Sign Restrictions in Structural Vector Autoregressions: A Critical Review

Abstract

Structural Vector Autoregressions (SVARs) have become one of the major ways of extracting information about the macro economy. One might cite three major uses of them in macro-econometric research.1. For quantifying impulse responses to macroeconomic shocks.2. For measuring the degree of uncertainty about the impulse responses or other quantities formed from them.3. For deciding on the contribution of different shocks to fluctuations and forecast errors through variance decompositions.To determine this information a 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 which 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 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 structuralequations. Parametric restrictions on these equations can vary according to whether particular variables appear in the latter (Cowles Commission), whether there is a recursive causal structure (Wold (1951), Quenouille (1957) and Sims (1980)), and whether shocks have known short-run (Gali (1992)) or long-run (Blanchard and Quah (1989)) effects. In each case the parametric restrictions free up enough instruments for the contemporaneous endogenous variables in the structural equations, thereby enabling the parameters of those equations to be estimated. Recently, a fifth method for estimating SVARs has arisen that employs sign restrictions upon the impulse responses as a way of identifying shocks - Faust (1998), Uhlig (2005), Canova and De Nicolo (2002). Applications of this method have been growing, as seen in the papers listed in Table 1. The table is a sub-set of published studies and adopts a taxonomy which distinguishes between cases where only sign restrictions are used (often there are mixtures of sign and parametric restrictions), the type of shock (permanent or transitory), the number of shocks identified, and whether the sign restrictions come from a formal model or not. Consequently, it is worth examining this literature in more detail, and the aim of our paper is to exposit how the method works and to identify some of the difficulties that can arise in its application.