Chapter Thirteen
Modern
Macroeconomic
Models
Dynamic Models
• A dynamic model is one in which actions that
occur at one time affect what happens at other
times
• A static model focuses on just one point in time.
• Advantages of dynamic models
– Allow modeling of expectations, thus avoiding the
Lucas critique
– Examine how people are affected by government
policy actions by including microeconomic
foundations of the macroeconomy
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Dynamic Models (cont’d)
• Dynamic models are ones with
microeconomic foundations, or are
based on decisions of economic agents
– Economic agents include households, firms,
governments, and foreigners who make exchange
decisions
• The main disadvantage of dynamic
models is that they are more complicated
than static models
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Two-period Model
of Consumption & Saving
The following example considers a single
household and the decisions it makes in two
time periods
• Income is known
– Period 1 income = $50,000
– Period 2 income = $75,000
• Can borrow or lend at fixed interest rate
– Interest rate = 50 percent
• There is one consumer good, which always
costs $1.00
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Two-period Model
of Consumption & Saving (cont’d)
• The household’s budget constraint
– If household does not borrow or lend in period
1, spending is 50,000 in period 1 and 75,000
in period 2
– If household spends nothing in period 1, it
saves $50,000, invests for one year at 50%,
so has $25,000 in interest + $50,000 principal
+ $75,000 income, so can buy 150,000 goods
in period 2
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Two-period Model
of Consumption & Saving (cont’d)
Many possibilities exist for the household
Period 1
• Could spend 0-$50,000 on goods
• Could save 0-$50,000, earning interest
• Could spend > $50,000, borrowing at 50%
interest, to be repaid in period 2
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Two-period Model
of Consumption & Saving (cont’d)
Any point along the line above is a spending/saving possibility for the
household. It cannot, however, go beyond this line; this is the
household’s budget constraint
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Household’s Budget Constraint
• The household can spend the entire
present value of its income in each period
• In Period 1, the present value of the
household’s budget is
$50,000 $75,000

 $50,000  $50,000  $100,000
0
1
(1.50)
(1.50)
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Two-period Model
of Consumption & Saving (cont’d)
• Where will the household consume? E.g.,
at what point along its budget constraint
line?
– It depends on their preferences
– Some households will be patient and
consume more in period 2
– Other households will be impatient and
consume more in period 1
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Changes in Income
• Consumers with different incomes have
different budget constraints
• A change in income shifts the entire budget
constraint
• The budget constraint shifts by the exact
amount as the change in income
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Changes in Income
(cont’d)
Figure 13.2 Higher Household Income in the Two-Period Model
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Changes in Interest Rates
• A change in the interest rate will cause the
slope of the budget constraint to change
• The point where households neither
borrow nor save in unaffected, at such a
point they neither pay nor receive interest
• The slope of the budget constraint is –
(1+i), so a lower interest rate makes the
line flatter
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Changes in Interest Rates (cont’d)
Figure 13.3 A Lower Interest Rate in the Two Period Model
As interest rates fall, the budget constraint line rotates
counterclockwise around the point at which the household neither
borrows nor lends
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Changes in Interest Rates (cont’d)
• Is a household better off or worse off if the
interest rate is lower?
– It depends on whether the household would have
been a borrower or a saver at each interest rate
– Someone who would have been at point A (more
consumption in period 1) is better off with a lower
interest rate
– Someone who would have been at point B (lower
consumption in period 1) is most likely worse off,
but could be better off, if their preferences were
such that they switched to being a borrower
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Changes in Interest Rates (cont’d)
• Consumption in each period depends on income
in both periods and the interest rate
– People prefer to smooth consumption spending over
their lifetimes
– Households anticipate future income increases, and
spend more in period 1, assuming their income will be
higher in period 2
– Increased income in either period likely leads to
greater consumption in both periods
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Adding Realism to the Model
• The model may seem unrealistic with only two
periods
• It is possible to increase number of periods
under analysis
• In reality, households could have higher interest
rates when borrowing than when lending (The
budget constraint will be steeper when
borrowing and flatter when saving)
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Adding Realism to the Model (cont’d)
Figure 13.4 The Budget Constraint in the Two-Period Model When the Interest
Rate On Borrowing Is Higher Than the Interest Rate on Lending
With different interest rates for borrowing and saving, a kink results at
the point where neither borrowing nor saving occurs
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Precautionary Savings
• When households are uncertain about income,
they often decide to save more as a precaution
• This “extra” amount of saving is known as
precautionary saving
• Greater uncertainty generally results in more
precautionary savings
• A household must therefore decide how much to
spend without knowing exactly where their
budget constraint will lie
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Precautionary Savings (cont’d)
Figure 13.5 Uncertainty About Household Income in the Two-Period Model
With uncertain income, the household does not know where its budget
constraint will be
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General Equilibrium
• Analysis thus far has focused on single
households, but should extend to the
macroeconomy to be a useful model
• General equilibrium is a situation in which all
markets are in equilibrium and all economic
agents have made decisions in their own best
interest
– To find general equilibrium, we need assumptions
about incomes and numbers of different households
and how much they decide to spend; then we must
find the equilibrium interest rate and the values of
other endogenous variables
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General Equilibrium (cont’d)
• Example: 50 households, all with period 1
income = $50,000
• Assumptions
– 25 poor households have period 2 income of
$75,000
– 25 rich households have period 2 income of
$105,000
– Each household spends half the present
value of its lifetime income on consumption in
period 1; the rest in period 2
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General Equilibrium (cont’d)
Solution method
1. Find consumption and saving of all
households as a function of interest rate
2. Since net saving of all households must be
zero (if someone borrows, someone else
must lend), use savings equations to find
equilibrium interest rate
3. Solve for other endogenous variables
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General Equilibrium (cont’d)
– Step 1: Find consumption and saving of all
households as a function of interest rate
– PV (poor) = $50,000  $75,000
1 i
–
C1 (poor) = ½ × PV (poor)
=
1
$75,000
$37,500
 {$ 50,000 
}  $25,000 
2
1 i
1 i
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General Equilibrium (cont’d)
– The household’s savings equals its income
in period 1 minus its spending, so:
– S (poor) = income – consumption
$37,500
$37,500
$50,000  {$ 25,000 
}  $25,000 
1 i
1 i
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General Equilibrium (cont’d)
– By similar analysis, a rich household has
savings equal to:
– S (rich) = income – consumption
$52,500
$52,500
$50,000  {$ 25,000 
}  $25,000 
1 i
1 i
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General Equilibrium (cont’d)
•
Since total saving in the economy must
be zero (borrowing by some = lending by
others), and there are 25 of each type of
household, then
$37,500
$52,500
{25  [$25,000 
]}  {25  [$25,000 
]}  0
1 i
1 i
– Solve this to get: i = 0.8 = 80%
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General Equilibrium (cont’d)
– Step 3: Solve for other endogenous
variables
$37,500
– C1 (poor) = $25,000 
1 i
= $25,000 
$37,500
 $45,833.33
1 .8
– S (poor) = $50,000 - $45,833.33 = $ 4,166.67
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General Equilibrium (cont’d)
–
$52,500
C1 (rich) = $25,000 
1 i
$52,500
 $54,166.67
= $25,000 
1.8
–
S (rich) = $50,000 - $54,166.67 = - $4,166.67
–
In this model, the rich borrow from the poor in
period 1 because they know their incomes will be
higher in period 2
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General Equilibrium (cont’d)
–
–
–
–
–
–
Borrowing by rich = lending by poor = $4,166.67
Interest paid = 0.8 × $4,166.67 = $3,333.33
Rich repay interest + principal in period 2 in amount
of $4,166.67 + $3,333.33 = $7,500
So,
C2 (poor) = $75,000 + $7,500 = $82,500
C2 (rich) = $105,000 - $7,500 = $97,500
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Expectations
•
Expectations are people’s beliefs about
future economic variables
–
–
–
–
People have rational expectations when they
form expectations using all available information
Expectations are best modeled as endogenous
variables; decisions depend on future variables
For example, households might care about future
inflation and form rational expectations of inflation
Since inflation depends on monetary policy, it
follows that households will monitor what
monetary policymakers say and do
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The Impact of Changes in
Government Policy
Consider a change in fiscal policy
–
–
–
–
Suppose the government gives everyone in the
two-period model a tax rebate of $1,000 in period
1 (household income rises by $1,000)
Do the households think the present value of their
incomes has risen by $1,000?
Not if they realize that the government will
increase taxes in period 2 to pay for the rebate in
period 1
Realizing that the government will tax them
$1,800 in period 2 (= $1,000 × 1.8), people will
save the entire tax rebate, as the present value of
their lifetime after-tax income is unchanged
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The Impact of Changes in
Government Policy (cont’d)
• The Ricardian equivalence proposition states that the
result of change in the timing of taxes does not affect
people’s consumption
– Whether Ricardian Equivalence holds or not depends on
people’s expectations and whether the present value of their
income changes
– Under Ricardian Equivalence, a government tax rebate has
no effect; people just save the rebate, so it does not lead to
increased spending
– Under some conditions, such as different interest rates on
borrowing and lending, or if people are unable to borrow, or if
people have uncertain future incomes, Ricardian
Equivalence may not hold exactly
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DSGE Models
• Dynamic, Stochastic General-Equilibrium
Models …include expectations to explain how
variables change over time
– Dynamic implies change over time
– Stochastic means including uncertainty
– General equilibrium assumes that price level, wages,
and interest rates adjust to bring all markets into
equilibrium
– First introduced as Real Business Cycle (RBC)
models
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Real Business Cycle Models
• “Real” shocks to productivity are the main
determinants of business cycles
• Both growth and business cycles are
explained by movements of a single
variable- total factor productivity (TFP)
• The level of TFP is the engine of growth;
fluctuations in TFP generate business
cycles
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Real Business Cycle Models (cont’d)
• RBC researchers used different methods
than earlier macroeconomists
– work with models incorporating
microeconomic foundations
– models are calibrated to match key business
cycle facts
– models are simulated on computers, not
estimated with econometric analysis like other
models
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Real Business Cycle Models (cont’d)
• Early RBC models were quite successful
– Showed why investment spending fluctuated so
much over the business cycle
– Showed the close relationship between output
growth and hours worked
– Showed that TFP shocks accounted for about 70%
of output fluctuations
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Real Business Cycle Models (cont’d)
• Some economists remained skeptical
about RBC models
– Government TFP data is poor, so the
apparent relationship between TFP and
output arises from measurement error
– The data also do not reflect how intensively
capital and labor are used, thus erroneously
leading to correlations between output and
productivity
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Real Business Cycle Models (cont’d)
• RBC theory suggests little role for
government policy
– TFP shocks, not government policy, are the
main cause of business cycles
– Government should do sensible things and
stay out of the way of the private sector,
keeping tax rates constant and inflation low
and stable
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Modern DSGE Models
• The development of RBC models found roles for
government policy, so a name change to DSGE
models was in order, as models were no longer
entirely “real”
• Increasing power of computers allows
complicated heterogeneous-agent models, with
many different households, firms, etc.; much
more complicated and realistic than older
homogeneous-agent models in which all agents
were the same
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Modern DSGE Models (cont’d)
•
Researchers using DSGE models
1. Pose the question to be answered
2. Develop a model with the core elements to be
analyzed; look at the decisions made by the
agents
3. Match the model to the data, and calculate the
size of the shocks that occur to exogenous
variables
4. Simulate the model and compare its properties to
those of the data. If the model closely matches
the data, answer the question in step 1. If the
model does not closely match the data, modify
the model and try again
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Statistical Models of the Economy
• Use statistical theory, not economic theory,
to build an economic model because of a
belief that earlier theories were based on
insufficient data
– The simplest is an univariate time-series
model: a variable today depends on its own
past and an error term
Ct  a0  a1Ct 1  a2Ct 2  a3Ct 3  a4Ct 4  et
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Statistical Models of the Economy (cont’d)
• Statistical models provide
reasonably good forecasts,
because the world is so
complicated that dynamic
models can’t capture
everything
• More complicated statistical
models, based on many
variables, do even better
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Statistical Models of the Economy (cont’d)
• Vector auto-regression models are ones in
which the value of a variable depends on its own
past, past values of other variables, and an error
term
– Example: equation for consumption spending with income Y and
interest rate r:
Ct  a0  a1Ct 1  a2Ct 2  a3Ct 3  a4Ct 4
 b1Yt 1  b2Yt 2  b3Yt 3  b4Yt 4
 c1rt 1  c2 rt 2  c3 rt 3  c4 rt 4  et
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Vector Autoregression Models
Advantages of VAR models
1. all variables are endogenous
2. can examine how a shock to one variable affects all
other variables
3. can see how important one variable is in affecting
movements of other variables
Disadvantages of VAR models
1. hard to use them to interpret historical events
2. models lack structure, so we cannot see how some
shocks affect other variables (more in next section)
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Do Modern Macro Models Have Any
Value for Policy?
• Lucas critique: changes in how policy is
formed may change equations of a model
• So a researcher cannot take an equation
that describes policy out of a large macro
model or VAR model and replace it with a
different equation to see how such a
change would affect the economy
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Do Modern Macro Models Have Any
Value for Policy? (cont’d)
• Solution for making VARs usable for policy
analysis…give them some structure
– Structural VAR: adds economic structure by
imposing restrictions on a VAR
– Short-run restrictions: how variables affect each other
in the short run
• Example: assume that money affects output only with a lag,
which is consistent with the data
– Long-run restrictions: how a change in one variable
today affects another in the distant future
• Example: money does not affect output in the long run,
according to both theory and data
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Do Modern Macro Models Have Any
Value for Policy?
• A structural VAR with long-run and shortrun restrictions provided by theory and
data, provides a better interpretation of
what happens to the economy when policy
changes
• Eventually, economists will build models
usable for forecasting, policy analysis, and
interpreting historical events
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