Projection Estimators for Structural Impulse Responses

In this paper we provide a general two‐step framework for linear projection estimators of impulse responses in structural vector autoregressions (SVARs). This framework is particularly useful for situations when structural shocks are identified from information outside the VAR (e.g. narrative shocks). We provide asymptotic results for statistical inference and discuss situations when standard inference is valid without adjustment for generated regressors, autocorrelated errors or non‐stationary variables. We illustrate how various popular SVAR models fit into our framework. Furthermore, we provide a local projection framework for invertible SVAR models that are estimated by instrumental variables (IV). This class of models results in a set of quadratic moment conditions used to obtain the asymptotic distribution of the estimator. Moreover, we analyse generalized least squares (GLS) versions of the projections to improve the efficiency of the projection estimators. We also compare the finite sample properties of various estimators in simulations. Two highlights of the Monte Carlo results are (i) for invertible VARs our two‐step IV projection estimator is more efficient compared to existing projection estimators and (ii) using the GLS projection variant with residual augmentation leads to substantial efficiency gains relative to standard OLS/IV projection estimators.