Information Criteria for Selecting Instrumental Variables in Conditional Moment Restriction Models

• Activity Number: 477
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Gunce Eryuruk*+ and Bruce E. Hansen
• Companies: ITAM and University of Wisconsin
• Keywords: generalized method of moments ; mean squared error ; information criterion ; instrument selection ; moment selection

Abstract

The efficiency of GMM estimation is sensitive to the choice of instruments. Increasing the number of instruments decreases the asymptotic variance but increases the finite sample bias of the GMM estimator. A major breakthrough is the work of Donald, Imbens and Newey (2009), who have derived a general expression for the higher-order asymptotic mean square error (MSE) of GMM estimators, allowing for nonlinear simultaneous models with unknown heteroskedasticity. They also suggested an estimator of the MSE to be used as a finite-sample instrument selection criterion, but did not fully justify or investigate this criterion. Our focus is on the construction of an appropriate finite-sample instrument selection criterion. First, we generalize their MSE expression to allow general weight matrices. Second, using asymptotic expansions we formally investigate the bias in the natural plug-in estimator of the MSE. Third, we propose and evaluate bias-corrections for the MSE estimators, in analogy to the classic Mallows criterion for regression models. We investigate the performance of our proposed instrument selection criterion via asymptotic expansions and finite sample simulations.