A Critique of Structural VARs Using Real Business Cycle Theory

The main substantive finding of the recent structural vector autoregression literature with a differenced specification of hours (DSVAR) is that technology shocks lead to a fall in hours. Researchers have used these results to argue that standard business cycle models in which technology shocks leads to a rise in hours should be discarded. We evaluate the DSVAR approach by asking the following: Is the specification derived from this approach misspecified when the data is generated by the very model the literature is trying to discard, namely the standard business cycle model? We find that it is misspecified. Moreover, this misspecification is so great that it leads to mistaken inferences that are quantitatively large. We show that the other popular specification which uses the level of hours (LSVAR) is also misspecified with respect to the standard business cycle model. We argue that an alternative approach, the business cycle accounting approach, is a more fruitful technique for guiding the development of business cycle theory. ∗The authors thank the National Science Foundation for support. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. The goal of the Structural Vector Autoregression (SVAR) approach is to identify promising classes of business cycle models using a simple time series technique. The approach has two popular specifications both of which use data on labor productivity and hours. The differenced specification, called the DSVAR, uses the first difference in hours while the level specification, called the LSVAR, uses the level of hours. We evaluate the SVAR procedure under both specifications by applying it to data generated from a standard business cycle model and find that both specifications are misspecified. With respect to the DSVAR our key finding is that the misspecification leads to quantitatively large mistaken inferences about standard business cycle models. With respect to the LSVAR our key finding is that in samples as long as those for postwar U.S. data the misspecification leads to uninformative inferences while for much longer samples the misspecification leads to mistaken inferences. The SVAR approach begins with the idea that it is possible to obtain impulse responses from the data using only a minimal amount of economic theory.1 These impulse response functions are the responses of the model’s economic system to innovations in various shocks. The hope is that the SVAR assumptions nest most business cycle models, at least approximately, so that the impulse responses obtained from the VAR set the standard for the theory: any promising model must produce impulse responses similar to those from the VARs. We focus on the DSVAR and the LSVAR literatures that study what happens after a technology shock. The findings of the two literatures are quite different. The main finding of the DSVAR literature is that a technology shock leads to a fall in labor input. Gali (1999), Francis and Ramey (2003), and Gali and Rabanal (2004) use the DSVAR procedure to draw 1See, among others, Shapiro and Watson 1988, Blanchard and Quah 1989, Gali 1999, Francis and Ramey 2003, Christiano, Eichenbaum and Vigfusson 2003, Uhlig 2003, and Gali and Rabanal 2004. the inference that this evidence dooms existing real business cycle models as unpromising and points to other models, such as sticky price models, as a more promising class of models. For example, Francis and Ramey (2003, p.2) say, “...the original technology-driven real business cycle hypothesis does appear to be dead.” Likewise, Gali and Rabanal (2004, conclusion) state, “The bulk of the evidence reported in the present paper raises serious doubts about the importance of changes in aggregate technology as a significant (or, even more, a dominant) force behind business cycles ...” In the LSVAR literature the range of results reported by researchers is very wide. Francis and Ramey (2004) argue that the LSVAR evidence shows that real business cycle models are dead. Christiano, Eichenbaum and Vigfusson (2003) argue that their LSVAR results imply that these models are alive and well. Gali and Rabanal (2004) argue that their LSVAR results, by themselves, are inconclusive. As we document below, while all three studies use slightly different methodologies, their sharply contrasting results are driven almost entirely by differences in the underlying data. It is worth noting that all three of these studies use very similar conceptual measures of productivity and Christiano, Eichenbaum and Vigfusson and Gali and Rabanal use very similar conceptual measures of hours. That the LSVAR results are so sensitive to seemingly minor differences in measuring productivity and hours raises doubts about the reliability of the LSVAR procedure for drawing inferences about underlying models. Both branches of the SVAR literature make several assumptions to identify the underlying shocks, often labelled as demand and technology shocks. This literature views two identifying assumptions as key: (i) demand shocks have no permanent effect on the level of labor productivity while technology shocks do and, (ii) the demand and technology shocks