The transformation of macroeconomic policy and research prize Lecture, December 8, 2004 by

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Step 7: Simulate the Model Economy

The equilibrium stochastic process is used to generate a time series realiza-

tion of the model economy. If the number of observations in the period

being considered is N, a time series of length significantly greater than N is

generated and the last N observations considered. A longer time series is 

generated because we wanted a draw from the invariant distribution for the

state of the economy as a starting point of the model’s sample path.

Step 8: Examine the Key Business Cycle Statistics and Draw Scientific Inference

The last step is to compare the key business cycle statistics for the model and

the actual economy. I emphasize that the identical statistics for the model

and the actual economy are compared.

One important statistic is the standard deviation of the cyclical component

of output. What we defined to be the cyclical component of output is first

computed for the actual economy and the standard deviation determined.

The identical procedure is followed for realizations of the equilibrium process

of the model economy. This means the model is simulated to generate the 

time series of output and other series. Next the cyclical component of output

is computed and its standard deviation determined. This is done many times

so that the first two moments of the sampling distribution of the standard 

deviation of the model’s cyclical output statistic can be determined.

If the sampling distribution of this statistic in question is concentrated

about some number, this number relative to the statistic specifies how variable

the economy would have been if TFP shocks were the only shocks. If the 

sampling distribution of this statistic is not concentrated, theory does not 

provide a precise accounting. But the sampling distribution is highly concen-

trated provided the number of quarterly observations is at least 100.

I emphasize that this is not a test in the sense of Neyman–Pearson statistical

hypothesis tests, which are useful in the search for a model or law through 

induction. The way theory is tested is through successful use. The neoclassical

growth model is tested theory.

4. USING THE METHODOLOGY IN BUSINESS CYCLE RESEARCH

Kydland and Prescott (1982) found, as reported in our paper “Time to Build

and Aggregate Fluctuations,” that if elasticity of substitution of labor supply is

3 and TFP shocks are highly persistent and of the right magnitude, then 

business cycles are what the neoclassical growth model predicts. This includes

the amplitude of fluctuation of output, the serial correlation properties of 

cyclical output, the relative variability of consumption and investment, the

fact that capital stock peaks and bottoms out later than does output, the 

cyclical behavior of leisure, and the cyclical output accounting facts.

Subsequently, Prescott (1986) found that the shocks were highly persistent

and the TFP shocks of the right magnitude. Conditional on a labor supply

elasticity close to 3, TFP shocks are the major contributor to fluctuations in

the period 1954–1981 in the United States.

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This finding turned out to be highly robust. Greenwood, Hercowitz, and

Huffman (1988) find that if, on average, TFP shocks are non-neutral with 

regard to consumption and investment, the conclusions hold. Rotemberg

and Woodford (1995) introduce imperfect competition and show that the

finding is overthrown only if monopoly rents are far in excess of what they

could be. With imperfect competition restricted to be consistent with labor

cost share, Hornstein (1993) and Devereux, Head, and Lapham (1996) show

that the importance of TFP shocks for business cycle fluctuations hardly

changes. With the introduction of monopolistic competition, model-TFP

shock variance is picked so that the model Solow-TFP variance matches the

actual economy’s Solow-TFP variance. In these monopolistic competitive

worlds, Solow-TFP is a complex statistic and is not total factor productivity.

Investment in the model economy varies smoothly, as does aggregate 

investment in the actual economy. Investment at the plant level, however, is

not smooth, and a natural question is whether this has consequences for 

modeling business cycles. Fisher and Hornstein (2000) find that having

plants that make lumpy inventory investment in equilibrium does not change

the estimates of the contribution of TFP shocks to fluctuations. For invest-

ment in plant and equipment, Thomas (2002) develops an economy that 

displays lumpy investment at the plant level. When calibrated to the growth

facts and establishment investment statistics, the findings for business cycles

using her abstraction are virtually the same as those using the neoclassical

growth model.

Ríos-Rull (1995) uses a carefully calibrated overlapping generations model

and finds that the estimated importance of TFP shocks for business cycle fluc-

tuations does not change. Within this framework, Ríos-Rull (1994) then shuts

down financial markets, so physical capital holdings is the only way to save.

This extreme version of market incompleteness does not affect the estimate

of the importance of TFP shocks. Introducing uninsurable idiosyncratic risk

(see Krusell and Smith, 1998) does not affect the estimate either. Hansen and

Prescott (2005) deal with capacity utilization constraints that are occasionally

binding. With their introduction, the nature of the predictions for business

cycles changes a little, but in a way that results in observations being in even

closer conformity with theory.

Using this methodology, Danthine and Donaldson (1981) and Gomme

and Greenwood (1995) investigate the consequences of various non-Walrasian

features for business cycle fluctuations. There are interesting implications for

relative variability of consumption for those with large capital ownership and

those with no capital ownership.

Freeman and Kydland (2000) and Cooley and Hansen (1995) find that 

introducing money and a transaction technology does not alter the conclusion

as to the importance of TFP shocks. Chari, Kehoe, and McGrattan (2000)

find that nominal contracting does not either. They introduce staggered 

nominal contracting into the basic business cycle model and find that in such

worlds, monetary shocks have effects that are persistent but too small to be an

important contributor to business cycle fluctuations. In summary, introducing

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