parameter ® (and the fact that capital and labor input enter multiplicatively in the production function). Not that for this case technology does not change over time. The amount of inputs K(t) and L(t) may vary over time, and hence the amount of output produced may change over time, but given inputs the way output is produced does not change over time (one easy way to see this is to realize that the only place t enters in the production function is in K(t) and L(t)). The situation is di¤erent when the production function is given by 1¡® Y (t) = K(t)® (A(t)L(t)) A(t) is an index of technology that the economy has access to in period t: If A(t) changes over time, then technology changes over time. Suppose in period T A(T ) is twice as big as A(t) in period t: Then, even if the economy uses the same amount of labor and capital in both periods, in period T the economy produces 21¡® times the output in period t. An easy way to see that in this case technology is not constant is to realize that t enters not only in K(t) and L(t); but also in A(t): Increases in the technology index A(t) are called technological progress. When new ideas are created, new knowledge is added to the existing stock of knowledge and more output can be produced with a given amount of labor and capital. New ideas can come in the form of new procedures to put more and more tansistors onto a computer chip of given size (Moore’s Law states that the number of transistors that can be packed onto a given chip doubles roughly every 18 months), the development of new drugs against diseases, a new strategy to run chain stores etc. The important insight of economists that worked in the area of growth and ideas was not so much that new ideas can induce economic growth, but rather that ideas do not usually simply fall from heaven, but are the result of costly e¤ort to discover new ideas. Firms, governments and individuals spent time and money on activities that are designed to generate new ideas that then bene…t economic growth. Our next task is to investigate why (and under what circumstances) resources are spent on the development of new ideas. 3.6.2 Ideas A key feature of ideas are that they are nonrivalrous goods. If one person uses calculus, another person is not precluded from using exactly the same idea. This makes ideas very di¤erent from most goods. If I consume a pizza, you cannot consume the same pizza. Pizza, as most consumption goods are rivalrous, but ideas are not. A nonrivalrous good is a good whose use by one person does not preclude the use of this same good by another person. An important consequence of this fact is that usually nonrivalrous goods only have to be produced once: once an idea has been developed it is there for use, and 78 CHAPTER 3. ECONOMIC GROWTH it needs not be discovered again. This fact will turn out to have important consequences. Another key feature of ideas are they are, at least partially, excludable. A good that is excludable is a good for which the owner of the good can charge another person a fee for the use of it. A good can very well be excludable but nonrivalrous: think of computer software. The fact that I use Windows NT does not preclude you from using it, but for sure Microsoft tries to make sure that they can charge a fee for the use of Windows NT. The legal system of most countries has provisions that make sure that developers of new ideas have the right to charge users of these ideas a price by providing copyright and patent laws. Dividing goods along the two dimensions of nonrivalry and nonexcludability we can distinguish four groups of goods 1. Rivalrous goods that are excludable: almost all private consumption goods, such as food, apparel and consumer durables fall into this group. 2. Rivalrous goods that have a low degree of excludability: an example is the …sh in international waters. When the …sh is caught by American …shermen, Japanese …shermen are precluded from catching and selling them. Hence these …sh are rivalrous goods. But American …sherman have no possibility to exclude Japanese …shermen from …shing in international waters. Rivalrous, nonexcludable goods often su¤er from the tragedy of the commons. The classic textbook example stems from middle age England. English towns had plots of land, called commons, where all peasants of the town were allowed to graze their cattle free of charge. Since no farmer was excluded, but there was only a …xed amount of grass available, the grass in the commons falls under this category. What happened was that, since grazing an additional cow yielded bene…ts for a farmer and the cost was shared among all farmers (less grass available), the commons were completely overgrazing and became useless. A similar development threatens to happen with the stock of …sh in international waters. To avoid the tragedy of the commons usually government intervention or private agreements to avoid overgrazing or -…shing are needed. 3. Nonrivalrous goods that are excludable: examples include the computer code for software programs or blueprints for the production of machines, cameras, lasers etc. Most of what we call ideas in this section would fall under this point. 4. Nonrivalrous and nonexcludable goods: these goods are often called public goods because they are mostly produced, or at least provided, by the government. The prime example is national defense: the fact that the U.S. government protects you from an aggression of some other country does not preclude me from being protected; also usually nobody is excluded from this good national defense (the times of outlaws are gone). Some ideas fall under this point, too. Basic scienti…c research is such an example. 3.6. IDEAS AS ENGINE OF GROWTH 79 It is obviously nonrivalrous and I can hardly exclude you from learning about the Solow model (even if I tried very hard so far). As we will see, the fact that a lot of basic research is done in public or publicly funded institutions is no accident, but follows from basic economic principles. The distinction into excludable/nonexcludable and rivalrous/nonrivalrous goods is not only academic. It has a huge impact on the economics of ideas. Consider nonrivalrousness …rst. Since an idea is a nonrivalrous good, it can be used by many people without precluding other people from using it. This just means that the cost of providing the good to one more consumer, the marginal cost of this good, is constant at zero (or at least very low, if the idea has to be put on some physical object, like a ‡oppy disk). But developing the idea at …rst may involve substantial resources, i.e. high start-up or …xed costs. Hence the production process for ideas is usually characterized by substantial …xed costs and low marginal costs.13 Now comes in the issue of excludability. Suppose a …rm can’t exclude another …rm from adapting and also selling the idea (or the good based on the idea). Competition would then drive down the price of the good to marginal cost (remember your micro class). But because of the original …xed cost the …rm that invented the idea would lose money by developing and then selling the idea at marginal cost. So would any …rm ever develop an idea if it can’t exclude it from competitors? Most likely not. Hence for the development of new ideas by private companies it is crucial that ideas are excludable. Therefore the existence of intellectual property rights like patent or copyright laws are crucial for the private development of new ideas, and hence for the engine of growth. It is also not surprising that ideas that can’t be made excludable by these laws (or for which society decides that these ideas are so desirable that everybody should have unlimited access to them) are usually developed by publicly …nanced institutions. In fact, some economic historians have made the point that this force is so strong that it explains part of the industrial revolution. Remember that sustained economic growth is a very recent phenomenon. Before the middle of the 18-th century, economic growth was an unknown phenomenon. Then, so the hypothesis of economic historian and Nobel price winner Oliver North, institutions developed that protected intellectual property rights. Only after this had happened could private …rms and individuals be sure that their investment into developing new ideas would be rewarded by warranting patents that then could be sold for fees covering the initial …xed cost of development. The number of new ideas developed increased, sustained technological progress occurred and the world, for the …rst time, experienced sustained economic growth. The initial period of economic growth in the late 18-th and early 19-th century is called the industrial revolution; its timing coincides pretty closely with the drafting of the US constitution, the French revolution and following Declaration 13 This cost structure for the production of ideas is closely linked to the fact that the production process for ideas is usually characterized by increasing returns to scale. See Jones for details. CHAPTER 3. ECONOMIC GROWTH 80 of the Rights of Man and of the Citizen, and the publishing of the …rst book on economics stressing private property rights, self-interest and private markets, Adam Smith’s “An Inquiry into the Nature and The Causes of the Wealth of Nations”. 3.6.3 Data on Ideas How can we measure technological progress directly, i.e. not just as Solow residual in our accounting exercises? To the extent that we attribute technological progress to the evolution of new ideas, this translates into the question of how we can measure the amount of new ideas being produced. There are two ways: we can try to count the number of new ideas directly or (since this may be easier) we can try to measure the amount of resources that are spent in producing new ideas. If more resources mean more ideas, this gives us indirect evidence about the number of new ideas that should have been produced during a particular time period. How can we measure the number of ideas? One close proxy may be the number of patents issued. Jones provides data for the number of patents the have been issued in the US, from 1900 to 1991. The data show the following general features: ² the number of patents issued has increased substantially: in 1900 roughly 25,000 patents were issued in the US, in 1990 the number was 96,000 ² more and more patents issued in the US are issued to foreign individuals or foreign …rms. The number of patents issued to US …rms or individuals has been roughly constant at 40,000 per year between 1915 and 1991. Obviously these data don’t tell us anything about the importance of each patent. The patent for the light bulb is supposedly hundred times more important than the patent for the self-rotating hamster cage. The data do not re‡ect this di¤erence of importance and therefore obviously give only a limited account of how the level of ideas has evolved over time. Ignoring this caveat it seems that the level of technology, as measured by the stock of ideas, has increased rapidly in the US over the last century. Jones also provides data on resources devoted to the development of new ideas. His Figure 4.6 shows how the number of researchers engaged in research and development (R&D) evolved in the US and in other industrialized countries over the last 40 years. Not only did the absolute level increase substantially (from around 200,000 to about 1,000,000 between 1950 and 1990 for the US), but also the fraction of the labor force involved in R&D increased from about 0.25% in 1950 to about 0.75% in 1990. This also indicates, to the extent that more researchers develop more ideas, that the number of ideas and hence the level of technology has increased rapidly over the last 40 years or so. So what have we accomplished in this section? We …rst de…ned what exactly we mean by technology. We then associated improvements in technology with the discovery of new ideas. We then argued that by its very nature ideas are 3.7. INFRASTRUCTURE 81 nonrivalrous goods and discussed what this implies for the cost structure of producing goods based on new ideas. We then argued why it is important for the development of new ideas that ideas are, or are made, excludable goods and …nally we presented some data showing that indeed the number of ideas has rapidly increased over the time horizon we have reliable data for. By doing all this we have provided an explanation for sustained technological progress that was the underlying force of economic growth in the Solow model. Our discussion was purely verbal in nature. In the mid 80’s and early 90’s models have been developed that formalized our reasoning, in particular by Stanford’s Paul Romer (1990). Jones’ Chapters 5 and 6 discuss these models in detail and the interested reader is invited to consult the book. 3.7 Infrastructure In the last section we looked at how we can justify one assumption of the Solow model, namely that the level of technology grows over time. Now we want to look at another assumption, namely the assumption that each country saves and invests a certain fraction of output (and consumes the rest). Why is this important? Remember that the Solow model explains di¤erences in income levels across countries by di¤erences in saving or investment rates. The question is then: why do some countries save and invest such a high fraction of income, whereas other countries don’t. Our answer will roughly be that some countries have political institutions that make investing more pro…table than others. For the purpose of this section we will interpret s as the investment rate rather than the saving rate (in the Solow model both are equivalent). We will also interpret the capital stock as including not only physical capital, but also human capital, the skill and education that the labor force has acquired. So by investment we will mean investment in physical capital (building new factories and the like) as well as investment in human capital such as schooling.14 Each investment has costs and bene…ts: a …rm that contemplates building a new factory weighs the cost of construction against the bene…ts of being able to produce and sell products with the new factory; in your decision to invest in your Stanford education you weigh the cost (tuition, opportunity cost of your time) against the bene…ts (better pay and more interesting work in the future). The reason why some countries invest more than others is then due to the fact that either the costs of investment are lower or the bene…ts are higher (or both) in these countries. So let’s have a look at the determinants of costs and bene…ts of investment. 14 It is quite easy to introduce human capital into the standard Solow model, and Chapter 3 of Jones does exactly that. I skipped it because I think it does not add much to the basic insights that can be gained from the basic Solow model. CHAPTER 3. ECONOMIC GROWTH 82 3.7.1 Cost of Investment The cost of investment may not only involve the resources to come up with a new business idea and the purchase of buildings and equipment, but also the cost of obtaining all legal permissions. That this may involve signi…cant costs (in particular time spent) is demonstrated in the famous book by Hernando de Soto “The Other Path” (1989). De Soto started a small business in Lima, with the purpose of measuring the cost of setting up a small business, in particular those costs due to bureaucracy and compliance with regulations. He was confronted with several o¢cial requirements such as obtaining a zoning certi…cate and registering with tax authorities. Meeting these requirements took an equivalent of 289 working days and required two bribes. Overall, only the cost of meeting these o¢cial requirements amounted to about 32 monthly minimum wages, i.e. for the same money one worker of this company could have been paid for almost three years. Similar stories can be told for a lot of countries and they may provide part of the explanation for why the investment share of output is relatively low. They almost always involve a de…cient or corrupt bureaucracy that impedes pro…table investment activities. 3.7.2 Bene…ts of Investment What determines the pro…tability of an investment project, over and above its costs and the inherent quality of its idea. We will follow Jones and single out several factors 1. The size of the market. The larger the pool of potential buyers of a products (or skill of a person), the larger are the potential bene…ts from an investment. Suppose Netscape’s only market would be the Bay Area. My educated guess is that its stock price wouldn’t be where it is now (better: where it was six months ago). But with potential buyers of Netscape all over the world, the bene…ts for the founders of Netscape are potentially huge. The size of the potential market for a product does depend crucially on political decisions within the country. Countries like the US are very open to international trade, and since the US allows foreign …rms to sell their products in the US, usually US …rms are allowed to sell in foreign countries. A country that decides to remain relatively closed to international trade restricts the market for their …rms to the domestic market and therefore reduces potential bene…ts from setting up a new or expanding an existing business. 2. The extent to which the bene…ts from the investment accrue to the investor. Suppose the investment project actually earns some money. The extent to which institutions in the country guarantee that the pro…t remains with the owner is an important determinant of the decision to invest. Reasons of why pro…ts are diverted from the owner range from high taxes to theft, corruption, the need to bribe government o¢cials or the payment of protection fees to the Ma…a or Ma…a-like organizations. These 3.7. INFRASTRUCTURE 83 features not only tax the investment project, but also may lead to ine¢cient production just to avoid the diversion of pro…ts. It also may channel investment into unproductive sources, such as protection against crime, so as to avoid extortion of pro…ts. To what extent pro…ts are diverted from private investors is largely determined by the government. Hence, roughly, countries with policies and institutions that favor investment bene…ts being diverted from investors make investments less bene…cial and hence will have a lower fraction of output being invested. 3. Rapid changes in the economic environment in which …rms and individuals operate may increase uncertainty of investors. Who would invest in a country for which there is a reasonable chance that tomorrow a new radical government will take power that nationalizes all private …rms? This list of potential determinants of the costs and bene…ts of investment projects is probably not complete. The next task is to determine whether, in the data, these determinants actually have an in‡uence on the share of output that is invested in these countries. Jones provides some …gures that shed light on this question (see his …gures 7.1 and 7.2). In his …gure 7.1. he plots the share of output that is invested (on the y-axis) against a variable that is a weighted average of two variables: one that measures the degree of openness, the other that broadly measures to what extent the government of a particular country tries to stop diversion of pro…ts from private investment. From the …gure one can clearly see that countries that are more open to international trade and stop diversion of private pro…ts more e¤ectively have a higher investment share of output. Figure 7.2 does the same, but focuses on investment in human rather than physical capital. The measure of human capital accumulation (plotted on the y-axis) is the average years of schooling in a particular country, the variable on the x-axis is the same as before. Again we see that the more open and more e¤ective in stopping diversion a country is, the more on average do its citizens invest in school education. So again, what have we accomplished? We explained income di¤erences of countries, following Solow, by di¤erences in investment rates. In this section we have discussed why investment rates are higher in some countries than in others. The basic answer was: some countries have institutions (bureaucracy, policies and politicians) that favor investment to a greater extent. But now the question arises: why do some countries have better institutions (better at least for encouraging investment and therefore economic growth) than others? It is not that economists are completely clueless about this question15 , but instead of speculating at this point it’s time to punt and leave this to the political scientists. 15 There is some exciting work done in the area of political economy, which tries to explain economic policies and institutions as the outcome of explicit or implicit voting procedures. CHAPTER 3. ECONOMIC GROWTH 84 3.8 Endogenous Growth Models In this section I brie‡y want to expose you to a rather di¤erent class of growth models. The Solow model (and all its extensions) are called exogenous growth models, as the engine of growth, technological progress, is itself exogenous to the model. The models that explain technological progress (I alluded to them when talking about ideas, but didn’t expose you to the formal models) are sometimes called endogenous growth models since they explain technological progress within the model. Most of these models share one very important feature with the Solow model: a change in the saving (investment) rate has e¤ects on income levels, but not on growth rates. Therefore policies that increase the saving rate have only level, but no growth rate e¤ects. I will now present a simple model in which policies that a¤ect the saving rate will a¤ect the growth rate of the economy. This model (and the class of models based on it) were the …rst type of endogenous growth models. As we will see they do not at all rely on technological progress to generate growth: in these models sustained growth is possible even without any technological progress. The model consists of two equations as before, a production function and a capital accumulation equation. Already written in per worker terms, the capital accumulation is identical to the Solow model _ k(t) = sy(t) ¡ (n + ±)k(t) The only di¤erence is the production function, which takes the form y(t) = Ak(t) where A is a technology parameter that does not change over time (we have no technological progress). The only (very crucial) di¤erence to the Solow model is that k(t) doesn’t have an exponent ® (or you may set ® equal to 1 in the Solow model). Because of the form of the production function these types of models are also referred to as Ak-models. The important economic assumption that di¤erentiates it from the Solow model deals with the marginal product of capital: in the Solow model the e¤ect on output per worker from one unit more of capital per worker was given by ® dy(t) = dk(t) k(t)1¡® and now it is given by dy(t) =A dk(t) The key di¤erence is that in the Solow model the marginal product of capital was decreasing when k(t) was increasing. The additional e¤ect of one unit more capital gets smaller and smaller, and this is the reason for the economy to …nally come to rest at the steady state. In this model the marginal product of capital 3.8. ENDOGENOUS GROWTH MODELS 85 is constant, independently of the level of k(t): This will cause the model to not have a steady state!! But let us proceed. We can substitute the production function into the capital accumulation equation to obtain _ k(t) = sAk(t) ¡ (n + ±)k(t) and now can draw a diagram similar to the Solow diagram. First we make the assumption that sA > n + ±: We then plot the sAk(t) curve and the (n + ±)k(t): Both are straight lines, one with slope sA the other with slope n + ±: Under our assumption the …rst curve is steeper than the second curve. Figure 26 shows both curves. sAk(t) (n+δ)k(t) . k(t) k(0) k(t) Figure 3.20: Suppose the initial capital stock per worker is k(0): At k(0), since the sAk(t) _ is positive and the capital curve lies above the (n+±)k(t) curve, we have that k(t) 86 CHAPTER 3. ECONOMIC GROWTH stock is growing. The important fact in this model is that, under the assumption that sA > n + ±; this is the case for all levels of the capital stock per worker k(t); so the capital stock per worker continues to grow forever. And this is true without may technological progress, it just comes from the fact that capital has a high marginal product that does not decline over time as the economy accumulates more and more. The growth rate of capital per worker is given by _ k(t) = sA ¡ (n + ±) k(t) which also equals to the growth rate of output. Two important facts: the growth rate of the economy is constant and positive (always, not only in a balanced growth path) and the growth rate is increasing in the saving rate. In other words, in this model a country with a higher saving rate has a permanently higher growth rate, not only a higher income level!!! It also follows that all policies that increase the saving rate increase the growth rate. Hence such a policy has growth rate and not only level e¤ects. Note that this model can provide an alternative explanation for di¤erences in growth rates across countries than the Solow model: di¤erences in growth rates are due to di¤erences in saving rates, according to this model. What do the data have to say about this prediction? Figure 27 plots the average investment rate between 1980 and 1990 against the average growth rate of real GDP between 1960 and 1990 for the di¤erent countries in the Summers-Heston data set. We see that investment and growth rates tend to be positively correlated, as predicted by the Ak-model, but only weakly so. I would interpret Figure 27 carefully, as weak, but not convincing support of the Ak model. Jones (in his section 8.4) quotes other empirical results that question the Ak-model. In particular, the rate of investment into human capital has increased rapidly in the US over the last 100 years (as measured by the years of schooling the average American received). The Ak model would predict a strong increase in the growth rate of the economy over the last hundred years. The data, however, indicate that growth rates at the turn of the century for the US have been as high as they are now, contradicting the prediction of the model.16 3.9 Neutrality of Money Before summarizing our main results from the study of the theory and data of economic growth there is one important point to be made about all of growth theory in the way we discussed it. All the variables we looked at, real GDP, real GDP per worker, the capital stock, the real interest rates were real variables. In the whole last chapter not once did we talk about money, nominal interest rates, in‡ation and the like. This is due to what is called the classical dichotomy 16 Other studies have tried to investigate whether the form of the production function (constant returns to scale with respect to capital alone) can be backed up by data. The data seems not to be supportive of this assumption. 3.9. NEUTRALITY OF MONEY 87 Growth Rates and Investment Rates Average Growth Rate 1960-1990 0.06 0.04 0.02 0 -0.02 -0.04 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Average Investment Rate 1980-1990 Figure 3.21: or the neutrality of money. It is fair to say that today most economists believe that in the long run (the time horizon for growth theory) money has no e¤ect on real variables. A doubling in the money supply by the Federal Reserve Bank in the long run just leads to a doubling of the price level, but leaves real variables una¤ected. It is this neutrality of money in the long run that allows us to do growth theory and never talk about money, since growth theory is the theory of output and output growth determination in the long run. We will see that when we talk about economic ‡uctuations, or the determination of output in the short run, the classical dichotomy will not always hold. In the short run money potentially matters in determining real output, and with it monetary policy becomes an interesting topic to study. 0.45 CHAPTER 3. ECONOMIC GROWTH 88 3.10 Summary Let us sum up what we learned in the last chapter. From Kaldor’s stylized growth facts we learned that over the long run capital and output per worker grow at roughly equal and constant positive rates. From the Summers-Heston data set we saw that there are enormous di¤erences in per-worker income levels across countries and that countries also vary widely with respect to growth rates of per worker GDP. We then constructed the Solow model with technological progress. In a balanced growth path the Solow model reproduces Kaldor’s stylized growth facts. In particular the sustained growth of per worker GDP is explained by technological progress, which itself has the origin in the discovery of more and more ideas as engine of growth. The di¤erences in income levels can be explained within the Solow model with di¤erences in saving (investment) rates, whose di¤erences in turn can be explained by di¤erences in institutions across countries that a¤ect the pro…tability of investment projects. A question mark remains whether the Solow model, although capable of explaining the direction of income di¤erences, can explain the magnitude of income di¤erences across countries. For di¤erences in growth rates the Solow model points to transition dynamics and the principle of conditional convergence: countries that are far away from their balanced growth path should grow faster than those close to their balanced growth path. The data show some support for the conditional convergence hypothesis. Finally we looked at a model in which changes in saving rates have e¤ects not only on income levels (as in the Solow model), but e¤ects on growth rates of income. These Ak-type models were found to be somewhat de…cient when confronting their predictions with the data. Overall I think it is fair to say that the Solow model (and its extensions) has been an great success in addressing most of the puzzles in the data on economic growth and development. This may explain that there is substantial agreement among economists about what to study and teach in the area of growth theory. As we will see in a bit, the same cannot be said for the study of economic ‡uctuation, for business cycle theory. Chapter 4 Business Cycle Fluctuations The modern world regards business cycles much as the ancient Egyptians regarded the over‡owing of the Nile. The phenomenon recurs at intervals, it is of great importance to everyone, and natural causes of it are not in sight. (John Bates Clark, 1898) 4.1 Potential GDP and Aggregate Demand Remember the …gure that plots real GDP per capita over the last 30 years. For your bene…t it is reproduced here as Figure 28. Real GDP (and also real GDP per capita) on average grows at a positive rate. We constructed the Solow growth model to explain this fact of sustained econonomic growth. In the Solow model all factors of production (labor and capital) were fully employed to produce output (real GDP) according to the aggregate production 1¡® Yt = Kt® (At Lt ) I switched back to discrete time as for the rest of the course we will work in discrete time. The amount of output that can be produced at time t according to the Solow model is called potential GDP or trend GDP: it is the level of real GDP that can be produced in the economy if all factors of production are fully employed, and it corresponds to the line labeled “Trend” in Figure 28. When it is necessary to distinguish potential GDP from actual GDP we use Ytp as a symbol for potential GDP and Yt for actual GDP. At this point a word of caution: when I say that all factors of production are fully employed I do not mean that the unemployment rate is zero and …rms operate at 100% capacity. People voluntarily quit jobs and it takes time until they start a new job; this relocation process generates a positive unemployment rate even when economist speak of a situation of full employment. Losely, for our purposes full employment means that all factors of production are used as in “normal” times. The unemployment rate in normal times is often referred to 89 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 90 as the Natural Rate of Unemployment (and we will come back to it when we discuss unemployment). So now we know what factors determine potential GDP or trend GDP (Y p ), the amount of output that all …rms together can produce. In this part of the course we want to explain why actual GDP (Y ), the amount of output that actually is produced, can temporarily and cyclically deviate from potential GDP, i.e. we want to explain why there can be business cycles and what causes them. Or, to use Figure 28, we want to explain the ‡uctuations of the solid line around the dotted line. Real GDP in the United States 1967-2001 9.2 Log of real GDP 9 8.8 Trend 8.6 GDP 8.4 8.2 8 1970 1975 1980 1985 Year 1990 1995 Figure 4.1: There are several competing business cycle theories. We will …rst explore a theory that is based on the idea the prices are not fully ‡exible in the short run.1 1 This class of theories that relies on sticky prices or wages is usually referred to as Keynesian or New Keynesian business cycle theory. We will later take a look at a business cycle theory that is neoclassical in spirit, i.e. has fully ‡exible prices and wages, the so-called Real Business 2000 4.1. POTENTIAL GDP AND AGGREGATE DEMAND 91 The idea goes like this: The economy (i.e. all its …rms together) can supply total output equal to potential output.2 The total demand for output, called Aggregate Demand is the sum of demands by all households, …rms, the government and foreign countries for domestic output. If prices were completely ‡exible in the short run, then they would adjust instantenously to equate aggregate demand to potential output, just as in you’ve learned in microeconomics. The key of Keynesian business cycle theory is the assumption that in the short run prices are not ‡exible, they are …xed (or sticky). We assume that at these …xed prices …rms are ready to supply whatever output is demanded. In other words, prices are assumed to be sticky in the short run, but production is assumed to be able to adjust very rapidly to aggregate demand. New Kenesian business cycle theory works hard to provide explanations for why prices are sticky in the short run; please refer to Hall and Taylor’s Chapter 15 for further (quite interesting) details. To repeat: in the short run aggregate demand determines realized GDP; realized GDP may be smaller, may equal or may be bigger than potential GDP. How reasonable is this assumption? For the US …rms on average work at a level of capital utilitization of about 80%, i.e usually only 45 of all the available machines are actually used (or used in as many shifts as they could). Firms usually are also able to adjust labor input to changing aggregate demand by hiring new workers (although this may be di¢cult in a tight labor market like the one we have now) or inducing workers to work overtime, etc. So the assumption that …rms can adjust production instantenously to demand seems quite reasonable. The assumption of sticky prices in the short run seems harder to defend, and the interested reader is referred to Chapter 15 in Hall and Taylor. Business cycle ‡uctuations then come about by ‡uctuations in aggregate demand: recessions are periods in which aggregate demand falls below potential output at the …xed price level whereas booms are times in which aggregate demand is above potential GDP at a …xed price level. The situation is exempli…ed in Figure 29. The aggregate demand curve is downward sloping since at lower prices consumers and …rms demand more goods and services (we will return to this point later). Potential output is independent of the price level; it is determined purely by the availability of production factors in the long run. Suppose the price level is …xed in the short run at P1 . At this price level aggregate demand is lower than potential output, part of the available inputs labor and capital are left idle (more than in normal times) and the economy is in a recession. In the long run prices are assumed to be ‡exible so that in the long run the price level adjusts to P0 and realized GDP equals potential GDP. So in order to develop a uni…ed macroeconomic theory of growth and business cycle our task is to provide a theory of aggregate demand. Growth theory provided the explanation for the growth of potential GDP, and since business cycle ‡uctuations are explained as short-run deviations of aggregate demand from potential GDP, with sticky prices being responsible for these deviations Cycle theory (RBC-theory). 2 Some economists, e.g. Gregory Mankiw in his Macroeconomics textbook, refer to potential output as (long-run) aggregate supply. CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 92 Price Level (P) Potential Output Gap between Potential Output and Aggregate Demand P 1 P 0 Aggregate Demand Output (Y) Figure 4.2: being sustained, we need to explain aggregate demand. We will proceed in two steps: 1. We will determine what aggregate demand is for a given …xed price level P (i.e. we will determine single points on the aggregate demand curve). In doing so we will develop the famous IS-LM-model, due to Sir John Hicks, who formalized the ideas of John Maynard Keynes. 2. We will investigate how changes in the price level change aggregate demand (i.e. we will trace out the entire aggregate demand curve). 4.2. THE IS-LM FRAMEWORK 4.2 4.2.1 93 The IS-LM Framework The Balance of Income and Spending: Keynesian Cross and Multiplier Now we take the price level in the economy as …xed. Therefore we don’t (as of now) have to distinguish nominal from real GDP, but for concreteness let Y be real GDP. Multiplying Y by the …xed price level P gives nominal GDP. Remember that actual GDP is determined by aggregate demand in the short run. We start our analysis of aggregate demand (which equals realized GDP) by remembering that GDP equals total income and equals total spending in the economy (remember that this is an accounting identity, i.e. is always true). From the spending side we have Y = C + I + G + (X ¡ M ) (4.1) On the other hand, how much consumers spend on consumption goods and import goods depends on their income Yh , so C and potentially M are functions of income, i.e. C = C(Yh ) and M = M (Yh ). But by our identity spending Y always has to equal income Yh , and both equal GDP. So (given a price level P ) realized GDP is that level of income Yh for which total income equals total spending Y , i.e. that level of Y that solves Y = C(Y ) + I + G + (X ¡ M (Y )) The situation in which Y = Yh is called Spending Balance by Hall and Taylor. We will now start to model each component of spending. The Aggregate Consumption Function We start with C; the consumption expenditures of private households. So for now we assume that investment I; government spending G and net exports (X ¡M) are just some constant numbers, and in particular do not depend on the level of income in the economy. We posit a very simple theory of consumption in this section: we assume that C = a + bYd (4.2) where a and b are …xed positive constants and Yd is (personal) disposable income of private households. Remember that disposable income is (roughly) total income (GDP) less taxes, i.e. Yd = Yh ¡ T; where T are total taxes. Several things should be noted: 1. The equation in (4:2) is called the aggregate consumption function and gives total consumption as a function of current disposable income. It is a whole contingency plan: if disposable income is 200; then total consumption equals a + b ¤ 200; if disposable income is 500; then total consumption equals a + b ¤ 500 and so forth. 94 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 2. As every model, the aggregate consumption function is a very simple approximation of actual consumption. It is likely that actual consumption depends on other variables besides current disposable income, as future income expectations, current wealth, interest rates and the like. But it is exactly its simplicity that makes the aggregate consumption function tractable. 3. As the name says, the aggregate consumption function models aggregate, or total consumption. It is not meant to model any speci…c household, but all households together. Obviously, if all individual households have individual consumption functions of the form (4:2); then the aggregate consumption function also has this form. But it may be true that even if individual consumption functions look di¤erent, summing them all up gives an aggregate consumption function of the form above.3 4. The constant b is call the marginal prospensity to consume. Note dC = b; i.e. b is equal to the extra amount that households consume that dY d if their disposable income increases by $1: For example, if b = 0:8; then an extra dollar of disposable income makes household spend 80 cents more on consumption. This explains the name marginal prospensity to consume: it is the response of consumption to a marginal (small) increase in disposable income. It is assumed that b < 1: The constant a is sometimes called autonomous consumption, it is that part of consumption that does not depend on income. Let us plot the aggregate consumption function in Figure 30. On the x-axis we have disposable income Yd and on the y-axis we have aggregate consumption. Given the form of the aggregate consumption function, consumption is a linear function (straight line) with intercept a and slope b: The actual constants chosen are a = 220; b = 0:9: This is about what ones gets if one …ts US data on consumption and disposable income for the last 30 years.4 The Keynesian Cross Let us make another simplifying assumption and assume that income is taxed at a constant marginal tax rate ¿ : out of each dollar of total income a fraction ¿ has to be paid in taxes. For example if ¿ = 0:2 then for every dollar of income the household has to pay 20 cents in taxes. With this assumption the relation between total income Yh and total disposable income Yd is given by Yd = (1 ¡ ¿ )Yh 3 The question under which conditions individual consumption functions give an aggregate consumption function of a particular form is actually a deep theoretical question. Aggregation theory deals with these issues that are well beyond the scope of this course. 4 The procedure used is OLS (ordinary least squares) estimation. You will (or have learned) this procedure in great detail in your econometrics classes. 4.2. THE IS-LM FRAMEWORK 95 Aggregate Consumption (in billion $) 2,000 C=a+bY d 1,000 Slope b 1,000 2,000 3,000 Disposable Income (Y ) d (in billion $) Figure 4.3: Substituting this relationship into the aggregate consumption function yields C = a + b(1 ¡ ¿ )Yh (4.3) Our very simple model consists of two equations, (4:3) and (4:1); which determine the two endogenous variables C and Y: We now determine income and spending where we have spending balance. Remember that total spending was given by Y = C + I + G + (X ¡ M ) We assumed that I; G; (X ¡ M ) are some …xed, exogenously given numbers and substitute the aggregate consumption function to get Y = a + b(1 ¡ ¿ )Yh + I + G + (X ¡ M ) (4.4) 96 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS Now we use the fact that at the point of spending balance we have that spending equals income, or Y = Yh : Imposing this condition in (4:4) yields Y = a + b(1 ¡ ¿)Y + I + G + (X ¡ M ) We can now solve for income (spending) Y (1 ¡ b(1 ¡ ¿ )) = a + I + G + (X ¡ M) a + I + G + (X ¡ M) Y = Yh = 1 ¡ b(1 ¡ ¿) The value for aggregate consumption at the point of spending balance is obtained by plugging in for Yh in (4:3): This yields C =a+ b(1 ¡ ¿ ) (a + I + G + (X ¡ M )) 1 ¡ b(1 ¡ ¿) We can also solve for the point of balanced spending graphically. In Figure 31 we draw the famous Keynesian Cross diagram that determines income (spending) in the balanced spending situation.5 On the x-axis we have total income Yh and on the y-axis we have total spending Y: Income and spending are equal at the point of spending balance, so this point has to be somewhere on the 45-degree line (since the 45-degree line is the collection of all points at which Yh = Y ): But which point? This is determined by the total spending equation. Plotting this equation we note that is a straight line with intercept a + I + G + (X ¡ M ) (all the components of spending that do not depend on income) and slope b(1 ¡ ¿) < 1: Hence the line starts above zero and has smaller slope than the 45-degree line. Therefore it necessarily intersects the 45-degree line once and only once. At this point income coincides with spending and aggregate consumption is described by the aggregate consumption function: as we found algebraically, at this point Y = Yh = a + I + G + (X ¡ M) 1 ¡ b(1 ¡ ¿) You may ask yourself: haven’t we said that the fact that income equals spending is an identity, i.e. always true. So what is the signi…cance of the spending balance income? Remember that the aggregate consumption function is a whole contingency plan: for each possible perceived income it gives the amount consumed. Spending balance is the point at which total income is exactly at its right level so that consumption spending plus all the other spending components, which are treated as exogenous at this point exactly equals that income. In other words it is that income for which consumers can actually afford to spend what they want to spend according to the consumption function, because total spending generates exactly that income. 5 John Maynard Keynes was the founder of macroeconomics and was the …rst to discuss the aggregate consumption function. 4.2. THE IS-LM FRAMEWORK 97 Total Spending Y 45-degree line: Y=Y h Slope 1 Spending Y=a+(1-τ)bY +I+G+(X-M) h Slope (1-τ)b a+I+G+(X-M) Y=Y h Total Income Y h Figure 4.4: This also makes clear why we always have to be at spending balance: suppose in Figure 32 the economy is at a point where income Yh = Y1 : In this situation total spending is higher than total income: consumers spend too much relative to their income, a situation that is not sustainable, since consumers would realize this imbalance. The same is true for a point like Y2 ; where income is too high relative to what consumers want to spend. Therefore the economy always has to be in spending balance where income equals spending. To make this point more rigorous one has to specify an adjustment process that takes the economy from points like Y1 or Y2 to spending balance. It is quite straightforward to do this, but we have to introduce time (and therefore dynamics) in our analysis. Assume that the consumption function takes the form Ct = a + b(1 ¡ ¿ )Yh;t¡1 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 98 Total Spending Y 45-degree line: Y=Y h Slope 1 Spending Y=a+(1-τ)bY +I+G+(X-M) h Slope (1-τ)b a+I+G+(X-M) Y 1 Y=Y h Y 2 Total Income Y h Figure 4.5: i.e. consumption this period depends on income last period. On the other hand …rms produce whatever the sectors in the economy want to spend, so Yt = Ct + It + Gt + (Xt ¡ Mt ) For the moment let us assume that It = I; Gt = G; (Xt ¡ Mt ) = (X ¡ M ) ; i.e. all components apart from consumption are constant over time and exogenously given. Plugging the consumption function into the spending equation yields Yt = a + b(1 ¡ ¿ )Yh;t¡1 + I + G + (X ¡ M) From our identity Yh;t¡1 = Yt¡1 : and therefore Yt = a + b(1 ¡ ¿ )Yt¡1 + I + G + (X ¡ M ) (4.5) This is a linear di¤erence equation that gives spending (income) this period as a function of income (spending) last period. It is very similar in spirit to our 4.2. THE IS-LM FRAMEWORK 99 basic di¤erential equation in the Solow model, just in discrete time. Let us graphically analyze this di¤erence equation. Total Spending Y 45-degree line: Y=Y t h,t Spending Y=a+(1-τ)bY +I+G+(X-M) t h,t-1 Y 2 Y 1 a+I+G+(X-M) Y h,0 Y Y Y=Y h h,1 h,2 Total Income Y h Figure 4.6: In Figure 33 we have on the x-axis income of households at period Yh and on the y-axis we have total spending Y: We plot two relationships, our identity Yt = Yh;t and the equation for total spending Yt = a + b(1 ¡ ¿)Yh;t¡1 + I + G + (X ¡ M ) Now suppose we start with total income Yh;0 : In period 1 aggregate consumption is given by C1 = a + b(1 ¡ ¿)Yh;0 and aggregate spending is given by Y1 = a + b(1 ¡ ¿ )Yh;0 + I + G + (X ¡ M) Graphically we get this point by starting from Yh;0 , going to the spending line and from there to the y-axis, as indicated by the arrows. But from our identity 100 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS Yh;1 = Y1 i.e. income in period 1 equals spending in period 1 since all spending generates income. Graphically we …nd Yh;1 by starting at Y1 on the y-axis, going to the 45-degree line (where Y = Yh ) and then down to the x-axis. Now we have income in period 1: We can now repeat the same logic to …nd Y2 ; Yh;2 ; Y3 and so forth. As the …gure indicates over time income and spending go the point where Y = Yh and then stay there forever. This point is our steady state in which income and spending does not change anymore. We can solve for this point, call it Y ¤ ; analytically. At this point Y does not change anymore, so Yt¡1 ¡ Yt = 0 (this is the analog to k_ = 0 in the Solow model), so Yt¡1 = Yt = Y ¤ : Using this in (4:5) we have Y ¤ = a + b(1 ¡ ¿)Y ¤ + I + G + (X ¡ M ) or Y¤ = a + I + G + (X ¡ M) 1 ¡ b(1 ¡ ¿) which is exactly our income at spending balance. So the dynamic model provides the foundation for assuming that we are always in spending balance: if we start with income below, then spending of the economy in period 1 is above income in period 0, …rms produce to satisfy the demand and generate income in period 1 which is higher than in period 0, this leads to further spending and income increases until the economy hits Y ¤ : Note that the previous analysis crucially depends on the assumption that b < 1; (or better, (1 ¡ ¿ )b < 1). Repeat the analysis with (1 ¡ ¿)b > 1 and you will see that, unless we start at Y ¤ ; we will never get there and hence the dynamic model is not adequate for providing an underpinning for the assumption that we always are in spending balance.6 From now on we will assume that the adjustment process to Y ¤ is rapid enough so that we, without losing anything substantial, can assume that we will always be at spending balance. For this we should interpret the time periods as short, maybe a month or so. We will not consider the adjustment process explicitly in our further analysis. The Multiplier We now know how the level of income (and spending) is determined, given exogenously given values for I; G and (X ¡ M): The next question is: what happens to income and spending if there is an exogenous change in investment, government spending or net exports? So suppose that the government decides to increase government spending, say because the Reagan administration fears a nuclear attack by the Russians and decides that one should have SDI to protect 6 Note that, since the di¤erence equation (4:5) is linear, we can actually solve it analytically. Doing so yields Yt = Y ¤ + (Y0 ¡ Y ¤ ) (b(1 ¡ ¿ ))t Obviously Yt goes to Y ¤ as t becomes large as long as b(1 ¡ ¿ ) < 1: 4.2. THE IS-LM FRAMEWORK 101 its citizens. For concreteness, suppose that G increases by $50 billion to G0 . Let ¢G = G0 ¡ G denote the change in government spending ¢Y the resulting change in income (and spending). Let us …rst analyze the situation graphically. Total Spending Y 45-degree line: Y=Y h New Spending Y=a+(1-τ)bY +I+G’+(X-M) h Spending Y=a+(1-τ)bY +I+G+(X-M) h a+I+G’+(X-M) ΔG a+I+G+(X-M) Y’* Y* ΔY Total Income Y h Figure 4.7: From Figure 34 we see that income (and spending) increase, due to the increase in government spending, from Y ¤ to Y 0¤ : We can actually use our model for the adjustment process to describe how the economy moves from Y ¤ to Y 0¤ over time. For now we are interested in the size of the change in income ¢Y: From the picture we see that ¢Y > ¢G; i.e. income and spending go up by more than the initial increase in government spending. We will now show that this not an accident of the picture, but will be true in general. From our CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 102 algebraic solution we have Y¤ = Y 0¤ = a + I + G + (X ¡ M) 1 ¡ b(1 ¡ ¿) a + I + G0 + (X ¡ M) 1 ¡ b(1 ¡ ¿ ) Hence ¢Y = Y 0¤ ¡ Y ¤ a + I + G0 + (X ¡ M ) a + I + G + (X ¡ M ) ¡ = 1 ¡ b(1 ¡ ¿) 1 ¡ b(1 ¡ ¿ ) G0 ¡ G = 1 ¡ b(1 ¡ ¿ ) ¢G = 1 ¡ b(1 ¡ ¿ ) Since 0 < (1 ¡ ¿ )b < 1; we have that 1 ¡ b(1 ¡ ¿) < 1 and therefore ¢Y > ¢G: Suppose that the marginal prospensity to consume equals b = 0:9 and the tax rate equals ¿ = 0:2: Then ¢Y = = ¢G 1 ¡ 0:9(1 ¡ 0:2) ¢G = 3:57 ¤ ¢G 0:28 So if government spending goes up by $50 billion, total income and spending 1 (GDP) in the economy goes up by $178.5 billion. The term 1¡b(1¡¿ ) is called the government spending multiplicator: it tells us by how much GDP goes up if government spending goes up by $1. Similarly we can derive the investment and the export multiplicator, where instead of an increase in government spending we consider an exogenous increase (or fall) in investment or exports. These 1 multipliers turn out to both equal 1¡b(1¡¿ ) ; i.e. are equal to the government spending multiplicator. What is the economics behind these results. This is most clearly demonstrated by using the adjustment process explicitly. Remember that the two equations were Yt Yh;t = a + b(1 ¡ ¿ )Yh;t¡1 + I + G + (X ¡ M) = Yt Now we start at Yh;0 = Y ¤ ; i.e. the old steady state corresponding to government spending G: Now Reagan and his SDI come along and government spending increases by ¢G to G0 : Then total spending increases from Y1 = Y ¤ to Y1 = Y ¤ + ¢G: Firms supply the desired new additional products, here the SDI system. The additional production generates additional income, so income increases from 4.2. THE IS-LM FRAMEWORK 103 Yh;0 = Y ¤ to Yh;1 = Y ¤ + ¢G: But this is not the end of the story. Although G does not increase further, total spending does: since income is now higher by ¢G and consumers consume a fraction b(1 ¡ ¿ ) out of every additional dollar of income, consumption spending in the second round increases by b(1 ¡ ¿ )¢G: Hence Y2 = Y1 + b(1 ¡ ¿)¢G = Y ¤ + ¢G + b(1 ¡ ¿ )¢G = Y ¤ + (1 + b(1 ¡ ¿ )) ¢G Again …rms stand by to produce the additional goods demanded and additional income of size b(1 ¡ ¿ )¢G is generated: Yh;2 = Y2 : And again a fraction b(1 ¡ ¿ ) of this additional income is used for additional consumption, so that Y3 = Y2 + b(1 ¡ ¿) ¤ b(1 ¡ ¿ )¢G = Y2 + (b(1 ¡ ¿ ))2 ¢G ´ ³ = Y ¤ + 1 + b(1 ¡ ¿) + (b(1 ¡ ¿ ))2 ¢G This process of additional income generation and additional spending continues ad in…nitum, until Y 0¤ is reached: additional spending generates additional income from the production process; this additional income leads to further additional spending and so forth. Note, however, that the income and spending increments become smaller and smaller over time (and eventually become so small that they are negligible); eventually we get arbitrarily close to Y 0¤ : This adjustment process is demonstrated in Figure 35. In Table 9 we summarize all the e¤ects of the change in government spending from G to G0 : Again we assume b = 0:9 and ¿ = 0:2: For concreteness we assume that Y ¤ = $1; 000 billion CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 104 Total Spending Y 45-degree line: Y=Y h New Spending Y=a+(1-τ)bY +I+G’+(X-M) h Spending Y=a+(1-τ)bY +I+G+(X-M) h a+I+G’+(X-M) (1-τ)bΔG ΔG a+I+G+(X-M) ΔG Y’* Y* ΔY Total Income Y h Figure 4.8: Table 9 Time t 0 1 2 3 .. . t large Additional Spending 0 ¢G = 50 b(1 ¡ ¿ )¢G = 0:9(1 ¡ 0:2)50 = 36 (b(1 ¡ ¿))2 ¢G = (0:9(1 ¡ 0:2))2 50 = 26 .. . (b(1 ¡ ¿ ))t ¢G ¼ 0 Total Change in Income Yt ¡ Y0 0 ¢G = 50 (1 + b(1 ¡ ¿ ))¢G = (1 + 0:9(1 ¡ 0:2))50 = 86 (1 + b(1 ¡ ¿) + (b(1 ¡ ¿ ))2 )¢G = (1 + 0:72 + (0:72)2 )50 = 112 .. . (1 + b(1 ¡ ¿) + ¢ ¢ ¢ + (b(1 ¡ ¿))t )¢G ¼ 1 1¡b(1¡¿ ) ¢G = 178:5 Yt = Yh;t 1; 000 1; 050 1; 086 1; 112 .. . Y 0¤ = 1; 178:5 4.2. THE IS-LM FRAMEWORK 105 As argued above, in the …rst round income and spending increase exactly by the amount of additional government spending. Additional income triggers additional consumption spending, $36 billion in the second round, $26 billion in the third round and so forth. Summing up all these e¤ects yields a total increase in income and spending of $178:5 or exactly 3:57 times the initial increase in government spending. Remember that this was exactly what we got using our government spending multiplier. This, again is no accident: mathematically this comes from the fact that the sum of all income increases in all rounds, if we allow in…nitely many rounds 2 t (1 + b(1 ¡ ¿ ) + (b(1 ¡ ¿ )) + ¢ ¢ ¢ + (b(1 ¡ ¿ )) + ¢ ¢ ¢ )¢G 1 ¢G = 1 ¡ b(1 ¡ ¿ ) equals exactly the multiplier. So again the dynamic analysis provides the justi…cation for our shortcut results.7 In all of our exercise we ignored the fact that we government has to somehow …nance the additional government spending. The SDI project was …nanced by issuing more government debt (which is being repaid at the moment). If instead the increase in government spending is …nanced by increasing taxes, the multiplier analysis is changed and the multiplier is much smaller. In fact I may ask you in a homework to derive the famous Haavelmo multiplier, the multiplier that results from a tax-…nanced increase in government spending.8 It is an easy modi…cation to analyze what happens if not only the amount of consumption goods that are purchased domestically depends on current income, but also the imported consumption goods. Suppose that imports are given by the function M = mYh where m is the marginal prospensity to import. Now our key equations for spending balance become Y Yh = a + b(1 ¡ ¿ )Yh + I + G + X ¡ mYh = Y Doing exactly the same analysis as before this yields as income (spending) level 7 Shortcut as we ignore the adjustment process to spending balance. The formula comes from the mathematical fact that, for any number c strictly between 0 and 1 we have = 1 + c + c2 + c3 + ¢ ¢ ¢ 1 1¡c The expression 1 + c + c2 + c3 + ¢ ¢ ¢ is called a geometric sum (since the terms in the sum decline geometrically to zero). 8 Named after Swedish economist and Nobel price winner (in 1989) Trygve Haavelmo the result is that a tax-…nanced increase in government spending increases income 1 for 1, i.e. the multiplier is exactly 1. CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 106 in spending balance Y¤ = a+I +G+X 1 ¡ b(1 ¡ ¿) + m 1 and a government spending (investment, export) multiplicator of 1¡b(1¡¿ )+m : Note that the multiplicator is smaller now because the fraction m of additional income generated by ¢G is not spent on domestic consumption and therefore does not additional income domestically (but rather in the country from where the additional import goods come). Further details will be investigated in some homework problems. 4.2.2 Investment, the Interest Rate and the IS Curve In the previous subsection we …xed the price level and investment I; government spending G and exports X at some exogenously given numbers. Now we look more carefully at what determines investment demand. When we modeled consumption demand we posited a very simple, highly tractable model of consumption: consumption demand depends only on current disposable income. When modelling investment we follow the same strategy: we posit that investment demand only depends on the real interest rate r and we write I = e ¡ dr where e and d are positive constants. Our reason for why investment demand depends negatively on the interest rate is the following. Most businesses don’t have the funds available to …nance a new factory, an expensive new machine and so forth. Therefore they have to take out a loan from a bank to …nance this new investment. The higher the real interest rate, the more expensive it is for …rms to borrow and the less investment projects are actually undertaken. Therefore investment demand depends negatively on the real interest rate.9 In Figure 36 we draw the aggregate investment function. It is a straight line that is downward sloping since aggregate investment demand depends negatively on the real interest rate. We now have all the ingredients together to analyze the determination of income and interest rates jointly. Still we assume that the price level P is …xed. Also the components G and X of total spending are assumed to be exogenously given …xed numbers. Aggregate consumption is given by C = a + b(1 ¡ ¿)Yh Aggregate investment is given by I = e ¡ dr 9 We use the real interest rate since, although banks pay the nominal interest rate speci…ed in the loan contract, in the period of repayment one dollar is worth less than in the period where the contract was agreed upon, due to in‡ation. Hence the real return on the loan for the bank (and the real cost for the …rm) is given by the nominal interest rate minus the in‡ation rate, i.e. the real interest rate. 4.2. THE IS-LM FRAMEWORK 107 Aggregate Investment (in billion $) 800 Slope -d 400 3 6 9 Real Interest Rate (in %) Figure 4.9: Aggregate imports are given by M = mY Spending balance requires Yh = Y Therefore total spending is given by Y = a + b(1 ¡ ¿ )Yh + e ¡ dr + G + X ¡ mYh Using the identity that income equals spending we get Y = a + b(1 ¡ ¿)Y + e ¡ dr + G + X ¡ mY CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 108 or Y = r a+e+G+X ¡d 1 ¡ b(1 ¡ ¿ ) + m 1 ¡ b(1 ¡ ¿ ) + m (4.6) We can also solve for the interest rate. This yields r= 1 ¡ b(1 ¡ ¿ ) + m a+e+G+X ¡ Y d d (4.7) Remember that the only two variables in this equation are income Y and the real interest rate r; all the other stu¤ are …xed numbers. Equation (4:7) or (4:6) is called the IS-curve (for income=spending): it is a relation between income Y and the real interest rate r and consists of all points (Y; r) so that income equals spending and consumption is described by the aggregate consumption function, investment by the aggregate investment function and imports by the aggregate import function. Figure 37 draws the IS-curve. It is downward sloping since a higher interest rate decreases investment demand (by d) and therefore spending (income) by an d amount given by d times the investment multiplier, i.e. by 1¡b(1¡¿ )+m : Since )+m : we draw Y on the x-axis, the slope is the inverse of this, 1¡b(1¡¿ d We can derive the IS-curve directly from the Keynesian Cross diagram. This is done in Figure 38 The top graph is our typical Keynesian cross from before. We start with a given real interest rate r: For this interest rate investment demand is given by I = e ¡ dr and the resulting spending and income is given by Y: So in the lower graph we found one point on the IS curve: the smily face corresponding to the point (Y; r): Now we want to construct a second point on the IS curve, so we vary the real interest rate. In particular we reduce the interest rate to r0 : This increases investment demand from I = e ¡ dr to I 0 = e ¡ dr0 : Since investment increases with lower interest rates, I 0 > I: In the Keynesian Cross diagram the spending curve shifts upwards and income (spending) increases to Y 0 (by ¢I d ¢Y = 1¡b(1¡¿ )+m = 1¡b(1¡¿ )+m ¢r: In the bottom graph we mark a second point (Y 0 ; r0 ) on the IS-curve. Continuing to do this we can trace out the entire IS-curve by varying the interest rate and determining the income (spending) level corresponding to this interest rate from the Keynesian Cross diagram. We can now investigate what happens to the IS curve if the government increases government spending by ¢G from G to G0 : We already did the analysis in the Keynesian Cross diagram, so now our life is easy. Figure 39 shows what happens. Again we draw two graphs. Suppose that in the bottom graph we …gured out the IS-curve for a given level of government spending G: This line is labeled as old IS-curve. Now G increases from G to G0 : What happens to the IS-curve. Let is look at a single point on the new curve. Fix the interest rate at r: For this interest rate and the old level of government spending G; the point on the old IS-curve is the smily face corresponding to (Y; r): But where is the point corresponding to the same interest rate r and the new level of government spending G0 : Fixing r and increasing G by ¢G to G0 shifts the spending curve 4.2. THE IS-LM FRAMEWORK 109 Real Interest Rate (in %) 10% Slope (1-b(1-τ)+m)/d 5% Income Y 5000 6000 7000 (GDP) Figure 4.10: in the Keynesian Cross diagram up by ¢G: The new income level is given by Y 0 : We remember from above that ¢Y Y0 ¢G 1 ¡ b(1 ¡ ¿ ) + m ¢G = Y + 1 ¡ b(1 ¡ ¿ ) + m = Y0¡Y = i.e. the new income level associated with the old r; but new G0 is exactly ¢G times the government spending multiplier higher than the old income level. We found one point on the new IS-curve: it is the smily face corresponding to (Y 0 ; r): Again doing this for all possible interest rates yields the new IS-curve. ¢G The new IS-curve looks like the old, but is shifted by 1¡b(1¡¿ )+m to the right, exactly because income increases by ¢G times the multiplier for every interest rate. CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 110 Y =Y h Spending Y Y=a+(1-τ)bY +e-r’d+G+X-mY h h Y=a+(1-τ)bY +e-rd+G+X-mY h h Income Y Y Y’ h Real Interest Rate r r r’ Income Y Y Y’ h =Spending Y Figure 4.11: Obviously a decline in government spending shifts the IS-curve to the left; similar shifts are caused by changes in exports X or changes in the parameters a and e: 4.2.3 The Demand for Money and the LM-Curve Our macroeconomic model so far consists of the following equations. Some of them are behavioral equations, i.e. describe the behavior of consumers or …rms. These are the aggregate consumption, investment and import functions. C I M = a + b(1 ¡ ¿)Yh = e ¡ dr = mYh 4.2. THE IS-LM FRAMEWORK 111 Y =Y h Spending Y Y=a+(1-τ)bY +e-rd+G’+X-mY h h Y=a+(1-τ)bY +e-rd+G+X-mY h h ΔG Y ΔY Income Y Y’ h Real Interest Rate r ΔY r New IS Curve Old IS Curve Income Y Y Y’ h =Spending Y Figure 4.12: We also have equations that are true by de…nition or by accounting rules. These are the de…nition for total spending and the identity that income always equals spending. Y Y = C + I + G + (X ¡ M ) = Yh We still assume that G; X are just given numbers and that the price level is …xed at some predetermined level P: Hence we have …ve equations and six endogenous variables to be determined, namely Yh ; Y; C; I; M; r (note that a; b; d; e; m; ¿ are parameters, i.e. numbers that we will treat as …xed for all future purposes). That means that we cannot yet solve for the equilibrium values of our variables altogether (by equilibrium values I mean values of endogenous variables that satisfy all equation that describe our economy, given some values for the parameters and exogenous variables G; X; P ). So far the best we can do CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 112 is to substitute C; I; M; Yh into the spending equation and derive the collection of all income (spending) levels and interest rates (Y; r) that satisfy all equations. This was the IS-curve. The formula for the IS-curve is given (see the last section) as 1 ¡ b(1 ¡ ¿ ) + m a+e+G+X ¡ Y d d Now we will add one additional equation that will enable us to solve exactly for one single combination (Y ¤ ; r¤ ) of equilibrium income and interest rates. Now we bring in money into our analysis. Note that so far we measured all our variables in real terms, i.e. in physical units: Y is real GDP and so forth. But in order to spend, people need money, at least in general.10 By money in this course I will mean …at currency, i.e. pieces of paper issued by the government that have no intrinsic value.11 These pieces of paper are money because the government decrees that they are money. Although …at money is the primary form of money in modern societies, historically most societies have used as money a commodity with intrinsic value. This type of money is called commodity money. A famous example are WW II prison camps where cigarettes became the common form of money between inmates. Cigarettes were used as medium of exchange to trade soap for food, but they were also consumed. The most prevalent form of commodity money historically was gold. In the early 20-th century a lot of countries used pieces of paper as money, but these pieces of paper were backed by gold: everybody could go to the bank and exchange these pieces of paper for gold at a rate that was …xed and guaranteed by the government. Such a monetary system is referred to as the gold standard. The US left the gold standard when the Breton Woods system collapsed in 1973. We will now add a behavioral equation to our economy that intends to describe the market for money. Let us …rst think about the demand for money. People need money to purchase goods, i.e. to make transactions. We will develop three hypotheses about money demand. To understand these hypotheses it is crucial to understand that households can hold their wealth in di¤erent forms: in money or in assets that bear interest. So the question here is not how much money households want (everybody prefers more to less), but how households divide their wealth into money holdings and other assets (stocks, bonds) that, in contrast to money, yield interest rate. Such a decision is called a portfolio decision. Back to our three hypotheses. r= 1. People want to hold more money when the price level is higher and less money when the price level is lower. Since people do not care about money 10 Sometimes goods are exchanged for goods. For example in college I traded tutoring sessions against cases of beer (instead of for money). Such trades are called barter. Barter trade requires “double coincidence of wants”, i.e. my collegue wanted tutoring lessions and I wanted beer. If there is no double coincidence of wants for trade to happen we need a medium of exchange - money. 11 When measuring money economists include as money all assets that are readily available to make transactions, which includes not only currency, but also checking accounts that households hold with private banks. For now it is conceptually easier to think of money just as currency in circulation. 4.2. THE IS-LM FRAMEWORK 113 per se, but only as a medium of exchange for real consumption goods, if all goods double in prices, households need a doubled amount of money to purchase the same consumption goods. If we let M d denote the demand for money and P the (…xed) price level, this hypothesis just states that M d and P are proportional to each other. 2. Suppose people want to spend more in consumption goods, so that total spending in real terms Y (or real GDP) increases, then people need more money to carry out the additional trades. Therefore we assume that money demand M d increases in Y; the desired real spending in the economy. 3. What is the opportunity cost for holding money, instead of interest bearing assets? Money does not pay any interest rates, whereas interest bearing assets pay the nominal interest rate. Therefore we assume that money demand is decreasing in the nominal interest rate. Since, for the moment, we assume that the price level is …xed and therefore the in‡ation rate is zero in the short run, this translates into the assumption that money demand is decreasing in the real interest rate r: For now we follow Hall and Taylor and disregard the di¤erence between the nominal and the real interest rate for the moment and denote by r just the interest rate. We therefore model the demand for money as M d = P ¤ L(Y; r) or Md = L(Y; r) P The function L is called the real money demand function and gives the demand for real money balances, i.e. for money adjusted by the price level. We assume that the function L is linear, i.e. Md = L(Y; r) = kY ¡ hr P where k and h are positive constants. The constant k measures by how much real money demand goes up if real spending goes up by one dollar, the constant h measures by how much real money demand goes down if the interest rate goes up by 1%: This completes our description of the demand for money. What about the supply of money. The supply of money, M s ; is determined by the Federal Reserve System, by the government agency that is responsible for conduction monetary policy. We have to postpone a discussion of how exactly the FED goes about conducting monetary policy. For now we assume that the supply of money is …xed and exogenously given (as is the price level). We assume that the money market is always in equilibrium, so that Ms = Md CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 114 or Ms P Ms P = Md P = kY ¡ hr (4.8) Equation (4:8) is called the LM-curve (since it relates the demand for real money balances L to the supply of money, M s : It is important to distinguish which variables are endogenous and which are exogenous in this equation. We assume that money supply M s is …xed by the FED and therefore exogenously given. Also the price level P is …xed by assumption. The only endogenous variables in the LM-curve are Y and r: Rewriting (4:8) yields r= 1 Ms k Y ¡ h h P This closes our economic model: the IS-curve and the LM- curve can be used jointly to determine the equilibrium values of (Y; r). Once we have these we can deduce all other endogenous variables C; I; M; Yh from the other equations. Therefore, given a price level P and a money supply M s (and given G; X), we can …gure out total spending, income, consumption, investment, imports and interest rates that prevail in the economy in the short run. We will do this graphically in a bit. But …rst let’s analyze the LM-curve in more detail. In Figure 40 we draw the LM-curve. The LM curve shows the interest rate as a function of spending (GDP). The slope of this curve is given by hk > 0: What is the intuition for this? Remember that since the money supply and the s price level are …xed, the real supply of money MP is …xed. Now suppose that spending Y goes up, so real money balances demanded increase. But the supply is …xed. The only way to bring demand and supply to equilibrium again is a rise in the interest rate, making the amount of real balances demanded decline, o¤setting the increase due to higher Y: Changes in the money supply M s and the price level P shift the LM-curve. So let us consider what happens to the LM-curve if M s increases (but P stays constant). This is important for the analysis of the e¤ects of monetary policy. Suppose the money supply increases from M s to M s0 : How does GDP have to change to leave the interest rate unchanged? Since real money supply increases, real money demand must increase. If the interest rate is unchanged, to increase real money demand, Y must increase. The LM-curve shifts to the right.12 This is shown in Figure 41. 12 By how much does the LM curve shift to the right? Suppose money supply increases by ¢M s . To leave the interest rate unchanged it has to be the case that the change in GDP, ¢Y has to satisfy 0 = = = ¢r ¶ µ ¶ µ k 1 M s0 k 0 1 Ms ¡ Y ¡ Y ¡ h h P h h P k ¢M s ¢Y ¡ h hP 4.2. THE IS-LM FRAMEWORK 115 Interest Rate (in %) LM-curve 10% Slope k/h 5% Income Y 5000 6000 7000 (GDP) Figure 4.13: An increase in the price level has thes opposite e¤ect. Keeping the money supply …xed, an increase in P decreases MP ; the real supply of money. Therefore the demand for real money balances has to decrease. For a …xed interest rate now GDP Y has to decrease to bring the money market back into equilibrium. The LM-curve shifts to the left for an increase in the price level. This is crucial for the derivation of the aggregate demand curve below. Figure 42 shows this e¤ect.13 Therefore ¢Y = s ¢M s kP i.e. the LM-curve shifts to the right by ¢M kP 13 By how much does the LM curve shift to the left? Suppose the price level increases by ¢P . To leave the interest rate unchanged it has to be the case that the change in GDP, ¢Y CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 116 Interest Rate (in %) Old LM-curve 10% New LM-curve Slope k/h 5% M s Income Y 5000 6000 7000 (GDP) Figure 4.14: has to satisfy 0 = = = ¢r ¶ µ ¶ µ k 0 k 1 Ms 1 Ms Y ¡ Y ¡ ¡ h h P0 h h P µ ¶ k M s ¢P ¢Y ¡ h h P 0P Therefore ¢Y = ¡ i.e. the LM-curve shifts to the left by Ms k ³ Ms k ¢P P 0P µ ´ : ¢P P 0P ¶ 4.2. THE IS-LM FRAMEWORK 117 Interest Rate (in %) New LMcurve 10% Old LM-curve Slope k/h 5% P Income Y 5000 6000 7000 (GDP) Figure 4.15: 4.2.4 Combination of IS-Curve and LM-Curve: ShortRun Equilibrium We can combine the IS-curve and the LM-curve to determine short-run GDP (income, spending) and interest rates. Remember that the IS-curve is given by r= 1 ¡ b(1 ¡ ¿ ) + m a+e+G+X ¡ Y d d (4.9) whereas the LM-curve is given by r= k 1 Ms Y ¡ h h P (4.10) These are two equations in the two unknowns (Y; r): Given that the IS-curve is downward sloping and the LM-curve is upward sloping these to curves intersect CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 118 once and only once, as shown in Figure 43. This intersection determines the short run level of GDP, Y ¤ and the short run interest rate r¤ : Interest Slope Rate (in %) (1-b(1-τ)+m)/d LM-curve 10% Slope k/h r* 5% IS-curve Income Y 5000 6000 Y* 7000 (GDP) Figure 4.16: Let us solve for (Y ¤ ; r¤ ) algebraically. Combining the IS-curve and the LMcurve yields 1 Ms a+e+G+X 1 ¡ b(1 ¡ ¿) + m k Y ¡ = ¡ Y h h P d d Solving this mess for Y yields µ ¶ k 1 ¡ b(1 ¡ ¿ ) + m + Y h d Y¤ = = 1 Ms a+e+G+X + d h P ¢ ¡ a+e+G+X 1 Ms +h P d ³ ´ 1¡b(1¡¿ )+m k h + d 4.2. THE IS-LM FRAMEWORK 119 Note that GDP (or total spending, total income) in the short run increases with the level of government spending G and exports X as well as with money supply M s and decreases with the price level P: Remember that in the short run real GDP equals aggregate demand. So the fact that Y ¤ decreases with increases in P justi…es that the aggregate demand curve is downward sloping as drawn in Figure 29. It now follows that Yh¤ r¤ I¤ C¤ M¤ = Y¤ k ¤ 1 Ms Y ¡ = h h P = e ¡ dr¤ = a + b(1 ¡ ¿)Y ¤ = mY ¤ These formulas give the short run equilibrium values of the endogenous variables Y; Yh ; r; I; C; M as functions of the exogenous variables G; X; M s ; P and the parameters a; b; d; e; m; ¿: We have now formulated and solved our complete model of the macroeconomy in the short run. Now we can address policy questions in the next section. 4.2.5 Monetary and Fiscal Policy in the IS-LM Framework Monetary Policy Let us start with monetary policy. In our simple model monetary policy amounts to the FED picking the money supply M s : Suppose we want to analyze statements of the form (which could be found in recent issues of the economist) The US is going to a recession. A possible remedy: increase real GDP by softening monetary policy Let us try to analyze this statement with the tools we have. First we assume that the US economy is well-described by the macroeconomic model we developed in the last section. Second, we focus on the short run e¤ects of monetary policy (remember that in the long run money did not a¤ect real output, according to the classical dichotomy). Third, we translate “softening monetary policy” to mean an increase in the money supply M s : We use our IS-LM diagram to see what is going on. As usual, we …rst ask ourselves which curves, if any, shift. The IS-curve (4:9) does not shift, but sthe LM-curve (4:10) shifts, as we argued in the last section to the right (by ¢M kP ). From Figure 44 we see that short-run equilibrium real GDP Y ¤ increases to Y ¤0 and the interest rate r¤ falls to r¤0 . Given values for the exogenous variables and parameters we can also compute by how much real GDP and the interest rate change in response to an increase in the money supply. This is straightforward and I will leave this for a problem set. CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 120 Slope Interest (1-b(1-τ)+m)/d Rate (in %) Old LM-curve New LM-curve 10% Slope k/h r* r*’ 5% IS-curve s M Income Y Y* Y’* (GDP) Figure 4.17: What is the economic intuition for this (this intuition is somewhat loose, and in order to make it tighter we would need a fully dynamic model, which to develop is beyond the scope of this course): An increase in M s increases the supply of money. For households to be willing to hold this additional money the interest rate must fall. A lower interest rate spurs higher investment and the multiplier sets in, leading to higher real GDP Y ¤ : From the …gure we also see what determines the magnitude of the response of real GDP to an increase in money supply. Suppose the IS-curve is really steep, almost vertical. Then a given increase in the money supply has very little e¤ects on real GDP Y ¤ and a strong e¤ect on the interest rate. Why this. A steep IS-curve means a low d; i.e. investment demand is not very responsive to declines in the interest rate. So an increase in the money supply leading to a drop in the interest rate does not increase investment by a whole lot and therefore real GDP does not increase by much. On the other hand, if investment 4.2. THE IS-LM FRAMEWORK 121 demand is very sensitive to the interest rate (a high d), the IS curve is very ‡at and an increase in money supply and the resulting drop in the interest rate have a large e¤ect on investment and hence real GDP. The e¤ect on real GDP induced by an increase in the money supply is also the bigger the steeper the LM curve is. The LM-curve is steep when h is low, i.e. when real money demand responds only weakly to the interest rate. In this situation a large drop in r is required for money demand to absorb the additional money supply. But large drops in interest rates induce large increases in investment demand and hence real GDP. Therefore the e¤ectiveness of monetary policy to increase real GDP (by increasing money supply) depend on how sensitive investment is to the interest rate and how sensitive money demand is to the interest rate. The e¤ect on real GDP of an increase in money supply are weak (but positive) if investment demand is insensitive to changes in the interest rate and/or money demand is very sensitive to the interest rate. The e¤ect is strong (and positive) if investment demand is very sensitive to the interest rate and real money demand is relatively insensitive to changes in the interest rate. You should convince yourself of that by drawing several IS-LM diagrams with di¤erent slopes of the IS-curve and the LM-curve (or by looking at Hall/Taylor, pp. 194-95). We can do the reverse experiment of a decline in money supply. I will leave this as an exercise for a problem set, but it is worth mentioning that the two recessions in 1980-82, the so-called Volcker recessions, are attributed to the tight monetary policy that the FED carried out under then new chairman Paul Volcker. Fiscal Policy Let us again study the Reagan SDI policy experiment. This program was probably not primarily designed to move the economy out of the Volcker recessions, but rather motivated by strategic national defense reasons, but let us analyze its e¤ect on the US economy anyway. Again we assume that the US is described well by our model and that we only analyze the short-run e¤ects of the policy. We also ignore the question how SDI was …nanced. Fiscal policy in our model basically amounts to the government choosing how much to spend, i.e. how to pick G: So initiating the SDI program amounts to an increase in G in our model. Let us use IS-LM analysis to see what happens. Again, what curves shift? It is obvious that the LM-curve (4:10) does not shift, but that the IS-curve (4:9) shifts to the right (we actually saw this in the section where we developed the ¢G ¤ IS-curve) by 1¡b(1¡¿ )+m . We see from Figure 45 that real GDP Y increases to Y ¤0 and the interest rate r¤ increases to r¤0 : Again, what is the economic intuition? An increase in government spending starts the multiplier process and increases total spending. We discussed that when we talked about the multiplier. But now our model is richer, it includes money and has investment depending on interest rates. So when consumption spending increases, money demand increases. But money supply is …xed, so the interest rate has to increase to bring the money market back into equilibrium. CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 122 Interest Rate (in %) Old IS-curve LM-curve New IS-curve 10% Slope Slope k/h (1-b(1-τ)+m)/d r*’ r* G Income Y Y* Y’* (GDP) Figure 4.18: But higher interest rates mean a reduction in investment demand. So part of the stimulus of real GDP due to an increase in G and the multiplier process is o¤set by a fall in private investment demand, induced by rising interest rates. This process is called crowding-out: higher government spending leads to higher interest rates and therefore crowds out private investment. Nevertheless real GDP on net increases with an increase in government spending, but by less than what is predicted by the naive multiplier analysis. Again, the magnitude of the increase in real GDP induced by an increase in government spending depends on how steep the IS-curve and the LM-curve are. This has good economic intuition again. The e¤ects of an increase in government spending are strong if the IS-curve is steep and/or the LM-curve is ‡at and are week if the IS-curve is ‡at and/or the LM-curve is steep. The IS-curve is steep if d is small. Small d means that investment does not react strongly to an increase in the interest rate. If this is the case, then the 4.3. THE AGGREGATE DEMAND CURVE 123 crowding out-e¤ect is small. Even though higher government spending leads to higher interest rates, this does not reduce private investment by much. The LM-curve is ‡at if h is big, i.e. money demand responds strongly to the interest rate. Then only a small increase in the interest rate is needed to bring the money market back into equilibrium (money demand had increased because of higher consumption spending induced by higher G and the multiplier process). But if interest rates rise only modestly, not much investment is crowded out and the e¤ects of an increase in G are large. Reverse arguments hold if d is large and h is small. The previous discussion also explains why the model we developed so far was so popular until the 70’s. It gave monetary and …scal policy an active role in managing the business cycle. If the economy is in a recession, then the model prescribes soft monetary policy and/or expansionary …scal policy (high government spending). The economist and the politician is like a social engineer that can …ne-tune the economy with the appropriate policy, and the only problem left is to …gure out when and by how much exactly to change monetary and …scal policy. The Keynesian model of business cycles was so popular that even Nixon confessed that “we are all Keynesians now”. But it was also in the mid-70’s that these simple recipes started to fail, which not only led to a change in economic policies in the 80’s and 90’s, but also to a dramatic change in economics as a science, away from Keynesianism and back to neoclassical ideas (back to the future, so to speak). We will pick up this theme in more detail in a bit. 4.3 The Aggregate Demand Curve Given our IS-LM apparatus it is now simple to derive the aggregate demand curve from Figure 29. For a …xed price level P we know how to derive aggregate demand Y ¤ (which equals real GDP in the short run), using the IS-LM diagram. Now suppose we want to …nd aggregate demand for a di¤erent price level, say P 0 > P: If the price level increases, what happens in the IS-LM-diagram? As we saw in the last section, the LM-curve shifts to the left. The IS-curve remains unchanged (the price level does not enter the IS-curve). Therefore the aggregate demand (GDP) associated with the higher price level P 0 ; Y ¤0 is lower (and the interest rate is higher) than before. Doing this exercise for a lot of di¤erent price levels one can trace out the entire aggregate demand curve. Figure 46 exempli…es this. Again, what is the economics? A higher price level decreases real money supply. Therefore real money demand has to fall which requires an increase in the interest rate. A higher interest rate reduces investment and real GDP, partly because of the direct e¤ect, partly because the multiplier kicks in. There is one big question remaining: what is the process that lead us from a short-run situation, where aggregate demand (and hence realized GDP) is di¤erent from potential output (or aggregate supply) to the long run equilibrium in which potential output equals to aggregate demand. The answer obviously CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 124 Interest Rate r New LM-curve Old LM-curve for P for P’>P P IS-curve Y*’ Y* Price Level P Real GDP Y (Aggregate Demand) P’ P Aggregate Demand Curve Y*’ Y* Real GDP Y (Aggregate Demand) . Figure 4.19: must have something to do with adjustment of prices. We will discuss this after we are …nished with a little digression. When aggregate demand falls below potential output, some labor is left unutilized and there is unemployment. We …rst want to discuss some basic facts about unemployment before we turn to the price adjustment mechanism. 4.4 Unemployment The Keynesian business cycle theory can explain unemployment. In the short run prices are sticky, realized GDP equals aggregate demand, which may very well be below potential GDP. Factor inputs, in the short run, are left unutilized: machines are left idle and some workers who desire to work for the market wage can’t …nd a job. In this section we will look at the data about the labor market. Even though the news usually reports only one number from the labor market, 4.4. UNEMPLOYMENT 125 namely the unemployment rate, there is much more going on. Even in good times a large number of workers are …red or voluntarily leave their job and a large number of new jobs are created and workers are hired. We will look at some numbers from the US labor market and then we will build a simple, purely descriptive model of the ‡ows into and out of unemployment. A fantastic source of information about the ‡ow of workers into and out of jobs is the book “Job Creation and Destruction” by Steven Davis, John Haltiwanger and Scott Schuh. We will report their main …ndings. 4.4.1 Concepts and Facts Let us start with some basic de…nitions De…nition 3 The labor force is the number of people, 16 or older, that are either employed or unemployed but actively looking for a job. We denote the labor force at time t by Nt De…nition 4 Let W Pt denote the total number of people in the economy that are of working age (16 - 65) at date t : The labor force participation rate ft is de…ned as the fraction of the population in working age that is in the labor force, i.e. ft = WNPt t : Note that for the U.S., in 1994 the labor force consisted of about 131 million people whereas about 197 million people were of working age. That gives a labor force participation rate of about 66.5%. This number has not changed much over the last 7 years. It has become a bit higher since the prospectus of entering a very good labor market in the second half of the 90’s has persuaded some people to make themselves available for a job. De…nition 5 The number of unemployed people are all people that don’t have a job. We denote this number by Ut : Similarly we denote the total number of people with a job by Lt : Obviously Nt = Lt + Ut : We de…ne the unemployment rate ut by ut = Ut Nt De…nition 6 The job losing rate bt is the fraction of the people with a job which is laid o¤ during a particular time, period, say one month (it is crucial for this de…nition to state the time horizon). The job …nding rate et is the fraction of unemployed people in a month that …nd a new job. Note that we use one month as our time horizon. This is due to the fact that new employment data become available each month. The agency responsible for measuring and reporting labor market data is the BLS, the Bureau of Labor Statistics. Between 1967 and 1993 the average job losing rate was 2.7% per month, whereas the average job …nding rate was 43%. The average unemployment rate during this time period was about 6.2%. CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 126 In Figure 47 we plot the unemployment rate for the US from 1967 to 1999.14 We see that in recessions the unemployment rate increases, whereas in expansion it decreases. A variable that shows such a behavior is called “countercyclical”: it is high when real GDP is low (relative to trend) and it is low when real GDP is high. Also note that unemployment in 2000 was on its lowest level since 1970. Unemployment Rate for the US 1967-2001 12 1980-82 back-to-back recessions 11 1974-75 recession Unemployment Rate 10 9 1990-91 recession 8 7 1970-71 recession 6 5 4 3 2 1970 1975 1980 1985 Year 1990 1995 Figure 4.20: But where does it come from that in recessions the unemployment rate is higher than in booms. At …rst sight this seems obvious: less is produced, hence less workers are needed in recessions. But the net decline in job masks what happens to gross ‡ows out of and into unemployment. High unemployment in recessions can be due to the fact that more people are …red in recessions or that less people are hired in recessions. So let us look more closely. 14 The unemployment rate is measured by the Bureau of Labor Statistics (BLS). Go to their homepage at http://stats.bls.gov/top20.html if you want to have a look at the original data. 2000 4.4. UNEMPLOYMENT 127 Let us de…ne four more concepts that will help getting a handle at these questions. De…nition 7 We have the de…nition of the following concepts: 1. The gross job creation Crt between period t¡1 and t equals the employment gain summed over all plants that expand or start up between period t ¡ 1 and t: 2. The gross job destruction Drt between period t ¡ 1 and t equals the employment loss summed over all plants that contract or shut down between period t ¡ 1 and t: 3. The net job creation N ct between period t ¡ 1 and t equals Crt ¡ Drt : 4. The gross job reallocation Rat between period t ¡ 1 and t equals Crt + Drt : Note the following things. Job creation and destruction measures are derived from plant level information, i.e. by asking …rms. Unemployment data are derived from household data, i.e. by asking individual households. Obviously these data are related, but one set of data cannot be reconstructed from the other. And both data sets are immensely important in discussing what goes on in the labor market, so we will report facts from both data sets. Let us start with the plant level data examined in detail by Davis et al. They use data from all manufacturing plants in the US with 5 or more employees from 1963 to 1987. In the years they have data available, there were between 300,000 and 400,000 plants. Studying these data four major …ndings emerge: ² Gross job creation Crt and job destruction Drt are remarkably large. In a typical year 1 out of every ten jobs in manufacturing is destroyed and a comparable number of jobs is created at di¤erent plants. This implies a large number for gross job reallocation Rat , but a modest number for net job creation N ct . ² Most of the job creation and destruction over a twelve-month interval re‡ects highly persistent plant-level employment changes. This persistence implies that most jobs that vanish at a particular plant in a given twelvemonth period fail to reopen at the same location within the next two years. ² Job creation and destruction are concentrated at plants that experience large percentage employment changes. Two-thirds of job creation and destruction takes place at plants that expand or contract by 25% or more within a twelve-month period. About one quarter of job destruction takes place at plants that shut down. ² Job destruction exhibits greater cyclical variation than job creation. In particular, recessions are characterized by a sharp increase in job destruction accompanied by a mild slowdown in job creation. CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 128 The last point answers our earlier question: in recessions the unemployment rate goes up because unusually many people get …red, not because unusually few people are newly hired. 4.4.2 Some Theory and the Natural Rate of Unemployment Let us formulate a little descriptive model of the unemployment rate. Suppose last month the number of unemployed people was Ut¡1 and the number of employed people was Lt¡1 = Nt¡1 ¡ Ut¡1 : Suppose for simplicity that the labor force grows at the population growth rate n; so that Nt = (1 + n)Nt¡1 : Let us compute the unemployment rate at date t: How many people are unemployed at date t? A fraction e (the job …nding rate) of the previously unemployed …nd a job, so this leaves (1 ¡ e)Ut¡1 previously unemployed still unemployed. In addition a fraction b (the job losing rate) of the people with work Lt lose their job and augment the pool of unemployed. Hence Ut = (1 ¡ e)Ut¡1 + bLt¡1 = (1 ¡ e)Ut¡1 + b(Nt¡1 ¡ Ut¡1 ) Dividing both sides by Nt = (1 + n)Nt¡1 yields ut = = = Ut (1 ¡ e)Ut¡1 b(Nt¡1 ¡ Ut¡1 ) = + Nt (1 + n)Nt¡1 (1 + n)Nt¡1 1¡e b(1 ¡ ut¡1 ) ut¡1 + 1+n 1+n 1¡e¡b b ut¡1 + 1+n 1+n This is a …rst order di¤erence equation that gives the unemployment rate this month as a function of the unemployment rate of last month. Remember that we loosely de…ned the natural rate of unemployment as the unemployment rate in normal times. In the light of our simple theory we now de…ne it more concisely as that unemployment rate that would prevail , if the population growth rate n; the job …nding rate e and the job losing rate b are at their normal, long run average level and would not change over time. We can then de…ne the natural rate of unemployment as the steady state u¤ of our di¤erence equation; as that unemployment rate that, in the long run, would be attained in the economy, absent any shocks to n; e; b: Let us solve for u¤ : Set ut¡1 = ut = u¤ to get u¤ = n+e+b ¤ u 1+n = u¤ = 1¡e¡b ¤ b u + 1+n 1+n b 1+n b n+e+b 4.4. UNEMPLOYMENT 129 Using the long run average numbers from before, i.e. b = 2:7%; e = 43% and n = 0:09% (note that the time period is one month here). Hence, according to the data, the natural rate of unemployment is 5:9%; which is almost identical to the average unemployment rate during the last 30 years (which justi…es the de…nition of the natural rate of unemployment as unemployment rate in normal times). In Figure 48 we show the dynamics of the unemployment rate. Suppose the economy starts at an unemployment level u0 lower than the natural rate. Then, barring any changes in b; e; n over time the unemployment rate approaches the natural rate of unemployment, where it remains forever, if there are no changes in job …nding or losing rates. u t u=u t t-1 slope (1-e-b)/(1+n) b/(1+n) u 0 u 1 u u* 2 u t-1 Figure 4.21: From our dynamic equation it is also clear what factors determine the natural unemployment rate: the natural unemployment rate increases with the job loosing rate b and declines with the job …nding rate e: But what are the fac- 130 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS tors that determine these numbers. Answers to these questions could provide us with some explanation of why, for example, Europe had consistently higher unemployment in the last 15 years than the U.S. Since this does not appear to be a temporary phenomenon, one may conjecture that the natural rate of unemployment is higher in Europe than in the U.S. So what are the determinants of job …nding and job losing rates? 1. Unemployment Insurance: Workers that get laid o¤ receive unemployment insurance. Length and generosity of unemployment insurance vary greatly across countries. Whereas in the US the replacement rate (the fraction of the last net wage that the unemployment insurance covers) is about 34%, and this only for the …rst six months, in countries like Germany, France and Italy the replacement rate is about 67%, with duration well beyond the …rst year of unemployment. Given these di¤erent incentives to …nd a new job it seems clear that job …nding rates are higher in the US than in Europe. To the extent that voluntary quits do happen, job losing rates may also be higher in Europe than in the US. 2. Minimum Wages: High minimum wages would mainly a¤ect job …nding rates. If the minimum wage is so high that it makes certain jobs unprofitable, less jobs are o¤ered and job …nding rates decline. I would think that in the US the minimum wage has no bite (at least now) since even industries which tend to be low-wage industries these days pay wages above the minimum wage (for example fast food chains -you may imagine which companies I mean). In other countries this may be more of a factor, but I think the importance of the minimum wage is hugely overstated. 3. Union Wage Premiums: The classical insider-outsider theory posits that unions maximize the well-being of their members, meaning high wages and good working conditions in highly unionized sectors. To the extent that …rms in these sectors have to pay higher wages, less jobs are profitable, reducing the possibility of …nding a good job for the outsiders, the unemployed. Furthermore the prospect of …nding a good job may lead unemployed workers to forgo other, not so good job o¤ers. Both e¤ects reduce job …nding rates. Unionization is much more prevalent in Europe, so this may explain part of the European unemployment dilemma, or “Eurosclerosis”. 4. E¢ciency Wages: The e¢ciency wage theory starts with the presumption that worker-employer matches work best when the worker knows what he has to lose. Therefore employers may want to pay more than the market wage to make workers perform well, since, if they wouldn’t they know they could get …red and lose their privilege to work for a high wage, with others standing in line for the job. But higher wages mean less pro…table jobs. Hence, although each existing job is well paid, there are relatively few of those jobs, so although job losing rates are low (no voluntary quits), job …nding rates are extremely low as everybody that sits on a good job does everything to keep it. 4.4. UNEMPLOYMENT 131 So far we have discussed the main determinants of the natural rate of unemployment -roughly the unemployment rate in the long run. Now let’s turn to the behavior of the unemployment rate over the business cycle. 4.4.3 Unemployment and the Business Cycle So why is the unemployment rate high in a recession and low in a boom. The plant level data from Davis et al. indicated that during recession it is not the case that fewer than normal new workers are hired by establishments. What is the case is that much more workers get …red during recessions than booms. So gross job creation is relatively stable over the business cycle, whereas gross job destruction moves strongly countercyclical: it is high in recessions and low in booms. In severe recessions such as the 74-75 recession or the 80-82 back to back recessions up to 25% of all manufacturing jobs are destroyed within one year, whereas in booms the number is below 5%. For our model this implies that in recessions b increases, whereas in booms it decreases. The time a worker spends being unemployed also varies over the business cycle, with unemployment spells being longer on average in recession years than in years before a recession. Note that we said earlier that job creation rates do not vary much over the business cycle. These two facts are not contradictory, since in recessions there are much more people being laid o¤ and looking for a new job, so even though …rms hire at a roughly normal pace it takes longer for the average person to …nd a new job. In Table 10 we show how the length of unemployment spells vary across the business cycle. We show data from 2 years, 1989 and 1992. The year 1989 was the last good year before the 90-92 recession (that cost George Bush his job), the year 1992 is the last bad year of the recession. Table 10 Unemployment Spell < 5 weeks 5 - 14 weeks 15 - 26 weeks > 26 weeks 1989 49% 30% 11% 10% 1992 35% 29% 15% 21% We see that the average unemployment spells increase during a recession. In the recession year 1992 one …fth of all unemployed worker was unemployed for longer than half a year, whereas in the decent year 1989 only one out of 10 unemployed workers faced that situation. If we compare this to other countries, for example in Germany, France or the Netherlands about two thirds of all unemployed workers in 1989 were unemployed for longer than six months!! Why are more people …red in recessions than in booms? Our Keynesian business cycle model gives the answer: in recessions aggregate demand is below potential GDP because prices are sticky, …rms need less workers to satisfy the demand of their customers and therefore lay o¤ part of their workforce. In fact, 132 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS the relation between the unemployment rate and the GDP gap (the gap between potential GDP and realized GDP (or aggregate demand)) is so strong that it has its own name. Okun’s law, named after economist Arthur Okun, asserts that for every percentage point that the unemployment rate is above its natural rate, real GDP is about 2.5-3% below potential GDP. Note that Okun’s law is a classical misnomer: it is not a law in that it always has to hold, it is more like an empirical regularity that happens to roughly hold for the US in the last 50 years or so (and does not perform too badly for other countries as well). Formally stated, Okun’s law says that Y ¡ Yp = ¡3(u ¡ u¤ ) Y where Yp is potential GDP, Y is actual GDP, u¤ is the natural rate of unemployment and u is the actual unemployment rate. Note that it is not straightforward to measure this relation in the data, since data on the natural rate of unemployment and on potential GDP are required. Nevertheless we plotted Okun’s law from US data in Figure 49. On the x-axis we have the unemployment rate in deviation from 6%, on the y-axis we have the percentage deviation of realized GDP from long term trend (i.e. we identi…ed long term trend GDP with potential GDP, which is somewhat problematic, but can’t be easily avoided). We see that indeed unemployment and output gap are negatively correlated, with a coe¢cient of roughly 2.5-3. The data are from 1967 to 1999. We also so that, although Okun’s law holds on average, it is far from a law in the strict sense: in single years reality may be quite far from Okun’s law. 4.5 The Price Adjustment Process Our model of the macroeconomy so far consists of two parts: the neoclassical growth model that determines potential GDP and the Keynesian business cycle model (the IS-LM model) that determines aggregate demand and hence real GDP in the short run, under the assumption that the price level is …xed and may not be at a level for which aggregate demand equals potential output. By assuming price stickiness we could also explain unemployment. The missing ingredient of our model is the process by which the price level, assumed to be …xed in the short run, in the medium run adjusts so that eventually the economy returns to a situation in which aggregate demand equals potential GDP, i.e. to the long run equilibrium of the economy. It is obviously somewhat unrealistic to assume that …rms will not change their prices if demand is below the output that they can produce. What we have really assumed so far is that producers do not change their prices immediately in reaction, but rather meet all the demand by consumers at the pre-speci…ed …xed price level. But in situations in which aggregate demand is below potential output, by cutting prices …rms may increase demand for their products and therefore improve their utilization of capacities and increase profits/reduce losses. Similarly, in situations in which aggregate demand is above 4.5. THE PRICE ADJUSTMENT PROCESS 133 Real GDP in Deviation from Potential GDP Okuns Law for the US between 1967-99 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -4 -3 -2 -1 0 1 2 3 4 Unemployment Rate in Deviation from Natural Rate Figure 4.22: output, instead of increasing capacity to higher levels …rms may just increase the price. The Keynesian model rules immediate price adjustment out, but rather assumes that the price that …rms charge in the next period will react to the gap between potential output and aggregate demand. Two caveats are in order: …rst, it is really crucial to specify the length of a period. In order for the price stickiness assumption of the Keynesian model to have any bite, the period has to be long enough, say at least a quarter, or better a year. Second, we lead our discussion from the perspective of a single …rm, but talk about macroeconomic aggregates like aggregate demand and potential output. So the …rm that we are implicitly invoking in our discussion is the “average …rm”. On average, …rms are assumed to behave as described, which, when averaging over …rms, give rise to the aggregate behavior. As with the aggregate consumption, the issue of aggregation is a di¢cult one and we can’t explicitly deal with it in this course. So for the price adjustment process we assume that the (percentage) change 5 6 134 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS in the price level from last period to today (the in‡ation rate) is a function of the (percentage) gap between yesterday’s realized output (aggregate demand) and potential output. The relationship can be written mathematically as ¼t = f Yt¡1 ¡ Yp;t Yp;t (4.11) where f is a positive constant. Remember that Yp;t was potential output. Now Y ¡Y from Okun’s law we can substitute for t¡1Yp;t p;t the term ¡3(ut¡1 ¡u¤ ); so that (4:11) becomes ¼t = ¡g(ut¡1 ¡ u¤ ) (4.12) where g = 3f is a constant. Equation (4:12) is called the Phillips curve, named after British economist A.W. Phillips.15 It states that the in‡ation rate depends negatively on the unemployment rate: higher unemployment brings about lower in‡ation and vice versa. Up until the early seventies, the Phillips curve was probably the single most important empirical relationship between two macroeconomic variables and a great deal of research was done in writing down economic models whose outcome was a relation like the Phillips curve. It also seems to provide an intriguing problem for policy makers: if there is a trade-o¤ between in‡ation and employment, then the policy maker has a choice: does she accept a little more in‡ation in order to bring down the unemployment rate? And, believing in the Keynesian business cycle model we know how to increase aggregate demand for a given price level: expansionary monetary or …scal policy will do it. Figure 50 plots the Phillips curve (i.e. unemployment rates against in‡ation rates) for the year 1967-1973. One can clearly see the negative relationship between the unemployment and the in‡ation rate - a relation that was also quite stable in the 50’s and early 60’s. In Figure 51 we plot the Phillips curve for the entire sample from 1967 to 1999. There is no systematic relationship between in‡ation and unemployment rate whatsoever. For some, yet to be explained reason the Phillips curve broke down completely and has not reappeared (at least not in its original form) since. Even worse, the 70’s were a period of so-called “Stag‡ation”, high unemployment with high in‡ation. The two oil price shocks provide a partial explanation for this misery, but expansionary monetary and …scal policy to combat the high unemployment rates have done their share of bringing in‡ation up. One remark: both (4:11) and (4:12) are called the Phillips curve, which, given Okun’s law, is justi…ed since unemployment and the gap between potential and actual GDP have such a stable relationship. In the late 60’s, before the simple Phillips curve actually broke down in the data, Milton Friedman from Chicago and Edmund Phelps from Columbia criticized the Phillips curve on theoretical grounds, arguing that it ignores in‡ation 15 Phillips himself studied the relationship between percentage changes in wages and the unemployment rate, rather than percentage change in prices. In his study for the UK from 1861-1957 he found that the Phillips curve …t the data extremely well. 4.5. THE PRICE ADJUSTMENT PROCESS 135 Phillips Curve for the US between 1967-73 0.08 0.07 Inflation Rate 0.06 0.05 0.04 0.03 0.02 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 Unemployment Rate in Deviation from Natural Rate Figure 4.23: expectations. The so called expectations-augmented Phillips curve reads (we augment (4:11) rather than (4:12)) ¼t = ¼et + f Yt¡1 ¡ Yp Yp where ¼et is the in‡ation rate that households and …rms expect for period t in period t ¡ 1: One of the justi…cations for including in‡ation expectations as determinant for actual in‡ation goes like this: if …rms and unions expect the in‡ation rate to be 5% rather than 2%; then in their bargaining over wages they will agree on a 3% higher wage increase to compensate for higher in‡ation (which so far is just expected, not realized in‡ation). But if wages rise by 3% more (due to higher in‡ation expectations), then …rms, in order to get reimbursed for the increasing costs, have to increase their prices for next period by 3%; so that in fact realized in‡ation rises by 3%: In this sense do in‡ation expectations 1 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 136 Phillips Curve for the US between 1967-99 0.18 0.16 0.14 Inflation Rate 0.12 0.1 0.08 0.06 0.04 0.02 0 -0.02 -4 -3 -2 -1 0 1 2 3 4 Unemployment Rate in Deviation from Natural Rate Figure 4.24: help determine actual in‡ation. The work by Friedman and Phelps basically marks the …rst instance in macroeconomics where expectations explicitly enter a macroeconomic model. But now we face a dilemma: we have to model how people form in‡ation expectations. Early contributors to the literature, including Phelps and Friedman, made their lives somewhat easy and assumed “adaptive expectations”: the expectation for the in‡ation rate for time t at time t ¡ 1 is assumed to equal the actual in‡ation rate at date t ¡ 1 (or a weighted average of past in‡ation rates in a more sophisticated model), so the Phillips curve becomes ¼t = ¼t¡1 + f Yt¡1 ¡ Yp Yp If we plot this relationship for 1967 to 1999, as in Figure 52 we see that our negative conclusion from Figure 52 disappears: we now can see somewhat of an 5 6 4.5. THE PRICE ADJUSTMENT PROCESS 137 (expectation-augmented) Phillips curve. Inflation Rate in Deviation from Inflation Expectation Phillips Curve for the US between 1967-99 0.08 0.06 0.04 0.02 0 -0.02 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 Real GDP in Percentage Deviation from Potential GDP Figure 4.25: Two remarks: to model the expected in‡ation rate as being determined by past experience is clearly unsatisfactory: it is the future that should count for your expectations, not the past. A lot of work as been done to overcome this shortcoming, because it assumes that households are somewhat dum in making their in‡ation forecasts. A second, even more important point is that the expectations-augmented Phillips curve is not an easy-to-exploit policy menu anymore, as monetary and …scal policy may a¤ect in‡ation expectations and hence the realized in‡ation rate. That is what a lot of economists believe happened in the 70’s. By the 70’s households by and large had roughly …gured out how the government does Keynesian business cycle policy. Given a recession people expected that the government will try to exploit the simple Phillips curve and curb unemployment, taking into account a bit higher in‡ation. But this now entered in‡ation 138 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS expectations of private households and …rms: they expected higher in‡ation and this resulted in higher in‡ation -in fact much higher than the simple Phillips curve would have predicted, because of the expectation e¤ect. And this is the crux with the simple Phillips curve: once the public understands it and the governments’ intention to exploit it, it can’t be exploited any longer successfully. Realizing that people are not stupid after all was a painful experience for policy makers and led to a complete paradigm shift in macroeconomics, away from Keynesian macroeconomics to “Rational Expectations Macroeconomics”. Real Business Cycle theory is the business cycle part of Rational Expectations Macroeconomics. Before discussing this, however, let us proceed and see how the Keynesian model, augmented by the Phillips curve, works. 4.5.1 Aggregate Demand, Potential GDP and the Price Adjustment Process For simplicity we keep the discussion to the simple Phillips curve ¼t = f Yt¡1 ¡ Yp Yp Suppose that, as in Figure 53, we start at a situation with price level P0 and a Y ¡Y corresponding percentage output gap 0Yp p : Then the Phillips curve indicates 0 < 0 and therefore P1 < P0 ; i.e. the that, since Y0 ¡ Yp < 0 we have ¼ 1 = P1P¡P 0 price level falls (a process that economists call de‡ation). But for price level P1 we still have a gap between aggregate demand and potential GDP (although smaller) since Y1 ¡ Yp < 0: So ¼2 < 0 and prices fall further until, absent any other shocks, over time the economy approaches the point where aggregate demand equals potential GDP. The same analysis can be applied for the study of the e¤ects of monetary and …scal policy on output and the price level and the adjustment process over time. 4.5.2 Monetary Policy We have already done half of the work in the IS-LM analysis. Suppose we want to analyze the e¤ect of a monetary expansion; i.e. suppose that the FED increases the money supply M s : What happens in our economy? Let’s proceed in steps 1. Fix the price level P: An increase in M s shifts the LM-curve to the right. The IS-curve does not shift. Hence aggregate demand Y increases, for the given price level. We did this analysis before, nothing new here. 2. The previous argument is true for every given price level P: Hence, in response to loosening monetary policy (increasing M s ) the aggregate demand curve shifts to the right (since aggregate demand is higher now for any given price level). 4.5. THE PRICE ADJUSTMENT PROCESS Price Level (P) 139 Potential Output Gap between Potential Output and Aggregate Demand P 0 P 1 P* Aggregate Demand Output (Y) Y Y 0 1 Y p Figure 4.26: 3. The rest of the analysis is new and uses the price adjustment process. In Figure 54 we show what happens. The aggregate demand curve shifts to the right, due to the monetary expansion. We assume that before the policy change the economy was at its long run equilibrium where aggregate demand equals potential output and the associated long run equilibrium price level is P0 : Since the price level is …xed, immediately after the expansion aggregate output jumps up to Y0 : Why this happens is answered by the IS-LM model: for a …xed price level the increase in money supply increases real money supply, the interest rate in the money market has to fall, this induces higher investment, the consumption multiplier sets in and aggregate expands. So far nothing new. Now the price adjustment via the Phillips curve comes into play. After the monetary expansion aggregate demand is above potential output, …rms will start increasing prices, say to P1 aggregate demand declines to Y1 : This decline is due to the fact that CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 140 with an increasing price level the real supply of money declines, the interest starts increasing and investment falls below the initial level after the money injection. The …rst round e¤ect is partly reversed. This process of price adjustment continues until aggregate demand eventually equals potential output again (this of course assumes that there are no further policy changes which would again shift the aggregate demand curve). So in the long run monetary policy is ine¤ective; in the long run the monetary expansion just leads to an increase in the price level without any e¤ect on real GDP, just as the classical dichotomy predicts. Along the adjustment process however, the expansion in monetary policy does a¤ect real GDP. Therefore sometimes potential output is also called the natural (rate of ) output since in the long run it is the level of output that the economy will return to. Price Level (P) Potential Output New Aggregate P 1 P 0 Demand Curve Old Aggregate Demand Curve Output (Y) Y =Y 0 p Y 2 Figure 4.27: Y 1 4.6. STABILIZATION POLICY 4.5.3 141 Fiscal Policy The analysis of a change in …scal policy is almost identical to that of monetary policy. Suppose there is a …scal expansion so that government spending increases. Let us repeat our three steps of reasoning 1. Fix the price level P: An increase in G shifts the IS-curve to the right. The LM-curve does not shift. Hence aggregate demand Y increases, for the given price level. We did this analysis before, nothing new here. 2. The previous argument is true for every given price level P: Hence, in response to expanding …scal policy (increasing G) the aggregate demand curve shifts to the right (since aggregate demand is higher now for any given price level). 3. Again the rest of the analysis is almost identical to the process induced by a monetary expansion. Again refer to Figure 54. The aggregate demand curve shifts to the right, due to the …scal expansion. We assume that before the policy change the economy was at its long run equilibrium where aggregate demand equals potential output and the associated long run equilibrium price level is P0 : Since the price level is …xed, immediately after the expansion aggregate output jumps up to Y1 : Why this happens is answered by the IS-LM model: for a …xed price level the increase in government spending induces the multiplier process and hence increases aggregate demand. In the process the interest rises and the crowding-out of private investment reduces the …rst round e¤ect somewhat. So far nothing new. Now the price adjustment via the Phillips curve comes into play. After the …scal expansion aggregate demand is above potential output, …rms will start increasing prices, say to P1 aggregate demand declines to Y1 : This decline is due to the fact that with an increasing price level the real supply of money declines, the interest starts increasing and private investment falls even further. The …rst round e¤ect is partly reversed. This process of price adjustment continues until aggregate demand eventually equals potential output again (this of course assumes that there are no further policy changes which would again shift the aggregate demand curve). So in the long run also …scal policy is ine¤ective; in the long run private investment is crowded out one for one by government spending. Along the adjustment process however, the expansion in …scal policy does a¤ect real GDP as before did monetary policy Given that we (hopefully) have understood how monetary and …scal policy work in the complete model, including the adjustment process, we can now analyze both types of policies more systematically. 4.6 Stabilization Policy What brings the economy away from the long run equilibrium in which aggregate demand equals potential GDP? We saw in the last section that monetary and 142 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS …scal policy can do so, but why should they. After all, monetary and …scal policy should be used to smooth out the business cycle, not to create them. In this section we will …rst identify shocks hitting the economy that may lead to deviations of aggregate demand form potential GDP and then discuss how monetary and …scal policy can counteract these shocks to smooth out or even prevent business cycles. Hall and Taylor identify two sources of shocks to the economy 1. Aggregate Demand Shocks: these are shocks that shift the entire aggregate demand curve and therefore move the economy temporarily out of its short-run equilibrium. Examples include all sources of shocks that either shift the IS-curve or the LM-curve: a decline in exports due to a recession in other countries, say in Asia, a decline in autonomous consumption spending due to a sudden drop in the stock market, a sudden decline in real money demand (due to the arrival of credit cards, for example), etc. 2. Price Shocks: these shocks do not shift the aggregate demand curve, but induce a jump along the aggregate demand curve. The most famous examples of price shocks are the oil price shocks in the 70’s and early 80’s. There are two steps to analyzing these shocks. First, we have to …nd out how they a¤ect the position of the economy in the aggregate demand - potential GDP graph, holding monetary and …scal policy …xed, and then we have to …gure out what monetary or …scal policy can do to counteract them. In all our analyzes we assume that we start at the long-run equilibrium in which aggregate demand equals potential GDP and that the shocks are permanent. 4.6.1 Aggregate Demand Shocks and Their Stabilization Every Shock that shifts the IS-curve to the right or the LM-curve to the right shifts the aggregate demand curve to the right. Examples include increases in exports, autonomous consumption or investment spending and so forth. Every shock that shifts the IS-curve or the LM-curve to the left shifts the aggregate demand curve to the left. Examples were given before. Since the major concern about stabilization policy is avoiding severe recessions we focus on examples which, without government intervention, would lead to recessions. So suppose that there is a …nancial crisis in Asia in 1997 and as a result Japan and other countries fall into a severe recession. This, in turn, leads to a decline of U.S. exports to Asia in 1997. Suppose the US government and the Federal Reserve Bank do not react. What happens? A decrease in exports shifts the IS-curve to the left, therefore for each price level aggregate demand falls, hence the aggregate demand curve shifts to the left. In the initial period of the decline, 1997, US real GDP drops from potential output Yp to Y0 (see Figure 55). The US falls into a recession. Over time prices decline and the economy returns out of the recession back to potential GDP. Can …scal (or monetary policy) be used to avoid the recession? The answer is yes, and there is an easy recipe. Suppose 4.6. STABILIZATION POLICY 143 the government increases government spending G by exactly the amount by which exports fall, immediately once Japan’s problem becomes public. Then, as indicated in Figure 56, the shift of the aggregate demand curve to the left is immediately o¤set by a shift back to the right, due to increased government spending. The economy remains at potential GDP and full employment (the unemployment rate equals its natural rate). Neither a recession nor an increase in the price level (higher in‡ation has occurred). Price Level (P) Potential Output P 0 Old Aggregate P 1 Demand Curve New Aggregate Demand Curve Output (Y) Y Y 0 1 Y p Figure 4.28: A similar story can be told when, for example, money demand increases. This would shift the LM-curve to the left, hence the aggregate demand curve to the left and push the economy into a recession if not the FED would increase the money supply by exactly the right amount to counteract this initial shift and avoid the recession. The fact that consumers, by developing a stronger preference for holding cash, could cause a recession was a major concern for Keynes. CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 144 Price Level (P) Potential Output Decline in Exports Increase in Government Spending Old Aggregate Demand Curve New Aggregate Demand Curve Output (Y) Figure 4.29: So how can any sensible mind dispute the usefulness of stabilization policy? Almost all economists would agree that it would be very desirable to eliminate business cycles with monetary and …scal policy if we could. So what is the criticism of Non-Keynesians of stabilization policy. It is two-fold: 1. First, all policies occur with lags. It takes time for politicians and central bankers to realize when an adverse demand shock has hit the economy (presumably politicians longer that central bankers). Then it takes time to decide on an appropriate policy, because congress or the Federal Open Market Committee (FOMC) has to assemble, deliberate and take a decision. Finally it takes time to implement the decision. Congress agreeing on SDI does not mean that the orders for the …rst satellites go out the next morning, there is a rather lengthy bureaucratic process involved. Given these time lags the stabilization policy may hit the economy when it is already recovering from the recession and may create the opposite problem, 4.6. STABILIZATION POLICY 145 an overheated economy. 2. Not only timing is di¢cult, but also to …nd the right magnitude of the policy is not a trivial task to …nd out. Friedrich August Hayek, an important neoclassical economist criticized the belief that politicians and central bankers can overcome these practical problems and carry out e¤ective stabilization policy as hubris. These points do not dispute the principle usefulness of stabilization policy, but question its implementability. In contrast real business theorists question the usefulness of stabilization policy, in particular monetary policy, altogether. Both fractions of opponents suggest instead that the best the government and the central bank can do is keep monetary policy transparent and stable so as not to cause additional shocks over and above the ones already present in the economy; and otherwise trust the magic of free markets to bring the economy back to its long-term equilibrium. 4.6.2 Price Shocks and Their Stabilization Now suppose an adverse shock hits the US economy that increases the price level suddenly. The two oil price shocks in 1973-74 and 1979-80 are classic examples of such events. Without any policy intervention Figure 57 shows what happens. A sudden increase in the price level, brought about by the increase in oil prices, lets the price level jump up from P ¤ to P0 . Output declines and the economy goes into a recession. Over time the price level starts declining and output comes back to potential output, but not without a recession in the meantime. For the two speci…c episodes the numbers are the following: in 1973-74 the price of gasoline increased by 35%, the CPI increased by 4.8% and real GDP from 1974 to 1975 shrank by 0.8%. For 1978-79 the gasoline price increased by 35%, the CPI by 3.7% and real GDP shrank 0.5% from 1979 to 1980. Can monetary or …scal do something in this case. Let us focus on monetary policy. Suppose monetary policy does not react at all. Such a monetary policy is called nonaccomodative. The situation is as in Figure 57: a severe recession, but real GDP and the price level …nally come back to their initial levels P ¤ and Yp: Now suppose the FED reacts to the price shock and increases the money demand. Such a policy is called accomodative. An increase in the money supply shifts the LM-curve to the right and hence the aggregate demand curve to the left. Again, due to the price shock, the price level jumps up to P0 ; but output declines only to Y0 ; a smaller decline compared with the nonaccomodative policy. This is shown in Figure 58. Hence the accomodative policy softens the recession. But this comes at a price. Over time in the nonaccomodative policy case the economy goes back to the original price level, whereas with the accomodative price level it goes to a price level P1 > P ¤ , with higher in‡ation rates (lower disin‡ation rates) along the way. Hence for a price shock not even the Keynesians have an easy answer what to do: one may use monetary policy to soften the recession, but this comes at the cost of higher in‡ation. CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS 146 Price Level (P) Potential Output Gap between Potential Output and Aggregate Demand P 0 P* Aggregate Demand Output (Y) Y 0 Y p Figure 4.30: This concludes our discussion of the Keynesian business cycle model. To recapitulate: 1. In the short run prices are sticky and aggregate demand determines GDP. Aggregate demand may fall short of potential GDP in which case there is unemployment. 2. In the medium run prices adjust, according to the Phillips curve. Prices go up if aggregate demand is higher than potential output and go down if aggregate demand is lower than potential output. 3. The adjustment process described by the Phillips curve in the long run leads prices back to a level at which aggregate demand equals potential GDP. 4. Active monetary and …scal policy are able to prevent or soften recessions 4.6. STABILIZATION POLICY 147 Price Level (P) Potential Output P 0 New Aggregate Demand P*’ P* Old Aggregate Demand Output (Y) Y 0 Y p Figure 4.31: that may arise because of adverse aggregate demand or price shocks. Severe information and implementation problems have to be solved to use these policies e¤ectively, though. Overall the Keynesian model was unambiguously successful until the 70’s when the Phillips curve broke down. Still today, a signi…cant fraction of practitioners and academic researchers trust the Keynesian model as their model of business cycles, which, I guess rightly so, is re‡ected in macroeconomics textbooks, in which this model is still the workhorse to explain business cycles. Before leaving business cycles completely, let’s have a brief look at a competing paradigm for business cycle research. 148 4.7 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS Real Business Cycle Theory Real business cycle theory builds on the basic insight that whatever is good for explaining economic growth should be good for explaining business cycles. In stark contrast to Keynesian business cycle theory it is assumed that prices are fully ‡exible even in the short run and that aggregate demand never falls short of potential GDP. How then can business cycles arise. The answer: technology shocks. In particular, let us assume that total output Y in the economy can be produced by the aggregate production function Yt = zt Kt® L1¡® t where zt is a technology shock and equals 0:95 with probability 0:5 and equals 1:05 with probability 0:5: But this is not the end of the story. In real business cycle theory we have households that live for, say 60 periods. These households like to eat consumption goods ct and like to have leisure. They have 16 hours of time in a day, 365 days a year and can decide how much of this time to work. Let by N denote the total hours in a year that a household can work and by lt the number of hours the household actually decides to work. Their utility function is then u(c0 ; N ¡ l0 ) + ¯u(c1 ; N ¡ l1 ) + : : : + ¯ T u(cT ; N ¡ lT ) So what happens if zt is low? The return from working (the real wage) is low and households optimally decide to work less in the current period and more later. So the e¤ect of the technology shock on output is ampli…ed by the labor supply decision of the households. There is no involuntary unemployment in this model: all households can work at the equilibrium wage, but this wage may be so low that some people don’t …nd it worthwhile to work or work full hours. By making the technology shocks really persistent (if today is bad, then the likelihood of tomorrow being bad is very high) Kydland and Prescott (1982) showed that around 70% of all business cycle ‡uctuation can be accounted for by technology shocks and the ensuing e¤ects on labor supply. It is also important to note that in this model there is no role for monetary policy, since the source of the ‡uctuations, technology shocks, can’t be cured with monetary policy, and conditional on having the shocks in the economy everybody, …rms and households are behaving optimally and there are no market failures. Monetary policy would just make matters worse. My assessment of the model: is has a big methodological plus: it is soundly based on the microeconomic principles of consumer and …rm maximization and market clearing. No ad-hoc assumptions as in the Keynesian model are needed. The big problem is: what are these technology shocks exactly and how can they be identi…ed in the data? Given that these shocks are at the heart of the model one would expect the RBC’ers to have a satisfactory answer for this, but a convincing explanation is missing so far. For this course we have to leave it here. But some of the material covered next, namely a more detailed look at consumption and investment behavior shares the same principles with the RBC 4.7. REAL BUSINESS CYCLE THEORY 149 model: an explicit model of the decision problem that single households and …rms face. 150 CHAPTER 4. BUSINESS CYCLE FLUCTUATIONS Chapter 5 Microeconomic Foundations of Macroeconomics In this section we discuss the foundations for some of the behavioral equations we wrote down when developing the IS-LM model. In particular we will subject to more detailed analysis the aggregate consumption function and the aggregate investment function. We will discuss how good or bad they perform empirically and present other, more involved theories of consumption demand and investment demand. 5.1 Consumption Demand Consumption is the sole end and purpose of all production [Adam Smith] But consumption is not only the …nal purpose of all economic activity, but also constitutes about two thirds of GDP. Therefore economists have spent a great deal of time trying to understand the determinants of consumption demand. In this section we want to accomplish three things: we …rst want to look more carefully at the data on consumption, we then want to investigate empirically whether the simple Keynesian consumption function is in fact a good approximation to reality. Finally we will look at an alternative model of consumption demand, the life-cycle permanent income model, which is more soundly based on microeconomic principle, to see what other determinants of consumption beyond current disposable income there are. 5.1.1 Data on Consumption In this section we will describe the basic facts about aggregate consumption. In Figure 59 we plot real GDP, personal disposable income and total consumption expenditures for 1959 to 1999. The data are in billion 1996 chained dollars, 151 152CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS i.e. real quantities and of quarterly frequency, i.e. we have one new observation every quarter. What are the main observations? All three time series trend upward, due to growth in population and due to economic growth as described in the third section of this lecture. With respect to the cyclical properties of the data, we see that there are substantial ‡uctuations of all variables around their long term growth trend. More importantly, real GDP tends to ‡uctuate more than both disposable personal income and consumption expenditures, which exhibit a smoother time series. We also see that consumption makes up the bulk of GDP, a fraction that varies but is about 60-70% of GDP. Finally we see that consumption seems to track personal disposable income rather closely. This observation, after all, was the motivation for the Keynesian aggregate consumption function, which speci…ed consumption solely as a function of disposable income. In the next section we will see how well this consumption function does in the data. GDP, Disposable Income, Consumption 8000 Real GDP, Personal Disposable Income, Consumption Expenditures, 1959-99 7000 6000 5000 Personal Disposable Income 4000 Real GDP 3000 Consumption 2000 1000 1955 1960 1965 1970 1975 1980 Year Figure 5.1: 1985 1990 1995 2000 5.1. CONSUMPTION DEMAND 153 We can break consumption down into its components, expenditures on a) nondurable consumption items, durable consumption items and services. In 1997, 13.6% of all consumption expenditures were accounted for by purchases of consumer durables, 30.2% were due to purchases of nondurable goods and 56.2% accrued to services. Over time, the share of consumption expenditures going to services has increased substantially, as has the share of consumer durables, whereas the share of nondurables has declined over time. When plotting these components over time (see Hall/Taylor’s Figure 10.2) we see that, although consumer durables are the smallest item among total consumption expenditures, it is by far the most volatile part: purchases of consumer durables are particularly low during recessions and particularly high during booms, whereas purchases of nondurables and services are relatively stable over the business cycle. This fact is quite intuitive since consumer durables (cars, furniture) have investment goods character; they require a large outlay, are usually …nanced by credit and provide services for a prolonged period of time. This investment good character of consumer durables has led economists to think that we in fact mismeasure consumption by looking at consumption expenditures. When you buy a new car in 1999, the whole price for the car is counted in consumption expenditures for 1999. But the car delivers services for many years (unless you bought a real lemon). Therefore from a theoretical point of view the price of the car should be split up into, say, ten pieces (for ten years of usage), and only that part of the price that corresponds to the services that the car provides in the …rst year should be counted as consumption expenditures. This method is obviously somewhat hard to implement in practice. But once implemented it seems almost certain that expenditures on consumer durables, measured this way, would be way less volatile than it is now with the conventional measurement technique. Hence consumption expenditures would be even smoother over the business cycle that they already are. 5.1.2 The Keynesian Aggregate Consumption Function and the Data Now we will look in more detail at the Keynesian aggregate consumption function. Remember that in its simplest form it was given as C = a + b(1 ¡ ¿ )Yh = a + bYd where Yd is disposable income. Let us see how the function does in practice. In Figure 60 we plot total consumption expenditures as measured in the data and consumption expenditures predicted by the aggregate consumption function for 1959 to 1999. All data is in billion 1996 US dollars. We pick the parameters (a; b) in such a way as to minimize the di¤erence between actual and predicted data, i.e. we give the aggregate consumption function its best shot. Estimating the parameters that gives the best …t1 yields 1 Technically, we estimate the parameters by ordinary least squares, i.e. in order to minimize 154CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS 6000 Consumption Expenditures, Actual and Predicted, 1959-99 Consumption, Actaul and Predicted 5500 5000 4500 4000 3500 3000 2500 2000 Consumption Expenditures in the Data 1500 Consumption Expenditures Predicted by Aggregate Consumption Function 1000 1955 1960 1965 1970 1975 1980 1985 1990 1995 Year Figure 5.2: (a; b) = (¡106; 0:923): The fact that the estimated a is negative is a bit bothersome, but let’s ignore this for a second. The marginal prospensity to consume is estimated at 0:92; i.e. on average the US households spend 92 cents out of every additional dollar disposable income. Figure 60 may indicate that the Keynesian consumption function does rather well. But the magnitudes on the y-axis a re substantial. Let us in Figure 61 plot the deviation of actual consumption expenditures from the ones predicted by the consumption function. We see that the deviations are quite sizeable, amounting to under-or overestimation of actual consumption by up to 200 billion US dollar, or about 6% of total consumption expenditures in given periods. Given that consumption expenditures make up about two thirds of total real GDP, this under- or overprediction may easily lead to an under -or overprediction of real GDP by 3-4%. the sum of squared deviations of actual data from predicted ones. 2000 5.1. CONSUMPTION DEMAND 155 Deviation of Consumption Expenditures from Predicted, 1959-99 250 200 Consumption Deviations 150 100 50 0 -50 -100 -150 -200 1955 1960 1965 1970 1975 1980 Year 1985 1990 1995 Figure 5.3: Given that economic policy is carried out based on economic forecasts, these are huge numbers because the prediction may easily show a healthy economy when in fact the true data afterwards indicate that the economy was well under way into a recession. For example, in the 70’s and early 80’s realized consumption expenditures were quite smaller than predicted ones. According to the prediction …scal or monetary expansionary policy was not called for, but ex-post it turned out to be the case that the economy was or was going into a recession and an expansionary …scal or monetary policy, uncalled for based on the prediction, may have been able to prevent or at least soften the recession. The apparent malfunction of the Keynesian aggregate consumption function, plus its weak foundation on microeconomic principles of consumer optimization led to the development of an alternative model of consumption, the life cycle/permanent income model of consumption. 2000 156CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS 5.1.3 The Life Cycle/Permanent Income Model of Consumption In this subsection we will present and then apply a simple version of AndoModigliani’s life-cycle model and Friedman’s permanent income model. The simple model we present is due to Irving Fisher (1867-1947), and the life-cycle as well as the permanent income model are relatively straightforward generalizations of Fisher’s model. At the end of this section we will apply Fisher’s model to the analysis of how a social security system a¤ects consumption demand of households. Consider a single individual, for concreteness call this guy Freddy Krueger. Freddy lives for two periods (you may think of the length of one period as 30 years, so the model is not all that unrealistic). He cares about consumption in the …rst period of his life, c1 and consumption in the second period of his life, c2 : His utility function takes the simple form u(c1 ; c2 ) = log(c1 ) + ¯ log(c2 ) (5.1) where the parameter ¯ is between zero and one and measures Freddy’s degree of impatience. A high ¯ indicates that consumption in the second period of his life is really important to Freddy, so he is patient. On the other hand, a low ¯ makes Freddy really impatient. In the extreme case of ¯ = 0 Freddy only cares about his consumption in the current period, but not at all about consumption when he is old. Freddy has income y1 > 0 in the …rst period of his life and y2 ¸ 0 in the second period of his life (we want to allow y2 = 0 in order to model that Freddy is retired in the second period of his life and therefore, absent any social security system, has no income in the second period). Income is measured in units of the consumption good, not in terms of money. As with the Keynesian aggregate production function we abstract from money in this analysis. Freddy also starts his life with some initial wealth A ¸ 0; due to bequests that he received from his parents. Again A is measured in terms of the consumption good, not in terms of money. Freddy can save some of his income in the …rst period or some of his initial wealth, or he can borrow against his future income y2 : We assume that the interest rate on both savings and on loans is equal to r; and we denote by s the saving (borrowing if s < 0) that Freddy does. Hence his budget constraint in the …rst period of his life is c1 + s = y1 + A (5.2) Freddy can use his total income in period 1, y1 + A either for eating today c1 or for saving for tomorrow, s: In the second period of his life he faces the budget constraint c2 = y2 + (1 + r)s (5.3) i.e. he can eat whatever his income is and whatever he saved from the …rst period. The problem that Freddy faces is quite simple: given his income and 5.1. CONSUMPTION DEMAND 157 wealth he has to decide how much to eat in period 1 and how much to save for the second period of his life. The is a very standard decision problem as you have studied left and right in microeconomics, with the only di¤erence that the goods that Freddy chooses are not apples and bananas, but consumption today and consumption tomorrow. In micro our people usually only have one budget constraint, so let us combine (5:2) and (5:3) to derive this one budget constraint, a so-called intertemporal budget constraint, because it combines income and consumption in both periods. Solving (5:3) for s yields s= c2 ¡ y2 1+r and substituting this into (5:2) yields c1 + c2 ¡ y2 = y1 + A 1+r or c1 + c2 y2 = y1 + +A 1+r 1+r (5.4) Let us interpret this budget constraint. We have normalized the price of the consumption good in the …rst period to 1 (remember from micro that we could multiply all prices by a constant and the problem of Freddy would not change. 1 ; which is also the relative The price of the consumption good in period 2 is 1+r price of consumption in period 2; relative to consumption in period 1: Hence the gross interest rate 1 + r is really a price: it is the relative price of consumption goods today to consumption goods tomorrow (note that this is a de…nition). So the intertemporal budget constraint says that total expenditures on consumpc2 ; measured in prices of the period 1 consumption good, have tion goods c1 + 1+r y2 ; measured in units of the period 1 consumption to equal total income y1 + 1+r y2 good, plus the initial wealth of Freddy. The sum of all labor income y1 + 1+r y2 is sometimes referred to as human capital. Let us by I = y1 + 1+r + A denote Freddy’s total income, consisting of human capital and initial wealth. Now we can analyze Freddy’s consumption decision. He wants to maximize his utility (5:1); but is constrained by the intertemporal budget constraint (5:4): To let us solve max flog(c1 ) + ¯ log(c2 )g c1 ;c2 s:t: c2 c1 + 1+r = I One option is to use the Lagrangian method, which you should have seen in Microeconomics, and you should try it out for yourself. The second option is to substitute into the objective function for c1 to get ¾ ½ µ ¶ c2 max log I ¡ + ¯ log(c2 ) c2 1+r 158CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS This is an unconstrained maximization problem. Let us take …rst order conditions with respect to c2 1 ¡ 1+r ¯ =0 c2 + I ¡ 1+r c2 or c2 1+r c2 (1 + ¯)c2 c2 Since c1 = I ¡ c2 1+r µ ¶ c2 = ¯ I¡ 1+r = ¯ ((1 + r)I ¡ c2 ) = ¯(1 + r)I ¯ (1 + r)I = 1+¯ ¯ = ((1 + r)(y1 + A) + y2 ) 1+¯ (5.5) (5.6) we …nd c1 c2 1+r ¯ = I¡ I 1+¯ I = 1+¯ ¶ µ 1 y2 +A = y1 + 1+¯ 1+r = I¡ (5.7) Since saving s equals y1 + A ¡ c1 we …nd s= ¯ y2 (y1 + A) ¡ 1+¯ (1 + ¯)(1 + r) which may be positive or negative, depending on how high …rst period income and initial wealth is compared to second period income. So Freddy’s optimal 1 of total lifetime consumption choice today is quite simple: eat a fraction 1+¯ income I today and save the rest for the second period of your life. So on what variables does current consumption depend on? According to our model it is income today, income next period, initial wealth A and the interest rate r: All those variables, apart from income today, did the simple Keynesian aggregate consumption function ignore. But even the simplest model that has consumers deciding optimally on their consumption predicts that future income, the intertemporal price of consumption (the interest rate) and initial wealth holdings should enter the consumption function. More complex models based on consumer optimization add even more variables. 5.1. CONSUMPTION DEMAND 159 For now let us stick with our simple model. As in microeconomics we can analyze the decision problem of Freddy graphically, using budget lines and indi¤erence curves. First we plot the budget line (5:4): This is the combination of all (c1 ; c2 ) Freddy can a¤ord. We draw c1 on the x-axis and c2 on the y-axis. Looking at the left hand side of (5:4) we realize that the budget line is in fact a straight line. Now let us …nd two points on the line. Suppose c2 ; i.e. Freddy y2 does not eat in the second period. Then he can a¤ord c1 = y1 + A + 1+r is the y2 a a …rst period, so one point on the budget line is (c1 ; c2 ) = (y1 + A + 1+r ; 0): Now suppose c1 : Then Freddy can a¤ord to eat c2 = (1+r)(y1 +A)+y2 in the second period, so a second point on the budget line is (cb1 ; cb2 ) = (0; (1+ r)(y1 +A)+ y2 ): Connecting these two points with a straight line yields the entire budget line. We can also compute the slope of the budget line as cb2 ¡ ca2 cb1 ¡ ca1 (1 + r)(y1 + A) + y2 ´ ³ y2 ¡ y1 + A + 1+r slope = = = ¡(1 + r) Hence the budget line is downward sloping with slope (1 + r): Now let’s try to remember so microeconomics. The budget line just tells us what Freddy can a¤ord. The utility function (5:1) tells us how Freddy values consumption today and consumption tomorrow. Remember that an indi¤erence curve is a collection of bundles (c1 ; c2 ) that yield the same utility, i.e. between which Freddy is indi¤erent. Let us …x a particular level of utility, say u (which is just a number). Then an indi¤erence curve consists of all (c1 ; c2 ) such that u = log(c1 ) + ¯ log(c2 ) Solving for c2 yields log(c2 ) = c2 u ¡ log(c1 ) ¯ = e u¡log(c1 ) ¯ u ¡1 = e ¯ c1¯ Hence as c1 becomes bigger and bigger, c2 approaches 0: As c1 approaches 0; c2 becomes bigger and bigger. See Figure 62 for a typical shape of an indi¤erence curve. The slope of the indi¤erence curve is given as dc2 dc1 = = = ¡1 ¡1 u¯ ¡1 e c1¯ ¯ ¡1 u¯ ¡1 e c1¯ ¯c1 ¡c2 ¯c1 160CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS c 2 Slope c / βc 2 1 (1+r)(y +A)+y 1 2 Slope 1+r c* 2 Indifference curve log(c )+βlog(c )=constant 1 2 y 2 Saving s c* 1 Budget line y +A 1 y +A+y /(1+r) 1 2 c 1 Figure 5.4: Incidently this slope equals the (negative of the) marginal rate of substitution (as always) MRS = c2 uc1 (c1 ; c2 ) = uc2 (c1 ; c2 ) ¯c1 where uci indicates the partial derivative of u with respect to ci : From the …gure we note that Freddy should pick his consumption such that the indi¤erence curve is tangent to the budget line. This means that at the optimal consumption choice the slope of the indi¤erence curve and the budget line are equal or uc1 (c1 ; c2 ) = 1+r uc2 (c1 ; c2 ) uc1 (c1 ; c2 ) = (1 + r)uc2 (c1 ; c2 ) (5.8) This equation has a nice interpretation. At the optimal consumption choice the 5.1. CONSUMPTION DEMAND 161 cost, in terms of utility, os saving one more unit should be equal to the bene…t of saving one more unit (if not, Freddy should either save more or less). But the cost of saving one more unit, and hence one unit lower consumption in the …rst period, in terms of utility equals uc1 (c1 ; c2 ): Saving one more unit yields (1 + r) more units of consumption tomorrow. In terms of utility, this is worth (1+ r)uc2 (c1 ; c2 ): Equality of cost and bene…t implies (5:8): Using the particular from of the utility function yields as the condition for an optimal consumption choice c2 =1+r ¯c1 This, together with the intertemporal budget constraint (5:4) can be solved for the optimal consumption choices, which obviously gives the same result as before. Income and Interest Changes Now we can investigate how changes in today’s income y1 ; next period’s income y2 and initial wealth A change the optimal consumption choice. From (5:7) and (5:5) we see that both c1 and c2 increase with increases in either y1 ; y2 or A: In contrast to the Keynesian consumption function, an increase in tomorrow’s income will increase today’s consumption as well as tomorrow’s consumption. The marginal prospensity to consume out of today’s income or initial wealth is dc1 1 dc1 = >0 = dA dy1 1+¯ and the marginal prospensity to consume today out of tomorrows income equals 1 dc1 >0 = dy2 (1 + ¯)(1 + r) We see this e¤ect graphically in Figure 63. The e¤ect of increases in both c1 and c2 in reaction to increases in y1 ; y2 or A is called an income e¤ect. More complicated are changes in the interest rate, since this will entail income e¤ects and substitution e¤ects. A substitution e¤ect comes about since the gross interest rate 1 + r is the relative price of consumption in period 1; relative to consumption in period 2: So as the interest changes, not only does income y2 changes), but also the relative price of consumption goods change (because 1+r in the two periods. Let us analyze an increase in the interest rate from r to r0 and let us start graphically. What happens to the curves in Figure 62 as the interest rate increases? The indi¤erence curves do not change, as they do not involve the interest rate. But the budget line changes. Since we assume that the interest rate increases, the budget line gets steeper. And it is straightforward to …nd a point on the budget line that is a¤ordable with old and new interest rate. Suppose Freddy eats all his …rst period income and wealth in the …rst period, 162CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS c 2 Slope c / βc 2 1 (1+r)(y +A)+y 1 2 Slopes 1+r ’ c*’ 2 c* 2 y 2 Budget lines c* 1 c*’ 1 y +A 1 1 c Figure 5.5: c1 = y1 + A and all his income in the second period c2 = y2 ; in other words, he doesn’t save or borrow. This consumption pro…le is a¤ordable no matter what the interest rate (as the interest rate does not a¤ect Freddy as he neither borrows nor saves). This consumption pro…le is sometimes called the autarkic consumption pro…le, as Freddy needs no markets to implement it: he just eats whatever he has in each period. Hence the budget line tilts around the autarky point and gets steeper, as shown in Figure 64. Consumption in period 2 increases and consumption in period 1 decreases. Saving increases. This is also apparent from equations (5:7) and (5:5). What is the reason? There are two e¤ects from an increase in the interest rate. First there is an income e¤ect: if Freddy is a saver (as we assume in the picture) then a higher interest rate, for given savings, increases his income in the second period. The in‡uence of this e¤ect on both c1 and c2 is positive and is called the income e¤ect. Also, an increase in the interest rate makes consumption today 5.1. CONSUMPTION DEMAND 163 c*’ 2 Slope c / βc 2 1 Slope 1+r c* 2 y 2 Budget lines c*’ c* 1 1 y +A 1 c 1 Figure 5.6: more expensive compared to consumption tomorrow, so individuals substitute substitute consumption today with consumption tomorrow. This is the substitution e¤ect: it is negative for c1 and positive for c2 : Hence c2 unambiguously increases; for c1 it depends on the size of the income and the substitution e¤ect. For the particular utility function we chose and the assumptions on income we made c1 decreases and saving increases. Note that if the consumer is a borrower then the income e¤ect is negative rather than positive: a higher interest rate increases the interest payments on his loan. The substitution e¤ect works as before. Hence for a borrower we can conclude that consumption in the …rst period declines in a response to an increase in the interest rate (both income and substitution e¤ects are negative). Consumption in the second period may increase or decline, depending on whether the positive substitution e¤ect is stronger or weaker than the negative income e¤ect (again for our assumptions the substitution e¤ect is stronger). 164CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS So far we assumed that Freddy could borrow freely at interest rate r: But we all (at least some of us) know that sometimes we would like to take out a loan from a bank but are denied it. Let us analyze how the presence of so-called borrowing constraints a¤ect the consumption choice. So let us assume that Freddy cannot borrow, so he is constrained by s ¸ 0: Obviously if Freddy is a saver anyway, nothing changes for him since the constraint on borrowing is not binding. The situation is di¤erent if, without the borrowing constraint, Freddy would be a borrower. Now with the borrowing constraint, the best he can do is set c1 = y1 + A; c2 = y2 : He would like to have even bigger c1 ; but since he is borrowing constrained he can’t bring any of his second period income forward by taking out a loan. Note that in this situation Freddy’s …rst period consumption does not depend on second period income or the interest rate. In particular, if y2 goes up, c1 remains unchanged if Freddy is borrowing-constrained. This can be seen from Figure 65. c 2 Slope c / βc 2 1 Slope 1+r c’ = y’ 2 2 Budget line c =y 2 2 Indifference Curves c = y +A 1 1 Figure 5.7: c 1 5.1. CONSUMPTION DEMAND 165 The budget line with the presence of borrowing constraints has a kink at (y1 + A; y2 ): For c1 < y1 + A we have the usual budget constraint, as here s > 0 and the borrowing constraint is not binding. But with the borrowing constraint Freddy cannot a¤ord any consumption c1 > y1 + A; so the budget constraint has a vertical segment at y1 + A; because regardless of what c2 ; the most Freddy can a¤ord in period 1 is y1 + A: If Freddy was a borrower without the borrowing constraint, then his optimal consumption is at the kink. And with an increase of second period income y2 ; Freddy just increases second period consumption, with …rst period consumption unchanged. Also not that (as long as the borrowing constraint remains binding, Freddy will consume every cent of an income increase in the …rst period immediately in the …rst period, i.e. his marginal prospensity to consume out of current income is 1 if Freddy is borrowing-constrained. Hence with borrowing constraints the consumption function of Freddy looks much more Keynesian: consumption only depends on current income and is independent of the interest rate and future income. Since in the overall economy there are individuals that face borrowing constraints and others who do not, we can expect the aggregate consumption function to depend heavily on current income, but also on future income and the interest rate. We saw in the …rst section how the Keynesian aggregate consumption function fared with respect to the data. A huge amount of empirical work has been done to test more elaborate versions of the simple Fisher model. We come back to this later. Borrowing constraints may be one explanation of why the Japanese saving rate is higher than the US saving rate. Individuals that are borrowing constrained consume less (and save more) than they otherwise would, without the borrowing constraint. The biggest expense, particularly for young families is usually the purchase of the …rst home. In the US, a down payment of about 10% on a house is quite common, the rest is borrowed. In Japan down payments of 40% or higher are common, hence households are much more borrowing constrained in Japan than in the US, at least with respect of this particular transaction. Hence Japanese have to save more in advance to …nance home purchases, which explains part of their higher saving rate. Note that, although a lot of economists argue that a high saving rate is good for growth, the particular feature of the Japanese economy that brings the higher saving rate about (high down payments) is usually not regarded as desirable. Social Security in the Life-cycle model Now we use the model to analyze a policy issue that has drawn large attention in the public debate. The personal saving rate -the fraction of disposable income that private households save- has declined from about 7-10% in the 60’s and 70’s to 2.1% in 1997. Since saving provides the funds for investment a lower saving rate, so a lot of people argue, harms growth be reducing investment.2 Some economists argue that the expansion of the social security system has 2 This argument obviously ignores increased government saving in the US and the increased in‡ow of foreign funds into the US. 166CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS led to a decline in personal saving. We want to analyze this claim using our simple model. We look at a pay-as-you go social security system, in which the currently working generation pays payroll taxes, whose proceeds are used to pay the pensions of the currently retired generation. The key is that current taxes are paid out immediately, and not invested. We make the following simpli…cations to our model. We interpret the second period of a person’s life as his retirement, so in the absence of social security he has no income apart from his savings, i.e. y2 = 0: For simplicity we also assume A = 0: Without social security3 we have from before c1 = c2 = s = y1 1+¯ ¯(1 + r)y1 1+¯ ¯y1 1+¯ Now suppose we introduce a pay as-you-go social security system. As a consequence in the …rst period of his life Freddy has to pay payroll taxes. Let us assume that the tax rate on labor income is ¿ ; so Freddy’s after tax wage is (1 ¡ ¿ )y1 : Note that currently the payroll tax for social security is 15:3%; paid half by the employer and half by the employee. This includes contributions to medicare and disability insurance. In the second period of his life he now receives social security payments SS: Let us assume that the population grows at rate n; so when Freddy is old there are (1 + n) as many young guys around compared when he was young. Also assume that pre-tax-income grows at rate g; so the income of the young people, when Freddy is old, equals (1 + g)y1 the income that Freddy had when he was young. Finally assume that the social security system balances its budget, so that total social security payments equal total payroll taxes. This implies that SS = (1 + g)(1 + n)¿ y1 Freddy bene…ts from the fact that population and wages grow over time since when he is old there are more people around to pay his pension from higher wages of theirs. Now Freddy has the budget constraints c1 + s = (1 ¡ ¿ )y1 c2 = (1 + r)s + SS Again we can write this as a single intertemporal budget constraint c1 + c2 SS = (1 ¡ ¿)y1 + =I 1+r 1+r (5.9) 3 Conceptually a fully funded system is as if everybody saves for him- or herself. We abstract from uncertainty about the length of life and hence from insurance aspects of a socail security system. 5.1. CONSUMPTION DEMAND 167 Maximizing (5:1) subject to (5:9) yields, by the same logic as before c1 = c2 = I 1+¯ ¯ (1 + r)I 1+¯ Now we use the fact that SS = (1 + g)(1 + n)¿ y1 since the budget of the social security system has to be balanced. Therefore I SS 1+r (1 + g)(1 + n)¿ y1 = (1 ¡ ¿ )y1 + 1+r µ ¶ (1 + g)(1 + n) = y1 ¡ 1 ¡ ¿y1 1+r = y~1 = (1 ¡ ¿ )y1 + where we de…ned y~1 to be the mess on the right hand side. Hence c1 = c2 = y~1 1+¯ ¯ (1 + r)~ y1 1+¯ Comparing this with the result from before we see that consumption in both periods is higher with social security than without if and only if y~1 > y1 ; i.e. if > 1: Hence people are better o¤ with social security if and only if (1+g)(1+n) 1+r (1 + g)(1 + n) > 1 + r This condition makes perfect sense. If people save by themselves for their retirement, the return on their savings equals 1 + r: If they save via a social security system ( are forced to do so), their return to this forced saving consists of (1 + n)(1 + g) (more people with higher wages pay for the old guys). This result makes clear why a pay-as-you-go social security system may make sense in some countries (those with high population and wage growth), but not in others, and that it may have made sense in the US in the 60’s and 70’s, but not in the 90’s. Just some numbers: the current population growth rate is about n = 1%; growth of wages and salaries is about g = 2%; and the average return on the stock market for the last 100 years is about r = 7% (and obviously much higher recently). This is the basis for many economists to call for a reform of the social security system, most prominently Martin Feldstein, chief of the National Bureau of Economic Research, the most important economic think tank in the US. There is an intense debate over how one could privatize the social security system, i.e. create individual retirement funds so that basically each individual would save for her own retirement, with return 1+r > (1+g)(1+n): The biggest 168CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS problem is one missing generation: at the introduction of the system in the 30’s there was one old generation that received social security but never paid taxes for it. Now we face the dilemma: if we abolish the pay-as-you go system, either the currently young pay double, for the currently old and for themselves, or we just default on the promises for the old. Both alternatives seem to be di¢cult to implement politically and problematically from an ethical point of view. The government could pay out the old by increasing government debt, but this has to be …nanced by higher taxes in the future, i.e. by currently young and future generations. Hence this is problematic, too. The issue is very much open, and since I did research on this issue in my thesis I am happy to talk to whoever is interested in more details. But back to the original question: what does pay-as-you go social security do to saving? Without social security saving was given as s= ¯y1 1+¯ with social security it is given by s= ¯(1 ¡ ¿ )y1 ¡ 1+¯ SS 1+r and obviously private saving falls. Note that the social security system as part of the government does not save, it pays all the tax receipts out immediately as pensions. So saving unambiguously goes down with social security. To the extent that this harms investment, capital accumulation and growth the payas-you-go social security system may have substantial negative long-run e¤ects, over and above the e¤ects due to its lower return as compared to private saving for retirement.4 This analysis shows that, although or model is very simple, it is quite powerful in addressing an array of interesting policy questions. Now we turn to a description of more involved models of consumption choice that build on this simple model. Extensions of the Basic Model In the mid-50’s Franco Modigliani, jointly with Albert Ando and Richard Brumberg developed the life-cycle hypothesis of consumption. The basic insight of the simple model above builds the corner stone of the life-cycle hypothesis: individuals want a rather smooth consumption pro…le over their life, but their labor income varies substantially over their lifetime, starting out low, increasing up until about the 50’th year of a person’s life and then slightly declining until 65, with no labor income after 65. The life-cycle hypothesis then states that by saving (and borrowing) individuals achieve it that they turn a very nonsmooth labor income pro…le into a very smooth consumption pro…le. Therefore the life 4 In this simple model there is really no bene…cial role for a pay-as-you-go system. This changes as one introduces mortality risk or income distribution considerations into the model. 5.1. CONSUMPTION DEMAND 169 cycle hypothesis predicts that current consumption (as well as future consumption) depends on total lifetime income and given initial wealth, as in the simple model. The life-cycle model stresses the importance of saving: in particular saving should follow a very pronounced life-cycle pattern with little saving (or even borrowing) in the early periods of an economic life (which usually is assumed to begin around 16-20), signi…cant saving in the high earning years from 35-50 and dissaving in retirement years as the accumulated wealth is used to provide consumption in old age. The life-cycle version of the model seems to fare quite well when confronted with data from the Consumer Expenditure Survey or other data sources that record individual households incomes and consumption expenditures. One empirical fact that puzzles life-cyclers is the observation that older, retired household do not dissave to the extent predicted by the theory. There are several explanation for this puzzle. One is that, contrary to the assumptions of the theory, individuals are altruistic and want to leave bequests to their children. A di¤erent explanation is that it is highly uncertain how long one lives and whether one stays healthy. If older households are extremely risk-averse and fear the possibility of living very long and hence not having saved enough -or if they fear the risk of getting sick and the resulting huge medical bills, then it may be rational to keep almost all savings intact to be prepared for this very unlikely, but very deeply feared event. Milton Friedman’s permanent income hypothesis is also an immediate extension of the basic model discussed above. Instead of stressing the life-cycle aspect of consumption and saving Friedman focussed on the fact that future labor income is uncertain to a certain degree. He posited that the income of an individual household, y consists of a permanent part, yp and a transitory part yt ; i.e. y = yp + yt : One may think of the permanent part as expected average future income and of the temporary part as the random ‡uctuations around this average income. Examples may help: your usual salary makes up the largest fraction of your permanent income. A win in the lottery is the typical component of transitory income, or a particularly good summer for an ice-cream vendor, something that increases (or decreases) your income, but is not a permanent event. Friedman observed correctly that individuals would react quite di¤erently to an increase in permanent and an increase in transitory income. Suppose you start a new, permanent job that doubles your salary up into the inde…nite future. By how much would you increase your consumption expenditures? Now suppose you win $1,000 in the lottery, and the chances of that happening again are very small. By how much would you increase your consumption expenditures? Friedman claimed that an increase in the permanent component of income would bring about an (almost) equal response in consumption, whereas individuals would smooth out transitory income shocks over time: you take the 1,000 bucks and spend $50 to see Stanford beat Berkeley and the rest you put in your saving account for future usage. It then follows that individual consumption is almost entirely determined by permanent income, i.e. 170CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS by the average income you think you will make for the rest of your life. Formally c = ®yp where ® is a parameter close to 1: Again we have the insight that consumption today depends on future income (expectations) rather than on current income, which may be unusually high (because of a positive transitory shock) or unusually low (because of a negative transitory shock). A large empirical literature has investigated the life-cycle and permanent income theories of consumption demand.5 Although the book is not closed yet, it appears that the data seem quite favorable to these theories. Because of this and because of the fact that these theories have sound foundations in microeconomics they are the leading theories in current research on consumption and saving behavior. 5.2 Investment Demand Before turning to the theoretical analysis of investment demand let us have a look at the data. Although investment is a much smaller fraction of total GDP than consumption, the analysis of investment demand is is crucial for the analysis of business cycles as investment demand is much more volatile than consumption demand and GDP. Remember that we could divide total gross investment into three categories: 1. Residential Fixed investment: this is the spending of private households on the construction of new houses and apartments 2. Nonresidential Fixed Investment; this is the spending of …rms on new plants and equipment 3. Inventory investment: this is the change of the value of inventories held by businesses. Inventory investment can be positive (inventories increase) or negative (inventories decline). 5.2.1 Facts about Investment In Figure 66 we plot real GDP and real gross investment over tiem for the US. Note that the scale on the two sides of the graph is di¤erent. The scale on the left side is the relevant scale for real GDP, whereas the scale on the right side is relevant scale for gross investment. This techinque of plotting the time series is chosen to enable better comparison between the ‡uctuations of GDP and gross investment. Comparing the two plots we observe the following features 1. Gross Investment is about 15% of real GDP on average. This fraction, the so called investment-output ratio ‡uctuates over the business cycle, going down in recessions and up in booms, but is fairly constant in the long run. 5 An excellent book that discusses the theories as well as their empirical tests is Angus Deaton’s (1992) “Understanding Consumption”. 5.2. INVESTMENT DEMAND Real GDP, Gross Investment, 1959-99 10000 GDP and Gross Investment 171 2000 5000 1000 Real GDP Gross Investment 0 1955 1960 1965 1970 1975 1980 Year 1985 1990 Figure 5.8: 2. Gross Investment ‡uctuates much more severely than real GDP, with more pronounced declines in recessions and more pronounced increases in booms. In this sense gross investment is that part of GDP that is mostly responsible for the business cycle. Now we break down gross investment into its components, residential …xed investment, nonresidential …xed investment and changes in business inventories. In Figure 67 we plot gross investment and its …rst two components over time, leaving for Figure 68 the plot changes in inventories. From Figure 67 we see that over time nonresidental …xed investment (plant and equipment purchases of …rms) have become relatively more important compared to residential …xed investment. Whereas in 1959 made up about 50% of total gross investment, in 1999 nonresidential …xed investment made up around 74% of total gross investment and residential …xed investment around 23% (the rest going to changes in inventories). It also appears from this …gure that both residential as well as 1995 0 2000 172CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS Real Gross Investment and Components, 1959-99 1800 1600 Investment and Components 1400 1200 1000 800 Gross Investment 600 Nonresidential Fixed Investment 400 200 0 1955 Residential Fixed Investment 1960 1965 1970 1975 1980 Year 1985 1990 1995 Figure 5.9: nonresidential …xed investment ‡uctuate less over time as total gross investment. The last fact obviously implies that the remaining part of investment, namely changes in business inventories, has to ‡ucutate a lot over the business cycle. This conjecture is veri…ed in Figure 68, where we plot total investment and inventory investment. Again notice that we have used di¤erent cales for both variabl;es to enable easier comparison. In paricular the scale on the left side is for total investment, whereas the scale on the right side is for inventory investment. We see that inventory investment ‡ucuates much more than total investment, or, for that matter, much stronger than any ohter component of real GDP. Hence, although inventory investment makes up only about 1% of GDP, it is a strong contibutor to business cycles and inventory investment of …rms is heavily studied by both theoretical as well as empirical economists trying to explain the business cyle. Also note that during recessions inventory investment typically becomes (or at least gets close 2000 5.2. INVESTMENT DEMAND Gross Investment and Change in Inventories, 1959-99 2000 Gross Investment, Change in Inventories 173 100 Change in Inventories 1000 0 Gross Investment 0 1955 1960 1965 1970 1975 1980 Year 1985 1990 1995 Figure 5.10: to) negative: during recessions …rms tend not to produce for inventory. After this little tour overviewing the basic facts with respect to investment data let us now look at soem theory trying to explain the investment behavior of …rms. 5.2.2 The Theory of Investment Nonresidential Fixed Investment Demand To start our study of investment demand of a single we proceed in two steps. We …rst assume that our …rm rents all capital that it uses in the production process from other …rms that are in the business of equipment and plant renting for industrial purposes. Although in reality most equipment and plants used are in fact owned by the …rms who use it, this assumption will turn out not to matter. Let the rental price for one unit of the capital good be denoted by rk and the -100 2000 174CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS wage for one worker be denoted by w: We normalize the price of the output good to 1, so rk and w are the real rental price of capital and the real wage, respectively. Let us assume that the …rm can produce output Y according to the following production function Y = K ® L1¡® where K is the amount of capital rented and L is the number of workers hired. To determine the …rm’s demand for rented capital we have to solve the …rm’s pro…t maximization problem max K ® L1¡® ¡ rk K ¡ wL K;L The …rst part of the above equation is the revenue the …rm takes in (remember that we normalized the price of the …nal output good to 1), and the second and third part are the total costs for renting capital and hiring workers, respectively. Taking the …rst order condition with respect to capital yields rk = ®K ®¡1 L1¡® = ®Y ®K a L1¡® = K K solving this for K gives the optimal demand for capital to be rented, K; as K= ®Y rk (5.10) Hence, if the …rm decides to produce output Y and faces a rental price of capital rk ; then the optimal amount of capital to rent out is given by K = ®Y rk : This is the standard pro…t maximization condition from micro: the …rm should hire inputs, in particular capital, to the point where the additional cost for one unit rented, rk , equals the additional bene…t, the marginal product of capital, ®K ®¡1 L1¡® : This gives a demand curve for capital that is increasing in the desired amount of output produced, Y; and decreasing in the rental rate of capital rk : In Figure 69 we plot the demand for rented capital as a function of the rental rate of capital. As good (actually bad!) tradition in microeconomics we plot the price (the rental rate rk ) on the y-axis and the quantity of rental capital demanded on the x-axis. In this graph we hold the desired level of output constant. As indicated in (5:10) the quantity demanded of capital decreases with the rental rate rk : The optimal quantity demanded at the price rk is given by K ¤ ; because at this level of the capital stock the marginal cost from renting an additional unit, rk is equal to the marginal product ®Y K ; for a given level of output Y: Figure 70 shows what happens to the demand curve for rented capital if the planned level of output increases. Again as (5:10) shows an increase in Y; for …xed rk increases K: But this is true for every rk ; indicating that the entire demand curve shifts to the right. If the rental price of capital doesn’t change, 5.2. INVESTMENT DEMAND 175 Rental price of capital r Marginal Cost of Capital k Marginal Product of Capital K* Demand for Rented Capital (K) Figure 5.11: the new optimal choice of capital is now K 0¤ > K ¤ ; i.e. the …rm reacts to higher desired output by demanding more rented capital (and more workers). So far we have ignored the fact how the rental price of capital is determined. So let us consider the hypothetical problem of a …rm engaged in the business of renting out capital, i.e. equipment and plants. For concreteness let us consider the choice of such a …rm buying a particular piece of equipment. Let pk denote the relative price of equipment (relative to the price of the …nal output good), r denote the real interest rate and ± the depreciation rate. What are the costs and what are the revenues from purchasing this machine and renting it out in the current period? The revenues in the current period equal rk : The costs are composed of two parts. The …rm has to …nance the purchase by borrowing the money to purchase the machine. The interest on the loan is a cost, equal to rpk : Furthermore a part ± of the machine wears out in the production process. The loss of value due to this wearing out amounts to ±pk in the current period. 176CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS Rental price of capital r Marginal Cost of Capital k Y K* K’* Marginal Product of Capital Demand for Rented Capital (K) Figure 5.12: Since there is free entry into the business of renting out capital pro…ts are bit down to zero and therefore it must be the case that rk = (r + ±)pk So the rental price of capital equals the interest rate plus the rate of depreciation, times the relative price of investment goods to consumption goods, pk : This relative price in turn depends on the technology that speci…es how much of the …nal output good is needed to produce one unit of the investment good. In a lot of macro models we assume that output can be used both for consumption and investment on a 1-1 basis (remember the Solow model) in which case pk = 1: These types of models are called one-sector models as there is only one production sector that produces both consumption and investment goods. We will focus on these types of models as they are most tractable. We then have a direct relation between the rental rate of capital and the real interest rate of 5.2. INVESTMENT DEMAND 177 the form rk = r + ± and the demand for rented capital depends negatively on the real interest rate. The remaining step is to relate the desired rented capital stock and investment demand. Consider a hypothetical …rm that does two things: it purchases capital goods and rents it to itself and it produces output. Suppose this …rm enters the period with capital stock K¡1 : The demand of the …rm for rented capital services is given by K= ®Y r+± and the investment demand of the consolidated …rm (taking the output producing and the capital renting division together) equals I = K ¡ (1 ¡ ±)K¡1 ®Y ¡ (1 ¡ ±)K¡1 = r+± This is the investment demand for a single …rm. It depends positively on the output that this …rm produces and negatively on the real interest rate. Summing over all …rms in the economy we get the total demand for nonresidential …xed investment. As for the individual …rm the aggregate nonresidential …xed investment demand depends positively on the level of output in the economy and negatively on the real interest rate. Hence our more careful study of investment demand has revealed that our simple investment function from above was correct in that the real interest rate entered negatively, but it disregarded the in‡uence of current output Y on aggregate investment demand. Residential Fixed Investment Demand For residential …xed investment we can carry out a similar analysis. We start by assuming that the demand for housing H decreases as the rent rh increases. The relation between rh and H is identical to the relation between rk and K; just relabel the axes in Figure 69. Also by the same reasoning the price for a new apartment building ph ; the depreciation rate for buildings ± h and the real interest rate r are related by rh = (r + ± h )ph and the investment demand for residential …xed investment is, as above, a negative function of the real interest rate. To the extent that the demand for housing depends positively on income (equal to spending), the demand for residential …xed investment also depends positively on Y; hence has the same qualitative features as nonresidential …xed investment demand. Inventory Investment Demand A small fraction of total investment demand (usually not more than 1% of GDP) comes from changes in inventories. Although the change in inventories may be 178CHAPTER 5. MICROECONOMIC FOUNDATIONS OF MACROECONOMICS small (but very volatile over the business cycle), the total inventories held in the entire economy are quite substantial. Hall and Taylor report that in 1995 inventories amounted to about 17% of GDP. Note that holding inventories is not costless for …rms. Suppose the production of the goods in inventories has been …nanced by credit, then if the price all for the goods held in the inventory is pk ; the current period cost of holding the inventory is (r + ± i ) pk ; i.e. equals to the cost of capital bound in the inventory as well as the depreciation of the goods being held in inventories. Note that ± i may be small (in the case of highly durable goods), very large (in the case of, say, vegetables) or even negative (for goods that appreciate, like wine). What are the bene…ts of inventories. One …rst observation is that inventories may be required in the production process. Whiskey is an example. Whiskey has to be stored for a while before it reaches its best quality. So putting Whiskey into inventory for some time is a requirement of the production process. Oil is a second example. Unavoidably large fractions of all oil produced and sold is in transit in pipelines, in involuntary inventory, so to speak. More traditional examples includes inventories in the manufacturing industry, where certain intermediate goods are stored in inventories before being used in the production process. Just-in-time production techniques have sharply reduced inventories of this kind in the last 15 years or so. Secondly inventories serve a bu¤er function against unexpected ‡uctuations of demand. Final goods are put into inventory so that they are available upon demand. The bene…t from having an inventory is to be able to serve demand immediately and hence to avoid losing the customer to a competing supplier. Of course these bene…ts have to be balanced against the cost of holding the inventory, as discussed above. Empirically changes in inventory investment is a strongly procyclical variable, it tends to increase with overall production and tends to decline with overall production. A higher level of production requires more goods “in the pipeline” and in intermediate inventories. Booms are also times where …rms expect high demand that they want to bu¤er with high inventory of …nal goods. Occasionally …rms are caught by surprise in that their sales expectations are not met and inventories are accumulated involuntarily. This explains the few occasions where we observed a strong positive change in inventory investment and a recession (as in 1974). For more details see Hall/Taylor’s Figure 11.8 on p. 321. To summarize, our analysis of investment demand has recon…rmed our previous assumption that aggregate investment demand depends negatively on the real interest rate. It has added the insight that investment demand should depend positively on the level of output, a fact that was ignored in the traditional aggregate investment function and the IS-LM analysis based on it. Chapter 6 Trade, Exchange Rates & International Financial Markets Foreign trade is a central policy issue. The high and increasing US trade de…cit is of immediate concern to policy makers and there is a lot of controversy how to reduce it. Since the trade de…cit is closely related to the exchange rate (the value of the dollar compared to other currencies), some economists believe that, in order to control the trade de…cit, the exchange rate has to be controlled. Hence the discussion of the trade de…cit leads us directly to the discussion about …xed vs. ‡exible exchange rates and the international …nancial system. 6.1 Terms of Trade, the Nominal and the Real Exchange Rate In order to organize our thoughts we need a few de…nitions De…nition 8 The trade balance is total value of exports minus the total value of imports of the US with all its trading partners. In symbols TB = X ¡ M Hence the trade balance is an important component of total spending in the economy. For the US the trade balance has been negative for the last 20 years, as can be seen from Figure 71. For 1997 the trade balance for the US is around -100 billion dollar, i.e. the US had a trade de…cit of about 1.2% of GDP. For 1999 the trade de…cit is projected to reach about 3.5% of GDP De…nition 9 The current account balance equals the trade balance plus net 179 180CHAPTER 6. TRADE, EXCHANGE RATES & INTERNATIONAL FINANCIAL MARKETS Trade Balance for the US 1967-2001 (in Constant Prices) 0 -50 Trade Balance -100 -150 -200 -250 -300 -350 -400 1970 1975 1980 1985 Year 1990 1995 Figure 6.1: unilateral transfers CAB = T B + N U T The main ingredient of net unilateral transfers are interest payments to people living in the US holding government bonds of foreign countries, net of interest payments on US government debt to foreigners. For the US net unilateral transfers are slightly negative, about 0.3% of GDP in 1997. For some highly indebted countries, in particular in South America and South East Asia, net unilateral transfers can be signi…cantly negative, amounting to about 5% to 10% of GDP. Remember again what a negative current account balance means. For this we have to understand another de…nition De…nition 10 The Capital Account Balance is the change in the net wealth position of the US during a year. 2000 6.1. TERMS OF TRADE, THE NOMINAL AND THE REAL EXCHANGE RATE181 It follows from basic rules of accounting that the current account balance always equals the capital account balance. A negative current account balance means a negative capital account balance, and this means that the net wealth position of the US, the amount that the US (the government and its citizens) is owed, net of what it owes, decreases. The persistent current account de…cits of the US have led to the fact that in the early 80’s the US, traditionally a net creditor (having a positive net wealth position with the rest of the world) turned into a net debtor (having a negative net wealth position with the rest of the world). This tendency seems to continue without sign of reversal. An important determinant of the trade balance is the relative price of US goods to foreign goods. If US goods are expensive relative to Japanese goods, a lot of Japanese goods will be imported by the US and few US goods will be exported to Japan. Therefore, in order to understand the trade balance we have to understand exchange rates De…nition 11 The nominal exchange rate e is the relative price of two currencies. For example, if the exchange rate between the dollar and the euro is 0:98; then one has to pay 0:98 euros to purchase one dollar, or reversely, one has to pay 1:02 dollar to buy one euro. These days most exchanged rates are ‡exible: they are determined on international capital markets beyond the direct control of national governments (obviously monetary and …scal policy will in‡uence the exchange rate of the domestic currency, but under a ‡exible exchange rate regime the government does not directly …x the exchange rate). The opposite is a regime of …xed (sometimes called pegged) exchange rates: via international agreements exchange rates between certain countries are …xed. Before the collapse of the Breton Woods system in 1973, for example, the exchange rates of the western industrialized countries were pegged. These days, for example, the Argentinian peso is pegged to the dollar: the exchange rate between the dollar and the peso is 1 and the Argentinian government committed to defend this exchange rate.1 De…nition 12 The real exchange rate " is the relative price of goods in two countries. As it turns out it is the real exchange rate that is the key for net exports, i.e. the trade balance. To see this, consider the following example. Think of a good that is produced in many countries, say cars. Suppose a Ford Escort costs $12,000 and a similar car, a Honda Civic costs 1,890,000 yen. How expensive is a Ford relative to a Honda, i.e. how many Fords do we have to exchange for one Honda Civic. This is exactly what the real exchange rate tells us (if all that is traded between the US and Japan were Ford Escorts and Honda Civics). Now we have to bring in the nominal exchange rate, since the price of the Japanese car is measured in yen, the price of US cars in dollars. Suppose the exchange 1 By buying Argentinian pesos at exchange rate 1:1 if necessary. Obviously this requires potentially substantial dollar reserves on the side of the Argentinian government. It is not clear whether this peg would survive a major speculative attack against the peso. 182CHAPTER 6. TRADE, EXCHANGE RATES & INTERNATIONAL FINANCIAL MARKETS rate between the yen and the dollar is 105; i.e. one needs 105 yen to buy one dollar. Then the price of a Honda Civic, in dollar terms is 1; 890; 000 yen = $18; 000 105 yen per $ Hence the real exchange rate (for the two cars) is "cars = = $12; 000 per US car $18; 000 per Jap. car 2 Japanese car per US car 3 To summarize "cars = = = $12; 000 per US car 1; 890; 000 yen per Jap. car/105 yen per $ (105 yen per $) ¤ ($12; 000 per US car) 1; 890; 000 yen per Jap. car 2 Japanese car per US car 3 In other words, in order to buy 2 Honda Civic one has to exchange in return 3 Ford Escort. We can generalize this example to obtain a formal relation between the nominal and the real exchange rate. Obviously not only cars are sold in the US and Japan. Let P denote the price level (i.e. the price of a representative basket of goods) in the US, measured in $: Similarly, denote by P ¤ the price level in the foreign country, in terms of the foreign currency. For concreteness take Japan and the yen and denote by " the real exchange rate between the US and Japan and by e the nominal exchange rate. Then "=e¤ P P¤ These are all the de…nitions we need in this section.2 . There are two obvious questions to be answered: 1. How do real exchange rates a¤ect the trade balance? 2. What are the determinants of the real exchange rate? 2 Sometimes the real exchange rate is referred to as “Terms of Trade” (abbreviated t.o.t.). This is usually done when P is interpreted as the price of export goods and P ¤ as the price of import goods (rather than the price for a basket of goods that also includes goods that are nontraded, like services). The terms of trade indicate at what exchange rate the US can exchange their goods against foreign goods. 6.2. EFFECTS OF THE REAL EXCHANGE RATE ON THE TRADE BALANCE183 6.2 E¤ects of the Real Exchange Rate on the Trade Balance The …rst question appears to have an obvious answer. If the real exchange rate increases US products become expensive relative to foreign products. This leads to an increase in imports and a decline in exports. Hence the trade balance should be a decreasing function of the real exchange rate, (X ¡ M ) = (X ¡ M)("). Note that this argument often provides the rationale for countries to devalue their currency. Suppose price levels P and P ¤ are …xed in the short run, as mostly assumed during this course. Then a decline in the nominal exchange rate ( a devaluation of the currency) leads to corresponding decline in the real exchange rate and an increase in net exports. In particular for small, export-oriented countries this used to be a popular method to avoid or get out of a recession. With exchange rates mostly ‡exible and determined on world capital markets governments cannot directly devalue their currencies, so this type of policy has become signi…cantly more di¢cult to implement under ‡exible exchange regimes. If we look at the data net exports and the real exchange rate are in fact negatively related (see Hall/Taylor, Figure 12.4). One reason why the e¤ect described above may not be so direct as asserted is the following. Fix the price levels P; P ¤ and think about a decline in the nominal exchange rate. For the Japanese customers it becomes cheaper to acquire dollars to purchase American goods. But prices of US goods sold in Japan are usually quoted in yen, and unless Ford, say, doesn’t cut the yen price for its cars, nothing will happen to their sales. For a given yen price, a decline in the exchange rate increases Ford’s revenue in dollar terms, allowing them to sell their cars cheaper or make a higher pro…t on their existing sales. In a world with perfectly competitive markets the former should happen, but in particular with our assumption of sticky prices it is not clear why, at least in the short run, US …rms would not just take the windfall pro…ts from a better exchange rate. Leaving aside these concerns we accept that net exports depend negatively on the real exchange rate. For concreteness we use as our equation for net exports X ¡M = g ¡ mY ¡ n" eP = g ¡ mY ¡ n ¤ P = g ¡ mY ¡ n" (6.1) where g; m; n are positive constants. We now turn to the question of what determines the real exchange rate. 184CHAPTER 6. TRADE, EXCHANGE RATES & INTERNATIONAL FINANCIAL MARKETS 6.3 6.3.1 Determinants of the Real Exchange Rate Purchasing Power Parity One of the basic principles in economics is the law of one price: absent transportation costs the same good cannot sell at di¤erent prices in di¤erent locations. If a bushel of wheat sold for less in New York than in Chicago, then arbitrageurs would take advantage of this riskless opportunity to make money and buy wheat in New York and sell it in Chicago. Prices in New York will go up and/or prices in Chicago down, removing this arbitrage opportunity. The law of one price, applied to the international marketplace is called purchasing power parity: absent transportation costs a BMW should cost the same in New York and Munich, once we converted the dollar price in New York into Deutsche Mark, using the nominal exchange rate. Otherwise there would be again arbitrage opportunities, buying the car in one place and selling it in another place a making a riskless pro…t. This principle provides us with a theory for the real exchange rate and the nominal exchange rate. Suppose all goods are traded and there are no transportation cost. Then the real exchange rate should equal one: the same good sold in di¤erent countries should have the same price. Second, changes in price levels in the US and abroad, i.e. changes in PP¤ should be fully re‡ected in the nominal exchange rate. This can formally be expressed as follows. The real exchange rate is given by "=e P P¤ If purchasing power parity were to hold the real exchange rate should not change and (taking logs and di¤erentiating with respect to time) g(e) = ¼¤ ¡ ¼ i.e. the percentage change of the nominal exchange rate should be equal to the di¤erence between in‡ation rates in the two countries. Suppose, for example, that the in‡ation rate between 1999 and 2000 in Germany is 2% and in the US it is 5%: Then, according to purchasing power parity, the exchange rate between the dollar and the Mark should decline by 3% between 1999 and 2000, i.e. more dollars are required to buy one mark and less mark are required to buy one dollar. Again, the intuition is simple: suppose a Ford costs $10; 000 in 1999 in New York and 20; 000 mark in Berlin and suppose (as purchasing power parity would predict) that the exchange rate is 2 (2 mark per dollar). The same car sells at the same price in both locations. Now there is in‡ation: the 5% in‡ation rate in New York implies that in 2000 the car costs $10; 500 and the 2% in‡ation rate in Berlin implies that the car costs 20; 400 mark. But the absence of arbitrage requires that both cars sell for the same price, hence mark = 1:943; a drop of in 2000 the nominal exchange rate has to be 20;400 $10;500 1:943¡2 ¼ 0:03 = 3%: Here we have a simple theory of the nominal and the real 2 exchange rate. 6.3. DETERMINANTS OF THE REAL EXCHANGE RATE 185 Let us look at the data. Consider the example of the Big Mac. This high point of American cuisine is sold in just about every country in the world by now. Making all the assumptions needed for purchasing power parity (no transportation costs, most importantly) the price of the Big Mac should be the same all over the world, once local currencies are converted into US currency. Let us apply the theory and predict nominal exchange rates, based on the Bic Mac price. Again applying the formula for the real exchange rate yields PBM;U S PBM;Abroad PBM;Abroad PBM;US 1 = e e = In order to predict the nominal exchange rate between the US and an arbitrary country \Abroad" we just need to know the price of a Big Mac in the US, PBM;US and the price of a Big Mac abroad, PBM;Abroad : The economist did this in 1993 and got the results summarized in Table 11. The price of a Big Mac in the US was about $2:28 This table demonstrate that the purchasing power parity theory is not completely out of line, but that there are substantial deviations. Obviously we looked at only one example, Big Macs, and this particular commodity does not make up a major fraction of GDP of the countries we considered. But looking at plots for real exchange rates (see Hall/Taylor, Figure 12.3) we see that real exchange rates ‡uctuate quite heavily, in contrast to what the purchasing power parity theory predicts. So what are the problems that prevent the law of one price from applying. ² Transportation costs: it may be quite costly to ship, say, cars from Europe to the US and vice versa I would guess around $500 to $1,000 per car) ² Nontraded goods: a lot of goods that enter GDP (and hence the price levels P; P ¤ ) are not traded across borders. Services are the most important example. Hence the law of one price holds only for traded goods, and the purchasing power parity theory of exchange rate is more successful if P; P ¤ are taken to be price indices for exports and imports ² Trade restrictions as tari¤s and quotas: these things act like transportation costs, they drive a wedge between the price of a good domestically and the same good sold in other countries. Although the purchasing power parity theory has limited success with respect to the data it is an important benchmark. And its most basic prediction that real exchange rates should be somewhat stable in the long run is born out in the data. 186CHAPTER 6. TRADE, EXCHANGE RATES & INTERNATIONAL FINANCIAL MARKETS Table 11 Country US Argentina Australia Belgium Brazil Britain Canada China Denmark France Germany Hong Kong Hungary Ireland Italy Japan Malaysia Mexico Netherlands Russia South Korea Spain Sweden Switzerland Thailand 6.3.2 Currency Dollar Peso Dollar Franc Cruzeiro Pound Dollar Yuan Crown Franc Mark Dollar Forint Pound Lira Yen Ringgit Peso Goulder Ruble Won Peseta Crown Franc Baht Price of BM 2.28 3.60 2.45 109.00 77,000.00 1.79 2.76 8.50 25.75 18.50 4.60 9.00 157.00 1.48 4,500.00 391.00 3.35 7.09 5.45 780.00 2,300.00 325.00 25.50 5.70 48.00 e (predicted) 1.00 1.58 1.07 47.81 33,772.00 0.79 1.21 3.73 11.29 8.11 2.02 3.95 68.86 0.65 1,974.00 171.00 1.47 3.11 2.39 342.00 1,009.00 143.00 11.18 2.50 21.05 e (actual) 1.00 1.00 1.39 32.45 27,521.00 0.64 1.26 5.68 6.06 5.34 1.58 7.73 88.18 0.65 1,523.00 113.00 2.58 3.10 1.77 686.00 796.00 114.00 7.43 1.45 25.16 Real Exchange Rates and Interest Rates We will pursue a di¤erent explanation of the nominal, and hence the real exchange rate that is based on international …nancial markets. Think of a big player in international …nancial markets, a George Soros or the manager of a big mutual fund. Given that money can travel borders almost without any cost in the western world, these investors face the choice of where, i.e. in what country to invest. Suppose these investors hold a certain portfolio and now the real interest rate in the US, compared to other countries where the investors hold positions, goes up. At the prevailing nominal exchange rate it becomes more attractive to invest in the US, and this would cause huge (and fast) in‡ows of …nancial capital into the US and out of other markets (because it is almost costless to transfer money from one market to the other). Flows of funds between countries are substantial, but not as large as one would expect, following increases in the interest rate, say, in the US after the 6.4. THE INTERNATIONAL FINANCIAL SYSTEM 187 FED raised interest rates. What prevents foreign and domestic investors to move their portfolio into US interest bearing securities. The answer: an appreciation of the dollar, i.e. an increase in the nominal exchange rate. Investors have to acquire dollars to purchase US securities, the demand for US dollars increases and hence the price increases. But if the dollar gets more expensive, then, even if US securities now earn a higher interest rate, investors may not be tempted to buy more of them. Hence the reaction of the nominal interest rate keeps international capital ‡ows in check. Hence we theorize that the nominal exchange rate is determined by the real interest rate, both domestic and foreign. A higher domestic real interest rate leads to a higher nominal exchange rate. Taking price levels as sticky in the short run yields a positive relation between the real exchange rate and the domestic real interest rate.3 Formalizing this we posit "= eP = q + vr P¤ (6.2) where q; v are positive constants. Combining (6:2) and (6:1) we see that net exports are a negative function of the interest rate. The intuition: a higher real domestic real interest rate increases the nominal and hence the real interest rate, therefore makes US products more expensive relative to products from the rest of the world, hence reduces net exports. Now that net exports depend negatively on the interest rate, this modi…es our IS-curve and hence our policy analysis using the IS-LM framework. For example, the latest increase in interest rates by the FED (accomplished by a reduction in money supply) should, in theory, lead to an increase in the nominal exchange rate. This has already happened. It should translate into an increase in the real exchange rate (which has happened, too, from what we know yet) and a reduction of net exports, i.e. a widening of the already big US trade de…cit. This shows that sometimes economic policy is quite problematic, and to accomplish one goal (preventing the economy from overheating) compromises another goal (bringing down the large trade de…cit). 6.4 The International Financial System [To be completed] 3 See, for example, Figure 12.3 in Hall/Taylor, for the fact that the real excahnge rate tracks the nominal exchange rate very closely. 188CHAPTER 6. TRADE, EXCHANGE RATES & INTERNATIONAL FINANCIAL MARKETS Chapter 7 Fiscal and Monetary Policy in Practice Economic policy can be broadly divided into monetary and …scal policy. Fiscal policy is carried out by the government at di¤erent levels: by the President and Congress at the federal level, by the governor and the state congresses at the state level and by majors on the local level. The …scal policy instruments include government purchases and transfers as well as taxes. In contrast to …scal policy monetary policy is conducted by appointed bureaucrats, not elected politicians. The instruments of monetary policy include the money supply as well as certain interest rates. In the following chapter will discuss how monetary and …scal policy are conducted in practice. As usual we will look both at some theory and at data. 7.1 Fiscal Policy 7.1.1 Data on Fiscal Policy The Structure of Government Budgets We start our discussion with the federal budget. The federal budget surplus is de…ned as Budget Surplus = Total Federal Tax Receipts ¡Total Federal Outlays Federal outlays, in turn are de…ned as Total Federal Outlays = Federal Purchases of Goods and Services +Transfers +Interest Payments on Fed. Debt +Other (small) Items 189 190 CHAPTER 7. FISCAL AND MONETARY POLICY IN PRACTICE The entity “government spending” that we considered so far equals to federal, state and local purchases of goods and services, but does not include transfers, such as social security bene…ts, unemployment insurance and welfare payments. The US federal budget had a de…cit every year since 1969 until 1998, and in fact it seemed so unlikely that this would change in the near future that Hall and Taylor, on p. 362 conjectured that the federal budget would be in de…cit at least until the turn of the century. How can the federal government spend more than it takes in? Simply by borrowing, i.e. issuing government bonds that are bought by private banks and households, both in the US and abroad. The total federal government debt that is outstanding is the accumulation of past budget de…cits. The federal debt and the de…cit are related by Fed. debt at end of year = Fed. debt at end of year +Fed. budget de…cit Hence when the budget is in de…cit, the outstanding federal debt increases, when it is in surplus (as in 1999), the government pays back part of its outstanding debt. Now let us look at the federal government budget for the latest year we have …nal data for, 1997. See Table 12 7.1. FISCAL POLICY 191 Table 12 1997 Federal Budget (in billion $) Receipts 1719.9 Pers. Income Taxes 769.1 Corporate Income Taxes 210.0 Indirect Business Taxes 93.8 Social Security Contrib. 518.5 Outlays 1741.0 Fed. Gov. Purchases 460.4 National Defense 306.3 Other Purchases 154.1 Transfer Payments 791.9 Grants to Local Gov. 225.0 Interest Paym. on Debt 231.2 Subsidies less Pro…ts 32.5 Surplus -21.1 We see that the bulk of the federal government’s receipts comes from income taxes and social security contributions paid by private households, and, to a lesser extent from corporate income taxes (taxes on pro…ts of private companies). The role of indirect business taxes (i.e. sales taxes) is relatively minor for the federal budget as most of sales taxes go to the steady are the city in which it is levied. On the outlay side the two biggest posts are national defense, which constitutes about two thirds of all federal government purchases (G) and transfer payments, mainly social security bene…ts (about 550 billion if one includes Medicare) and unemployment (about 220 billion). About 13% of federal outlays go as transfer to states and cities to help …nance projects like highways, bridges and the like. About 2% go as subsidies to public enterprises, net of pro…ts (if any) of public enterprises. A sizeable fraction (13%) of the federal budget is devoted to interest payments on outstanding federal government debt. The outstanding government debt at the end of 1997 was $5369; 7 billion, or about 67% of GDP. In other words, if the federal government could expropriate all income of all households for the whole year of 1997, it would need to thirds of this in order to repay all debt at once. The ratio between total government debt (which, roughly, equals federal government debt) and GDP is called the (government) debt-GDP ratio, and is the most commonly reported statistics (apart from the budget de…cit as a fraction of GDP) with respect to the indebtedness of the federal government. It makes sense to report the debtGDP ratio instead of the absolute level of the debt because the ratio relates the amount of outstanding debt to the governments ability to generate revenue, namely GDP. Let’s have a brief look at the budget on the state and local level. The de…nitions apply as before. The main di¤erence between the federal and state and local governments is the type of revenues and outlays that the di¤erent levels of government have, and the fact that states usually have a balanced budget 192 CHAPTER 7. FISCAL AND MONETARY POLICY IN PRACTICE amendment: they are by law prohibited from running a de…cit, and correspondingly have no debt outstanding. The only state in the US that currently does not have a balanced budget amendment is Vermont. But let’s look at the numbers in Table 13 Table 13 1997 State and Local Budgets (in billion $) Receipts 1094.3 Personal Taxes 219.9 Corporate Income Taxes 36.0 Indirect Business Taxes 533.4 Social Insurance Contrib. 79.9 Federal Grants 225.0 Outlays 960.1 State and Local Purchases 758.8 Transfer Payments 304.1 Interest Paid Less Dividends -92.2 Subsidies less Pro…ts -10.6 Surplus 134.1 The main observations from the receipts side are that the main source of state and local government revenues stems from indirect sales taxes. Personal Taxes are mostly the income taxes paid to the state and property taxes paid by homeowners. Also about 25% of all revenues of state and local governments come from federal grants that help …nance large infrastructure projects. On the outlay side the biggest item are purchases, which are basically comprised of outlays for paying government employees, notably public school teachers, police o¢cers and local bureaucrats and outlays for infrastructure. Transfer payments on the state and local level basically consists of welfare bene…ts. As mentioned above almost all states and cities have balanced budget requirements prohibiting running government de…cits. Consequently these governments have positive assets rather than debt in general, hence their interest payments are outweighed by their interest receipts and a negative entity appears on the spending side. Also state and city-owned enterprises seem to make more pro…ts than losses, so the net subsides to these enterprises are negative. Fiscal Variables and the Business Cycle In our discussion of …scal policy in the IS-LM framework we asserted that in recessions …scal policy may be called upon to increase government spending to lead the economy out of the recession. In this section we will investigate to what extent actual …scal policy is correlated with the business cycle. Since in this section we will only look at data, all the statements we can make are bout correlations, not about causality. In Figure 72 we plot the unemployment rate as prime indicator of business cycle and purchases of the government (federal, 7.1. FISCAL POLICY 193 state and local) as a fraction of GDP over time. One feature that appears in the data is that government spending, as a fraction of GDP, has declined over time from about 30% of GDP in the late 50’s to below 20% in the late 90’s (see the right scale). One also can detect that in recessions (in times where the unemployment rises, see the left scale) government spending as a fraction of GDP increases. This is consistent with the view that government spending is being used to a certain degree -successfully or not- to smoothen out business cycles. A similar, even more accentuated picture appears if one plots government transfers (such as unemployment compensation and welfare against the unemployment rate). The fact that government transfers are countercyclical follows almost by construction: in recessions by de…nition a lot of people are unemployed and hence more unemployment compensation (and once this runs out, welfare) is paid out. These welfare programs are sometimes called automatic stabilizers, as these programs provide more transfers in situations where incomes of households tend to be low on average, hence softening the decline in consumption expenditures and therefore the recession. In Figure 73 we plot the unemployment rate and government tax receipts as a fraction of GDP against time. We see that tax receipts are strongly procyclical, they increase in booms and decline during recessions. In this sense taxes act as automatic stabilizers, too, since, due to the progressivity of the tax code, in good times households on average are taxed at a higher rate than in bad times. In this sense the tax system stabilizes after-tax incomes and hence spending. A second reason for declines of taxes in recessions is discretionary tax policy: if we believe the IS-LM analysis then cutting taxes provides a stimulus for private consumption and may lead the economy out of a recession. For example, the tax cuts in the early 60’s under President Kennedy were designed for this purpose. So rather than being automatic stabilizers, taxes may be used deliberately to control the business cycle. Now let us look at the government de…cit over the business cycle. Figure 74 plots the federal budget de…cit as a fraction of GDP and the unemployment rate over time. The …rst observation is (see the right scale) that the federal budget had small surpluses in the late 50’s, then went into (heavy) de…cit for the next 35 years or so and only very recently showed surpluses again. One clearly sees the large de…cits during the oil price shock recession and the large de…cit during the early Reagan years, due to large increases of defense spending. Overall one sees that the budget de…cit is clearly countercyclical: the de…cit is large in recessions (as tax revenues decline and government spending tends to increase) and is small in booms. In fact the extremely long and powerful expansion during the 90’s resulted, in combination if federal government spending cuts, in the current budget surplus. How does one determine whether the federal government is loose or tight on …scal policy. Just looking at the budget de…cit may obscure matters, since the current government may either have generated a large de…cit because of loose …scal policy or because the economy is in a recession where taxes are typically low and transfer payments high, so that the large de…cit was beyond the control of the government. Hence economists have developed the notion of CHAPTER 7. FISCAL AND MONETARY POLICY IN PRACTICE 194 Government Purchases and Unemployment Rate, 1959-99 15 10 0.4 0.3 Unemployment Gov. Spending as % of GDP 5 0.2 Unemployment Rate 0 1955 1960 1965 1970 1975 1980 Year 1985 1990 1995 Figure 7.1: the structural government de…cit: it is the government de…cit that would arise if the economy’s current GDP equals its potential (or long run trend) GDP. The structural part of the de…cit is not due to the business cycle, it is the de…cit that on average arises given the current structure of taxes and expenditures. The cyclical government de…cit is the di¤erence between the actual and the structural de…cit: it is that part of the de…cit that is due to the business cycle. How loose or restrictive monetary policy is can then be determined by looking at the structural (rather than the actual) de…cit. Unfortunately the structural de…cit is not easily available in the data and we have to leave its discussion for later. Finally lets have a look at the government debt, the accumulated de…cits of the federal government in Figure 75. What is striking is the explosion of the government debt outstanding in the last 70 years. The picture is obviously somewhat misleading, since it does not take care of in‡ation (in‡ation numbers 0.1 2000 7.1. FISCAL POLICY 195 Taxes and Unemployment Rate, 1959-99 15 0.35 0.3 Unemployment 10 Government Tax Receipts as % of GDP 5 0.25 Unemployment Rate 0 1955 1960 1965 1970 1975 1980 Year 1985 1990 1995 Figure 7.2: before the turn of the century are somewhat hard to come by). But clearly visible is the sharp increase during World War II. Somewhat more informative is a plot of the debt-GDP ratio in Figure 76. The main facts are that during the 60’s the US continued to repay part of its WWII debt as debt grows slower than GDP, then, starting in the 70’s and more pronounced in the 80’s large budget de…cit led to a rapid increase in the debt-GDP ratio, a trend that only recently has been stopped and reversed 7.1.2 A Few Theoretical Remarks The standard IS-LM analysis indicates that current tax cuts should have expansionary e¤ects: current disposable income increases, hence consumption spending increases, hence income and output increases. This is the Keynesian rationale for active …scal policy. There is a powerful theoretical counter argument 0.2 2000 CHAPTER 7. FISCAL AND MONETARY POLICY IN PRACTICE 196 Federal Deficit and Unemployment Rate, 1959-99 15 0.05 Federal Budget Deficit as % of GDP 0 Unemployment 10 5 -0.05 Unemployment Rate 0 1955 1960 1965 1970 1975 1980 Year 1985 1990 1995 Figure 7.3: against this reasoning, known as the Ricardian Equivalence Hypothesis. Originally formulated by the classical 19’th century economist David Ricardo and rediscovered by Robert Barro from Harvard in 1974 the hypothesis states that for a given stream and timing of government spending the timing of taxes does not a¤ect real activity in the economy, i.e. consumption, saving, output or the real interest rate. You already reconstructed the argument in HW5: a current tax cut has to be …nanced by a higher budget de…cit today and hence higher taxes in the future. But, at least according to the life cycle/permanent income theory of consumption, what really matters for the intertemporal consumption choice is total discounted lifetime income, not when it comes. The private households, according to the Ricardian Equivalence Theorem, see through the government budget planning, anticipate the future tax hikes, adjust their savings accordingly to exactly o¤set the change in tax policy. In other words it is irrelevant whether the government …nances it expenditures with current taxes or -0.1 2000 7.1. FISCAL POLICY US Nominal Government Debt, 1791-1998 12 6 197 x 10 US Government Debt 5 4 3 2 1 0 1750 1800 1850 Year 1900 1950 Figure 7.4: a higher government de…cit (future taxes). Therefore the Ricardian Equivalence Theorem is also often called the Debt Neutrality Theorem. Note that the Ricardian Equivalence Theorem is in fact a theorem: given its assumptions the debt neutrality result follows. The main assumptions are: 1. Consumers behave as rational life-cyclers: if they were myopic Keynesians, obviously Ricardian equivalence breaks down 2. No borrowing constraints: you have seen in HW5 that temporary tax cuts may have real e¤ects on consumption for consumers that are right on their borrowing constraint 3. Consumers are in…nitely lived, i.e. they never die. Otherwise, if the future tax hikes needed to …nance current tax cuts come after the agent has died he does not take these tax hikes into account. Is it crazy to assume that 2000 CHAPTER 7. FISCAL AND MONETARY POLICY IN PRACTICE 198 Debt-GDP-ratio for US, 1960-1998 70 65 Debt-GDP-ratio in % 60 55 50 45 40 35 30 1960 1965 1970 1975 1980 Year 1985 1990 1995 Figure 7.5: people life forever. Here comes Barro’s contribution: if people care about their children as well as about themselves, then this is equivalent to them living forever. In some sense altruistic agents live on in their children. 4. No uncertainty with respect to future income or perfect insurance markets against future income uncertainty 5. Lump-sum taxation is possible The last two points are a bit too involved to explain at this point, but talk to me if you are curious about this. The real question is whether the Ricardian Equivalence theorem is a good description of reality. Almost certainly an actual economy like the US economy will not satisfy all the assumptions exactly. The question really is whether the theorem (once we think about it as a hypothesis about the real world, we 2000 7.2. MONETARY POLICY 199 shouldn’t really call it a theorem anymore) is a good approximation to the real world. Economists are split right through the middle. Keynesians don’t like Ricardian equivalence since it defeats tax cut as useful stabilization policy, neoclassical economists tend to like it for exactly the same reason. Not so surprisingly empirical analyses of the issue yield results all over the map, depending on the exact method (sometimes economists are quite creative in generating results they like, sometimes it is not so clear what the right method is). Since I do active research in this area feel free to come by for a chat if this issue is of interest to you. 7.2 Monetary Policy [To be completed]