Working Paper

Identifying Structural VARs with a Proxy Variable and a Test for a Weak Proxy

Abstract: This paper develops a simple estimator to identify structural shocks in vector autoregressions (VARs) by using a proxy variable that is correlated with the structural shock of interest but uncorrelated with other structural shocks. When the proxy variable is weak, modeled as local to zero, the estimator is inconsistent and converges to a distribution. This limiting distribution is characterized, and the estimator is shown to be asymptotically biased when the proxy variable is weak. The F statistic from the projection of the proxy variable onto the VAR errors can be used to test for a weak proxy variable, and the critical values for different VAR dimensions, levels of asymptotic bias, and levels of statistical significance are provided. An important feature of this F statistic is that its asymptotic distribution does not depend on parameters that need to be estimated.

Keywords: F Statistic; Productivity Shocks; proxy variables; Structural Vector Autoregression; total factor productivity; Weak IV;

JEL Classification: C12; C13; C32; C36; O47;

https://doi.org/10.26509/frbc-wp-201528

Bibliographic Information

Provider: Federal Reserve Bank of Cleveland

Part of Series: Working Papers (Old Series)

Publication Date: 2015-12-04

Number: 1528