The Consistent Method of Moments Estimator in Weak Instrument Cases

• 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): Ignacio Lobato*+ and Eduardo García Gómez-Tagle
• Companies: Instituto Tecnológico Autónomo de México and ITAM
• Keywords: consistency ; weak instruments ; method of moments ; instrumental variables

Abstract

This article studies the behavior of the consistent method of moments (CMM) estimator introduced in Dominguez and Lobato (2004) in the context of weak instruments for both linear and nonlinear cases. For the linear case when many instruments are available, we propose a two step estimator based on a modification of the CMM estimator that is simple to calculate and presents better finite sample performance. For the case where the parameters of interest are defined by nonlinear conditional moments, the CMM estimator is more robust in situations such as weak instruments, where some orthogonality conditions are close to zero. The reason behind this robustness is that the CMM estimator relies on an infinite number of orthogonal conditions to identify these parameters, in contrast to the traditional instrumental variable estimator. We illustrate this robustness with simulations in both linear and nonlinear cases, which compare the finite sample behavior of instrumental variable estimators and our proposed extensions of the CMM estimator.