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63

"See Altug (1989) and Christiano and Eichenbaum (1992a) for examples of traditional econometric estimation of real-business-cycle models.

The detrending procedure that is used is known as the Hodrick-Prescott filter (Hodrick and Prescott, 1980). As the discussion of permanent shocks and detrending in the previous section suggests, this procedure may not be innocuous (Cogley and Nason, 1995).

importantly, the part of fluctuations that is due to aggregate demand movements may also be quite persistent. A shift by the Federal Reserve to a policy of extended gradual disinflation, for example, may reduce output over a long period if nominal prices and wages adjust only gradually. And if technological progress results in part from learning-by-doing (see Section 3.4), output changes caused by aggregate demand movements affect technology.

Thus in the end, the main contribution of the literature on persistence is to sound some warnings about time-series econometrics: mechanically removing trends or otherwise ignoring the potential comphcations caused by persistent movements can cause statistical procedures to yield highly misleading results.

4.9 Additional Empirical Applications

Calibrating a Real-Business-Cycle Model

How should we judge how well a real-business-cycle model fits the data? The standard approach is calibration (Kydland and Prescott, 1982). The basic idea of calibration is to choose parameter values on the basis of microeconomic evidence, and then to compare the models predictions concerning the variances and covariances of various series with those in the data.

Cahbration has two potential advantages over estimating models econo-metrically. First, because parameter values are selected on the basis of microeconomic evidence, a large body of information beyond that usually employed can be brought to bear, and the models can therefore be held to a higher standard. Second, the economic importance of a statistical rejection, or lack of rejection, of a model is often hard to interpret. A model that fits the data well along every dimension except one unimportant one may be overwhelmingly rejected statistically. Or a model may fail to be rejected simply because the data are consistent with a wide range of possibilities.

To see how calibration works in practice, consider the baseline real-business-cycle model of Prescott (1986) and Hansen (1985). This model differs from the model we have been considering in two ways. First, govemment is absent. Second, the trend component of technology is not assumed to foUow a simple linear path; instead, a smooth but nonhnear trend is removed from the data before the models predictions and actual fluctuations are compared.*

We consider the parameter values proposed by Hansen and Wright (1992), which are similar to those suggested by Prescott and by Hansen.



U.S. data

Baseline real-business-cycle model

1.92

1.30

(Tc /(

0.45

0.31

Oj/o-y

2.78

3.15

(Ti/o-y

0.96

0.49

Corr(L, Y/L)

-0.14

0.93

Source: Hansen and Wright (1992).

Based on data on factor shares, the capital-output ratio, and the investment-output ratio, Hansen and Wright set a = 0.36, S = 2.3% per quarter, and p = 1% per quarter. Based on the average division of discretionary time between work and nonwork activities, they set b to 2. They choose the parameters of the process for technology on the basis of the empirical behavior of the Solow residual, InRt = InYf - [ahiKt + (1 - a)lnlfj. As described m Chapter 1, the Solow residual is a measure of all Influences on output growth other than the contributions of capital and labor through their pri-\ate marginal products. Under the assumptions of real-business-cycle theory, the only such other influence on output is technology, and so the Solow residual is a measure of technological change. Based on the behavior of the Solow residual, Hansen and Wright set pa = 0.95 and the standard deviation of the quarterly fs to 1.1%.

The models implications for some key features of fluctuations are shown m Table 4.4. The figures m the first column are from actual U.S. data; those in the second column are from the model. All of the numbers are based on the deviation-from-trend components of the variables, with the trends found using the nonhnear procedure employed by Prescott and Hansen.

The first line of the table reports the standard deviation of output. The model produces output fluctuations that are only moderately smaller than those observed m practice. This finding is the basis for Prescotts (1986) famous conclusion that aggregate fluctuations are not just consistent with a competitive, neoclassical model, but are m fact predicted by such a model. The second and third lines of the table show that both m the United States and in the model, consumption is considerably less volatile than output, and Investment is considerably more volatile.

In addition, Prescott argues that, under the assumption that technology multiplies an expression of form F{K, L), the absence of a strong trend in capitals share suggests that f () is approximately Cobb-Douglas. Similarly, he argues on the basis of the lack of a trend in leisure per person and of studies of substitution between consumption in different periods that (4.7) provides a good approximation to the instantaneous utility function. Thus the choices of functional forms are not arbitrary.

TABLE 4.4 A calibrated real-business-cycle model vs. actual data



Productivity Movements in the Great Depression

Technological shocks are one of the key ingredients of real-business-cycle models. The main piece of macroeconomic evidence for the presence of substantial technological shocks is the considerable short-term variation in the Solow residual. For example, as described above, Prescott and Hansen and Wright estimate the magnitude of technology shocks from the behavior of the Solow residual.

The alternative to the view that variations m the Solow residual largely reflect shifts tn technology is that output fluctuations arising from other sources affect the measured Solow residual. If there are increasing returns to scale, for example, an increase in output occurring for reasons other than technological change wiB cause a Solow residual computed under the assumption of constant returns to rise. Similarly, if firms use their labor and capital more intensively when output is high, a Solow residual calculated assuming constant utilization will rise when output increases.

If we can identify a source of output movements other than changes in technology, we can test between these two views of the source of short-run variation in the Solow residual. The real-business-cycle view predicts that the Solow residual will not move systematically in the face of output fluctuations that do not result from technology shocks. The alternative view-that the variation is caused by output movements and that technology shocks have little to do with short-run output fluctuations-predicts that the Solow residual will move just as much with aggregate output when the output movements are known not to be due to technology shocks as it does at other times.

Bernanke and Parkinson (1991) carry out a simple test along these lines. Given that output per person fell sharply m the Great Depression, and given that substantial technological regress is unlikely, the output movements in

The final two lines of the table show that the baseline model is less successful in its predictions about the contributions of variations m labor input and in output per unit of labor input to aggregate fluctuations. In the U.S. economy, labor input is nearly as volahle as output; in the model it is much less so. And in the United States, labor input and productivity are essentially uncorrelated; in the model they move together closely.

Thus a simple calibration exercise can be used to identify a models major successes and failures, doing so, it suggests ways in which the model might be modified to improve its fit with the data. For example, additional sources of shocks would be likely to increase output fluctuations and to reduce the correlation between movements in labor input and in productivity. Indeed, Hansen and Wright show that, for their suggested parameter values, adding government-purchases shocks along the lines of the model of this chapter lowers the correlation of I and Y/L from 0.93 to 0.49; the change has little effect on the magnitude of output fluctuations, however.



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