Identification and Estimation Issues in Structural Vector Autoregressions with External Instruments

Abstract

In this paper we discuss general identification results for Structural Vector Autoregressions (SVARs) with external instruments, considering the case in which r valid instruments are used to identify g ≥ 1 structural shocks, where r ≥ g. We endow the SVAR with an auxiliary statistical model for the external instruments which is a system of reduced form equations. The SVAR and the auxiliary model for the external instruments jointly form a ‘larger’ SVAR characterized by a particularly restricted parametric structure, and are connected by the covariance matrix of their disturbances which incorporates the ‘relevance’ and ‘exogeneity’ conditions. We discuss identification results and likelihood-based estimation methods both in the ‘multiple shocks’ approach, where all structural shocks are of interest, and in the ‘partial shock’ approach, where only a subset of the structural shocks is of interest. Overidentified SVARs with external instruments can be easily tested in our setup. The suggested method is applied to investigate empirically whether commonly employed measures of macroeconomic and financial uncertainty respond on-impact, other than with lags, to business cycle fluctuations in the U.S. in the period after the Global Financial Crisis. To do so, we employ two external instruments to identify the real economic activity shock in a partial shock approach.