Sign Restrictions in Structural Vector Autoregressions : A Critical Review

S vector autoregressions have become one of the major ways of extracting information about the macro economy. One might cite three major uses of them in macroeconometric research: for quantifying impulse responses to macroeconomic shocks; for measuring the degree of uncertainty about the impulse responses or other quantities formed from them; and for deciding on the contribution of different shocks to fluctuations and forecast errors through variance decompositions. To determine this information, a vector autoregression (VAR) is first fitted to summarize the data and then a structural VAR (SVAR) is proposed whose structural equation errors are taken to be the economic shocks. The parameters of these structural equations are then estimated by utilizing the information in the VAR. The VAR is a reduced form that summarizes the data; the SVAR provides an interpretation of the data. As for any set of structural equations, recovery of the structural equation parameters (shocks) requires the use of identification restrictions that reduce the number of “free” parameters in the structural equations to the number that can be recovered from the information in the reduced form. Five major methods for recovering the structural equation parameters (identifying the shocks) are present in the literature. Four of these explicitly utilize parametric restrictions. These involve the nature of the Sign Restrictions in Structural Vector Autoregressions: A Critical Review