Projection estimators for structural impulse responses

In this paper we provide a general framework for linear projection estimators for impulse responses in structural vector autoregressions (SVAR). An important advantage of our projection estimator is that for a large class of SVAR systems (that includes the recursive (Cholesky) identification scheme) standard OLS inference is valid without adjustment for generated regressors, autocorrelated errors or nonstationary variables. We also provide a framework for SVAR models that can be estimated by instrumental (proxy) variables. We show that this class of models (that includes also identification by long-run restrictions) result in a set of quadratic moment conditions that can be used to obtain the asymptotic distribution of this estimator, whereas standard inference based on instrumental variable (IV) projections is invalid. Furthermore, we propose a generalized least squares (GLS) version of the projections that performs similarly to the conventional (iterated) method of estimating impulse responses by inverting the estimated SVAR representation into the MA(∞) representation. Monte Carlo experiments indicate that the proposed OLS projections perform similarly to Jord`a’s (2005) projection estimator but enables us to apply standard inference on the estimated impulse responses. The GLS versions of the projections provide estimates with much smaller standard errors and confidence intervals whenever the horizon h of the impulse responses gets large.