Avoiding unintentionally correlated shocks in proxy vector autoregressive analysis

Noting that the shocks in vector autoregressive models can be correlated if a number of shocks is identified individually by multiple proxy variables, we propose a Generalized Method of Moments (GMM) approach for estimation that enforces uncorrelated shocks. We point out that if each proxy identifies exactly one shock and is uncorrelated with all other shocks, uncorrelatedness of the shocks provides over-identifying restrictions that can be used in our approach to improve the estimation efficiency of the structural parameters. It also opens up the possibility to use Hansen’s J-test to check the model specification. Our method generalizes other GMM proposals that work under more restrictive assumptions. We illustrate its usefulness by two empirical examples from the recent literature.