Comparing External and Internal Instruments for Vector Autoregressions

Abstract

In conventional proxy VAR analysis, the shocks of interest are identifiedby external instruments. This is typically accomplished by considering thecovariance of the instruments and the reduced-form residuals. Alternatively, theinstruments may be internalized by augmenting the VAR process by the instrumentsor proxies. These alternative identification methods are compared and itis shown that the resulting shocks obtained with the alternative approaches differin general. Conditions are provided under which their impulse responses arenevertheless identical. If the conditions are satisfied, identification of the shocksis ensured without further assumptions. Empirical examples illustrate the resultsand the virtue of using the identification conditions derived in this study.

Keywords: Structural vector autoregression, proxy VAR, augmented VAR, fundamental shocks, invertible VAR