On the Identification of Structural Vector Autoregressions

F ollowing seminal work by Sims (1980a, 1980b), the economics profession has become increasingly concerned with studying sources of economic fluctuations. Sims’s use of vector autoregressions (VARs) made it possible to address both the relative importance and the dynamic effect of various shocks on macroeconomic variables. This type of empirical analysis has had at least two important consequences. First, by deepening policymakers’ understanding of how economic variables respond to demand versus supply shocks, it has enabled them to better respond to a constantly changing environment. Second, VARs have become especially useful in guiding macroeconomists towards building structural models that are more consistent with the data. According to Sims (1980b), VARs simply represented an atheoretical technique for describing how a set of historical data was generated by random innovations in the variables of interest. This reduced-form interpretation of VARs, however, was strongly criticized by Cooley and Leroy (1985), as well as by Bernanke (1986). At the heart of the critique lies the observation that VAR results cannot be interpreted independently of a more structural macroeconomic model. Recovering the structural parameters from an estimation procedure requires that some restrictions be imposed. These are known as identifying restrictions. Implicitly, the choice of variable ordering in a reduced-form VAR constitutes such an identifying restriction. As a result of the Cooley-Leroy/Bernanke critique, economists began to focus more precisely upon the issue of identifying restrictions. The extent to which specific innovations were allowed to affect some subset of variables,