A Critique of Structural VARs Using 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 business cycle models in which technology shocks lead to a rise in hours should be discarded. We evaluate the DSVAR approach by asking, is the specification derived from this approach misspecified when the data are generated by the very model the literature is trying to discard? 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 that uses the level of hours (LSVAR) is also misspecified. We argue that alternative state space approaches, including the business cycle accounting approach, are more fruitful techniques for guiding the development of business cycle theory. ∗Chari, University of Minnesota and Federal Reserve Bank of Minneapolis; Kehoe, Federal Reserve Bank of Minneapolis and University of Minnesota; 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 procedure. The idea behind the procedure is to run vector autoregressions in the data and impose identifying assumptions to back out impulse responses to various shocks.1 These SVAR impulse responses are then, typically implicitly, compared with theoretical impulse responses from economic models. Importantly, this literature does not follow the procedure that Sims (1989) advocates, in which the same VAR is run on data from an actual economy as on data generated from a model and statistics from the VARs are compared. We focus on the branch of the literature that studies impulse responses to a technology shock. We subject the SVAR procedure to a natural economic test. We treat an economic model as the data-generating mechanism and calculate the population impulse responses obtained from applying the SVAR procedure to data from the model. We ask whether the impulse responses identified by the SVAR procedure are close to the model’s impulse responses. For a large class of parameters, including ones estimated from the data, we find they are not. In this sense, we provide counterexamples to claims in the literature that, as long as the model satisfies the key identifying assumptions, the procedure will uncover the model’s impulse responses. In addition, we show analytically when the SVAR procedure will produce responses close to the model responses and when it will not. This technology shock branch of the SVAR literature 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, and the level specification, called the LSVAR, uses the level of hours. Both branches of the SVAR literature make several assumptions to identify the underlying shocks, often labeled as demand shocks and technology shocks. This literature views two identifying assumptions as key: (i) demand shocks have no permanent 1See, among others, Shapiro and Watson (1988), Blanchard and Quah (1989), Gali (1999), Francis and Ramey (2003), Christiano, Eichenbaum, and Vigfusson (2003), Gali and Rabanal (2004), and Uhlig (2004). effect on the level of labor productivity while technology shocks do, and (ii) the demand and technology shocks are orthogonal. Both branches estimate a VAR with a small number of lags, typically four. The main finding of the DSVAR literature is that a technology shock leads to a fall in hours. Gali (1999), Francis and Ramey (2003), and Gali and Rabanal (2004) use the DSVAR procedure to infer that this finding 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. In the LSVAR literature researchers report a wide range of results. Francis and Ramey (2004) argue that the LSVAR evidence shows that real business cycle models are dead. Conversely, Christiano, Eichenbaum, and Vigfusson (2003) maintain that their LSVAR results imply that these models are alive and well, while Gali and Rabanal (2004) assert that their LSVAR results, by themselves, are inconclusive. As we document below, these sharply contrasting results are driven almost entirely by small differences in the underlying data. We tilt our test in favor of the SVAR procedure by focusing mainly on a stripped-down business cycle model, referred to as the baseline model, that satisfies the two key identifying assumptions of the SVAR literature. Most business cycle models do not satisfy these two assumptions. In this sense our model is a best-case scenario for the SVAR procedure. Our estimated model shares the feature of second generation business cycle models in that it has multiple shocks with stochastic processes estimated from the data. In order to abstract from small sample biases and sampling uncertainty, we mainly study population impulse responses obtained from applying the SVAR procedure to our model rather than impulse responses computed from short samples generated by our model. The population impulse responses from the DSVAR procedure imply that a technology shock leads to a decline in hours. This conclusion is mistaken because in our model a technology shock leads to a rise in hours. The population impulse responses from the LSVAR procedure imply that a technology shock leads to a rise in hours about three times that in the model.