On the Contribution of Technology Shocks to Business Cycles

This article contends that the various measures of the contribution of technology shocks to business cycles calculated using the real business cycle modeling method are not corroborated. The article focuses on a different and much simpler method for calculating the contribution of technology shocks, which takes account of facts concerning the productivity/labor input correlation and the variability of labor input relative to output. Under several standard assumptions, the method predicts that the contribution of technology shocks must be large (at least 78 percent), that the labor supply elasticity need not be large to explain the observed fluctuation in labor input, and that the contribution of technology shocks can be estimated fairly precisely. The method also estimates that the contribution of technology shocks could be lower than 78 percent under alternative assumptions. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. The paper “Time to Build and Aggregate Fluctuations” by Kydland and Prescott (1982) has led to a controversy in the literature on business cycles concerning the extent to which technology shocks are responsible for aggregate fluctuations in the U.S. economy. Prescott (1986b, p. 29) has suggested that “technology shocks account for more than half the fluctuations in the postwar period, with a best point estimate near 75 percent.” Since then, several people have questioned this conclusion and suggested that the contribution of technology shocks is much lower than the figure calculated by Prescott. The policy importance of figuring out the relative contribution of different sources of economic fluctuations arises from the following considerations. Sometimes the choice of a policy instrument can depend on the relative contribution of different shocks to fluctuations. Sometimes the exact nature of a desirable policy rule can depend on the nature of shocks. That is, how government policy variables should respond to observable variables like output and investment can depend on whether fluctuations are due to technology shocks or some other shocks. If the root sources of fluctuations are not observable directly (unlike, say, the weather) or indirectly, then the government has to solve a signal extraction problem to determine optimal government policy. The solution of any signal extraction problem depends on the relative contribution of different sources of fluctuations to observables. Therefore, it becomes important to determine the contribution of different shocks to economic fluctuations. In this article, I will argue that the various measures of the contribution of technology shocks to business cycles calculated using the real business cycle (RBC) modeling method are not supported by corroborating evidence. I should emphasize that this criticism is not specifically against the number put forth by Prescott but applies to most such studies regardless of whether the particular number they yield is large or small. One—or none—of these numbers may be right, but there is no way to know based solely on the properties of these models and the data. Then I will describe a different and much simpler method for calculating the extent to which technology shocks contribute to business cycles, which is the main focus of my article. This method is designed to take account of facts concerning the productivity/labor input correlation and the variability of labor input relative to output and has the following implications: • Under the standard assumptions of competitive markets, no external economies of scale, and no measurement errors, > Either the contribution of technology shocks must be large (at least 78 percent), or the predictions concerning the productivity/labor input correlation and the variability of labor input relative to output will be incorrect. > A large magnitude of the aggregate intertemporal labor supply elasticity is not necessary for explaining the observed fluctuation in labor input. Hence some of the work in RBC modeling that has attempted to modify the basic growth model by increasing the intertemporal labor supply elasticity has been quite unnecessary. Instead, work should have focused on incorporating shocks other than technology into these models. > Contrary to the argument of Eichenbaum (1991), the contribution of technology shocks can be estimated fairly precisely. • The point estimate of the contribution of technology shocks can be lower than 78 percent under alternative assumptions involving imperfect competition, external economies of scale, overtime wage premiums, and measurement errors (especially systematic errors in measuring labor input) while still resulting in correct predictions for the productivity/labor input correlation and the variability of labor input relative to output. In view of the second implication, the argument of Prescott’s critics that the contribution of technology shocks is much lower should be understood to imply some departure from the standard assumptions. I will conclude by suggesting that it may be possible to use empirical evidence from micro studies at the firm and household level to determine whether the standard assumptions or some alternative assumptions are appropriate. Thus it may be possible to narrow the range of disagreement regarding the contribution of technology shocks. Problems With Measures Based on Real Business Cycle Models Perhaps the best way to explain the problems with current RBC model–based measures of the importance of technology shocks is by analogy with the price and quantity determination in a single market, in terms of the usual supply/demand apparatus. Suppose that the supply and demand curves are being shifted by many random influences, one of these being random changes in technology. (For simplicity, I will assume that any particular shock affects either supply or demand, but not both, and that the various shocks are mutually independent.) Clearly, equilibrium price and quantity will be fluctuating randomly. A modeler of such a market, who is interested in how much technology shocks contribute to quantity fluctuations, could specify a supply/demand model in which only technology shocks enter (say, on the supply side), calculate the variance of quantity (which is a measure of how much quantity fluctuates in the model), express this as a ratio to the variance of quantity in the data, and report that as the contribution of technology shocks to quantity fluctuations. Let us call this ratio φ. How would one defend the calculated value of φ as plausible? One possibility is to compare the model’s predictions for the price/output correlation and the variance of price with the data. However, if φ is not close to unity, then such a comparison would not make sense since, admittedly, the model is omitting some shocks which are present in the data and which significantly affect the price/output correlation and the degree of price fluctuation. Therefore, there is no way to judge if the calculated value of φ is plausible or not. Further, given that the model is missing some quantitatively significant shocks, it would appear to be better if the model’s predictions were wrong. But, again, there is no way to say by how much they would have to be wrong in order for the calculated value of φ to be right. RBC models are basically similar to a supply/demand model except that the RBC analysis is of a general equilibrium nature and may include some shocks in addition to technology shocks. The RBC modeler specifies the technology and the preferences and endowments of the individuals in the model economy using particular functional forms and parameter values. These are used to calculate the unconditional variance of output in the model economy when only technology shocks are present. This is expressed as a fraction (denoted φ) of the variance of output in the U.S. economy, and φ is taken to be an estimate of the contribution of technology shocks to output fluctuation. The view underlying many RBC models (certainly those with only technology shocks in them) seems to be that the models are missing quantitatively important sources of fluctuations. As Prescott (1991, p. 6) has said, “To estimate the model is to implicitly assume that technology shocks are the only significant source of fluctuations. That is not a hypothesis we were willing to maintain.” That is, under this view, a close match of model statistics with those in the data cannot be used to corroborate the calculated value of φ. Indeed, as noted in the supply/demand example, it would appear to be better if the model statistics were not close to the values in the data. As Prescott has noted (1991, p. 6), “Mimicking is not always good.” However, as noted earlier, for this to be useful in practice, one needs to know by how much the model statistics should miss those in the data. Since this is often not possible, it is difficult to evaluate the plausibility of these models and thereby defend the contribution of technology shocks implied by them. The above comments apply also to the models of some of Prescott’s critics. Sometimes the output variance generated by their models is significantly lower than that of the data, suggesting that their models are missing some shocks that explain the remaining portion of output variance. One cannot then defend the calculated value of φ by comparing model statistics with those in the data (using either informal or formal econometric methods), since it is hard to maintain that the data were (even approximately) generated by the model at hand. As an example, consider the work of Burnside, Eichenbaum, and Rebelo (1993), who incorporate a labor hoarding feature (as suggested by Summers 1986) into an RBC model. Some versions of this model (with both technology shocks and government consumption shocks) generate output variance that is only 30–40 percent of that of U.S. data. (See the values of λ for “Labor Hoarding I” and “Laboring Hoarding II” in their Table 4.) Hence the contribution of technology shocks alone is implied to be even lower. On this basis, Burnside, Eichenbaum, and Rebelo (1993) argue that the contribution of technology shocks may be much lower than Prescott’s figure. And yet they suggest (p. 255) that “the labor hoarding model does at least as well as the Hansen-Rogerson model at accounting for the volatility of hours worked and the relative volatility of consumption, investment, average productivity, and government consumption” (Hansen 1985, Rogerson 1988). Elsewhere (p. 260) they state, “Burnside et al. (1991) argue that the labor hoarding model is better able to account for the joint behavior of average productivity and hours worked than the standard model.” It cannot be a good feature of a model that it matches various correlations in the data while missing shocks that account for possibly as much as 70 percent of output variance. Clearly, the contribution of technology shocks to business cycles calculated using RBC models is unsupported by corroborating evidence. A Simpler Method of Measuring Here I will present a different and much simpler method that is based on a variance decomposition procedure, imposes a minimum of theoretical structure on the data, uses only information on contemporaneous correlations, and does not rely on measures of Solow residuals. This is in contrast to the elaborate dynamic theoretical structure imposed in RBC modeling methods and the use of measured Solow residuals. In my method, a lower bound for the contribution of technology shocks is derived by calculating the relative strength of technology versus other shocks, which is required to match two key features of the data: the contemporaneous productivity/labor input correlation and the variability of labor input relative to output. (These two numbers determine all the other standard deviations and cross-correlations among the three variables: output, labor input, and productivity.) The intuition behind how the observed values of the productivity/labor input correlation and the variability of labor input relative to output can be used to deduce the contribution of technology shocks and nontechnology shocks to business cycles is as follows. Suppose, for the sake of illustration, that the production technology satisfies diminishing returns to labor input. If nontechnology shocks were the only source of fluctuations, then clearly labor input would fluctuate more than output, and the productivity/labor input correlation would be close to negative unity. If technology shocks were the only source of fluctuations, however, then labor input would generally fluctuate less than output, and the productivity/labor input correlation would be close to unity. Therefore, the empirically observed values of these two statistics can be used to deduce the relative strengths of technology versus nontechnology shocks and hence the contribution of technology shocks to business cycles. There are three key steps in my analysis. The first is the specification of technology. This is specified as