Incontro Identification and Inference in proxy-SVARs with non-Gaussian shocks

Abstract

Two prevalent strategies for identifying structural VARs are external instruments, which carry economic motivation but are often weak, and the non-Gaussianity of the shocks which provides statistical identification but carries no economic meaning. We combine the two methods in a single generalized method of moments framework that stacks proxy exclusion restrictions with higher-order moment conditions of the structural shocks. This hybrid identification point-identifies the target shocks and identifies the non-target shocks up to sign and ordering. Under certain rank conditions, the higher-order moments anchor the identification uniformly over the proxy strength: under local-to-zero proxy relevance, the estimator remains consistent with standard asymptotic inference, and the Anderson-Rubin confidence sets are substantially narrower than those based on the instrument alone. The hybrid estimator is also more efficient than either source used in isolation: at any fixed proxy relevance, even a weak instrument increases efficiency through its covariance with the non-Gaussian moment block. Under local proxy endogeneity, we provide asymptotic bias bounds and show that stronger non-Gaussianity of the shocks compresses the bias. Finally, the over-identified structure yields two mutually orthogonal specification tests, for proxy exogeneity and non-Gaussianity of shocks. We derive their limiting distributions and provide a bootstrap procedure for finite-sample critical values. Monte Carlo evidence and two applications with identification of oil news-shock and a Euro-area MP shock demonstrate the potential of our framework.