Macroeconomics

The Numerical Calibration and Simulation

my’s natural rate of interest 

r

is 2 percent. The

Phillips curve parameter 

f

= 0.25 implies that

when output is 1 percent above its natural level,

inflation rises by 0.25 percentage point. The

parameters for the monetary policy rule 

v

p = 0.5

and

v

Y

= 0.5 are those suggested by John Taylor

and are reasonable approximations of the behav-

ior of the Federal Reserve.

In all cases, the simulations assume a change

of 1 percentage point in the exogenous variable

of interest. Larger shocks would have qualitative-

ly similar effects, but the magnitudes would be

proportionately greater. For example, a shock of

3 percentage points would affect all the variables

in the same way as a shock of 1 percentage point,

but the movements would be three times as large

as in the simulation shown.

The graphs of the time paths of the variables

after a shock (shown in Figures 14-7, 14-9, and

14-11) are called impulse response functions. The

word “impulse” refers to the shock, and

“response function” refers to how the endoge-

nous variables respond to the shock over time.

These simulated impulse response functions are

one way to illustrate how the model works. They

show how the endogenous variables move when

a shock hits the economy, how these variables

adjust in subsequent periods, and how they are

correlated with one another over time.

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P A R T   I V

Business Cycle Theory: The Economy in the Short Run

In the periods after the shock occurs, expected inflation is higher because

expectations depend on past inflation. In period t

+ 1, for instance, the economy

is at point C. Even though the shock variable 

u

t

returns to its normal value of zero,

the dynamic aggregate supply curve does not immediately return to its initial

position. Instead, it slowly shifts back downward toward its initial position DAS

t

−1

as a lower level of economic activity reduces inflation and thereby expectations of

future inflation. Throughout this process, output remains below its natural level.

Figure 14-7 shows the time paths of the key variables in the model in response

to the shock. (These simulations are based on realistic parameter values: see the