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

Kurt Lunsford

No 1528, Working Papers (Old Series) from Federal Reserve Bank of Cleveland

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: Productivity Shocks; F Statistic; TFP; Weak IV; Structural Vector Autoregression; Proxy Variable (search for similar items in EconPapers)
JEL-codes: C12 C13 O47 C32 C36 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2015-12-04, Revised 2015-12-04
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