Download Chapter 1: Introduction

Chapter 1
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Chapter 1: Introduction
J. Bradford DeLong
--Draft 1.0-1999-01-30: 3,090 words
1-1: What is macroeconomics?
1-1-1: Business cycles, unemployment, inflation, and growth.
Questions.
Are we richer than our parents were when they were our age? How much richer
will our children be than our grandparents were? Will we find it easy to get new
jobs if we want to change jobs in five years? How likely is it that the business we
work for will go bankrupt and dissolve? Will inflation leave us poorer as
increases in the general level of prices erode the real value of our savings? Or
will inflation leave us richer as increases in the general level of prices erode the
real value of the debts we owe?
These are the questions that macroeconomics tries to answer--questions about the
behavior of the macroeconomy, of the economy as a whole.
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Why they matter.
These questions matter. One or another of us may be individually interested in
what is happening in the market for and to the price of wheat, or peaches, or
VCRs (or economics professors). But we are all interested in the macroeconomy.
As long as there have been industrial market economies there have been the
large-scale fluctuations in output, employment, inflation, and interest rates that
we call business cycles. And the state of the business cycle has a big effect on the
quality of our lives.
[Picture: people having their lives affected by the business cycle]
Think of how your life is affected by the business cycle. it is much easier to get a
job during a boom than a recession. Real wages rise much faster when
governments pursue policies favorable to long-run growth. Becoming one of the
long-term unemployed is a very unpleasant economic fate.
Definition of macroeconomics.
Macroeconomics is the branch of economics that studies such questions: that tries
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to understand long-run growth, the business cycle, unemployment, and inflation.
1-1-2: Macroeconomics different from microeconomics.
The two branches of economics.
For more than half a century economics has been divided into two branches-microeconomics and macroeconomics.
Microeconomics is the part of economics that deals with supply and demand in
the markets for particular commodities and industries. It focuses on how
competitive markets can work to efficiently allocate resources and create
maximum producer and consumer surplus (and also on how markets can
become non-competitive, and go wrong).
Macroeconomics deals not with individual markets and industries but with the
economy as a whole. It focuses on feedback loops that lead from one component
of the economy to another. It studies how different kinds of market "failure"
affect the total level of production and employment.
[Diagram: the two branches of economics]
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Microeconomics assumes that imbalances between demand and supply are
resolved by changes in prices--rises in prices that bring forth additional supply,
or falls in prices that bring forth additional demand. Macroeconomics considers
the possibility that imbalances between supply and demand can be resolved by
changes in quantities rather than in prices: that businesses may be slow to change
the prices they charge but faster to expand or contract production until supply
balances demand. Thus less may carry over from micro to macro than one might
expect or hope.
[Two lists: characteristics of microeconomics and macroeconomics]
Unsettled microfoundations.
Every generation of economists attempts to integrate the two--to provide
"microfoundations" for macroeconomic topics of inflation, business cycles, and
long-run growth. But so far they have had only limited success, and so
knowledge gained in one branch is not necessarily a good guide to the other. Be
careful when you try to apply principles and conclusions gained in micro to
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macro questions--and vice versa!
Macroeconomics and policy.
Macroeconomics deals with those areas in which government policy toward the
economy is perhaps the most powerful. Today's governments have amazing
abilities to improve the state of the business cycle—to reduce the magnitude of
short-run fluctuations in demand and production that cause high
unemployment--or to mess things up and make the business cycle much, much
more severe. Good macroeconomic policy can make almost everyone's life better.
Bad macroeconomic policy can make almost everyone's life much worse.
[Picture: newspaper headlines showing bad macroeconomic policy making
almost everyone's life worse]
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1-2: Why would you want to learn about macroeconomics?
1-2-1: Most of the newspaper financial pages are about macroeconomics.
Cultural literacy
The first reason to study macroeconomics is that it one of the things you have to
know to be culturally literate in the twenty-first century. The economy is the
most successful of the institutions that our society has inherited from the
twentieth century, and so a lot of conversation--in the newspapers, on television,
and at cocktail parties--deals with the economy.
If you want to understand these debates and discussions, or to know why you
should care and what it means when newscasters read from their scripts about
the stock market, interest rates, unemployment rates, consumer price inflation, or
exchange rates, you first need to understand macroeconomics.
[Graphic: newspaper headlines concerned with the economy]
1-2-2: Macroeconomic events change your life-chances.
Macroeconomics and your life.
The second reason to learn about macroeconomics is that what happens to the
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macroeconomy affects what happens to you. It is much, much easier to get a
good job after college if you graduate during a boom than during a deep
recession. Taking out a mortgage at a lower interest rate but with a large number
of "points" attached--essentially a front-end payment by you back to the bank-may be extremely unwise and costly if interest rates are likely to fall. The
prudent allocation of your pension and tax-deferred savings money depends on
the current state of the macroeconomy, as does your bargaining power vis-à-vis
your employer--or if you are on the other side of the table your bargaining power
vis-à-vis your employees.
Understanding if not control.
You cannot by yourself control what the macroeconomy is doing. But you can
understand what the macroeconomy is doing. You can understand how
macroeconomic events will affect your options as you go about living your life.
And to some degree forewarned is forearmed: whether you judge the options
open to you appropriately may depend to some degree on how much attention
you pay in your macroeconomics classes.
For, to paraphrase the Russian revolutionary Leon Trotsky, you may not be
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interested in the macroeconomy, but the macroeconomy is interested in you.
[Graphic: unemployment relief line during the Great Depression]
1-2-3: Your political choices help shape macroeconomic outcomes.
Citizenship.
There is a third reason to be interested in macroeconomics. If you are not literate
in macroeconomics, you cannot be a good citizen.
You vote. You thus help choose the officials of our government. This is one of the
most precious rights and capabilities members of human societies have ever had.
One of the most important things the government does is manage the
macroeconomy--or, rather, try to manage the macroeconomy. In election after
election over your life, different candidates will present themselves seeking your
vote. After the election, the winning candidates will then have to try to manage
the macroeconomy.
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Being a good voter.
If you are literate in macroeconomics, you can judge which candidates for office
give signs of understanding the issues, and could possibly become effective
macroeconomic managers. You will be able to judge which candidates for office
are essentially clueless, or are cynically promising much more than they could
possibly deliver.
If not, not.
Now our civilization can stand a lot of uninformed voters electing clueless
candidates. As economist Adam Smith said more than two hundred years ago
(when a student cried out that the American Revolution meant that the country
of Great Britain was ruined), there is a lot of ruin in a nation. But isn't it better to
take your responsibility as a voter seriously? If so, you need to pay attention in
your macroeconomics classes.
[Graphic: voting booths]
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1-3: What is the macroeconomy doing?
1-3-1: Economic activity.
Economic statistics.
Macroeconomics could not exist without--and did not exist before--governments
began to systematically collect and disseminate economic statistics. Government
estimates of the value and composition of total economic activity, principally
those estimates contained in the so-called National Income and Product Accounts
[NIPA] are the fundamental data of macroeconomics. You cannot try to explain
fluctuations in production, unemployment, and prices unless you know what the
economy-wide fluctuations in production, unemployment, and prices are.
The NIPA were built to provide estimates of the overall level and composition of
economic activity. But what is this “economic activity”?
Economic activity.
When you work for someone and get paid, that is economic activity. When you
buy something at a store, that is economic activity. When the government taxes
you and spends its money building a bridge, that is economic activity. In general,
if there is a flow of money involved in any transaction, economists will count
that transaction as "economic" activity.
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[Picture: a whole bunch of different kinds of "economic activity"]
This set of patterns of production and exchange, flows of commodities and
money, and the ownership of assets is what economists mean when they talk
about economic activity. It is the flow of transactions in which things of real
useful value--resources, labor, goods, and services--are exchanged for money. If
it is not a transaction in which something of useful value is exchanged for
money, odds are that the NIPA do not count it as part of economic activity.
Six key variables.
Six key variables estimated as part of the NIPA and the associated other
economic statistics are of especially key importance in macroeconomics: real
Gross Domestic Product, the unemployment rate, the inflation rate, the interest
rate, the level of the stock market, and the exchange rate.
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GDP.
The first key quantity is the level of real Gross Domestic Product, usually
abbreviated GDP. Real GDP--"real" meaning that it attempts to correct for
changes in the level of prices that are not changes in the volume of the
production of useful goods and services--is the most commonly-used measure of
the production of final goods and services in the economy. It consists of the
production of consumption goods, things that are useful to consumers--things that
consumers buy, take home (or take out), and… consume--plus the production of
investment goods, things like machine tools, buildings, highways, and bridges that
amplify the country's productive capital stock and thus aid our ability to produce
in the future; plus what the government (acting as our collective agent, in some
sense) buys for public consumption and public investment purposes; plus a
balancing term (net exports: equal to the difference between what is exported
from and what is imported into the country) that is needed to make the accounts
come out even.
Real GDP (often divided by the number of people or the number of workers) is
our best available index of the status of the economy as a social mechanism for
producing goods and services that people find useful: the necessities,
conveniences, and--yes--luxuries of life.
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[Figure: Real GDP per worker in the U.S., c. 1890-present]
The unemployment rate.
The second key quantity is the unemployment rate: the number of people looking
for jobs who have not yet found one, or have not yet found one that they find
attractive enough to take rather than continue to look for a better. The number of
unemployed is usually divided by the total number of people either at work or
looking for work to produce the unemployment rate. In the United States the
Labor Department's Bureau of Labor Statistics carries out a very large survey-the Current Population Survey--every month, and calculates that month's
unemployment rate. Last month's unemployment rate is usually the big piece of
economic news on the first Friday of every month.
Some amount of unemployment in an economy is normal, and indeed beneficial.
We would all like the economy to do as good a job as possible of matching
people and jobs together. An economy in which each business grabbed the first
person who came in the door to fill a newly-open job and in which each worker
went and took the job associated with the first help-wanted sign that he or she
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saw would probably be a less productive economy than our economy is today.
We want workers to be somewhat choosy about what jobs they take--to be
willing to think that "this job pays too little", or "this job would be too
unpleasant", or "when the employers find out how unqualified I am to do this
they will be very unhappy." This means that a well-functioning economy will
have some unemployed workers and some vacancies--some workers looking for
good jobs at good wages that matches their skills and preferences, and some jobs
looking for good workers that match their skill requirements.
But there are times--recessions, and depressions--when the unemployment rate
rises very high above any level that anyone could claim reflects a normal and
healthy process of job search and job matching. The market economy's matching
of the supply of workers willing and able to work with businesses that could put
their skills and labor-power to making useful goods and services breaks down.
In the United States and in Germany during the Great Depression the share of
workers unemployed rose to between one-quarter and one-third: between
twenty-five and thirty percent.
Whenever the unemployment rate is high, the market economy is not working
well. The unemployment rate is perhaps the best indicator of how well the
economy is living up to the potential created by the current level of technology
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and the current stock of productive capital.
[Figure: unemployment rate, c. 1890-present]
The inflation rate.
The inflation rate is the third key quantity. The inflation rate is a measure of how
fast the overall level of prices is rising--how much more in money terms things in
general cost this year than they cost last year.
A very high inflation rate can cause massive economic destruction, as the price
system breaks down and the possibility of using profit-and-loss to make rational
decisions about what should be produced vanishes. Such so-called hyperinflations
are one of the worst economic disasters that can befall an economy.
[Picture: effects of hyperinflation]
Moderate inflation rates appear to be very unsettling to consumers and to
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business managers. This leaves economists scratching their heads to some
degree: moderate rates of inflation--less than twenty percent a year or so--should
not do too much damage to consumers' investors' and managers' ability to figure
out what the best use of their financial resources is. Yet all such groups appear
strongly averse to inflation, and they vote: politicians in the industrialized
economies have learned over the past generation that expressing a lack of
commitment to low and stable inflation gets them a quick ticket out of office.
[Figure: inflation rate, c. 1890-present]
The interest rate.
The fourth key quantity is the interest rate--or rather the whole complex of
interest rates, for different interest rates apply to loans that mature at different
times in the future, and to loans of different degrees of risk. (After all, the person
or business entity to whom you loaned your money may find themselves unable
to pay it back: that is a risk you accept when you make a loan.) Interest rates
govern the terms on which you can transfer purchasing power from the present
to the future. Those people or business enterprises who think that they could
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make good use of additional financial resources now borrow. Those business
enterprises or people who have no sufficiently productive or utilitarian use for
their financial resources today lend.
[Figure: short- and long-term real interest rates, c. 1890-present]
The stock market.
The level of the stock market is the key economic quantity that you likely hear
about most--you most likely hear about it every single day. The level of the stock
market is an index of expectations of how bright the economic future is likely to
be. When the stock market is high, average opinion expects economic growth to
be rapid, profits high, and unemployment relatively low in the future. (Note,
however, that there is a certain mirror-like and tail-chasing element in the stock
market: perhaps it would be better to say that the stock market is high when
average opinion expects that average opinion will expect that economic growth
will be rapid in the future.) When the stock market is low, average opinion
expects the economic future to be relatively gloomy.
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[Figure: real value of the stock market, c. 1890-present]
The exchange rate.
Sixth and last of the key economic quantities is the exchange rate: the rate at which
the moneys of different countries can be exchanged one for another. The
exchange rate governs the terms on which international trade and international
investment takes place. When the dollar is appreciated, the value of the dollar in
terms of other currencies is high: this means that foreign-produced goods are
relatively cheap to American buyers, but that American-made goods are
relatively expensive for foreigners. When the dollar has depreciated the opposite is
the case: American goods are cheap to foreign buyers--thus exports from
America are likely to be high or at least about to rise--but Americans' power to
purchase foreign-made goods is limited.
[Figure: real value of dollar, c. 1890-present]
Know the values today of these six key economic variables in their context--both
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their levels today relative to their average or normal levels, and their recent
trends and reversals of trends--and you have a remarkably complete picture of
the current state of the macroeconomy.
1-3-2: The current state of the U.S. economy: unemployment, inflation, and growth.
GDP: its level and long-run trend.
GDP: short-run fluctuations.
GDP and unemployment.
Inflation.
Interest rates and the stock market.
The exchange rate.
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[To be written last, and updated for each year within editions]
1-3-3: What's happening in the rest of the OECD.
GDP: its level and long-run trend.
GDP: short-run fluctuations.
Output stagnation in Japan.
High unemployment in Europe.
Inflation.
Interest rates and the stock markets.
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The exchange rate: the yen and the euro.
[To be written last, and updated for each year within editions]
1-3-4: What's happening in the NICs and in the rest of the world.
GDP: divergence.
GDP: growth miracles and convergence.
GDP and exchange rates: financial crises.
Inflation and hyperinflation.
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The stock markets and international investment.
[To be written last, and updated for each year within edition]
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Chapter 2: Thinking Like an Economist
J. Bradford DeLong
--Draft 0.9-1999-01-28: 7,073 words
2-1: How macroeconomists try to understand the macroeconomy
2-1-1: Subjects as patterns of thought.
New ways of thinking.
Each time you learn a new subject you learn a new pattern of thought.
Economists have their own ways of thinking about the way the world works.
Every intellectual discipline has its own ways of thinking about the world--that's
what makes it a system of thought, a subject of study, something worth learning
that can be taught. Thus each intellectual discipline is new and strange to those
who have not seen it before.
Economics is no exception: a number of things about economists' ways of
thinking will seem strange to you if this is the first time you have seen someone
thinking like an economist.
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Strangeness.
Do not let this strangeness lead you to immediately dismiss ideas and
interpretations as just plain weird. Instead, register this strangeness, for there is
no way of avoiding it--sort of like learning a new language and sort of like being
initiated into a club. And you will find that the economists' ways of thinking that
seemed strange at first allow you to see pieces of the economy more sharply and
clearly than you could have imagined. (Of course, you will also find that
economists' ways of thinking lead them--you--us--to miss large pieces of what is
going on in society; that is why economics is not the only social science, and we
have sociologists, political scientists, historians, psychologists, and
anthropologists as well.)
A problem.
There is one big problem with your learning to think like an economist. Those
who are teaching you--your graders--your discussion and section leaders--your
lecturer--your (ahem!) textbook writer--are all people who are used to thinking
like an economist. Thus for all of us the initial strangeness has melted away, and
it is hard for us to recapture it and to remember what it was like to see these
ideas fresh and new for the first time.
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Thus many ideas and assumptions that seem obvious and natural to us will seem
counterintuitive and strange to you. They may seem barely worth mentioning, or
not worth mentioning at all, to them--us--me. But to you they may well seem
badly in need of explication, and perhaps of defense.
This chapter tries to point out where some strangenesses in world-view and
difficulties in translation from one intellectual language to another may lie. This
chapter tries to point out explicitly some of what is involved in learning to speak
and think in economese.
2-1-2: Economics is not a natural science.
Economics is different.
If you are coming to economics from a background heavy in the natural sciences-physics, chemistry, and so on--you may believe that you have a good idea of
what economics is: economics is like a natural science, only less so. To the extent
that it works, it must work more-or-less like physics.
If so, you are half right and half wrong. Economics is a science, but economics is
not a natural science, it is a social science. Its subject matter is not made up of
electrons or elements, but of human beings: people and how they behave. And
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the fact that economics is not a natural but a social science has a number of
important consequences, some of which make the job of a social scientist easier
than that of a natural science, some of which make the job of a social scientist
harder, and some of which make the job of a social scientist just different.
Debates last longer.
First, the fact that economics is a social science means that intellectual debates
within economics can last a lot longer than in the natural sciences. Moreover,
they are less likely to come to clear and well-defined consensus conclusions.
The principal reason for this is that people care a lot about the subject matter of
economics: people have very different views of what a free, a good, a just, or a
well-ordered society would look like. (Indeed, They look for things in the
economy that are in harmony with their vision of what a society should be. They
ignore--or explain away-- facts they run across that turn out to be inconvenient
for their particular political views.
People are, after all, only human.
Economists try to approach the objectivity that characterizes most work in the
natural sciences. After all, they should be able to reach broad areas of agreement:
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for what is, is, and what is not, is not; even if wishful thinking or predispositions
contaminate the results of one single study, successor studies and reexaminations
will correct the error. But economists are unlikely to ever approach the effective
unanimity with which physicists embrace the theory of relativity, chemists
embrace the oxygen and reject the phlogiston theory of combustion, and
biologists reject the Lamarckian inheritance of acquired characteristics.
No experiments.
Moreover, the fact that economics is about people means that economists cannot-or cannot ethically--undertake large-scale experiments. Economists cannot set
up special situations in which potential sources of disturbance are reduced to a
minimum, examine what happens, and then generalize from what happens in
the experiment (where sources of disturbance are absent) to what happens in the
world (where sources of disturbance are common).
The absence of the experimental method makes economics harder than many of
the natural sciences. It makes economists' conclusions much more tentative and
subject to dispute.
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People have minds of their own
The third is that the particles that economists study--people--have minds of their
own. They take a look at what is going on around them, they plan for the future,
they take steps to avoid future consequences that they foresee and fear will be
unpleasant, and at times they do things just because they feel like it. This means
that in economists' analyses the present often appears to depend not just on the
past but on the future, or rather on what people expect the future to be.
This additional wrinkle makes economics in some sense even harder, for the
arrow of causality flows from the (anticipated) future back to the present. In the
natural sciences, at least you can rely on the arrow of causality and influence
flowing from the past to the future only.
2-1-3: But economics is a quantitative social science.
Economics is quantitative.
In spite of its political complications, its non-experimental nature, and its
peculiar problems of temporal causality, economics remains a science and a
quantitative science. Most of what economists study comes in easily-measurable
form, with numbers attached. Thus--as opposed to sociology and political
science--economics makes heavy use of arithmetic and algebra.
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Economics makes heavy use of arithmetic to measure economic variables of
interest. In economics you can always ask, and usually answer, the question how
much? And answering the question how much? requires counting things, requires
arithmetic.
Arithmetic and algebra.
But arithmetic by itself quickly becomes too limited and cumbersome. Thus
economists turn to algebra because algebraic equations are the best way to
summarize relationships between arithmetic magnitudes. It would be very
cumbersome to carry around a large table telling you how large consumption
spending tends to be for each of a thousand different possible values of
household income.
It is much easier to remember, and to work with, one algebraic equation relating
this year's consumption spending Ct to this year's total income Yt like:
2.1.3.1
Ct  $2,000  0.5  Yt (with both consumption and income in billions of dollars)
You will almost always choose to remember the equation, for one equation with
known coefficients (the $2,000, and the 0.5) can take the place of a very large
table detailing the relationship between income and consumption indeed.
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Not just one, but whole classes of algebraic relationships.
But there is yet another reason for economists to make intensive use of algebra.
Algebra allows you to think not just about the consequences of the one particular
systematic relationship between consumption and income given in (2.1.3.1):
2.1.3.1
Ct  $2,000  0.5  Yt (with both consumption and income in billions of dollars)
but about the consequences of each of a host of different possible systematic
relationships:
Ct  $1,000  0.5  Yt
Ct  $2,000  0.5  Yt
Ct  $3,000  0.5  Yt
Ct  $1,000  0.6  Yt
2.1.3.2
Ct  $2,000  0.6  Yt
Ct  $3,000  0.6  Yt
(with both consumption and income in billions of dollars)
...
Ct  $1,000  0.1  Yt
Ct  $2,000  0.1  Yt
Ct  $3,000  0.1 Yt
Algebra can do this by simply replacing the $2,000 and the 0.5 in equation
(2.1.3.1) with unspecified parameters c0 and c:
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Ct  c0  cYt
Then you can manipulate and analyze all of the entire class of possible
systematic relationships at once, and when you want to consider one particular
case then just substitute the numerical values for that particular case for the-abstract--parameters.
An example: the power of arithmetic.
Given the particular relationship between consumption and income in (2.1.3.1),
we can use it to analyze how an economy in which (2.1.3.1) was a good
approximation to how consumption spending was determined would behave. If
you combine (2.1.3.1) with the national-income identity that this year's
consumption spending Ct, government purchases Gt, investment spending It,
and net exports NXt together add up to total income Yt:
2.1.3.4
Yt  Ct  It  Gt  NXt
and with a particular level for total non-consumption spending G+I+NX:
2.1.3.5
It  Gt  NXt  $2,000 (with quantities measured in billions of dollars)
then you can substitute the right-hand sides of (2.1.3.5) and (2.1.3.1) into (2.1.3.5)
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in place of the expressions that match the left-hand sides of the first two
equations:
2.1.3.6
Yt  $2,000  0.5  Yt  $2,000 (with quantities measured in billions of dollars)
and then solve that equation to determine that:
2.1.3.7
Yt  $8,000 (billions of dollars)
that total income in that year in the economy as a whole is eight thousand billion-eight trillion--dollars.
[Figure: Income-Expenditure Diagram with numeric values of parameters
$2,000 and 0.5]
An example: the power of algebra.
However, we can think not just about this one particular systematic relationship
but about a whole family of different systematic relationships if we use algebra
and let letters stand for different parameters of our equations. If we think of the
systematic relationship between consumption and income not in the specific
terms of (2.1.3.1) but in the general terms of (2.1.3.3):
2.1.3.3
Ct  c0  cYt
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where the parameters c0 and c are placeholders that can take on any of a wide set
of different numerical values. Combining this equation with the national income
identity (2.1.3.4) leads us to:
2.1.3.8
Yt  c 0  cYt  It  Gt  NXt
and then to the conclusion that:
2.1.3.9
Yt 
c 0  It  Gt  NX t
1 c
Equation (2.1.3.7) was one single arithmetic statement about what the level of
national income Yt would be under thus-and-so specific conditions. Equation
(2.1.3.9) is much more powerful. It allows us to rapidly determine what the level
of national income Yt would be for any particular numerical values of the
parameters c0 and c that summarize what the thus-and-so specific conditions
happen to be. And (2.1.3.9) allows us to see what would happen to the
equilibrium level of Yt if the parameters were a little bit different: a $1 increase in
c0 increases equilibrium total output Yt by 1/(1-c) dollars, no matter what value c
happens to take on.
This is the power of algebra: to allow us to reach broad conclusions about what
might happen in any of an uncountably large number of different situations just
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by making a few squiggly marks on paper.
2-1-4: Modern economics is more of an abstract than a descriptive science.
Institutional detail vs. abstract analysis.
A complicated social science like economics could have developed in either of
two directions. First, it could have developed as a descriptive science--courses in
economics could contain long lists of economic institutions and practices, could
be devoted to cataloguing and detailing the institutional structure of the
economy. Second, it could have developed as a more abstract science--in which
case courses in economics would (as they do) spend most of their time on
relatively abstract and general principles that nevertheless had proved useful in
studying a number of situations.
Economics as we know it today has taken the second, more abstract road.
Much more time is spent on relatively general principles and how to apply them.
Relatively little time is spent on the detailed analysis and description of
institutions. Thus a remarkably large part of what economists have to say is tied
up in their particular set of tools: a particular way of thinking about the world
that is closely tied up with a particular technical language and a particular set of
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data that are most often examined. It is possible (at least, I have found it possible)
to get a lot out of sociology and political science courses without learning to
think like a sociologist or a political scientist because of their focus on the
detailed analysis and description of institutions. It is much less possible to get a
lot out of an economics course without learning to think like an economist.
Synergies between algebra and abstract analysis.
The reason that modern economics has become more of an abstract, toolapplying and less of an institutional, descriptive science is in large part the result
of the power of algebra. Had economists in the first half of the twentieth century
found that their mathematical tools were less useful than they in fact turned out
to be, economists in the second half of the twentieth century would have
developed the field in different directions--more like political science or
sociology. But abstraction--largely mathematical abstraction, largely algebra-turned out to be very useful indeed.
What economists' use of algebra and abstraction means for you.
Unfortunately for some of you, many students who wish to learn economics do
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not especially like algebra: long pages of derived equations are next to
incomprehensible, and the relationships between the equations with their Ct's
and their It's and their 's and the real economy quickly becomes obscure.
Economists have developed a number of tools--mostly graphical and
diagrammatic--to try to make the algebra more intelligible. But there is no
question that this textbook--and the course you are presumably taking--will be
easier for you the stronger and more intuitive is your grasp of mathematics.
2-2: Economists use metaphors
2-2-1: The rhetoric of economics.
Metaphors and similes.
Human beings think in metaphors and similes. They understand something that
they do not know by comparing and analogizing it to something that they do
know.
Economics is no exception.
Economics as a subject is riddled with metaphors. In economics, curves "shift."
National income and expenditure "flows in a circle." Money has a "velocity."
Changes in the state of the economy are described by saying that the economy
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crawls "up the IS curve" or "along the total expenditure line."
When the Federal Reserve raises interest rates and throws people out of work, it
"pushes the economy down the Phillips curve." When the Federal Reserve lowers
interest rates and the economy booms, it "pushes the economy up the Phillips
curve"--as if the economy were a dot on a diagram drawn on a piece of paper, as
if it were constrained to move along a particular curve on the diagram called the
Phillips curve, as if changes in Federal Reserve monetary policy really did push
this dot drawn on the diagram up and to the left or down and to the right.
Be conscious of metaphorical thinking.
It is important for you to be conscious of--and a little bit critical of--the
metaphors that economists use for two reasons.
First, if you don't understand the metaphors and their place much of economics
may simply be completely incomprehensible. Your professor may say that "the
velocity of money increased." You may think:
Velocity? Velocity of money? Money doesn't have a velocity. Cars have a velocity.
What can he possibly mean?
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But all will become clear… or at least clearer… if you remember that a dominant
metaphor in macroeconomics is the circular flow metaphor, that the flow (see-there it is, the metaphor) of spending is like the flow of some liquid through the
economy, that if the total amount of spending increases but the quantity of
money doesn't then the money must "flow" faster since the fixed quantity of
pieces of money must change hands more often: hence money must have a
higher velocity. Without the underlying context of the metaphor that spending is
a circular flow of purchasing power through the economy, references to the
"velocity" of money make no sense.
Classes of metaphors.
Most of the metaphors you will see in macroeconomics will fall into four classes:

The first is made up of hydraulic metaphors connected with the dominant
image of the circular flow of economic activity.

The second is economists' use of the word "market" to label incredibly
intricate processes of exchange--as if all the workers and all the jobs in the
economy really were being matched to each other in a single open-air market
like that of fifth century B.C. Athens.
Chapter 1

39
The third is economists' fondness for the idea of "equilibrium": their thinking
about economic processes as if they were somehow bringing the two pans of
an old-fashioned scale into balance (that's what "equilibrium" means: equilibrium, equal weights on the two pans of the balance)

The fourth and last is the way of metaphorical thinking that is the branch of
mathematics called analytic geometry-- economists' use of graphs and
diagrams as an alternative to algebraic equations by identifying equations
with curves, equilibrium with points, and changes in parameter values as
shifts in the positions of curves on a diagram. This use of metaphor is central
enough to economics that it is discussed not in this but the next section of this
chapter.
2-2-2: The Circular flow.
The hydraulic metaphor.
The most frequently encountered metaphor in economics is the hydraulic--a
fancy word for "water"--metaphor of thecircular flow of economic activity. When
economists speak of the "circular flow" of economic activity through the
economy, they have a definite picture in their mind's eye. Patterns of spending,
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income, and production are seen as flows of some liquid through different sets of
pipes. Categories of actors in the economy--the set of all businesses, or the
government, or the set of all households--are seen as pools into and out of which
the fluid of purchasing power (i.e., money) flows.
[Figure: the circular flow of economic activity]
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Circular Flow of Economic Activity
Flow of incomes from businesses to households
Households
Businesses
Flow of consumption spending
Flow of net taxes
net
imports
(= - net
exports,
= diversion
of demand
to foreign
producers)
Flow of government purchases
Government
Government
Surplus
Flow of investment spending
Private saving
Financial Markets
Net inflow of
capital
(= foreign
investment in
the U.S.)
=
net
imports
Rest of the World
One benefit of this hydraulic metaphor is to help us see that the economy is
made up of ongoing and ever-repeated patterns of activity: not one act of
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exchange or production, but a continuous process of the exchange and
transformation of flows of purchasing power and resources: patterns of activity
that both persist and change over time. The hydraulic metaphor is apt in that it
reminds us that economic variables like consumption spending or GDP are
ongoing flows--see, there the metaphor is.
Every economic transaction has two sides.
The circular flow metaphor contains another important truth--that every piece of
economic activity has two sides. When a business produces and sells something
of value, the money earned by the business is then paid out as income to
someone--the workers, the suppliers, the bosses, or all three. When a household
earns income, that purchasing power is then used somehow--taxed away by the
government, spent on consumption goods the household finds useful, or loaned
to a bank (or to the U.S. Treasury, if you take the cash and hide it under your
mattress) which then uses that purchasing power somehow.
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2-2-3: Markets and equilibrium
Markets.
Economists talk as if all economic activity--all purchases and acts of exchange-take place in something like the great open-air marketplaces of the merchant
cities of the preindustrial past.
They speak offhandedly of how all contracts between workers and bosses are
made in the "labor market," of how all the borrowing of money from and the
depositing of money into banks take place in the "money market," of how supply
and demand have to balance in the "goods market." In the market square of a
trading city of the pre-industrial past you could survey all the buyers and all the
sellers, and pretty quickly have a good idea of just what was being sold for how
much, and what quality it was.
In using the open-air markets of the pre-industrial past as metaphors for the
complex processes of matching and exchange that take place in our modern
industrial economy, economists are placing an intellectual bet: they are betting
that information travels fast enough and that buyers and sellers are well
informed enough that the prices and quantities that prevail in our modern
economy are as if we actually could walk around the perimeter of the
marketplace and examine all buyers and sellers in an hour. In most cases this will
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be a good intellectual bet to make--but sometimes (for example, in situations of
so-called structural unemployment) it may not be.
Equilibrium.
Economists spend most of their time looking for equilibrium--points of balance in
which some quantity or set of quantities have no tendency to either rise or fall.
The dominant metaphor is of an old-fashioned two-pan scale in balance.
Equilibrium. Equi-librium--literally, "even weights" so that both pans of the twopan scale are at the same height.
This search for equilibrium is a way to try to greatly simplify the process of
analyzing an ever changing, dynamic, complicated system. The underlying
principle is that things are much easier to analyze if you can first figure out
"points of rest," positions and states of affairs where pressures for economic
quantities to rise and to fall are evenly balanced--see, there is the metaphor
again. Once you have identified the potential points of rest, you can then figure
out how fast your stripped-down picture of the economy will converge to those
points of equilibrium.
This search for points of equilibrium, followed by an analysis of the speed of
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adjustment to equilibrium, is perhaps the most common way of proceeding in
any economic analysis.
Metaphors are aids to thinking about reality--not the reality itself.
But do not forget: these metaphors are just aids to understanding theories and
principles. They are not the theories and principles themselves. And the theories
and principles in turn are also just aids to understanding the reality--and are not
themselves the reality.
2-3: Analytic geometry
2-3-1: The relationship between algebra and geometry
Rene Descartes.
There remains a fourth class of metaphors: those taken from analytic geometry.
Analytic geometry translates algebra into geometry. Thus the algebraic
expressions of patterns of cause-and-effect are turned into geometric figures.
Rene Descartes (1596-1650) spent a good chunk of his life proving that graphs
and algebra are identically useful ways of proceeding: that there is a natural way
of identifying an equation with a curve, or a soluation with a point. Thus the
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metaphors of analytic geometry portray chains of cause and effect--links between
one economic variable and another--as lines drawn on a graph with axes, and
portray situations of balance--situations in which the economy has reached a
stable position--as points on the graph where different curves happen to cross.
Turning equations into lines--and vice-versa.
We use graphs to plot two economic variables on the two axes. We draw one line
(or "curve") for each behavioral relationships or equilibrium condition. The point
where the curves cross will be the solution: the values at which the two economic
quantities that you did not know are consistent with people's behavior and
market equilibrium.
Not only can you use analytic geometry to think of any equation relating two
quantities as a line on a graph, but you can think of the solution to a system of
two equations as the point on the graph where the two lines cross.
Economics courses use analytic geometry--lots of diagrams with curves and
intersecting points--in large part because Paul Samuelson had the good idea back
at the end of World War II that many students would be more comfortable
manipulating diagrams than manipulating algebraic equations. And he was
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right--with diagrams, you can see what is going on. It is often easier to think of
how a particular curve would shift than to think of the consequences of changing
the value of the constant term in an equation.
2-3-2: Understanding economics.
Three ways of understanding economics.
Thus you will find economics textbooks putting forward concepts and ideas in
no fewer than three ways. The concepts and ideas will be presented first in
verbal descriptions, second in equations, and third in the lines and curves of
graphs and diagrams. Much of the time the principal weight of the discussion
and explanation will happen in the graphical part--the lines and curves on
graphs and diagrams.
Thus, we can say "Consumers grew more pessimistic about the future and spent
less"; we can reduce the value of the constant term--the c0--in the consumption
function:
2.3.2.1
Ct  c0  cYt
or we can move the spending-as-a-function-of-income line downward on the
income-expenditure graph. All three are the same thing: consumers become
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pessimistic, a number in an algebraic equation is reduced, a line on a diagram
shifts downward. The first uses words, the second uses algebra, and the third
uses analytic geometry: the metaphor by which the systematic behavioral
relationship between consumers' incomes and their spending is seen as a line on
a graph--a line on a graph that can and does change position as circumstances
change.
What if you don't get analytic geometry?
Now if you find analytic geometry easy and intuitive, then Paul Samuelson's
intellectual innovation makes economics very accessible to you. Understanding
economists' theories and arguments becomes as simple as moving lines and
curves around on a graph, and looking for places where the right two curves
cross. It becomes easy to graphically solve systems of equations, and to see how
changing the presuppositions of the problem changes the answer. If you are
comfortable with analytic geometry, economists’ reliance on lines, curves, and
graphs makes understanding economics relatively easy.
If not. . . not.
Then you need to find other tools to help you think like an economist.
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Don't get me wrong: these metaphors from analytic geometry are very useful in
understanding the economy. It is truly helpful to think about changes in
behavioral relationships as if they were curves on a graph that shift about. And it
is helpful to think about positions of equilibrium as if the whole economy was a
dot on a graph--a dot located where two curves describing behavioral
relationships cross, and thus where both behavioral relationships are satisfied.
And it is helpful to think about changes in the state of the economy as
movements on a graph of a dot--a dot that represents the state of the economy as
a point on a diagram, and a dot that spends its time crawling around from one
position to another.
But remember that these too are metaphors, not the reality. They are tools to aid
your understanding. If the graphs are confusing, then you need to become better
at understanding and manipulating algebra, or better at following the verbal
descriptions of the argument. But use whichever feels most comfortable: grab
hold of whichever makes most sense to you, and recognize that these are really
three ways of trying to make the same points and reach the same conclusions.
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Lines and curves.
When economists translate their algebraic equations into analytical-geometric
diagrams, they do two things that may annoy you. First, economists (like
mathematicians) think of a "line" as a special kind of "curve" (and it is: it is a
curve with zero curvature, after all). So you may find words--in this book, or in
your lecture, or in your section--referring to a "Phillips curve," but when you
will look over at the accompanying diagram you see that it is a straight line. Do
not let this bother you. Economists use the word "curve" to preserve a little
generality. They want to keep open the possibility that a cause-and-effect
behavioral relationship between one economic variable and another may be a
little more complicated than can be captured in a simple linear equation like:
2.3.2.1
Ct  c0  cYt
Prices always go on the vertical axis.
Second, when economists draw a diagram they always put the price on the
vertical axis and the quantity on the horizontal axis. They do this no matter
which is the cause and which is the effect.
You are (probably) used to seeing diagrams in which the cause is placed on the
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horizontal axis and the effect placed on the vertical axis. That is the convention
everywhere else in the world.
Economists do not follow this convention. There is no good reason, save for
tradition, for them not to do so. But they don't.
Again, don't let this bug you, and don't let this surprise you when you see it.
2-4: Using models to understand the economy.
2-4-1: Narrow your focus and omit all unnecessary detail.
The American economy is complex.
The American economy is complex: 130 million workers, 10 million firms, and 90
million households buying and selling $24 trillion worth of goods and services a
year. Economists have placed the intellectual bet that the best way to understand
this complexity is to simplify.
The way that they simplify is to abstract from a great deal of variation and
institutional detail and to boil down the entire complicated economy to a handful
of key behavioral relationships--cause-and-effect links from one set of economic
quantities to another--and a handful of equilibrium conditions--conditions that
must be satisfied for economic activity to be stable and for supply and demand to
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be in balance in different markets. They then represent these behavioral
relationships and equilibrium conditions in simple algebraic equations (and
analytic-geometric diagrams).
Economists call this process of stripping-down of the complexity and variation of
the economy into a handful of equations "building a model." And economists
then use these models that they have built to try to understand what is going on
in the real, complex economy out there..
Simple models are understandable.
Economists do not just use models--systems of equations that in some way are
supposed to mimic the behavior of people and institutions--economists use
simple models.
Economists use simple models for two reasons. First, no one can understand
what is going on inside complicated models. A model is of little use if it
generates a prediction, but if you then do not understand the logic behind the
prediction.
Second, predictions generated from simple models are nearly as good as ones
from complex models. The economic models used in real life by the Federal
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53
Reserve or the Congressional Budget Office are more complex than the models in
this textbook. But at the bottom they are clearly cousins of the models used here.
The same Phillips curves, IS curves, and consumption functions you see in your
textbook underpin staffwork behind meetings of the Federal Reserve Open
Market Committtee [FOMC] when it tries to decide whether the management of
the economy requires a change in the level of interest rates.
Economists' intellectual bet.
Thus in their love of algebra economists have placed an intellectual bet that the best
way to understand the economy is to quantify and to simplify. Capture a few
behavioral relationships in equations. See how the mathematical system made up of
those equations behaves. Then try to apply the properties of the system back to the
real world. All along hope that all the quantifying and simplifying have not made
the model a bad guide to how the world really works.
This is a powerful way of thinking--if the detail that you omitted is indeed
unnecessary, if the features that your particular model focuses its attention on
are in fact the most important features for analyzing the issues at hand.
If not… then not.
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Should you hear someone say that economics is more of an art than a science,
they are saying that the rules for how to build effective and useful models-models that omit unnecessary detail but retain the necessary and important
factors--are nowhere written down. In this important aspect of economics,
economists tend to learn by doing--or learn not at all.
2-4-2: Representative agents.
Everyone in the economy is the same.
One simplification that macroeconomists--but not microeconomists--invoke at
almost every opportunity is the simplification that all participants in the
economy are the same, or rather that the differences between businesses and
workers do not matter much for the issues that macroeconomists study. The
convention is to analyze a situation by examining the decision-making process
that would be followed by a single representative agent--a single representative
business, representative worker, representative saver, whatever--and then
generalize to the economy as a whole the conclusions reached about how the
decisions of that single representative agent are affected by the economic
environment.
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This use of the construct of the representative agent makes macroeconomics
much simpler.
Difficulties with the "representative agent."
It also makes some areas of the field of study next to impossible to analyze.
Consider unemployment, for instance: the key fact of unemployment is that
some workers have jobs and other workers do not. Thus it is hard to say
anything coherent about unemployment if one has previously adopted the
simplifying assumption of a representative worker.
This assumption of a representative agent also means that much of
macroeconomics is helpless in situations where the distribution of income and
wealth--and thus differences between different people in the economy--are
important.
Most of the time our judgments about social welfare are deeply tied up with
distribution: an economy in which everyone works equally hard but a million
lucky people received $1,000,000 a year in income and 99 million received
$10,000 a year in income would be judged by most of us to be worse off than an
economy in which all 100 million people received $80,000 a year in income, even
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though total incomes in the first economy amounted to $10.9 trillion and total
incomes in the second economy amounted to only $8 trillion.
As I wrote at the beginning of this chapter, every intellectual discipline sees some
things very clearly and some things very fuzzily or not at all: distribution and its
impact on social welfare is one thing that macroeconomics has trouble bringing
into focus.
2-4-3: Decision making and opportunity costs.
Opportunity costs.
Perhaps the most fundamental principle of economics is that there is always a
choice and that making a choice excludes alternatives. If you keep your wealth in
the form of easily-spendable cash, you pass up the chance to keep it earning
interest in the form of bonds. If you keep your wealth in the form of interestearning bonds, you pass up the capability of immediately spending it on
something that suddenly strikes your fancy. If you spend on consumption goods,
you pass up the opportunity to save.
Economists call the value of the best alternative to any choice that someone is
making that choice's opportunity cost.
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At the root of every behavioral relationship in an economic model will be
somebody's decision. In analyzing that decision--and thus building up the
behavioral relationship--economists will always think about the decision maker's
opportunity costs: if you do or get this, what opportunities and choices are you
thereby excluding? How much of X will the decision maker choose given his or
her other alternatives?
A substantial number of students make economics a lot harder than it has to be
by not remembering that this opportunity cost way-of-thinking is at the heart of
every behavioral relationship in an economic model.
Expectations
Much of the time the opportunity cost of taking some action today will not be an
alternative use of the same resources today, but will involve some saving or
husbanding of resources for the future. A worker trying to decide whether to
quit his or her job and search for another will be thinking about what the future
wages will be in the job that will be found in the future, after a period of
searching. A consumer trying to decide whether to spend or save will be
thinking about the rate-of-return on saving, which depends on what the rate of
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inflation and the level of the stock market will be in the future.
But no one knows what the future will be. At best we can form more-or-less
rational-and-reasonable expectations of what the future might be.
Hence nearly every behavioral relationship in an economic model will depend
on expectations of the future. The processes by which expectations are formed--the
amount of time that individuals have to devote to thinking about what the future
might be like, the information they have to process, and the rules-of-thumb they
use to turn the information they have into expectations--are a central, perhaps the
central piece of macroeconomics.
Economists tend to consider three types of expectations:

Static expectations--in which the future in the relevant dimension is not
thought to be uncertain or predictable enough that it is worth spending any
time thinking systematically about how the future will be different.

Adaptive expectations--in which time and attention is spent thinking about
the future, and the rules-of-thumb adopted relate expectations of the future
values of variables to their values now and in the recent past.

Rational expectations--in which a lot of time and attention is spent thinking
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about the future, and in which the decision-makers in the economic model
know as much (or more) about the structure and behavior of the economy as
the economist building the model does.
Depending on which type of expectations is believed to hold, the behavior of the
economic model can be very, very different.
As I wrote above, the fact that behavioral relationships depend on opportunity
costs--that opportunity costs depend on expectations of the future--that
expectations are formed by individuals and decision-makers who are as smart as
we are (indeed, they are us)--makes economics potentially very complicated and
very hard. The present depends on what people expect the future to be, and
people's expectations of the future are almost surely tied up with what is going
on in the present. Analyzing situations in which cause-and-effect are potentially
scrambled in this way can become very difficult very quickly.
2-4-4: An example: a simple model.
The Keynesian cross.
We have already presented the bulk of one of the simplest models used by
macroeconomists--the so-called Keynesian Cross--in the earlier sections of this
chapter. The Keynesian Cross consists of the consumption function:
Chapter 1
2.4.4.1
60
Ct  c0  cYt
the national income identity:
2.4.4.2
Yt  Ct  It  Gt  NXt
and the statement that investment It, government purchases Gt, and net exports
NXt are exogenous--exo-genous, literally "outside-generated"--that is, that they are
values that the model doesn't try to account for but that takes as already
determined and set by outside forces.
Types of equations.
The assumptions that I, G, and NX are generated outside; and that consumption
spending has the simple systematic behavioral relationship of (2.4.4.1) are the
simplifying assumptions of the model: the things that make it possible to analyze
it--and the simplifying assumptions that we hope have not dropped so much of
reality out of the model as to make it useless. The consumption function (2.4.4.1)
is a behavioral relationship--a cause-and-effect prediction that if income is at level X
consumption will be at level Y, and that if income changes by an amount X
(where "" is a Greek letter, capital delta, often used to symbolize changes) then
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consumption will change by an amount Y. And the national income identity
(2.4.4.2) is an equilibrium condition--something that must hold for the economy to
be in balance.
Solving the model three different ways.
We can analyze this model in any of three ways.
First, we can draw the so-called income-expenditure diagram, with the sum of
spending (C+I+G+NX) on the vertical axis and the level of total income Y on the
horizontal axis. Then we can use the consumption function and the exogenouslygiven values of I, G, and NX to draw a line representing the expenditure
function: how much total spending (C+I+G+NX) there is for each possible value
of total income Y. And the point at which the expenditure function lies on a 45degree line along which the national income identity is satisfied--along which
C+I+G+NX=Y--is the economy's equilibrium position.
[Figure: income-expenditure diagram]
Thus we can use analytic geometry to analyze this model. And if our hand is
steady enough and our eye good enough, we can read quantitative answers off
of our graph.
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Second, we can do the algebra: combine the national income identity and the
consumption function to produce:
2.4.4.3
Yt 
c 0  It  Gt  NX t
1 c
and then simply substitute in the (exogenously-given) values of the variables on
the right-hand side and the two parameters c0 and c to solve the model and
determine the level of total income Y. Thus we can use algebra to analyze this
model.
Or we can describe this model in words:
In order for the economy to be in equilibrium, total spending must be equal to
total income. Total spending is made up of four components, three of which
(investment, government purchases, and net exports) are determined outside
this simple model. The fourth component of spending, consumption
spending, is an increasing function of income: the higher are total incomes,
the higher is consumption spending, but consumption spending increases
less than dollar-for-dollar with increases in income.
Thus to determine the equilibrium level of total spending and income, start
with the level that total spending would have if income were zero. In this first
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round, at this level of income--zero--spending is greater than income. So next,
in the second round, consider what would happen if income were at a level
equal to first-round spending. In this second round income will still be less
than spending--because spending in this second round will be higher because
incomes are higher, and higher incomes generate higher consumption
spending. So next, in the third round, consider income at a level equal to the
level of second-round spending.
Continue this process and eventually it will converge because each dollar
increase in income increases spending by less than a dollar. The equilibrium
level of income (and spending) will be that at which total spending (as a
function of the level of total income) is equal to the level of total income itself.
All three ways of proceeding are equally valid (though some may be easier or
more useful to certain people or in certain circumstances).
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Chapter 3: Measuring the Economy
J. Bradford DeLong
--Draft 0.9-1999-02-01: 14,977 words
3-1: Economics and measurement
3-1-1: Social science and introspection.
Economics is a social science. That means that it is about us: what we do and
what happens to us as a result. Because economics is a social science, one of our
important sources of information is simple introspection. The appeal to
introspection--what would you do in this particular situation, with these
opportunities and working under these constraints?--is a very common and very
powerful intellectual move for economists to make. We will make it often in this
book.
But introspection alone is not enough to make macroeconomics possible.
3-1-2: Economics and data.
Uses of data.
Most importantly, macroeconomics would be impossible without data. Without
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data we could not figure out how to apply our theories to the economy: forecasts
would be impossible. And without data we could not figure out which theories
were correct: testing alternative approaches--comparing what they predicted to
what is actually the case--would be impossible as well.
The NIPA.
The principal source of data used by economists is a system of measurements
and estimates by the U.S. Department of Commerce's Bureau of Economic
Analysis, the national income and product accounts [NIPA]. The NIPA evolved in a
symbiotic relationship with modern macroeconomics. The NIPA was created to
measure and estimate the quantities that macroeconomic theory suggested
would be interesting. And variables of interest measured by the NIPA and by
other data-collection efforts then sparked economists to try to theorize about
how to understand their behavior.
Six key variables.
Of all the statistics collected by the NIPA and other data-collection efforts, six are
the most important: the level of total production (and of income) in the economy,
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GDP, Gross Domestic Product; the unemployment rate; the price level (usually
as measured by the Consumer Price Index, the CPI), the level of the stock market,
the interest rate, and the exchange rate. Know these six measurements of the
economy--what their current values are, what their time trends have been, and
what their future values are projected to be--and you have an excellent
knowledge of the state of the economy.
Your own situation.
A potentially dangerous source of information about the overall state of the
economy is your own particular set of circumstances, or those of your family.
The United States is a very, very big place. What is going on in your life, or in
your neighborhood, or for your family may well not be in any sense typical of
what is going on in the country as a whole.
3-1-3: Types of economic data
Stocks and flows.
Economic data come in many different flavors: net and gross, real and nominal,
stocks and flows.
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Stock and flow--see, there is the hydraulic circular-flow metaphor again--are
closely related. The rate of change of a stock is a flow. The cumulated integrated
value over time of a flow is a stock. Think of the stock variable as being like the
total amount of water in a reservoir, and the flow variable as the flow of water
into or out of the reservoir.
Thus flows are measures of ongoing processes. A flow will be measured as so
many dollars per unit of time--per day, per month, per year. GDP or the rate of
net investment--how much businesses are spending in additions to the total
capital of a country--are flow quantities.
You can tell a flow quantity if it needs a "per unit of time" attached to a number
in order for it to make sense
Stocks are measures of quantities in being at some particular exact moment of
time. The capital stock is the total amoun tof useful machines, buildings, and
other past investments that add to the economy's productivity. The capital stock
is--no surprise--a stock. The money stock is the total value of liquid assets in the
economy at some particular moment.
You can tell a stock quantity if adding a "per unit of time" to its number would
produce nonsense. The U.S. capital stock is $24 trillion, not $24 trillion per year.
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GDP--a flow--is $8 trillion per year.
Notionally, at least, you could bring a stock quantity together into one big pile
and count it. The total capital stock of a country at a particular moment is one
example of a stock quantity. This includes the total value of all the machines that
have been installed, all the buildings that have been built, all the infrastructure
that has been created, and all the inventories that have been built up to support
production.
Real and nominal magnitudes.
Nominal quantities are quantities that have not been adjusted for overall changes
in the average level of prices--have not been adjusted for inflation a deflation.
They are quantities measured in terms of dollars, paying no mind to any changes
in the value of the dollar, and making no attempt to get an estimate of what they
would have been had the average level of prices been more-ore-less unchanging.
A nominal quantity is expressed in terms of current dollars, or is simply one
current-dollar sum divided by another. In 1995 total nominal GDP (at 1995's
prices) was $7,254 billion; in 1996 total nominal GDP (measured at 1996's prices)
was $7,581 billion. The nominal GDP growth rate between 1995 and 1996 was 4.5
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percent.
Real quantities are quantities that have been adjusted for changes in the overall
price level, for episodes of deflation or inflation. They have been divided by the
current price level in order to produce an estimate of what spending would have
been if the price level had been constant.
When measured using 1995's prices, GDP in 1996--real GDP--was not $7,581
billion but only $7,410 billion. The difference--the gap between $7,410 and $7,581-was due to the 2.0 percent general inflation in the level of prices between 1995
and 1996.
Nominal and real magnitudes are related by the price level. Between 1992 and
1996 the nominal prices of consumer services in the United States increased by
12.8%. Meanwhile, the nominal price of machines-producers' durable
equipment-increased by only 0.7%. The Commerce Department's Bureau of
Economic Analysis combined these two estimates with estimates for all the other
components of GDP and calculated that between 1992 and 1996 the overall price
level increased by 9.9%.
How did the BEA come up with that number? By constructing an index number.
It took the rate of inflation for each good or category and multiplied it by the
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share of final expenditure in that good or category to produce an appropriatelyweighted index of overall, general inflation.
Gross and net magnitudes.
Gross magnitudes are quantities that have not been corrected for
counterbalancing magnitudes. Net investment--the rate at which the capital stock
is changing is equal to total spending on investment goods minus depreciation-the wearing-out, scrapping, and retirement of old capital. Gross investment is
total spending on investment goods. Net investment is gross investment minus
depreciation.
Similarly, net exports are the net flow of goods out of the United States to other
countries. Gross exports are the total flow of goods out of the United States.
Imports are the total flow of goods into the United States. Net exports are equal
to gross exports minus imports.
Almost always we economists would prefer to have the "net" quantity to work
with and think about. But sometimes we don't. Usually the reason that we don't
is that the estimating agencies do not trust their estimates of the "net" quantity.
Thus the Department of Commerce's Bureau of Economic Analysis greatly,
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greatly prefers to report GDP--gross domestic product--than NDP--net domestic
product--because they do not trust their estimates of depreciation.
3-1-4: The estimating process.
Estimating agencies.
All economic magnitudes reported--from GDP to the unemployment rate down
to consumer confidence and new investment orders--are estimates. In the United
States today, most such estimates come from two places: the Bureau of Economic
Analysis (BEA), a part of the Department of Commerce, and the Bureau of Labor
Statistics (BLS), a part of the Department of Labor.
The BLS.
The Bureau of Labor Statistics compiles the Consumer Price Index (CPI)--the
most frequently used gauge of inflation--and also calculates the unemployment
rate. Each month the BLS announces two different estimates of employment and
unemployment, coming from two different surveys. The official unemployment
rate is calculated from what the BLS calls the Current Population Survey, which
is a survey of households by BLS workers that asks them whether they have or
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are looking for jobs. The official estimate of employment comes from the BLS's
survey of business establishments, which asks them how many people are at
work.
The BEA.
The Bureau of Economic Analysis, part of the Department of Commerce,
compiles the National Income and Product Accounts and publishes the Survey of
Current Business once a month, which contains more statistics than you would
ever wish for.
Sources of information.
There are more manageable sources for BEA-produced estimates that you are
likely to be interested in or need. These are the annual Economic Report of the
President, which includes some 110 tables of economic variables; the annual
Statistical Abstract of the United States; the Paris-published OECD Economic
Outlook; and--most accessibly--the final few pages in each issue of the British
newsweekly The Economist.
The White House has a World Wide Web site--http://www.whitehouse.gov/--
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that includes an economic briefing room where the most frequently-cited and
often-used government-produced economic statistics are presented.
3-2: Gross domestic product and the circular flow
3-2-1: Gross Domestic Product--GDP.
GDP as the most-used economic statistic.
The most often used frequently cited measure of how the economy is performing
is Gross Domestic Product (GDP). GDP is a measure of the circular flow of
economic activity: it is measured in real (that is, adjusted for changes in the price
level) dollars per year, and tells us the rate at which useful goods and services
are being produced. Because it is a measure of the circular flow, GDP is a
measure not only of the flow of production, but also of the total incomes
generated in the economy, and of the total amount of spending as well.
Near synonyms for GDP.
GDP, however, is just the most frequently-cited measures: you will see other
measures, near-synonyms to GDP like GNP (Gross National Product), NNP (Net
National Product), NDP (Net Domestic Product), and NI (National Income) used
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as well. You will also hear “total output,” “total production,” “national product,”
“gross national product,” “net domestic product,” and “national income.” Except
when the discussion is focusing on the details of the NIPA, whenever you hear
any of these expressions think “GDP.”
At the level of intermediate macroeconomics, economists pay little attention to
the differences between domestic product, national product, and national
income.
Indeed, in this book we will use "total income" and "total output" and "total
spending" all as synonyms for "GDP": our summary measure of the circular flow
of economic activity.
3-2-2: The circular flow.
The circular flow metaphor.
Economists think of economic activity--the pattern of production and spending
of the economy--as a circular flow of purchasing power thorough the economy.
This circular flow metaphor allows us confidently to predict that changes in one
piece of the economy will affect the whole, and how such changes will affect the
whole. It allows us to simplify economic behavior, to understand the entire
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complex set of decisions taken by different actors in different parts of the
economy by thinking of a few typical decisions taken by representative agents
that govern one or the other parts of economic activity's circular flow.
[Figure: Circular Flow Diagram Once Again]
What happens in the circular flow of economic activity? Money payments flow
from firms to households as businesses pay their workers and their owners for
their labor and their capital--this is the income side of the flow. Money payments
then flow from households to firms as households buy consumer goods, pay
taxes, and save, and as their taxes and savings then are spent by the government
on goods and services that it buys and are loaned to and then spent by firms
engaged in investments to boost their capital stock--this is the expenditure side
of the flow.
Measuring the circular flow.
This circular flow is measured at three different points in the circular flow.
Economists measure GDP at the point in the circular flow where consumers,
exporters, the government, and firms making investments purchases goods and
services from businesses: this is called total output—the total economy-wide
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production of goods and services--the expenditure-side measure of the circular
flow.
Economists measure the level of economic activity at the point in the circular
flow where businesses pay households for factors of production. Businesses need
labor, capital, and natural resources to make things. All these factors of
production are owned by households. When businesses buy them, they provide
households with their earned incomes: this is called total income or national
income.
[Figure: Circular Flow Diagram and the Three Points of Measurement]
Third, economists measure the level of economic activity at the point where
households decide how to use their incomes: How much do they save? How
much do they pay in taxes? How much do they spend buying consumption
goods? This is the uses of income measure of economic activity.
The measure used most often is the expenditure side measure: the Gross
Domestic Product produced by firms and demanded by purchasers, estimated
by counting up the four components of spending (and sales): consumption,
government purchases, investment, and net exports.
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All measures of the circular flow are equal.
If we compare the expenditure side measure of GDP with the income-side or
uses-of-income-side measures of the circular flow, we find that they are equal.
They are equal because the circular flow principle is designed into the National
Income and Product Accounts (NIPA). Every expenditure on a final good or
service is accounted for as a payment to a business. Every dollar payment that
flows into a business is then accounted for as paid out to somebody. It can be
paid out as income--wages, fringe benefits, profits, interest, or rent. It can be paid
out to buy goods from another business, which then pays it out to somebody.
Thus, ultimately every dollar of spending on goods produced by a business
flows out of the business sector to the household sector, for ultimately it will be
paid out as income to somebody, after some series of transactions with suppliers
of intermediate goods and raw materials.
3-2-3: Accounting definitions and statistical discrepancies.
The statistical discrepancy.
Now the different measures of the circular flow will not exactly balance. First,
there is the so-called statistical discrepancy. All pieces of GDP reported by the
Commerce Department are estimates. All estimates are imperfect. It is not
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unusual for $100 billion a year to go "missing" in the circular flow.
Accounting definitions.
Second, different measurements will differ because of differences in exact
accounting definitions. For example, measures of Net Domestic Product (NDP)
and National Income (NI) exclude depreciation expenditures. NI excludes
indirect business taxes. Domestic Product (DP) includes and National Product
(NP) excludes incomes earned in the United States by people who are not
citizens or permanent residents here.
3-2-4: The circular flow diagram.
Understanding the diagram.
Economists illustrate the circular flow principle with a simple diagram: the
circular flow diagram.
Along the top of the diagram, expenditures by businesses as they purchase labor
and other factors of production become the components of household incomes:
wages and salaries, benefits, profits, interest, and rent. Along the bottom of the
diagram, household uses-of-incomes--consumption spending, savings, and taxes--
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become the components of aggregate demand: consumption spending, investment
spending, government purchases of goods and services, and net exports.
Within the business sector, businesses buy and sell intermediate goods from each
other as they strive to produce goods and services and make profits. Within the
household sector, households buy and sell assets from and to one another. These
within-the-business-sector and within-the-household-sector transactions are
important components of the economy. But because they net out to zero within
the business sector or within the household sector, they are not counted as part
of the circular flow of economic activity.
Following the circular flow.
Let's take a look at one particular piece in the circular flow: a dollar paid out by a
business as a dividend to someone who had previously invested in the company
by buying a share of stock when the company had undertaken its initial public
offering, or IPO.
[The circular flow diagram: following the flow]
When the dividend check is deposited, it becomes part of that shareholder's
household income. Suppose that the household doesn't spend it but simply
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keeps the extra money in the bank--saves it. The bank will soon notice that it has
an extra dollar of deposits, and it will loan that dollar out to a business seeking
cash to add to its inventory. That business will then spend the dollar buying
goods and services as it builds up its inventory, and it may buy them from the
very company that originally issued the dividend check. In any event, as soon as
the dollar shows up as a component of investment spending, the circular flow is
complete.
3-3: GDP estimates and national income identities
3-3-1: Counting GDP.
Quarterly estimates of GDP.
The Department of Commerce's Bureau of Economic Analysis computes
estimates of GDP every three months, each estimate covering a three-month
period--a quarter of a year. When you hear the newscasters announce the GDP
estimate, they will report it in one of two ways. They may report a level at an
annual rate--a statement that if production for an entire year took place at the
same rate as in the particular quarter being measured, then $7,854 billion worth
of goods and services would be produced: a GDP of $7,854 billion per year. They
may report a growth rate--a statement that GDP in the particular quarter being
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measured was higher than in the immediately preceding quarter by an amount
such that if GDP grew over an entire year at the same rate, then after a year GDP
would be 5.6% higher: a growth rate of 5.6% per year.
Components of GDP.
So what is the NIPA actually measuring when it reports a measure of GDP? The
Bureau of Economic Analysis estimates, and includes in GDP [Y], the value of:

Goods and services that are ultimately bought and used by households
(except for newly constructed buildings) make up consumption spending [C].

Goods and services (including newly constructed buildings) that become part
of society's business or residential capital stock are investment spending [I].
Investment is divided into two parts: depreciation simply replaces worn-out
or obsolete capital; net investment increases society's total capital stock.

Government purchases [G] of goods and services make up the third
component of GDP. Government purchases do not include any transfer
payments: do not include any payments to individuals the government
makes not in payment for anything provided to the government (whether a
dam or an hour of a bureaucrat's time) but simply as a free transfer of money
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to the recipient.

And as a balancing item to make the national income and product accounts
consistent, net exports [NX]--the difference between exports and imports--are
also included in GDP.
Add all of these up to arrive at the level of GDP. This definition is called the
national income identity:
3.3.1.1
Y  C  I  G  NX
It is the equation that you will write down most frequently as you take any
macroeconomics course.
3-3-2: The income side.
Types of income earned.
Another way of arriving at the same number for GDP--or at the same number
except for the "statistical discrepancy" caused by the fact that measurements are
imperfect, and NIPA estimates are just that, estimates--is to count up not total
goods produced but total incomes earned. (Note that this must be incomes
earned--unearned income that comes from government transfer payments cannot
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be included here, or it won't work.)
Add together:

workers' wages and salaries (including benefits like health insurance purchased
by companies for their workers)

entrepreneurs' and businesses' profits (noting that any money earned as
corporate profits that is not distributed to shareholders--so-called retained
earnings--are shareholders' property, and should be imputed as income to the
shareholders)

money lenders' interest

landlords' rent.
Accounting definitions.
And add in as well so-called "indirect business taxes" paid by businesses and not
by households, plus depreciation allowances--expenditures to replace worn-out
or obsolete capital that are not counted as part of anyone's income but that
nevertheless set in motion real purchases of useful goods--and find that you have
arrived back (save for the statistical discrepancy) at the same GDP estimate as
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you found by adding together consumption C, investment I, government
purchases G, and net exports NX.
Why? Because of the circular flow principle.
3-3-3: The uses-of-income side.
Total expenditure equals total income equals uses of income.
The circular flow of activity has not only an expenditure side and an income side
but a uses-of-income side as well. The total earned incomes received by
households, which we will call Y (the same Y as the total level of production: at
this level of generality we are ignoring the facts that indirect business taxes and
depreciation allowances are deductions from production before it is translated
into anyone's income), must be used in some way or another by the households
that receive them.
Because every dollar of household income shows up somewhere in household
uses-of-income, because every dollar flowing out of the household sector shows
up as a purchase of goods or services from the business sector, and because every
dollar spent on business products eventually shows up as someone's income, the
flow of economic activity is--surprise!--circular.
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Uses of income.
This means that a household that earns income must use it by either:

Having it taxed away by the government, a total amount that we will call T, for
net taxes. Note that the government doesn't just take money, it gives money out-food stamps, disability payments, social security payments, and other
government transfers partially offset the total amount removed from income by
the government. When we speak of "taxes" in macroeconomics, we always mean
"net taxes": tax collections minus these transfer payments that add to household
resources.

Spending it on consumption goods, the amount C that we have seen before.

Saving it by putting it in the bank or using it to buy some financial investment or
some newly-produced investment good or other. We will use the letter S for such
private savings--private because they are undertaken by private households.
No leakages from the circular flow.
What if you do not want to do any of these three things with a piece of your
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income? Suppose you simply take the dollar bills that are your income and use
them to buy something old and precious from another household--a bar of gold,
say--that you then keep in your basement. Then you no longer have your
income, but the household that you bought the gold ingot from does have your
income. They will then either spend it on consumption goods, save it, or have it
taxed away.
What if you do not want to do any of these three things, and decide that you are
just going to take the dollar bills themselves and hide them in your basement?
When the Bureau of Engraving and Printing notices that the total number of
dollar bills circulating in the economy has dropped, they will print up more. The
government will spend these extra dollar bills that replace the ones you have
hidden. The net effect would be the same as if you had saved that portion of your
income by loaning it out to the government and bought a Treasury bond--a
promise by the government to repay your principal plus interest at the set time
that marks the duration of the loan. The only difference is that you have a stack
of dollar bills in your basement rather than a piece of paper with the words
"Treasury bond" written on it--and that the government doesn't pay interest on
dollar bills hidden in the basement.
Thus even if you try not to use your income, the household sector as a whole still
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winds up using all of its income Y as either consumption spending C, private
savings S, or net taxes T. This is another identity true by definition, the uses of
income identity:
3.3.3.1
Y CST
Why does this work? Because of the circular flow principle.
3-3-4: The national savings identity and international trade.
Deriving the national savings identity.
If we combine the uses-of-income identity (3.3.3.1) and the national income
identity () we can immediately discover an interesting principle relating
international tarde and national savings: the so-called national savings identity.
On the expenditure side, consumption plus investment plus government
purchases plus net exports are equal to total output:
3.3.4.1
Y  C  I  G  NX
On the uses-of-income side, consumption plus private savings plus net taxes are
equal to total income:
3.3.4.2
Y CST
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Since the circular flow principle tells us that total output is equal to total income:
3.3.4.3
C  S  T  C  I  G  NX
Since "C" is on both sides of the equation, we can simply cross it out. And if we
then move everything except net exports to the left hand side, we find that:
3.3.4.4
(T  G) (S  I)  NX
This is the national savings identity. It tells us that if we add together the
government's surplus (the difference T-G between net taxes and government
spending) and the excess of private saving over investment (the difference S-I
between private saving and investment spending), then the sum is equal to net
exports NX.
What we mean by "identity."
This principle 3.2.4.4 is an identity. That is, it must hold always. It is a consequence
of the way that the NIPA are defined.
The national savings identity and the determinants of the trade balance.
This national savings identity is of interest because we usually think of net
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exports--the economy's trade balance--as simply the difference between exports
and imports, each of which has largely independent causes. Instead, the national
savings identity tells us that net exports are determined by two things not
usually seen as affecting foreign trade--the government's budget, which
determines T-G, and the difference between private savings and investment, S-I
When net exports are negative, you can count on newspapers, columnists, and
those hoping for protection against foreign competitors to decry this trade
deficit--exports less than imports--as a sign of the collapse of American industry
or as the consequence of the unfair trade practices of foreign countries. When net
exports are positive you can count on politicians in office to triumphally declaim
on the strength and competitivenss of the American economy.
The national savings identity tells us: not so--not so in either case. A trade deficit-net exports less than zero--is the result of (a) investment running ahead of
private saving, or (b) a government in deficit that is spending more than it is
taxing. A trade surplus--net exports greater than zero--is the result of a
government in surplus, or of investment that is strong relative to private saving.
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3-3-5: A few danger spots.
Economists' strange definition of "investment."
There are two points that are potential sources of confusion that are worth
flagging. First, what economists mean when they say "investment" is probably
not what you mean when you say "investment." Second, the distinction between
"gross" and "net"--as in gross and net investment, gross and net taxes, or gross
and net domestic product--is an important one for you to be aware of.
First, it is important to make note of the fact that when economists refer to
investment or investment spending, they are using the words as a technical term
that does not correspond to everyday language. To economists, an investment is
the purchase and installation by a business of a machine that increases
productivity, the construction of a building, or an increase in the total value of
inventories. A purchase of a stock or a bond--what most people would call an
investment--would be called an asset sale by an economist. Do not let yourself
become confused by this terminological oddity!
"Gross" quantities and "net" quantities.
Second, it is important to note the difference between "gross" and "net"
quantities. So far we have seen two examples of this. In the case of taxes, the
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national income accounts balanced and the national income identities worked
only if we used T to refer to so-called "net taxes"--taxes collected by the
government minus transfer payments made back to households--not gross taxes.
In the case of investment we have already run into the difference between gross
and net investment: depreciation.
Some purchases of machinery or construction serve to replace worn-out and
obsolete capital. Other purchases of machinery or construction of buildings
increase that capital stock of goods that amplify Americans' productivity. The
total sum of spending on machines, building structures, and adding toward
inventories is gross investment. The amount of such investment spending that
does not replace obsolete and worn-out capital but increases the capital stock is
net investment. The difference is depreciation--the economy's consumption of
capital.
If we are talking about GDP, it is more natural and convenient to think of
investment as "gross investment"--indeed, this reference to gross investment is
where the "G" in GDP comes from. But on the income side it would be more
natural to think of net investment, for depreciation allowances are a deduction
from production before it becomes income; depreciation allowances are no one's
income.
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In this textbook we will always use "I" to mean "gross investment" and "Y" to
mean Gross--rather than Net--Domestic Product. This means that whenever we
are thinking about the income side of the NIPA, we will have to remember that
we are implicitly adjusting total income by including depreciation allowances in
it.
3-3-6: What's in and what's out of GDP
Depreciation and net output.
Some things that NIPA measures and that are thus included in GDP should
probably not be. Every year a portion of the capital stock loses its value. It wears
out or becomes obsolete--it is no longer worth keeping it operating because the
cost of keeping it operating is higher than the value of the goods it produces.
Replacing such worn-out or obsolete capital is a cost of production. It is as much
a cost of production to a business (or a government) as is meeting the business's
payroll.
Yet the NIPA counts such depreciation expenditures as part of GDP. They are
seen not as a cost of production but instead as the near-equivalent of building a
new factory to expand the business's productive capacity. The investment
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component of GDP is total gross investment spending, not net investment
spending. The investment component of GDP includes both that part of
investment spending that actually adds to the value of the capital stock and that
part that merely keeps the economy's capital stock--and the firm's productive
potential--constant.
Depreciation expenditures are counted because the statisticians who compile the
NIPA have no confidence in their estimates of economy-wide depreciation.
Intermediate goods.
So-called "intermediate goods"--goods made by a company and then sold not to a
consumer or the government (or exported, or bought by some firm undertaking
to increase its capital stock) but to another business--are excluded from GDP.
Such intermediate should be excluded form GDP: a product made by one
business and sold to another will show up in the NIPA only when the second
business sells its products to a consumer, an investor, a foreign purchaser, or the
government.
Why should intermediate goods be excluded from GDP? Because the value of the
intermediate goods has already been counted in GDP. The value of the
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intermediate goods is included in the price of the final--that is, the sold-to-theconsumer--goods that the intermediate goods were used to make. If a home
builder buys wood from a lumber mill to build a house, the value of the wood is
then included in the value of the house.
To count the value of the wood again--to include the sale of the wood to the
home builder as well as the sale of the newly-constructed house to its first
purchaser--would be to count the value of the wood twice. And then what would
happen if the home builder bought the lumber mill? GDP shouldn't go down just
because two businesses have merged if the total amount produced remains the
same.
One good way to think about intermediate goods is to think that the goal of GDP
is to count up the value-added in the economy at every stage of production. The
value added by any one business is equal to the total value of the firm's products
minus the value of the materials and intermediate goods that the firm purchases.
As we add up value-added over all the businesses in the economy, we find that
each intermediate good and material is entering our calculations twice--once
with a plus sign, when we calculate the value-added by the business that made
the intermediate good; and once with a minus sign, when we calculate the valueadded by the business that uses the intermediate good in its own process of
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production.
Thus when we calculate GDP using this value-added approach, every good and
service in the economy cancels out except for those that are not sold to other
businesses which use them in the process of production. Which goods are not
intermediate goods? The final goods and services, of course--consumption
goods, goods purchased by the government, goods purchased as part of
investment, and net exports. Hence GDP--defined as the total value-added of all
firms in the economy--is equal to GDP--defined as the total value of final goods
and services produced in the economy.
Housing
About half the people in the United States rent their dwellings. About half the
people in the United States own their own homes. When a landlord rents a house
to a tenant, he or she is selling them a service--the usefulness of having a roof
over one's head--just as much as a barber is selling you a service when you get a
haircut. Thus rent is one item of consumer spending--consumer spending on
services. It is part of expenditure in the FIRE--"finance, insurance, and real estate"
sector, one of the largest sectors of demand in the economy.
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But suppose that you own your own home. You don't pay rent to yourself. Does
this mean that GDP goes down if a tenant buys the house he or she lives in from
the landlord? Before the purchase there was a month-by-month money flow-rent--from the tenant to the landlord; after the purchase there was no such flow.
Back when the NIPA were set up, it was decided that it would be too great an
anomaly for the level of GDP to depend on the relative proportions of renters
and homeowners. So it was decided that GDP would include "implicit" rent: the
BEA would calculate GDP as if all homeowners were schizophrenically divided
into renters and landlords, and that they would "impute" an amount of rent that
the renter-half of the person notionally paid each month to the landlord-half of
each person.
This "imputed rent on owner-occupied housing" component of GDP is perhaps
the most poorly estimated component of GDP, for it is th eonly component of
aggregate demand that does not correspond to any real flow of spending in the
economy.
The government.
Also counted in GDP are government purchases of goods and services. The
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government uses the goods and services it produces to provide some services of
its own: building roads, providing police protection and courts, maintaining
armies in West Germany to deter a Russian attack on Europe during the Cold
War, issuing weather reports, maintening the national parks.
Many of these services are of a kind that, if provided by private businesses,
would be counted as intermediate goods: things that are not goods-in-themselves
but instead are aids to private-sector production. As such, they would be
excluded from the GDP.
Think about it. Suppose that two companies made a contract. And suppose that
they agreed in their contract that so-and-so would be the judge of any disputes
that arose during the terms of the contract, and suppose that they paid so-and-so
a retainer. The services of the (private) judge that they hired would be counted in
the NIPA as an intermediate good--something that was not part of final demand
because it was part of the process of production.
But all government purchases of goods and services are counted as part of GDP,
including the money that the government collects in taxes and then pays to its
own judges, bailiffs, and clerks who decide business-to-business disputes. A
large chunk of government consumption expenditures are of this form--items
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that are counted as part of GDP, but that would not be counted had they been
made for analogous substantive purposes by private businesses.
What's not in GDP--but should be.
Moreover, many things are excluded from the NIPA system of measurement,
and thus from the GDP, that probably should not be. Production that takes place
within the household is excluded from GDP. That is, work that family members
do in order to keep the household going, but for which they are not paid, is
excluded from NIPA-based measures of the circular flow of economic activity.
This is surely a mistake that warps our picture of the economy. This year some
129 million Americans will work a total of some 206 billion hours (and some 7
million Americans will spend a total of 5 billion hours looking for jobs). But
Americans--overwhelmingly adult women--will also spend at least 100 billion
hours doing things that would count as service-sector employment and would
count in GDP if they were doing them for pay rather than for their families--such
as cooking, cleaning, shopping, and chauffeuring.
Within-the-household production has never been counted as part of GDP. Back
when the NIPA was designed, its designers believed that it would be too hard to
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obtain reasonable, credible, and defensible estimates of the economic value of
within-the-household production. The excuse remains that it would be hard to
measure.
The exclusion of within-the-household production makes a difference not just for
the level of national product but for its rate of growth. Over time the border
between market paid and nonmarket within-the-household unpaid work has
shifted. Be suspicious of economic growth rates that measure total GDP, or GDP
per capita, or GDP per adult, because they are distorted by the shifting dividing
line between what we do and how society arranges it. A meal cooked is a meal
cooked whether it is part of the market paid work of a chef at a restaurant, or
part of the nonmarket unpaid work of a housewife cooking for a family. Over
time the share of meals eaten prepared in the first way has grown, and the share
prepared in the second way has shrunk. This shift in the dividing line has raised
measured GDP. But it did not reflect an increase in society’s wealth.
Depletion, pollution, and "bads".
The NIPA system makes no allowance for the depletion of scarce natural
resources. To the extent that an economy produces a high volume of income at
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the expense of destroying valuable natural resources, such income is not true
income at all but is instead the dissipation of the economy's natural resource
capital. Kuwait, Qatar, and Saudi Arabia have high levels of real GDP per
worker. But a very large chunk of high current national incomes and products in
these resource-rich economies arise not out of sustainable production but out of
the sale of what are limited and depletable natural resources. A better system of
accounts for keeping track of the economy would have a category for the
depletion of natural resources.
Moreover, the NIPA contain no category for the production of "bads"--things
which are the opposite of economic "goods," things that you would rather not
have.
Producing more smog does not diminish GDP. Producing more cigarettes and
hence more cases of lung cancer does not diminish GDP. If the demand for locks
and alarm systems rises because crime increases, GDP increases. As noted, GDP
is a measure of productive potential only: not of economic welfare and not of
whether other social and economic changes are causing people to use up
resources attempting to neutralize them.
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3-3-7: The NIPA treatment of inventories.
Unwanted inventory buildup.
Suppose that a business produces too much of its output--then finds it cannot sell
it, and so the extra output piles up in the parking lot, protected from the rain by a
tarp. Doesn't this cause an interruption in the circular flow? After all, the
business has paid its workers to produce the stuff--hence income has been
generated--but the stuff sits there unsold, hence no sales or expenditures are
generated by it.
The accounting convention adopted by the NIPA is to treat the piling-up of
unsold inventory as an "investment" by the firm. The firm has expanded its
capital stock, in this case its stock of working capital tied up in goods already
made. Thus the firm is deemed to have "bought" its own inventory, and the
piling-up of inventory is treated as a form of investment.
Inventory investment and the NIPA.
The NIPA adopts this accounting convention so that the circular flow principle
will continue to hold. The payments of wages and salaries must be matched by
some final expenditure, and in this case they are matched by an (involuntary)
investment by the business in an extra-large inventory of its unsold goods.
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Changes in inventories and changes in economic activity.
Although they don't break the circular flow, such so-called involuntary
investments (or declines) in inventory are a principal cause of business cycles.
For buildups or drawdowns of inventory are an important cause of changes in
the magnitude of the circular flow, as changes in inventories induce businesses to
expand or contract production.
Suppose that in the economy as a whole inventories are growing rapidly.
Suppose that aggregate demand--again, the sum of consumption spending,
investment spending (not including inventory accumulation), government
purchases of goods and services, and net exports together--add up to
significantly less than total production. Then businesses as a whole will be
selling fewer goods than they are making, and economy-wide total inventories
will be rising.
How will businesses respond to such a sudden--and undesired--increase in their
inventories? Some businesses will respond by cutting their prices, thus reducing
inflation (or, if the inflation rate is low enough causing deflation--falls in the
general price level). Other businesses will contract production to match demand,
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and will fire workers because they no longer need to employ so many. Thus the
rate of the circular flow of economic activity will fall. The economy will contract.
Suppose, on the other hand, that aggregate demand adds up to more than total
production. Then businesses will be selling more than they are making. And total
economy-wide inventories will be falling. Some businesses will respond to
falling inventories by boosting their prices, trying to earn more profit per good
sold, and adding to inflation. Other businesses will expand production to match
demand, hiring more workers (and paying their existing workers higher
incomes). Thus the rate of the circular flow of economic activity will increase.
The economy will expand.
In the short run of months or a year or two, the changes in the magnitude of the
circular flow of economic activity that we see are mostly the result of expansions
and contractions of aggregate demand, and of the response of businesses as they
hire and fire workers in the process of trying to avoid either exhaustion of their
inventories or undesired buildup of surplus inventories of products that nobody
wants to buy.
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3-4: Making index numbers
3-4-1: Measures of material well being.
What would a good index of material well-being look like?
GDP per worker is our most frequently used measure of material well-being.
Presidents trumpet rapid growth and explain away declines in GDP per worker.
Columnists use GDP per worker to rank the relative desirability of life in
different countries.
But is GDP per worker a good index of material well-being and economic
productivity? What would a good index of material well-being look like?
If the economy produced just one and only one type of good--say, the meals of
ambrosia that the ancient Greek gods who lived on Mount Olympus were
supposed to consume--then there would be no conceptual problems at all in
measuring material well-being, or in constructing an index of GDP. Simply count
up how many meals of ambrosia were produced (and consumed) per worker.
That would be your quantitative index of material well-being.
Now such an index of material well-being might not tell you what you wanted to
know about human happiness. Perhaps the jump from one meal of ambrosia a
day to two meals a day leads to an important and significant increase in human
happiness, but that increases from two to three and three to four meals of
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ambrosia a day have only a trivial effect on psychological well-being. You would
like a good measure of human happiness to register that psychological fact. But
our index, created simply by counting meals created, would not do so.
Nevertheless such an index would be a perfectly adequate and satisfactory index
of economic productivity. If we were making the additional assumption that the
disutility of work--the blood, sweat, toil, and tears involved in production--did
not rise over time, then we could use our index of GDP per worker--meals of
ambrosia produced per worker--economic productivity--as a perfectly adequate
index of total material well-being as well.
More than one good.
Even if the economy produced more than one good--say, ambrosia on the one
hand and personal computers on the other--there still would be no problem
constructing a quantitative index of material well-being as long as the prices of
ambrosia and personal computers remained unchanged.
Suppose, for example, that one meal of ambrosia always cost $10 and that one
personal computer always cost $1000. Then it would be straightforward to add
up the different quantities of goods produced: simply multiply the number of
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computers produced by $1000, multiply the number of meals produced by $10,
add the dollar sums together, and you have a measure of economic productivity,
or GDP per worker.
An example.
Suppose that last year demand and producer supply said that each personal
computer was worth $1,000 while each meal of ambrosia was worth $10. If
average production and consumption in the economy consisted of one personal
computer plus two hundred meals of ambrosia per year for every worker, then
last year's GDP per worker was $3,000. If production (and consumption)
increased this year to two personal computers (plus two hundred meals of
ambrosia) per year for every worker, we would say that this year's GDP per
worker was $4,000--a year-over-year increase in GDP of 33%.
In the standard indifference-curve budget-set analysis of intermediate
microeconomics courses, as long as relative prices remain the same each increase
in the total value of goods produced is associated with a shift to a consumption
bundle on a better indifference curve for the representative consumer--a new
indifference curve that the consumer strictly prefers to the old indifference curve
which was the best that he or she could reach before the total value of goods
produced has increased. Once again the quantitative yardstick provided by the
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money value of the goods produced may not tell us much about changes in
human happiness (for that you would need to interview them, and to have a
psychologist on hand to interpret the interviews for you). But no one can take
exception to this quantitative yardstick of GDP per worker as a measure of
economic productivity, or (if we can once again conclude that the disutility of
work remains constant as productivity increases) as a measure of material wellbeing.
3-4-2: Real and nominal GDP.
General inflation with constant relative prices.
Even if the prices of goods in terms of dollars changed, there would still be no
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problem in constructing our quantitative index of material well-being--of GDP
per worker--as long as the changes in prices were restricted to a general inflation
or deflation that changed the level of all prices by the same amount, and left
relative prices--the price of one good in terms of the other--unchanged.
Consider our example in which production per worker rises from 1 personal
computer and 200 meals of ambrosia last year to 2 PC's and 200 meals of
ambrosia this year, and suppose that the government prints a lot of money,
distributes it to citizens to make them feel happy, and that inflation is the result:
so that this year the price of a PC is not the $1,000 it was last year but $2,000, and
the price of a meal of ambrosia is not the $10 that it was last year but $20.
Then the sum of the prices times the quantities of goods produced per worker-what economists call nominal GDP per worker--would have risen from $3,000 last
year to $8,000 this year--a year-over-year increase of 167%. This seems wrong.
Production of ambrosia has not increased at all. Production of PC's has increased
100%. Surely our index of output--which ought to be some kind of average of
production in all different industries--should increase by more than the biggest
increase in the production of any single commodity.
The problem is that measured nominal GDP, the sum of all the goods produced
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in the economy in a year multiplied by their prices, changes not just when the
amount of goods produced but when their prices change too. Yet such a change
in prices has no impact on the actual goods and services produced and
consumed, and should have no impact on human happiness (unless, of course,
you are made happier by consuming goods with larger price tags, even if they
are the exact same goods you saw before).
As long as all increases in prices are the same proportion, economists can solve
this inflation-or-deflation problem by calculating another measure, real GDP, a
measure of what nominal GDP would have been had there been no changes in
prices from one year to the next.
We would simply ask what the (new) bundle of goods produced and consumed
would have been worth at the (old) prices, and use the old prices to value
production and thus construct our estimate of real GDP per worker. Once again
we would have an unexceptionable measure of economic productivity, of real
GDP per worker, and--perhaps--of material well being.
The example
In the terms of our example, we would say that real GDP per worker measured
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at last year's prices has increased from $3,000 to $4,000, a 33% increase. Or we
could say that real GDP per worker measured at this year's prices has increased
from $6,000 to $8,000, a 33% increase. As long as relative prices do not change
and as long as we are clear about which year's prices we are using--which year
we are choosing for the base year--it doesn't matter which particular set of prices
we use to construct our estimates of real GDP per worker.
Many goods.
The same principal would apply no matter how many goods the economy
produces, as long as their relative prices remain unchanged. Multiply each good
by its price, and sum the totals to obtain the natural index of GDP per worker, or
economic productivity. If the overall price level has changed, make all
measurements in the prices that held in some suitably chosen base year. Once
again if we can make the additional assumption that the disutility of work--the
blood, sweat, toil, and tears involved in production--does not change, then our
index of GDP per worker--economic productivity--remains a perfectly adequate
index of total material well-being. And once again it is less satisfactory as a
measure of human happiness.
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3-4-3: The index-number problem.
Changes in relative prices.
But what if prices do not all increase or decrease by the same proportion? What if
relative prices change? What then would a good index of material well-being-and of GDP per worker--look like?
It is easy to see that there is at least the potential for big trouble. Let us extend
our previous example.
Suppose that this year the ambrosia harvest fails--no ambrosia meals at all. And
that the last leftover scraps of ambrosia are sold and eaten at a price of $100 per
meal this year. And suppose we look back not one year before the present, but
five years before the present back when personal computers were very scarce
and very expensive.
The table below shows prices and quantities of per worker annual production
and consumption in this model economy. What then do our attempts to produce
estimates of changes in real GDP produce?
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Year
Five years ago
Four years ago
Three years ago
Two years ago
Last year
This year
Ambrosia
200
200
200
200
200
0
Ambrosia
Price
$10
$10
$10
$10
$10
$100
Personal
Computers
.001
.01
.1
.5
1
2
PC
Price
$10000
$5000
$3000
$2000
$1000
$1000
And suppose that we take five years ago as our base year, so that we use the
prices of five years ago in calculating our index of total output, real GDP per
worker. Then production per worker today (measured at prices of five years ago)
is:
(3.4.3.1)
(2 PC' s  $10,000)  $20,000
And the value of production five years ago (measured at the prices of five years
ago) per worker was:
(3.4.3.2)
(200 ambrosia meals  $10)  (.001 PC' s  $10,000)  $2,010
At the prices of five years ago, the economy today is (in spite of the total failure of the
ambrosia harvest) more than nine times as productive as the economy of five years ago: in
dollars of five years ago, real GDP per worker (measured at the prices of five years ago) has
risen from $2.01 to $20 thousand.
But if we take prices today as the prices to use in calculating our index of total production,
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then production today (measured at today's prices) is:
(3.4.3.3)
(2 PC' s  $1,000)  $2,000
While production five years ago (measured at today's prices) was:
(3.4.3.4)
(200 ambrosia meals  $100)  (.001 PC' s  $1,000)  $20,001
And so at the prices of today, the economy today (with the failed ambrosia
harvest) is less than one-tenth as productive as the economy of five years ago:
real GDP per worker (measured at today's prices) has fallen from $20 to $2
thousand.
So which do we believe? Has real production shrunk by 90%? Or has it risen by
more than 900%?
The problem is that using the date five years ago as the base year puts an
extraordinarily high weight on PC's--for they were extraordinarily expensive
then. Because production of computers has boomed, real GDP with five years
ago as the base sees an extraordinary increase in production. By contrast, using
this year as the base year puts a high weight on ambrosia--for ambrosia is
expensive this year because it is very hard to find. Using this year as the base
year sees an extraordinary decline in production, because the ambrosia harvest
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has failed.
So the answer is that we believe neither. When prices are changing rapidly and
significantly, no choice of price weights corresponding to a particular base year
to measure changes in real GDP per worker will give a good and unambiguous
answer to the question "how much has real GDP per worker changed?"
Let me hasten to add that in the real world things are not nearly as bad as they are
in the cooked example above. Neverthless, it is not out of the question for
estimates of U.S. economic growth over a year to shift by a full percentage point
as the base year is moved from ten years in the past to five years in the past to the
present to five years in the future.
Chain indices.
In order to minimize the problems involved in measuring real GDP over time
spans in which prices change significantly, today the Commerce Department's
Bureau of Economic Analysis constructs estimates of real GDP through a process
called chain-weighting. Use 1997's prices to construct estimates of real GDP
growth between 1997 and 1998; use 1998's prices to construct estimates of real
GDP growth between 1998 and 1999; use 1999's prices to construct estimates of
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real GDP growth between 1999 and 2000; and then chain all of these growth
estimates together to produce a value for real GDP in 2000 relative to real GDP in
1997. The advantage of chain indices is that they make the index-number
problem small: since relative prices change little between one year and the next,
there is little opportunity for the different weights implicit in shifting prices to
cause differences in estimated growth from one year to the next.
These chain-weighted measures are superior to measures of real GDP that never
change the base year used to choose prices. After all, over time prices change. It
is very misleading to measure changes in productivity today using prices from
some long-ago base year in which the relative values of goods were much
different than they are today. As long as the chain-weighted index never allows
the prices it uses to drift far away from prevailing market prices, the chainweighted index will come as close as possible to solving index number problems,
and be close to a true cost-of-living based estimate of real GDP.
The GDP deflator.
From our estimates of real GDP (however derived) and our estimates of nominal
GDP we can derive a particular expression for the average level of prices: the
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GDP deflator. The GDP deflator is that number which turns nominal GDP into
real GDP.
No min al GDP P1  Qgood 1  ...  Pn  Qgood n 
GDP Deflator 
 base
now
base
now
Re al GDP
 Qgood
P1  Qgood
1  ...  Pn
n
now
3.4.3.5
now
now
now
It is defined implicitly as the quotient of the other two measures. Thus you may
sometimes see it referred to as the "implicit price (or GDP) deflator." The GDP
deflator suffers from the same sorts of ambiguity and dependence on the base
year as do the GDP measures from which it is derived.
Although easily calculated, the GDP deflator is not the most frequently used
measure of inflation. The most frequently used estimate of the changing price
level is the consumer price index--the result of a direct survey of the prices of
goods and services by the Department of Labor's Bureau of Labor Statistics.
3-4-4: The consumer price index.
Constructing the CPI.
The most commonly-used measure of the overall level of prices and inflation is
the consumer price index, calculated each month by the Bureau of Labor
Statistics. The Federal Reserve watches the CPI very closely. Private contracts
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with cost-of-living allowances built into them--adjustments that change the
number of dollars that one party has to pay as the overall price level changes-almost always use the CPI as their measure of the price level. The government as
well uses the CPI to adjust its programs: where the tax brackets are is indexed to
the CPI. Social Security benefits are adjusted upward each year by the same
proportional amount as the increase in the CPI.
The consumer price index attempts to summarize the information in the prices of
many different goods and services into a single number that measures the
"overall level" of prices paid by consumers.
How do economists construct the CPI? The Bureau of Labor Statistics surveys
consumers and constructs a list of the items purchased by the typical consumer.
It then constructs its market basket: each good having the same share of the
market basket as its share of the typical consumer's expenditure pattern. As the
prices of goods in the market basket change, so the consumer price index will
change in proportion.
Substitution bias in the CPI.
How good a measure of the inflation is the consumer price index?
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One problem with the CPI is that it is subject to substitution bias. The CPI
measures the price of one particular set of goods, the fixed market basket chosen
in the base year. Thus it does not take account of the power consumers have to
raise their welfare by shifting their consumption towards goods whose relative
prices have fallen. Indeed, this is why the CPI is called the consumer price index
rather than the consumer cost of living index.
The fact that the CPI considers only the cost of a fixed basket of goods (albeit a
basket of goods that is updated every five years or so) means that it tends to
overestimate the rate of inflation. Suppose that the price of ambrosia goes skyhigh because the quantity of ambrosia is greatly reduced--as in our example
above. The CPI would record a very large increase in the level of prices. But if
you asked a consumer how much of an increase in income would he or she need
in order to compensate for the increase in ambrosia prices, the answer you would
get would be a smaller number than the percentage increase in the CPI.
Why? Increasing income by the same amount as the increase in the CPI would
allow the consumer to purchase the same goods and services as before the price
rise. But when the customer took a look at the prices he or she was paying, he or
she would be very unlikely to want to purchase the same goods and services as
before. Look at how much ambrosia is costing! Do you really like ambrosia that
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much? Given that it is so expensive, wouldn't you rather cut back on ambrosia
purchases and spend your money on other, cheaper commodities that you like
more?
In response to a large increase in the price of any one good, consumers substitute
away from it--hence the name "substitution bias." Because consumers have the
ability to buy more of goods that have become relatively cheap--to shift their
consumption pattern in response to scarcities signalled by rises in prices--the cost
of living will have gone up by less than the consumer price index.
[Substitution bias figure]
Substitution bias is limited, however. The CPI is periodically rebased, every five
years or so. The hope is that this rebasing limits substitution bias to 0.2% per year
of understatement of inflation or so.
New goods and new kinds of goods.
A more important problem with the CPI is the fact that new goods and new
types of goods and continually being introduced, and the CPI cannot take
account of them until some time--usually some considerable time--after they
have been introduced. Whenever a new good that performs the same service for
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consumers as an old good--only better--is introduced into the marketplace, there
is a discrete upward jump in consumer well-being. But unless the CPI is rapidly
and carefully adjusted, at least some part of this upward jump in consumer wellbeing will be missed.
[New goods and new types of goods figure]
Things may well be worse when a new good is introduced that performs a
genuinely new service for consumers. Consumers are certainly better off--they
have more choice, and those of them who choose to consume the new good are
definitely happier. But this increase in well-being never makes its way into the
CPI.
Changes in quality.
Yet another problem is the fact that the BLS's ability to track changes in the
quality of different goods is limited. Whenever a firm changes the quality of an
existing product, or replaces an existing product with a new product that does
more at the same price, consumer welfare is enhanced. Yet do the estimators
have the information that they need to accurately track changes in quality?
Probably not.
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Government statisticians do their best to take account of quality changes. Some
parts of the process of constructing the CPI make explicit reference to the
characteristics of the goods priced.
[Changes in quality figure]
What bias remains?
But the belief is that all of these adjustments that can be reasonably made are a
partial solution only, and that the CPI does overstate the rate of inflation. By how
much--half a percent per year, a full percent per year, or one and a half percent
per year? Nobody really knows.
Most economists do, however, believe that the consumer price index (and other
price indices as well) do overstate inflation by some amount. If our price indices
overstate inflation, and if our nominal GDP and nominal spending measures are
more-or-less unbiased (as we believe them to be), then our real GDP and other
real output estimates are understating economic growth.
[Figure: effects of hypothetical biases]
The amount by which our real GDP, other real output estimates, and other real
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estimates (like our estimates of the real wage, or the real rate of interest) are
understating true economic growth is uncertain--it is simply the reverse side of
the coin that is our uncertainty about the magnitude of bias in our price indices.
This means that the true news about economic growth is slightly better than you
will read in the newspapers.
For how long have our estimates of economic growth been biased? There is no
reason to believe that the bias is any greater now than it has been at any other
time in the twentieth century. Before the last quarter of the nineteenth century,
however, the pace at which new goods--or at least new consumer goods--was
introduced was much slower. So there is reason to think that the bias in standard
statistical measures of economic growth was markedly less back before 1875, and
was probably effectively zero before 1700.
3-5: Measuring the international economy
3-5-1: Imports and exports.
Definitions of imports and exports.
Goods (and services) produced abroad yet consumed or used here at home are
our imports. Goods (and services) produced here and shipped abroad to be
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consumed or used there are our exports.
The growing relative importance of international trade.
In the years just after World War II, imports and exports from the U.S. were
about five percent of GDP--amounted to about one-twentieth of total economic
output. The United States then was more-or-less a closed economy, and
macroeconomics textbooks proceeded more-or-less ignoring the importance of
international trade and finance, save for one "open economy macro" chapter near
the end of the book that the course often did not get to.
[Imports and Exports as Shares of GDP, 1890-2000]
Today imports and exports from the U.S. are about fifteen percent of GDP--three
times as large a share as fifty years ago--and are headed higher. The American
economy is no longer a closed economy, and international economics issues can
no longer be relegated to a chapter at the back of the textbook.
Other major economies are even more open.
However, the U.S. economy is still one of the more closed economies in the
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world. Of the major industrial economies, only Japan has a lower share of
imports and exports in GDP.
[Imports and exports as shares of GDP in other countries]
3-5-2: The current account and the capital account.
Classifying international transactions.
Imports and exports together make up what international economists call the
current account: they are purchases and sales of goods and services for current
use. But there are other international transactions--capital account transactions-that involve not the purchase and sale of goods and services for current
consumption and other uses but the purchase and sale of pieces of property,
investments, assets valued because they hold the potential to generate income in
the future.
[Balance of payments diagram]
There is also--whenever governments get into the act, and conduct large foreign
exchange transactions of their own, an official settlements account.
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The balance-of-payments identity.
The current account, capital account, and official settlements account are all
related by the so-called balance-of-payments identity:
3.5.2.1
NX  (OI  OI )  OS  0
d
f
Net exports (NX) plus overseas investments abroad made by domestic residents
(OId) minus overseas investments in the U.S. made by foreign residents (OIf) plus
official settlements transactions (OS) must equal zero.
Why the balance-of-payments identity holds.
Why must this balance-of-payments identity hold?
Think of it this way. When Americans export goods to foreigners, they don't get
paid in dollars--foreigners pay for American exports using their own, foreign
currencies. Some of that foreign currency-denominated sum that American
exporters earn is then traded by them to those who want to import goods from
abroad. But imports don't match exports--the difference is net exports, NX. And
so American exporters are left with an amount NX of foreign currency that they
have earned by selling abroad, and that they have been unable to exchange for
dollars with those wishing to import goods into the United States.
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So what can exporters then do with these extra holdings of foreign currency, an
amount NX, that they have earned? They can either trade them to some
government (if some government is carrying out official settlements transactions)
or they can trade them to someone in America who wants foreign currency
because he or she wants to buy property abroad--wants to make a foreign
investment and so engage in a capital-account transaction. But people in America
seeking to invest overseas and demanding foreign currency could also get the
foreign currency they need from foreigners seeking to invest in America: only to
the extent that there are more Americans investing abroad than there are
foreigners investing here will the capital account be a source of demand for the
excess foreign currency earned by net exports.
[Diagram: possible uses of foreign currency earned by exporters.]
No leakages from the balance-of-payments.
But must the balance-of-payments identity hold? Suppose an exporter doesn't
want to trade his foreign currency to someone seeking to make overseas
investments, but instead hides his foreign currency under his mattress. Then--by
the same logic as in the analysis of the household trying to hoard dollar bills in
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the uses-of-income section above--the exporter has made an overseas investment:
by hoarding the foreign country's currency he or she has made an interest-free
loan to the foreign government that issued the currency.
3-5-3: Exchange rates.
The exchange rate is the relative price of two different kinds of money.
The exchange rate is the rate at which the currencies used in two different
countries can be traded or exchanged for each other. When economists talk of the
exchange rate, they try to distinguish between the nominal exchange rate and the
real exchange rate--between the relative prices of two currencies and the relative
prices of a certain amount of purchasing power or productivity in the two
countries.
[Diagram: the U.S. nominal exchange rate over time]
Nominal and real exchange rates.
The nominal exchange rate is the number reported on the financial pages of
newspapers. The nominal exchange rate is the relative price of two different
kinds of money. If the exchange rate between the dollar and the euro is $1.20,
that means that it takes one dollar and twenty cents of U.S. currency--1.2 of the
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U.S. currency unit, the dollar--to buy a single euro, to buy a single unit of the EC
currency unit. Conversely, it then takes 0.83 and change euros to buy a single
unit of the U.S. currency, the dollar.
The real exchange rate is the nominal exchange rate divided by the respective
countries' price levels. The real exchange rate is best thought of as the relative
price of goods made in the two different countries--the terms of trade at which
we can exchange the goods made in one country for the goods made I the other,
or at which we can exchange purchasing power over the goods made in one
country for purchasing power over the goods made in the other.
[Diagram: U.S. nominal and real exchange rates]
Calculating the real exchange rate.
We calculate the real exchange rate by (a) taking the nominal exchange rate and
(b) multiplying it by the ratio of the price levels in the two countries:
3.5.3.1
  e
P
P*
where  is the real exchange rate, e is the nominal exchange rate, P is the price
level here in the United States, in the home country, and P* is the price level
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abroad.
Beware! Economists follow two inconsistent conventions in measuring exchange
rates, both real and nominal. Some textbooks define the nominal exchange rate as
the price (in terms of the home currency) of the foreign currency (and define the
real exchange rate as the price in terms of home goods of foreign goods). Under
such a definition when the dollar is appreciated--when the dollar is more valuable-the measured exchange rate is low because the price of foreign currency is low.
Other textbooks define the nominal exchange rate as the value (in terms of
foreign currency) of the home currency, the dollar--and define the real exchange
rate as the value of home goods in terms of foreign goods.
[Diagram: the value of the dollar/the price of foreign currency]
The second convention goes much more easily with the terms used in day-to-day
conversation to describe exchange rate movements. It is much more natural to
say that as the dollar appreciates (becomes more valuable) the exchange rate rises.
At any rate, I think that the second convention has less potential to cause
confusion.
Thus in this book the (nominal) exchange rate is always the value of the home
currency, the (real) exchange rate is always the value of home goods in terms of
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foreign goods. An appreciation or revaluation of the dollar is a rise in the
exchange rate, and a depreciation or devaluation of the dollar is a fall in the
exchange rate.
3-5-4: Relative purchasing power.
Purchasing power parity.
Is there any economic principle that governs what fluctuations exchange rates
undergo? Economists believe that exchange rates are loosely--very loosely--tied
to the anchors provided by so-called purchasing-power-parity: the belief that if I
take a sum of dollars it ought to buy roughly the same amount of goods in San
Francisco as it would buy if turned into Hong Kong dollars and spent in Hong
Kong. After all, if the same amount of money at current exchange rates bought
much more in Hong Kong then in San Francisco then it would be to my
advantage to move to Hong Kong to spend my money, and it would be to the
advantage of entrepreneurs in Hong Kong to export to San Francisco and
undercut the current market price here.
The principle of purchasing power parity thus declares that exchange rates
should stay close to the values that gives a dollar--exchanged into the local
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currency--the same purchasing power everywhere. And the principle of
purchasing power parity places some limits on exchange rate fluctuations: toolarge exchange rate fluctuations should cause goods (and people!) to move across
national boundaries to take advantage of profit and consumption opportunities.
Barriers to trade and migration.
But people are hard to move across national borders. People generally like to live
among those who speak their birth-tongue. And governments are in the business
of making large-scale permanent migrations of large groups of people illegal.
And while some goods--portable computers, chairs, textiles, light fixtures--are
very cheap and easy to ship across oceans and borders, there are many other
goods and especially services (fresh tuna or crab, haircuts, guided tours of the
Grand Tetons, or someone to vacuum your car) that are next to impossible to
trade.
Purchasing power parity properly understood.
Thus purchasing power parity, properly stated, declares not that the purchasing
power of a dollar--exchanged into the local currency--should be the same
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everywhere, but that the purchasing power of a dollar over goods that can be
easily and cheaply traded across borders should be roughly the same anywhere.
[Diagram: real exchange rates and the Balassa effect]
In relatively rich countries factory productivity is relatively high and the wages
of unskilled labor are relatively high, and so the types of manufactured goods
that are easily traded are very cheap in terms of labor or of the price level as a
whole. In relatively poor countries factory productivity is relatively low and the
wages of unskilled labor are relatively low, and so the types of manufactured
goods that are easily traded are expensive in terms of labor or of the price level
as a whole. Purchasing power parity works to make the prices of easily-traded
manufactured goods the same in different countries, but in one--rich--country
labor is expensive relative to manufactures, and in another--poor--country labor
is cheap relative to manufactures.
Poor countries tend to have adverse terms of trade.
Thus we would expect the overall price level and real exchange rate in a poor
country to be lower than in a rich country because purchasing power parity
works to equalize the price across borders of the goods in which the rich country
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has a comparative advantage--internationally-traded manufactures--but not the
prices across borders in which the poor country has a comparative advantage-labor-intensive services. We would expect a dollar to go farther in a poor country
than a rich one, and for the poor country to have relatively disadvantageous
terms of trade.
3-6: Measuring unemployment
3-6-1: Who's unemployed?
Estimating the unemployment rate.
Keeping unemployment low--keeping workers who want to work employed at
jobs they like--is perhaps the chief goal of modern economic policy, and is one of
the most important indicators of economic performance. Every month the Labor
Department's Bureau of Labor Statistics [BLS] sends interviewers to talk to 60,000
households in a nationwide statistical survey of the U.S. population, the Current
Population Survey. And every month the BLS produces an estimate of the
current unemployment rate: the fraction of people who (a) wanted a job, (b)
looked for a job, but (c) could not find an acceptable job in the preceding month.
[Diagram: unemployment and its components]
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134
The BLS classified the people it interviews into four catagories:

(1) Those who were employed--had a job, of some sort.

(2) Those who were out of the labor force and did not want a job right now.

(3) Those who did want a job right now, but who had not been looking because
they did not think they could find one they would take.

(4) Those who did want a job right now, had been looking, but had not found a
job that they would take.
The BLS defines the labor force as the sum of group (1) and group (4): those who
had jobs plus those who looked for jobs. The unemployment rate that the BLS
reports is equal to the number of the unemployed divided by the labor force:
group (4)/{group(1) + group(4)}.
[Diagram: unemployment over time]
Alternative estimates.
Perhaps the BLS's report is an underestimate of the real experience of
unemployment in the United States today. Someone in group (3)--who wants a
job, but who has given up looking because he or she feels that it is hopeless--may
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well feel as unemployed as someone in group (4). Perhaps the press should
include such discouraged workers among the unemployed and should report a
higher unemployment rate, calculated as: {group(3) + group(4)}/{group(3) +
group(4) + group(1)}. And some of those who are in group (1) have part-time
jobs but wish for full-time jobs. Perhaps those who are part-time for economic
reasons should be counted as unemployed--or as half-unemployed--as well.
Labor force participation.
An alternative way of looking at the CPS survey is to look at the labor force
participation rate--the percentage of the adult population in the labor force.
Fluctuations in labor force participation mirror the fluctuations in the
unemployment rate: When the unemployment rate is relatively high, the labor
force participation rate is likely to be relatively low.
[Diagram: labor force participation]
Underneath those fluctuations in the labor force participation rate caused by the
business cycle, however, is the secular increase in labor force participation
largely driven by the increased labor force participation of women. Fifty years
ago sex discrimination was rife--and legal. It was not uncommon for a woman to
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be fired when she got married, just because she got married.
Today women's labor force participation is still lower than that of men for most
ages and ethnic groups. But it is much higher than it was even a single
generation ago.
Unemployment and race, sex, and age.
There are striking and persistent variations in unemployment by demographic
group and by class. Teenagers (16-19) have higher unemployment rates than
adults, blacks have higher unemployment rates than whites, high-school
dropouts have higher unemployment rates than those who have post-graduate
degrees. For most of the post-WWII period (but not recently) women have had
higher unemployment rates than men.
[Diagram: Unemployment by demographic groups over time]
One of the most important reasons for high unemployment among the lesseducated, the not-white, and the young has been that these groups are much less
likely than the married white prime-age well-educated to hold stable long-term
jobs. The non-white, the less-educated, and the young lose their jobs much more
often.
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A large part of this is the legacy of discrimination. Past discrimination leads to
present poverty, present poverty leads to underinvestment in education. Low
education, current discrimination, and little work experience tends to make it
more likely that one holds a 'dead-end' job, or a temporary job. These jobs don't
last, and so the young, the less-educated, and the non-white have to spend a lot
of time lookijng for work.
Women traditionally had higher levels of unemployment because they had a
high propensity to leave the labor force upon the birth of a child. Thus a large
proportion of their job tenures were cut short. And they too had to spend a
greater fraction of their time in the labor force looking for jobs, hence had higher
unemployment rates. Since the early 1980s, however, female unemployment
rates in the United States have been lower than male unemployment rates.
3-6-2: How long are they unemployed for?
The duration of unemployment.
The question "how long is the typical person unemployed for" turns out to be a
subtle one that is remarkably hard to answer. It is remarkably hard to answer
because the question is fundamentally ambiguous. Most people who first become
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unemployed on any one particular day--say January 15, 2001--will stay
unemployed for only a short time: more than half will find a job within a month.
Yet if we look at all the people unemployed on January 15, 2001, we will find that
some three-quarters of them will have been unemployed for more than two
months before they find another job.
[diagram: unemployment by duration of spells]
An analogy.
The reason for this is the same as the reason that your college's deans can tell
your parents that most courses taught are small and yet that you always seem to
wind up in enormous courses. Suppose that of every ten courses taught at a
university, nine have twenty students each and the tenth has 320 students. Then
the size of the average course that a professor teaches is fifty:
3.7.2.1
9  20   1 320 
10
 50
But the size of the average course that a student takes is much larger--for 180
students take a course of size 20, and 320 students take a course of size 320. The
size of the average course that a student takes is 212:
Chapter 1
3.7.2.2
139
320  320   180  20 
500
 212
Similarly, the average person who becomes unemployed will be unemployed for
only a short period of time. But the average unemployed person (at any one
moment) has probably been unemployed for a while, and probably will remain
unemployed for a considerable length of time.
3-6-3: Kinds of un and underemployment: frictional, structural, and cyclical.
Types of unemployment.
The kind of unemployment that falls and rises with the business cycle is cyclical
unemployment. But there are other kinds as well.
Frictional unemployment arises inevitably as people change jobs and as firms
hire workers in the same way that inventories of goods are needed as goods are
moved from place to place and sold to consumers.
"Structural" unemployment arises whenever there is a class of workers whom
employers fear lack the skills necessary for their work to be worth the wages they
would have to be paid.
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Frictional unemployment.
Think of frictional unemployment as the economy's "inventory" of workers. But
it is an inventory that changes in size. Some public programs (such as job search
assistance) reduce frictional unemployment by making it easier to match up
firms with workers. Others public programs (such as unemployment insurance)
increase frictional unemployment by giving workers the financial cushion to
search longer for better jobs.
Some amount of frictional unemployment is inevitable, and it is not necessarily a
bad thing. If the extra time frictionally unemployed people spend searching for
better jobs does land them one in which they are more productive, it is time well
spent.
[Diagram: types of and reasons for unemployment]
Structural unemployment.
The structurally unemployed are those whom employers think add less value
than their wage cost, and who believe that no potential employer would offer a
wage high enough to make employment worthwhile. People fall into this
category because the industries in which they used to work shut down, or
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something went wrong in their transition from school to work and they never
became attached to the labor force.
Structural unemployment remains even when the business cycle reaches its peak.
Cyclically unemployed people will, if their unemployment lasts too long, become
"structurally" unemployed. This happened in the U.S. in the 1930s, and it has
happened in Europe in the 1990s.
3-6-4: Cyclical unemployment and GDP
Okun's law.
Macroeconomics courses focus on the business cycle: shifts in inflation, in
unemployment (around its natural rate), and in national product relative to the
productive potential of the economy--the economy's potential output.
The link between business cycles and long-run growth is made through Okun's
law: a strong relationship between the unemployment rate and the level of
national product.
Okun's law holds that, when unemployment is at its natural rate, national
product is equal to potential output. Whenever national product output grows
faster than potential output, unemployment falls. Whenever national product
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output grows slower than potential output, unemployment rises.
The strength of Okun's law.
The Okun's law link between national product and unemployment is very
strong. Fluctuations in unemployment relative to its natural rate and in national
product relative to potential output are so highly correlated as to leave no
significant distinction between the two.
Thus economists sometimes talk about business cycles as fluctuations in
unemployment relative to the natural rate, and sometimes as fluctuations in
national product relative to potential output. Because of the strength of Okun's
law, there is no distinction between the two.
[Diagram: Okun's law]
Why are fluctuations in output proportionally larger than fluctuations in
unemployment?
This is not a 1-to-1 relation but a 2.5-to-1 relation. In other words, take the
difference between the natural rate and the current rate of unemployment and
multiply by 2.5: The result is the percentage gap between national product and
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143
potential output. So, for example, when unemployment is two percentage points
above its natural rate, national product will be 5% below potential output.
Why does it take such a large change in output to reduce unemployment?
Instead of a 2.5:1 ratio of a change in output to change in unemployment, why
not 1:1?
One part of the answer is that the unemployment rate as officially measured does
not capture all the people unemployed as a result of a recession. In a recession,
the number of people at work falls. The number of people looking for work rises.
And the number of "discouraged workers"-people who are not looking for work
because they do not think they could find jobs, but would be at work if business
conditions were better-rises.
The unemployment rate does not include these discouraged workers.
Moreover, when business is good, firms' initial response is not to hire more
employees, but to ask existing employees to work more hours. So, instead of
unemployment quickly going down, average hours of work per week go up.
[Diagram: Sources of the 2.5-1 Okun's law coefficient]
Second, some industries find that employing more workers increases production
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by more than a proportional amount: Product design and set-up tasks need to be
done only once no matter how much is produced. So they do not need twice as
many workers to produce twice as much output.
Why people fear recessions so much.
In an average recession, unemployment rises by 2%. Okun's law predicts that, in
such a case, national product relative to potential output falls by about 5%. That's
about three years' worth of economic growth. Yet people fear a recession much
more than they value an extra three years' of economic growth.
Why? Because recessions do not distribute their impact equally. Workers who
keep their jobs are only lightly affected, while those who lose their jobs suffer a
near-total loss of income. People fear a 2% chance of losing half their income
much more than they fear a certain loss of 1%. Thus it is much worse for 2% of
the people each to lose half of their income than for everyone to lose 1%.
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146
Chapter 4: The Theory of Economic Growth
J. Bradford DeLong
--Draft 0.9--
1999-02-02: 6,605 words
4-1: The Importance of Long-Run Growth
4-1-1: Long-run growth and macroeconomics.
The study of long-run growth has become an increasingly-large part of
macroeconomics in the past two decades.
4-1-2: Sources of long-run growth.
Macroeconomists tend to break the study of long-run growth into two parts. The
first part is the determination of an economy's steady-state capital-output ratio
(and the speed with which it will converge to that steady-state capital-output
ratio). The second part is the determination of the rate of invention and
innovation. An economy with a higher capital-output ratio will be a richer
economy (if it has access to the same inventions and innovations). But an
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147
economy with higher rates of invention and innovation--faster total factor
productivity growth--tend to become richer faster.
One way to increase real GDP per worker is to increase the capital stock per
worker. The capital stock per worker can be increased in many ways--more
investment, slower depreciation, or slower population growth. As the capital
stock per worker rises, the value of the machines and workspace available to the
average worker rises. With more assistance from capital, the average worker is
more productive.
4-1-3: Diminishing returns.
But boosting productivity by raising capital per worker is subject to diminishing
returns: each successive increase in capital per worker generates less of an
increase in production than did the one before. Eventually the boost to total
productivity given by further increases in the capital stock does not even amount
to enough to make up for the wear-and-tear on the extra capital employed. The
bulk of increases in productivity and material standards of living over the course
of decades or generations has to come from a different source than simply
"deepening" the amount of capital that the economy possesses.
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4-1-4: The key importance of technology.
This additional, extra source of increases in productivity and material standards
of living is technology.
Improvements in technology--and economists use "technology" in the broadest
possible sense to include improvements in the so-called technologies of
organization, government, and education--are the greatest amplifiers of
productivity. Yet economists have relatively little to say about what governs
technological progress. Why did we see better technology raise living standards
by 2 percent annually a generation ago, but by less than 1 percent annually
today? Why was the rate of technological progress only 0.25 percent per year in
the early 1800s?
Economists point to expanding literacy, better communications, the
institutionalization of research and development as causes of faster technological
progress now than in the distant past. But they have too little to say about the
causes of recent changes in the rate of productivity growth.
Thus discussions of economic growth by economists often end on an
unsatisfying note. Economists have a lot to say about the causes and effects of
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capital deepening, the sources of large differences in productivity levels and
material standards of living between countries, and the relationship between
economic policies and relative rates of economic growth. But they nevertheless
largely duck some of the big questions.
4-1: The Production Function
4-1-1: The production function.
Writing down an equation.
Economists summarize the relationship between the level of potential output (real
GDP) that the economy can produce in any year and the factor inputs--capital,
labor, the level of technology broadly defined--available in that year using a
mathematical tool called the production function:
4.1.1.1
Y  F(K,E  L)
Where:
F() -- a placeholder that stands for the idea that there is a production function -a rule that relates how large potential output is to how much of the factor inputs
are available--itself.
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150
E -- the efficiency of labor, taken as an indicator of the level of technology
broadly defined (not just engineering techniques and scientific knowledge, but a
whole range of other factors like management practices and social conventions
that also affect the aggregate productivity of the economy).
Y -- the level of output (real GDP).
L -- the economy's labor supply (the number of workers).
K -- the economy's capital stock (machines, bridges, buildings, and so on).
Thus:
Y/L -- output per worker
K/L -- the economy's capital-labor ratio: how much capital the average
worker has at his or her disposal to amplify his or her potential productivity.
The production function is an abstraction.
By even writing down such an aggregate production function we have already
made a number of breathtakingly-large leaps of abstraction. We have assumed
that it is useful to talk about a single measure of total output--that resources
could be switched from one sector to another without losing much of their
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productive value or causing big changes in relative prices that create insuperable
index-number problems. We have assumed that it doesn't matter (or doesn't
matter much within appropriate limits) what kinds of investments have been
made in the past. We have assumed that it useful to talk about a single measure
of the overall level of technology E, and that this level of technology can be
thought of as directly amplifying the productivity of the average worker, the
average member of the economy's labor force L.
All of these are big assumptions. (Indeed, fierce intellectual struggles were
waged during the 1950s and 1960s over whether writing down such a function
was useful at all, or just a sterile waste of time; at one point Robert Solow--who
won his Nobel Prize primarily for developing much of the theory of economic
growth outlined in this chapter--declared that he was on "both sides.")
Further simplifications.
Moreover, we want to make further assumptions. Calculations are made much,
much simpler (and little flexibility is lost) if we write this production function-this relationship between this year's level of potential output per worker and the
factors of production available to the economy--in one particular form:
Chapter 1
4.1.1.2
152

1
Y  K (E  L)
The economy's total output is proportional to the economy's stock of capital K
raised to the power , times the product of the size of the labor force L and the
efficiency of labor E, that product raised to the power 1-.
We hope that these abstractions and the simplifications involved in writing
down an aggregate production function and then choosing this one particular
algebraic form will not, later on, significantly mislead us in some way.
Advantages of this production function.
Three features of the particular production function (4.1.1.2) make using it
especially easy.

First, this production function exhibits constant returns to scale: double the
amount of capital K in the economy, and double either the efficiency of labor
E or the size of the labor force L (or maneuver both in any other way that
doubles their product E x L), and you have doubled total output Y. Such
constant-returns-to-scale mean that we can analyze the economy in perworker terms, so that there is a sense in which the absolute size of the
economy doesn't matter for most of the analysis.
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
153
Second, this production function is simple in the sense that how much output
is produced for each possible level of the economy's labor force and capital
stock depends on only two things: the parameter  and the level of the
technology parameter, the measure of the efficiency of labor E.

Third, this production is a simple power function--a variable or two raised to
a power. Thus we can use a large amount of the tools of algebra developed
three and four hundred years ago to help us analyze the properties of this
production function.
Useful algebraic tools.
Of these properties, four will be most important:

The general property that if y=k, then {the percentage change in y} will
(for small percentage changes) be equal to  x {the percentage change in
k}.

The general property that if y = z, then y = z.

The general property that if z = k/y, if k is growing at r percent per year,
and if y is growing at s percent per year, then z will be growing at r - s
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154
percent per year.

The general property that if x is small, then (1+x) is approximately equal
to 1 + x.
These algebraic rules prove very useful to us, but they are available for use
only if the production function takes a simple form like (4.1.1.2).
We analyze the production function (4.1.1.2); but we expect that the conclusions
we reach for this production function will be more general, will hold for other
production functions--including the economy's real production function, to the
extent that such a thing (approximately) exists--as well.
If we divide through by the number of workers in the economy so that our lefthand side is output per worker: the productivity of the economy.

4.1.1.3
1
Y K   E  L 

L  L   L 

 K 

E1
 L 
Advantages of simplicity.
This functional form is simple enough to keep analysis from becoming too
convoluted too quickly. Potential output per worker (Y/L) depends on only
Chapter 1
155
three things: the level of capital per worker (K/L), the level of technology (E),
and a parameter that is somewhere between zero and one labeled , the
exponent, the power to which K/L is raised in this algebraic expression for the
production function. Yet this functional form is also sufficiently flexible to allow
for a wide range of different cases. And it provides for a natural classification of
increases in output per worker. For increases in total product per worker have
two sources.
The first is an increased capital stock of machines, buildings, and infrastructure
produced by investment. The second is an improvement in the level of
technology: not more machines but better machines, and better organizations.
Think of increases in production per worker from an increased capital stock per
worker as shifts along a production function that tells you how much the average
worker can produce with the existing capital stock. Increases from better
technology are then upward shifts in the production function.
4-1-2: Potential output-per-worker as a function of the capital stock.
Capital accumulation and higher output.
Potential output per worker (Y/L) depends on the capital stock per worker
Chapter 1
156
(K/L). The higher the capital stock per worker--the more in the way of machines,
buildings, infrastructure, and so forth available to amplify worker productivity-the higher is potential output per worker. Whenever net investment is more than
enough to provide new entrants into the labor force with the capital they need,
the capital stock per worker rises: The value of the machines and work space
available to the average worker rises. With more assistance, the average worker
is more productive.
Diminishing returns.
However, because the  in the production function is smaller than 1, boosting
productivity by raising capital per worker is subject to diminishing returns: Each
successive increase in capital generates less of an increase in production than did
the one before. How fast potential output per worker increases with capital per
worker depends on the value of the parameter  in the production function: a
relatively low value of  (a value near zero) means that diminishing returns to
capital set in quickly, and that the point at which further increases in capital per
worker do little to raise potential output per worker arrives quickly; a relatively
high value of  (a value near one) means that diminishing returns to capital set in
only slowly, and that there is a large range within which increases in capital per
Chapter 1
157
worker generate large increases in potential output per worker.
Flexibility through varying .
Do you want to analyze a situation in which boosting capital per worker raises
output per worker at almost the same rate indefinitely? You can do that with the
form of the production function 4.2.1.2 and a value of  near one. Do you want to
analyze a situation in which boosting capital per worker beyond an initial,
minimal level does little to raise potential output per worker? You can do that
with the form of the production function 4.2.1.2 and a value of  near zero. Do
you want to analyze an intermediate case? You can do that too with an
intermediate value of the parameter  that tunes how quickly diminishing
returns to capital set in.
Chapter 1
158
Figure Legend: By changing the parameter --the exponent of (K/L) in the
algebraic form of the production function--you change the curvature of the
production function, and thus the point at which diminishing returns to further
increases in capital per worker set in.
4-1-3: Production-per-worker as a function of the level of technology.
Higher output through better technology.
Potential output per worker (Y/L) depends also on the level of technology or
Chapter 1
159
efficiency of labor E. Better technology means a higher level of efficiency of labor
parameter E, and thus a higher level of output per worker for any given level of
capital per worker.

4.1.1.3
Y K 

E 1


L
L
In the very long run, the fact that we have higher productivity levels and living
standards than did our distant ancestors, and that we expect such economic
progress to continue, is the result of invention, technological progress, and
improvements in total factor productivity. Without such improvements in total
factor productivity economic progress would grind to a halt: diminishing returns
would diminish the benefits to investments that further raised the capital-labor
ratio, and soon it would no longer be worthwhile to continue adding to the
capital stock per worker.
Chapter 1
160
Pot ential Outpu t per Worker as a Funct ion of
Capit al per Worker
E=3 x E0
$80 ,000
$60 ,000
E=2 x E0
$40 ,000
E=E0
$20 ,000
$0
$0
$50 ,000
$100 ,000
$150 ,000
$200 , 000
Capit al pe r Wor ker
Figure Legend: By changing the parameter E--the level of technology or the
efficiency of labor in the algebraic form of the production function--you raise or
lower how much potential output per worker is generated by each level of
capital per worker.
Chapter 1
161
4-1-4: Production per worker as a function of the capital-output ratio.
Finding a more convenient form for the production function.
The production function as we have written it so far expresses output per worker
as a function of the capital stock per worker. But this is not the most convenient
way of expressing it for our purposes: since we will be focusing on the capitaloutput ratio as our key variable in this chapter, we would prefer an expression
telling us how output per worker depended on the capital-output ratio.
We can translate our production function into such an expression by noticing
that the capital-labor ratio, K/L, is just equal to the capital-output ratio times
output per worker:
4.1.4.1
K K Y
 
L Y L
Substituting (4.1.4.1) into (4.1.1.2):

4.1.4.2

Y K Y 
1
K 



E 
Y 
L  Y L 

Y 
E1
L 
Dividing through to move all the output per worker terms to the left hand side:
1
4.1.4.3
Y 
 L

 K 

E1
 Y 
And then raising both sides to the 1/(1-) power to solve for the level of output
Chapter 1
162
per worker:

4.1.4.4
Y K 1

E
L  Y 
gives us what we wanted: output per worker as a function of the capital-output
ratio (and the level of technology A, and the parameter a governing the
curvature of the production function).
We can easily transform our diagram showing output per worker as a function of
capital per worker into one showing output per worker as a function of the
capital-output ratio by noticing that fixed values of the capital-output ratio are
straight lines radiating from the bottom-left corner of the figure.
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163
To figure out what level of output per worker (for a given, fixed level of the
efficiency of labor E) correspond to a capital-output ratio of one, look for the
point where the curve showing output per worker as a function of the capital
stock per worker crosses the ray corresponding to a capital-output ratio of one.
Chapter 1
164
Chapter 1
165
4-2: The steady-state capital-output ratio
4-2-1: The steady-state capital-output ratio.
What kind of equilibrium do we look for?
No matter what particular situation is being analyzed or issue is being explored,
the first instinct of an economist is to look for an equilibrium: some economic
quantity or group of quantities for which there are stable values. These
equilibrium values need to be stable in two senses. First, if the economy is in a
state in which these quantities are not at their equilibrium values, the economy
will tend to change and these variables will approach their equilibrium values.
Second, that if the economy is in a state in which these quantities are at their
equilibrium values, then the economy will tend to remain in that state.
But how are we to look for an equilibrium in the case examined in this chapter,
the case of an economy engaged in long-run growth? After all, it seems that in a
growing economy with improving technology and positive investment there is
no stable equilibrium--there is no stable equilibrium level for technology, or for
output per worker, or for the capital stock per worker. All these variables tend to
grow over time.
M.I.T. economics professor Robert Solow won his Nobel Prize in large part for
determining that there is a straightforward way to think about what an economic
Chapter 1
166
equilibrium is in a growing economy. The key is that even though there are no
stable values for the economy's stock of capital, or its level of output, or its level
of technology, there are stable relationships between these variables.
Focus on the steady-state capital-output ratio.
For our purposes the most convenient economic variable to focus on is the
capital-output ratio: the level of the capital stock per worker divided by potential
output per worker. For in a growing economy there will be a stable equilibrium
value for this capital-output ratio: And once we have determined this
equilibrium value--what economists call the call the steady-state capital-output
ratio--it is then straightforward to calculate the path of economic growth that the
economy will follow, a path that economists call the steady-state growth path.
Determining the steady-state capital-output ratio.
What is the steady-state capital-output ratio?
Consider an economy of which four things are true: First, potential output per
worker Y/L--Y for potential output, / for "per", and L for the number of workers
in the economy--is growing at some rate g: each year potential output per worker
Chapter 1
167
is g percent higher than it was last year. Second, the number of workers in the
economy is growing at rate n: each year the number of workers in the economy is
n percent higher than it was last year. Third, capital in the economy depreciates
at rate  (a Greek letter: lower-case delta): each year  percent of the economy's
capital stock wears out, breaks, becomes obsolete, must be replaced. Fourth, each
year some s percent of total output Y is saved by the economy as a whole, and
used to purchase investment goods to augment the economy's capital stock.
Since output per worker is growing at g percent per year, and the number of
workers is growing at n percent per year, then the economy's total output is
growing at n+g percent per year. Thus if the capital-output ratio in the economy
is going to be unchanging--if the economy is going to be in its long-run growth
equilibrium with the capital-output ratio at its steady state value and with output
per worker growing along its long-run steady-state growth path--then the capital
stock K must be growing at n+g percent per year too. This year's capital stock
must be bigger than last year's by n+g percent of last year's capital stock:
4.2.1.1
Knext
steady-state)
year
 Kthis
year
 (n  g)K this year (if the capital-output ratio is at its
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168
Is the capital stock growing at the appropriate rate?
How can we tell whether the capital stock is in fact growing at the rate needed
for the capital-output ratio to be stable? Remember that we also know that each
year an amount equal to s x Y, to the savings rate s times this year's output Y is
being added to the capital stock through new gross investment. And we also
know a fraction  of the current capital stock is being lost due to depreciation-wearing out, falling apart, breaking down, or just becoming too obsolete to be
worth using any more:
4.2.1.2
Knext
year
 Kthis
year
 sYthis
year
 Kthis
year
(by definition: always)
If the capital-output ratio is at its steady-state value, the amount that is being
added to the capital stock by net investment--that is, gross investment minus
depreciation--must be equal to the amount that is needed in order to match the
proportional growth rate of capital to the proportional growth rate of output.
Thus:
4.2.1.3
(n  g)Kthis
year
 sYthis
year
 Kthis
year
Moving all of the terms with the capital stock in them to the left-hand side:
4.2.1.4
(n  g   )Kthis
year
 sYthis
year
Chapter 1
169
Dividing through by this year's level of output:
4.2.1.5
K
(n  g   ) 
Y this
s
year
The answer: the steady-state capital output ratio?
Then dividing through by (n+g+) in order to get the capital-output ratio all by
itself on the left-hand side generates:
4.2.1.6
K 
 Y this

year
s
(if the capital-output ratio is at its steady-state
n  g 
value)
This is the equation to remember.
This is the payoff from the preceding short march through simple algebra.
The economy's steady-state capital-output ratio is equal to (a) the share s of
output saved and invested in new capital, divided by (b) the economy's
investment requirements--divided by the sum of the labor force growth rate n, the
long-growth rate of potential growth in output per worker g, and the rate of
depreciation of the capital stock .
Chapter 1
170
4-2-2: The capital-output ratio grows or shrinks if...
If the capital-output ratio is less than its steady-state value.
What if the economy is not at its steady-state capital output ratio? What if this
year's value of K/Y is less than s/(n+g+)? Then the proportional rate of growth
of the capital stock will be greater than n+g. To see this, notice that we can divide
both sides of (4.2.1.2) by this year's capital stock to determine the proportional
rate of growth of the economy's capital stock:
4.2.2.1
Knext
year
 Kthis
Kthis
year
year
s
Y 
K this

year
If K/Y is smaller than its steady-state value, Y/K will be larger than its steady
state value--and so the capital stock will be growing faster than the long-run
growth rate of output n+g. Thus the capital-output ratio will tend to rise--unless
we are in a very unusual situation (an unusual situation that we will rule out,
because it could happen given our production function only if were to be
greater than one) in which the fact that the capital stock is growing faster than
n+g boosts the economy's productive potential so much that output grows not
only faster than its long-run steady-state proportional growth rate n+g, but faster
than the capital stock.
Chapter 1
171
If the capital-output ratio is greater than its steady-state value.
Conversely, if K/Y is larger than its steady-state value, Y/K will be smaller than
its steady state value. The higher the capital-output ratio, the more gross
investment that must go simply to replace depreciated capital-machines and
buildings that wear out or become obsolete. And the smaller the share of
investment that is available to boost the capital stock. The capital stock will be
growing more slowly than the long-run growth rate of output n+g (and the
capital stock may even be shrinking). Thus the capital-output ratio will tend to
fall.
If the capital-output ratio is equal to its steady-state value.
And if K/Y is equal to its steady-state value, then--unless one of its determinants
s, n, g, or  changes--then K/Y will stay at its steady-state value.
The steady-state value of the capital-output ratio given in (4.2.1.6) thus fulfills all
the conditions economists want for an equilibrium. If the capital-output ratio is
at its steady-state value, it stays there. If it is less than its steady-state value, it
grows. If it is greater than its steady-state value, it shrinks.
Chapter 1
172
One way to calculate the steady-state capital-output ratio is to plot gross
investment and investment requirements as functions of the capital-output ratio.
When gross investment (the upper plot line) is greater than the investment
required to keep the capital-output ratio stable (the lower plot line), the capitaloutput ratio increases. When gross investment is less than investment
requirements, the capital-output ratio decreases. Where the curves cross, the
capital-output ratio is stable: National product and capital stock are growing at
Chapter 1
173
the same rate. This is the steady-state capital-output ratio.
4-2-3: The steady-state growth path.
Determining output per worker on the steady-state growth path.
If the economy has reached its steady-state growth path, we can substitute our
expression for the steady-state value of the capital-output ratio into the right
hand side of (4.1.4.4) to get:

4.2.2.1
Y 
Lthis
year,
 s
1
 
Ethis
n  g   
steady state
year
This is a very useful expression.
It tells us how to find the steady-state growth path of output per worker of the
economy--the path that it would be on if its capital-output ratio were at its
equilibrium value.
Using the steady-state growth path as a tool to analyze an economy.
(4.2.2.1) makes analyzing the growth of an economy relatively easily. First
identify the economy's savings rate, labor force growth rate, depreciation rate,
Chapter 1
174
and long-run rate of growth of potential output. Next calculate the steady-state
capital-output ratio--easy to find. And then you can calculate the steady-state
growth path.
From the steady-state growth path, you can forecast the future of the economy,
for the steady-state growth path is the path that the economy will be on in
equilibrium. If the economy is on its steady-state growth path today, it will stay
on its steady-state growth path in the future (as long as n, g, , s, and  do not
shift). If the economy is not on its steady-state growth path today, it will head for
its steady-state growth path in the future (as long as n, g, , s, and  do not shift).
Thus forecasting becomes easy: we know that if the capital-output ratio is not at
its equilibrium value, it is heading for its equilibrium value and will approach it
soon.
4-2-4: How fast is the efficiency of labor E growing?
Two loose ends remain. The first has to do with E, the efficiency of labor. We said
that output per worker Y/L had the potential to grow at a proportional rate g in
steady state. But we did not say how fast our measure of technology in the
broadest sense, the variable E, the efficiency of labor, had to be growing in order
Chapter 1
175
for that to be the case.
We can easily determine how fast E must be growing if we remember the form of
the production function:

4.2.4.1
Y K 1

E
L  Y 
and recall that the capital-output ratio K/Y is constant in steady-state. Then
output per worker Y/L is proportional to the efficiency of labor E. So if E is
growing at g percent per year, Y/L will be growing at g percent per year as well.
4-2-5: How fast does the economy head for its steady-state growth path?
The second loose end has to do with how fast the economy approaches its
steady-state growth path. Suppose that the capital-output ratio K/Y is not at its
steady state? How fast does it approach its steady state?
Calculating the out-of-steady-state behavior of the capital-output ratio.
We know that the proportional growth rate of the quotient K/Y is going to be
equal to the proportional growth rate of the capital stock K minus the
Chapter 1
176
proportional growth rate of output Y. So let us calculate both.
The proportional growth rate of the capital stock K is equal to net investment-gross investment minus depreciation--divided by the current level of the capital
stock:
4.2.5.1
growth rateof K 
K next year  Kthis
Kthis
year
year

sYthis
year
 Kthis
Kthis
year
year
 Y
 s 
K this

year
Since we know that:
4.2.5.2

1
Y  K (E  L)
We know that the growth rate of output Y is equal to  times the growth rate of
the capital stock K plus (1-) times the growth rate of the product (E x L), the
product of the efficiency of the labor force E and the size of the labor force L:
4.2.5.3
growth rateof Y   (growth rate of K)  (1   )(growth rate of E  L)
Solving the algebra.
But we know what the growth rate of the capital stock K is--it is (4.2.5.1)--and
with E growing at rate g and L growing at rate n, their product is growing at rate
n+g.
Chapter 1
177
Thus:
4.2.5.4
  Y
growth rate of Y   s 
  K this
year

   (1   )(n  g)

Subtracting (4.2.5.4) from (4.2.5.1):
4.2.5.5
 Y
growth rate of (K / Y)  (1  )s 
 K this

   (1 )(n  g)
year

 Y
growth rate of (K / Y)  (1  )s 
 K this

 (n  g   )
year

or
4.2.5.6
You can check that (4.2.5.6) is correct by asking what happens when K/Y is at its
equilibrium value of s/(n+g+). Then the terms inside the braces cancel, and the
growth rate of the capital-output ratio is zero--as it must be if it is at equilibrium.
Interpreting the answer.
How should we interpret equation (4.2.5.6)? A straightforward way of
interpreting it is that in a year an economy whose capital-output ratio is not at its
steady-state value will reduce the gap between its current and steady-state
Chapter 1
178
values by a fraction of approximately [(1-)(n+g+)]. A high capital share ()
means that convergence is slower; with diminishing returns, additional
investments yield smaller increases in production and make for more rapid
convergence. A low capital share means sharply diminishing returns on
investment, and thus rapid convergence.
A high growth rate (n+g) also means that convergence is faster; rapid growth
signifies that past output was small, and so can have little importance for the
present. A high depreciation rate () means that convergence is faster as well.
In an economy like that of the U.S., with a population-plus-productivity-growth
rate (n+g) of about 3% per year, a depreciation rate () of about 3% per year, and
a capital share () of about one-third, (1-)(n+g+) is 4%.
If an economy closes four percent of the gap between its current and its steadystate capital-output ratio in a year, then in a 30-year generation it will close about
70% of the gap--slow closure from the perspective of a year or a business cycle or
a presidential election cycle, but rapid closure from the perspective of
generations or of history. No matter where its level of national product per
worker starts, the level tends to converge to its steady-state growth path within
several decades.
Chapter 1
179
Consider the example of West Germany after World War II. The end of World
War II left Germany's cities and its economy in ruins. The allies had waged a
truly total war against the Nazi tyranny. Wartime destruction had wrecked the
German economy and pushed total output per worker far below its steady-state
growth path. But within less than four decades, West Germany had converged
again to its pre-World War II growth path. West Germany, at least, was once
again among the richest, most productive economies on earth.
4-3: Determinants of the steady-state capital-output ratio
4-3-1: Labor force growth.
The faster the growth rate of the labor force, the lower will be the economy's
steady-state capital-output ratio. Why? Because each new worker who joins the
labor force must be equipped with enough capital to be productive, and to on
average match the productivity of his or her peers. The faster the rate of growth
of the labor force, the larger the share of current investment that must go to
equip new members of the labor force with the capital they need to be
productive. Thus the lower will be the amount of investment that can be devoted
to building up the average ratio of capital to output.
Chapter 1
180
4-3-2: Depreciation.
The higher the depreciation rate, the lower will be the economy's steady-state
capital-output ratio. Why? Because a higher depreciation rate means that the
existing capital stock wears out and must be replaced more quickly. The higher
the depreciation rate, the larger the share of current investment that must go
replace the capital that has become worn-out or obsolete. Thus the lower will be
the amount of investment that can be devoted to building up the average ratio of
capital to output.
4-3-3: The rate of technological progress.
The faster the growth rate of productivity, the lower will be the economy's
steady-state capital-output ratio. This is correct but counterintuitive. The faster is
productivity growth, the higher is output now. But the capital stock depends on
what investment was in the past. The faster is productivity growth, the smaller is
past investment relative to current production, and the lower is the average ratio
of capital to output.
Chapter 1
181
4-3-4: The savings rate.
The higher the share of national product devoted to gross savings and
investment investment, the higher will be the economy's steady-state capitaloutput ratio. Why? Because more investment increases the amount of new capital
that can be devoted to building up the average ratio of capital to output. Double
the share of national product spent on gross investment, and you will find that
you have doubled the economy's capital intensity-doubled its average ratio of
capital to output.
4-4: The golden rule
4-4-1: Can the steady-state growth path be "too high"?: the golden rule.
Focus on consumption per worker.
Suppose that we have an economy on its steady-state growth path, and we are
interested not in the level of output per worker but in the level of consumption
spending per worker--where the share of total output Y devoted to consumption
is simply one minus the share devoted to saving, so that consumption spending
per worker is (1-s)Y.
Using the steady-state growth path version of our production function:
Chapter 1
182

4.4.1.1
4.4.1.2
consumption per wor ker (C / L)this
C 
 L this
Y
 (1  s) 
L this
year
year
 s
1
 (1 s)
Ethis
n  g   
  


1 

s

 (1 s)
n  g   
year, steady state
Ethis
year
Consumption per worker in steady-state as a function of the savings rate.
Now for the moment fix the growth rate of the labor force n, the efficiency of
labor g, the depreciation rate , the parameter , and consider what the level of
consumption per worker in the economy would be if one changed the steadystate savings rate. Examine low values of s near zero, high values of s near one,
and intermediate values, looking in each case at the level of consumption per
worker C/L relative to the efficiency of labor E along the economy's steady-state
growth path.
When s is very low, near zero, consumption per worker will be a very low--nearzero--fraction of E as well. The very low numerator of the fraction on the righthand side of (4.4.1.2) ensures that. When s is high, near one, consumption per
worker will also be a very low--near zero--fraction of E. The very low value of
the (1-s) in the initial parenthesis in (4.4.1.2) ensures that.
year
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Maximizing steady-state consumption per worker.
In between there is a value of the savings rate s at which consumption per
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worker along the steady-state growth path (measured relative to the current level
of the technology parameter E, the efficiency of labor) reaches a maximum. This
savings rate that sustains the maximum level (relative to E, the efficiency of
labor) of steady-state consumption per worker is in a sense the "best" savings
rate. Economists call it the golden rule savings rate, and they call the associated
steady-state growth path the golden rule steady-state growth path.
An economy can have "too much" savings.
So yes, there is a sense in which an economy can have "too much" savings: if an
economy's savings rate is higher than the golden rule savings rate, economists
call the economy dynamically inefficient: it would be possible to raise everyone's
level of consumption and thus of material well being if only the economy would
save and invest less, would save an invest a smaller proportion of output.
4-4-2: The marginal product of capital.
Building tools: determining the marginal product of capital.
In order to say anything else about the golden rule level of saving, we must first
determine what the marginal product of capital in the economy is--what the
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boost to output provided by an extra unit of capital happens to be. To do this,
begin with the production function (with all variables subscripted "o", for "old
value):
4.4.2.1

1
Yo  Ko (Eo  Lo )
and consider the effect on output of boosting the economy's capital stock by one
(with Y now subscripted "+1", for the effect of adding one unit of capital):
4.4.2.2

1 
Y1  (Ko 1) (Eo  Lo )
We can rewrite the term inside the first parenthesis as:

4.4.2.3

1 
 K o  (Eo  Lo )1 
Y1  1
 Ko 
Notice that the last two parentheses are simply our initial value of output Yo:

4.4.2.4

1 
 Yo
Y1  1
 Ko 
And use the algebraic principle that (1+x) is, if  is small, approximately equal
to 1+x:
4.4.2.5
  
Y1  Yo 1  
 Ko 
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Thus the marginal product of capital--the amount by which output is increased
by adding a unit to the economy's capital stock--is:
4.4.2.6
m arg inal product of capital  Y1  Yo 
 Yo
Ko
4-4-3: Determining the golden rule savings rate.
The effect of raising the capital stock by one unit.
With the marginal product of capital in hand, we can start to think about what
the golden rule savings rate s* is. Suppose that we increase the savings rate by
just enough to raise the capital stock by a single unit. If the economy is on its
steady-state growth path increase in the capital stock will increase output by an
amount equal to the marginal product of capital on the steady-state growth path:
4.4.3.1
n  g   
 Y
Y    


 s

K 
Does this increase in capital generate enough extra output?
Will this increase in output generated by the small increase in the capital stock
allow the economy to increase consumption per worker?
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The answer is maybe. Thereafter the economy must save an extra amount n+g in
order to keep the capital-output ratio at its new, slightly higher level. Thereafter
the economy must save an extra amount  to offset the extra depreciation on the
new, slightly higher capital-output ratio. There is enough extra output left over
to boost consumption if only if the marginal product of capital (on the steady-state
growth path) exceeds the investment requirements n+g+ generated by having a
single extra unit of capital.
Thus an increase in the capital intensity of the economy--an increase in the
savings rate--raises steady-state consumption per worker if and only if:
4.4.3.2
marg inal product of capital 
Y
K

(n  g   )
s
 (n  g   )  investment requirements
An increase in the capital intensity of the economy--an increase in the savings
rate--lowers steady-state consumption per worker if and only if:
4.4.3.3
marg inal product of capital 
The golden rule value.
And if:
Y
K

(n  g   )
s
 (n  g   )  investment requirements
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4.4.3.3
188
marg inal product of capital 
 (n  g   )
s
 (n  g   )  investment requirements
a small change in the savings rate neither raises nor lowers steady-state
consumption per worker. Then we are at the peak of the figure.
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189
We are at the golden-rule savings rate, which we can easily see to be:
4.4.3.4
s 
Is the golden rule a guide for economic policy?
Suppose that the savings rate is not currently at the golden rule value. Would it
be good economic policy to take steps to try to move the savings rate to its
golden rule value?
If the savings rate is higher than the golden rule value, then the answer is yes.
You could make everyone better off--now and in the future--by saving less and
reducing the economy's capital-output ratio.
Intertemporal and intergenerational tradeoffs.
If the savings rate is less than the golden rule value, then it is not so clear. Raising
the savings rate will in the long run increase consumption per worker, because it
will shift the level of consumption per worker (relative to the efficiency of labor)
associated with the economy's steady-state growth path upwards as it shifts the
steady-state growth path upwards. But in the short run it will decrease
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consumption per worker--because those alive today will have to cut back on
their consumption to generate the increase in the savings rate.
Moreover, those alive today are poorer--have lower consumption per worker-than is likely for future generations. Why should a poorer group of people
reduce their consumption to increase the consumption of a richer group?
But that's what we do--both individually and collectively--reduce our level of
consumption in order for our descendants to have higher levels of consumption
per worker. Few of us (few of us with children, at any rate) are comfortable with
the idea that our children won't live any better than we will.
However, it is clear that the case for policies to raise the savings rate (and lower
the consumption of the relatively poor current generation) gets weaker the closer
s comes to . When s is very close to , it is hard to imagine that it could improve
social welfare by cutting present-day consumption by a (significant) amount in
order to raise the consumption of future generations by (infinitesimal)
magnitudes.
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