Are Structural VARs Useful Guides for Developing Business Cycle Theories?

The main substantive finding of the recent structural vector autoregression literature with a difference 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 test 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 data analysis. ∗Chari, University of Minnesota and Federal Reserve Bank of Minneapolis; Kehoe, Federal Reserve Bank of Minneapolis; McGrattan, Federal Reserve Bank of Minneapolis and University of Minnesota. 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 test 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.