Download Macro1 Manual

Macro1 Manual
Purpose of the Module
Two of the major problems faced by national economies are inflation and unemployment.
Both of these have significant social costs, and it is generally considered the job of the
national government to keep those costs down. As a result, governments are constantly
trying to avoid recession (with rising unemployment), or get out of recession, or avoid
inflation, or reduce inflation. In their efforts to use the major tools at their command they
face the problem of deciding how much to do, since doing too little will leave them short
of their goals, and doing too much may cause new problems to arise.
In this module you face the problems that national governments face, but in a simpler
form. By acting as the whole government (President, Congress, Federal Reserve Board)
you can begin to see how each of the tools they have affect the inflation and
unemployment rates.
Nature of the Problem
In the real world, governments face more difficulties than are included in this module, but
the module does allow you to experience important aspects of their problems. One is the
difficulty in deciding which of the policy tools discussed under “Tools” below should be
used. For example, when a government wants to reduce unemployment each tool has
“side effects.” In other words, in addition to effects the government wants, there are other
things, such as a rise in the inflation rate, that it does not want, and some things it may, or
may not, consider desirable. The latter could involve changes in the relative amounts of
government, consumer, and investment goods produced, changes in the “burden of
taxation” and more. Since different tools have different side effects, consideration of
those effects should influence the choice of tools.
Governments also need to consider how much of a given tool to use. If the government
wants to cut unemployment, and wants to do so by increasing government spending, it
needs to determine how much of an increase in government spending will be needed in
order to get the desired change in unemployment. This aspect of the government’s
problem is made more difficult by the fact that whatever it does will cause gradual
changes in all aspects of the economy, and will take quite a while to have its full, final
effect. Consequently, it can’t just do a little, see what happens, and then maybe do a little
more. If it does try that, the problem will probably become the concern of a new set of
leaders -- people will not wait for many years to have a serious problem addressed.
Part of the problem faced by governments is that their policies can cause inflation.
Inflation is the rate at which prices are rising (e.g., the percentage change in the GDP
deflator). On the other hand, their policies can cause extra unemployment.
Unemployment is measured as the percentage of the nation’s labor force that wants to
work but currently is not working. Both inflation and unemployment cause costs for
society, but policies that reduce inflation may cause more unemployment, and vice versa.
The Model
This module is built around the basic Keynesian model. In this model everything
depends on decisions that affect aggregate spending plans to buy goods and services.
Every economic variable discussed in the module is given in “real” terms so that, for
example, GDP is real GDP.
Decisions to buy are made for different reasons by four different groups: households
(Consumption Expenditure or C), business (Investment Expenditure or I), foreigners (Net
Exports or NX), and the government (Government Expenditure or G). For simplicity, in
this module Net Exports are assumed to always be zero, that is, the nation sells exactly as
much to foreigners as it buys from them. Thus, there are three sources of spending
contained in the Aggregate Expenditure (AE) for the nation. Aggregate Expenditure can
be expressed as:
AE = C + I + G + NX
But since NX is assumed to be zero:
AE = C + I + G
In this model, spending plans will determine what happens to production, or GDP,
because producers will not produce more than what is going to be bought (not for long
anyway), nor will they produce less than can be sold. (Assume there are enough
resources to produce whatever amount is wanted, and that the profitability of producing –
the prices of products compared to the prices of resources—is not an issue.) As a result,
the aggregate expenditure decision will turn out to also be the same as GDP. When that
occurs the macroeconomy is in equilibrium and
GDP = C + I + G
If you want to know what GDP will turn out to be, you need to know what determines the
spending plans of each group. In this module government spending is either the default
(built-in) value or whatever you want it to be. The parts that need explaining are the
consumption and investment decisions.
Consumption
For purposes of this module assume household decisions on how much to spend depend
on two things—after tax income, and interest rates. After tax income is all the income
received from production (GDP) minus the amount the government takes for taxes. The
more income people have left after paying taxes, the more they will spend on goods and
services. In fact, the model assumes a fixed amount of extra spending will be done for
every extra dollar in after-tax, or disposable, income. The proportion between extra
spending and extra disposable income is the “marginal propensity to consume.”
2
The second influence on consumer spending is interest rates. Higher interest rates make
it more expensive for households to buy consumer durable goods, like cars or
refrigerators, that are often bought on credit. Higher rates also make it more desirable for
households to save (they get paid higher interest on the extra saving they do). As a result,
the higher interest rates go, the less consumer spending there should be.
Investment
In the real world business decisions on how much to spend on investment depends on
many things. In this module, it depends on only one thing -- interest rates. The higher
interest rates go, the higher the cost of buying machines, buildings, piling up inventory,
and the lower the profit expected from doing such things. As a result, higher interest
rates should mean lower investment spending.
Combining these three relationships would allow you to solve the model (see the Math
section) to determine, for any values of the tools, what GDP and all the other results will
turn out to be.
Besides the level of GDP, there are the inflation and unemployment rates to consider.
The unemployment rate has a negative relationship with GDP, the lower GDP is, the
higher the unemployment rate. While the exact relationship differs from that found in the
US economy, the basic behavior is as described in “Okun’s law.” The inflation and
unemployment rates are negatively, or inversely, related to each other, as in the standard
short run Phillip’s Curve. However, due to bias in the measurement of inflation
(described in more detail in the Math section) full employment in this module would be
at an inflation rate of 1.5%.
Finally, the delay between the time the government begins a new policy and the time
when the policy has its full impact is built into this module. In the model used:
1)
The new policy is implemented and the policy shifts Aggregate Expenditure.
2)
Aggregate output (GDP) increases or decreases in response to the initial
increase or decrease in AE, and the amount demanded changes in accordance
with the change in GDP. As a result, demand for goods and service still fails
to match actual production, so:
3)
GDP continues to rise (or fall) with similar effects on AE as in (2). The
process continues until final equilibrium is reached, and output equals planned
spending.
Running the Module
When you start up the module you have to decide the initial state of the economy. One
situation is an economy with inflation; the other is an economy with excessive
3
unemployment. Once you have decided which problem you want to investigate, click on
“Continue” in the toolbar, and you will be given the necessary information about the
macroeconomy, including the default values the three policy tools that determine GDP
and its components, as well as unemployment and inflation.
In the next step, you have to decide what policy tool you want to use. To make it easier
for you to learn the power of each policy tool, you only get to change one tool at a time.
You get to control government spending, the amount of taxes collected, or the prevailing
rate of interest. All your policy controls are “real,” meaning that inflation (rising price
level) and deflation (falling price level) do not affect their usefulness. Before starting to
make changes you should know what they are, how they work, and how to evaluate the
effects of changes you make.
Once you make your decision – which policy tool you want to use -- you need to enter a
value for that tool. Then you be given the long run equilibrium results of your policy
decision in numerical terms. You can elect to see how the economy moved toward that
new equilibrium over the following four years by clicking “annually.” (It won’t reach
equilibrium in four years, but it will get closer.) (If you leave the default value in place
you will just get the initial conditions information when you click on “Continue.”)
In addition to the numerical results you can see the adjustment process and final results in
graphical (Keynesian Cross) form. You can also see the final results in the Aggregate
Supply-Aggregate Demand diagram. (These graphs are explained later in this manual.)
The Tools
There are three major ways governments try to manage inflation and unemployment
problems. Government spending and taxes are referred to “fiscal policy” tools, and in the
US the President and Congress control them. The third macroeconomic stabilization tool
is monetary policy -- controlling either the money supply or interest rates. In the US the
Federal Reserve controls monetary policy.
Government Spending
When you change government spending, with tax collections and interest rates constant,
you should first look for how the change has affected the value of real GDP. Consider
the proportion of the change in real GDP divided by the change in government spending.
This proportion tells you the value of the government spending multiplier, and measures
the power of government spending as a macroeconomic stabilization tool. That is, if it
takes a big change in government spending to cause a small change in real GDP then
government spending is a weak tool -- maybe not even worth using.
The “spending multiplier” measures the effect of government spending on real GDP
when interest rates and taxes are kept constant: the spending multiplier is the ratio of the
change in real GDP divided by the change in government spending that caused that real
GDP change, or:
4
Spending Multiplier =  real GDP /  Government Spending
The same multiplier is relevant if there is a shift in investment or consumer spending, but
neither can happen in this module. The user can only change government spending and
observe the spending multiplier results of such spending.
In the real world, an increase in government spending, holding tax collections constant,
would cause interest rates to go up unless measures were taken by the Federal Reserve to
prevent that from happening. Such measures would involve increasing the supply of
money in the country. The results in this module therefore differ from the real world
results of only changing government spending. (Also, if real GDP started to go up (in
reality) because of a rise in government spending, tax collections would also start to go
up – unless tax rates were reduced. Higher real GDP means higher incomes, so more
income taxes are be collected, more sales, more sales taxes are collected, etc. This also
exaggerates the effects of changes in government spending compared to the real world.)
Taxes
In the module, when you cut taxes people have more disposable income to spend, so
consumption spending rises.
You should compare the effects of a given size tax cut (or increase) on real GDP with the
effects of an equal sized change in government spending. There will be a difference and
you should figure out why. You should also compare the effects of the two tools on the
composition of real GDP. That means comparing what proportions of real GDP are
consumer goods, investment goods, and government goods. There will be differences in
the effects of these two tools on these proportions.
(In the real world investment depends on the level of GDP as well as on interest rates and
business taxes. In this program investment depends only on interest rates. That makes
the comparison easier, but oversimplifies real world problems. Remember that the term
“investment” in this module means business firms buying equipment, buildings, and
inventory. It does not mean buying stocks, bonds or any other pieces of financial paper.)
Definition: The “tax multiplier” is the change in real GDP divided by the change in
taxes that caused that real GDP change (holding interest rates and government spending
constant):
Tax Multiplier =  Real GDP /  Taxes
In the real world governments cannot just change tax collections, they change tax rates
and that changes the amount of tax collections. Changing tax rates alters how much
someone owes in income taxes, sales taxes, corporate profits taxes, etc. Governments
have the difficult job of figuring out how much of a change in tax collections there will
be if they change tax rates in a certain way. Your job has been simplified by giving you
5
power the real government lacks -- direct control over the amount of tax revenue
collected. Also, as with government spending, a change in taxes will cause a change in
interest rates unless steps are taken to prevent this from happening. This means the
results you get exaggerate the power of tax changes to control real GDP.
Interest Rates (Monetary Policy)
In this module the monetary policy tool is the level of interest rates. Interest rates affect
business investment decisions and consumer decisions as to how much to save versus
how much to spend on consumer goods, so changing interest rates affects private demand
for goods and services, aggregate demand, and GDP. You should see how much of a
change in interest rates are needed to cause changes in GDP similar to those you got
changing the previous tools. You should also see what changing interest rates do to the
proportion of GDP going to investment, consumption, and government. Compare these
results with those obtained by changing the other tools.
In the real world, real interest rates influence investment and savings. The interest rates
the Federal Reserve controls are “nominal” interest rates. (Almost all interest rates
you’ve seen quoted are nominal rates.) The real interest rate is approximately the
nominal rate minus the inflation rate people expect. The approximation is OK as long as
expected inflation isn’t too large. (When analyzing countries with inflation rates even
close to 100% per year this approximation should not be used.)
Real Rate = Nominal Rate – Expected Inflation Rate
If people (for any reason) start expecting more inflation, having the same nominal interest
rate would mean real interest rates went down, and investment and consumer decisions
would change. In this module you control real interest rates directly, so you do not have
the problem the actual government has—that changes in expectations make it hard to
know what the actual current value of your “tool” is. This makes using interest rates to
control the economy easier in this module than in reality. In effect, this module can be
considered to hold the expected inflation rate constant -- so any change in the nominal
interest rate is equal to the change in the real interest rate.
Your Results
When you enter a value for whatever tool you have chosen, you get results -- the GDP,
consumption, investment, inflation, and unemployment values -- that your policy choice
will eventually produce. When you try to determine things like the value of the spending
multiplier, or the tax multiplier, these are the numbers you should be using. However,
you should notice that there is also a menu item labeled “Annual.” The reason it is there
is that policy changes do not work all at once, they take time to affect the economy. In
other words there are lags, delays from the time a policy is changed to when it has its full
impact on the economy.
6
Lags in Policy Effect
When government spending is changed, for example, government demand for goods and
services increases. However, it takes some time for that increase in demand to affect
GDP. It takes time because after the basic decision is made the government has to decide
just what to buy and from whom. Until contracts are negotiated and signed, and firms
and individuals start doing things, real GDP doesn’t change.
Once the government starts getting products and services, GDP has risen, and so have the
incomes of those supplying the goods and services. When their incomes increase people
start spending more, but it takes them some time to decide what to buy with their new
income. When they start to spend more, firms notice the increase in demand and start to
increase production. At this point GDP has increased again. With the increase in GDP
people’s incomes have gone up again, and they plan on further spending, leading to more
increases in GDP.
Keynesian Cross Graph
One way of illustrating the process is shown in the Keynesian Cross graph below, and
displayed in the module.
Figure 1
Keynesian Cross
45º line
AE
AE´
c
b
AE
a
0
Real GDP
Old GDPE
New GDPE
In Figure 1, the 45 line from the origin shows all the points where planned spending
equals planned output, or real GDP, the points where all income is spent. If planned
spending does not equal planned output (income), either people want to buy more than is
produced -- excess planned spending, or they want to buy less than is produced -- excess
planned output. Either way, when the two are not equal, real GDP will change. Only if
the two are equal, which happens on the 45 line, is there an equilibrium for real GDP.
7
In Figure 1, the old planned spending line, or AE, shows the amount consumers,
businesses, and government planned to spend at various levels of GDP with the default
values of government spending, taxes, and interest rates. Since consumer spending rises
when income rises, the line is upward sloping, the point where it crosses the 45 line is
the old macro equilibrium, or Old GDPE . A change in plans will shift this line and
eventually bring the economy to a new equilibrium, New GDPE. For example, if
government spending increases, the line shifts up to the new planned spending line, AE´.
The initial rise in planned government spending is the vertical shift in the line, and is
shown by the arrow labeled a. The first actual increase in real GDP, shown by arrow b,
is the same amount as the initial rise in planned spending (as the business produces the
goods and services the government wants). Then there is the next increase in planned
spending -- since it is due to the rise in income it is not a shift in the line, but a movement
along the line -- it is indicated by arrow c.
The arrows can be connected to a numerical sequence. Suppose the initial increase in
government spending was 100, and out of every $1 of extra income people spent $.50
(not true in this module). If only households increase spending when income rises, the
marginal propensity to consume (MPC) is 50%, or 0.50. The increases in GDP
correspond to the prior increases in planned spending, and the sequence can be seen in
the table below. The top row of the table marks out time periods -- which could be
months, quarters, or years. Only the first four are shown. In principle, there are an
infinite number of these terms, but most of the effects are seen in the first few terms (or
years in the module).
Time Period
Change in Planned Spending
Change in Real GDP
1
$100
$ 0
2
$ 50
$100
3
$25
$50
4
$12.5
$25
By the end of Period 4, the total effect of the government spending change on GDP is:
0 + $100 + $50 + $25 = $175. Since effects continue in later periods it is convenient to
be able to determine the eventual total impact. There is a formula used for calculating the
full effect. If MP is the “marginal propensity to spend”, or the extra spending from a
one-dollar change in real GDP, the size of the spending multiplier is:
Spending Multiplier =  Real GDP /  Government Spending = 1/(1 – MP)
If only consumer spending is affected by income changes, MP is the marginal propensity
to consume (MPC), and the spending multiplier is 1/(1-MPC). If the MPC is 0.5, as it is
in the example in the table, the spending multiplier is 1/(1-.5) = 2. In Figure 1, if the AE
line was shifted by an increase in government spending, the spending multiplier can be
seen as the ratio between the horizontal move from Old GDP to New GDP (length of
arrow b) and the vertical rise in AE (the length of the arrow a). The total impact on GDP
in the long run would be a change in GDP of $200.
8
The analysis of the effect of a tax change is similar. However, if taxes are cut by $100
and the MPC is 0.5, initially planned spending would rise by only $50 (the other $50
would go into saving). Since the initial effect on spending is smaller, the final effects on
GDP are also smaller. The formula for calculating the tax multiplier (when only
consumers react to income changes) is:
Tax Multiplier =  Real GDP /  Taxes = (1/(1 – MPC)) – 1 = MPC/(1 – MPC)
If the MPC is 0.5, then the tax multiplier is 1.
Aggregate Supply and Demand
Another way of presenting the results of changes in the policy tools is the AS-AD model.
In it, AD has an inverse relationship between changes in real GDP and changes in the
aggregate price level (P), or GDP deflator. The reason for the downward slope is that,
with a given nominal money supply, the higher the price level the lower the purchasing
power will be for the fixed number of dollars in the economy. The reduction in the real
value of the money supply at higher prices causes (among other things) higher interest
rates, which cause business and consumer spending to fall—so less quantity is demanded.
The model has an upward sloping AS curve because higher prices for final goods and
services (with no change in resource prices) imply production is more profitable.
The AD-AS model does not exactly fit the way this module works. In the module when
you change government spending the real interest rate stays constant, but the nominal
money supply does not. In fact, if government spending rises, in order to keep real
interest rates from rising, the nominal and real measures of the money supply must
increase. As a result the apparent shift in AD with a change in government spending is
the result of both the change in government spending and the change in the money
supply. The same caution applies to the effects of tax changes; a tax cut (real interest rate
constant) implies that the money supply increases. If you change the real interest rate
tool you are changing the money supply, the AD-AS model is a better fit for this case.
In addition, this module does not address the long run adjustment mechanism of the ADAS model, in which rising final good prices cause rising resource prices, shifting the AS
curve. Many presentations of the AD-AS model also assume that policy tools are set in
nominal terms, i.e., the government decides on a budget with a certain number of dollars
to be spent, and if prices go up the government gets fewer goods than it expected. In this
module you control real government spending, so changing the price level has no such
effect. The same is true for the tax tool you control.
The AD-AS Graph
Figure 2 shows how a rise in government spending, a tax cut, or cut in real interest rates
affect AD, the equilibrium price level, and GDP. P0 is the original price level, P1, the
new price level (after the policy change), GDP0 is the original GDP value, and GDP1 is
9
the new value. The vertical line indicates the full employment level of GDP, GDP FE.
The arrow shows the direction of shift in the AD curve. In Figure 2, both the old (AD)
and new (AD´) curves do not intersect AS at the full employment level of GDP and thus
do not reach full employment equilibrium.
Figure 2
Aggregate Supply and Demand
Price
Level
AS
P1
P0
AD´
AD
Real GDP
0
GDP0
GDP1
GDPFE
Mathematical Model
The results of this module come from the following set of equations:
1)
GDP = C + I + G
2)
C = a0 + a1 (GDP – T) + a2 (Interest rates)
a0 is the amount of consumption that would be done if interest rates and disposable
income were zero, The value of a0 is 201.818. T is the amount the government takes in
taxes, a1 is the marginal propensity to consume, set at 0.9, and a2 is the sensitivity of
consumption to interest rates, set at –1725 (negative).
3)
I = b0 + b1 (Interest Rates)
b0 is the amount of investment spending done if interest rates fell to zero, set at 285,
while b1 represents the effect of a unit change in interest rates on the level of investment
spending, it is set at –1775 (negative).
10
So:
4)
GDP = a0 + a1 (GDP – T) + a2 (Interest Rates) + b0 + b1 (Interest Rates) + G
To see how GDP is determined, solve (4) for GDP:
5)
GDP = [(a0+b0) / (1–a1)] + [(a2+b1)/(1–a1)](Interest Rates) + [(G–a2 T)/(1–a1)]
If you know the values of all the a’s and b’s, of interest rates, government spending, and
taxes, you can calculate the value of GDP. Once you know GDP you can calculate the
value of consumption (knowing interest rates is also necessary, but you needed that to get
this far). You could also calculate the amount of investment, knowing the values of b0,
b1, and interest rates.
To determine the unemployment rate you also need to know what this module uses for
“Okun’s Law,” the relationship between changes in GDP and changes in the
unemployment rate. In this module the unemployment rate and GDP are related through
this equation:
6)
Unemployment = 0.5 - (0.0001 * GDP)
To get unemployment to drop by one percent (0.01) it would be necessary to get GDP to
rise by 100.
In models of this type the inflation rate is usually discussed in terms of a “Phillips curve,”
a negative short run relationship between the inflation rate and the unemployment rate.
In this module the inflation rate is actually determined directly by the level of GDP (that
does give it a negative relationship with the unemployment rate). The module uses two
functions to determine the inflation rate—one for high value of GDP, the other for low
values, because in the real world inflation usually reacts less to changes in GDP at low
levels than at high ones. Where $4500 billion is the full employment level of GDP:
7a)
7b)
If GDP > 4500 Then inflation = 0.015 + 185 * (((GDP - 4500) / 4500) ^ 1.8)
If GDP <= 4500 Then inflation = 0.015 -0.5 * (((4500 - GDP) / 4500) ^ 3.3)
In both 7a and 7b the 0.015 (1.5%) incorporated in the relationship represents the built in
bias in the price index that is used to measure the inflation rate. This bias (including
quality changes, substitution bias, outlet bias) means the measured inflation rate
overstates the true inflation rate. At full employment in this module the true inflation rate
would be zero, but the measured inflation rate would be 1.5%.
The lag effects of policy changes are calculated as follows:
For period 1, there is no impact on actual spending (effect of any shift is zero):
GDP1=GDP0 + ΔGDP=GDP0 (GDP0 is the original equilibrium)
11
For period 2: ΔGDP = S (where S is the size of the initial shift in AE):
GDP2 = GDP1 + ΔGDP = GDP1 + S
For period 3: ΔGDP = S*MPC
GDP3 = GDP2+ ΔGDP = GDP2+S*MPC = GDP1+S+(S*MPC)
For period 4: ΔGDP=S*S*MPC
GDP4 = GDP3+ ΔGDP = GDP1+S+(S*MPC)+(S*S*MPC)
Once GDP is calculated, substitute into the Consumption equation to get consumer
spending, into the Okun’s Law equation for the unemployment rate, and into the Phillip’s
curve equation for the unemployment rate. If one of the fiscal policy tools was used there
will be no change in interest rates anywhere along the line, including in the final
equilibrium. If interest rates were used, the full change in investment spending will show
up in period 2, there will be no further change in investment after that.
12