Consistent moment selection procedures for generalized method of moments estimation

This paper considers a generalized method of moments (GMM) estimation problem in which one has a vector of moment conditions, some of which are correct and some incorrect. The paper introduces several procedures for consistently selecting the correct moment conditions. The procedures also can consistently determine whether there is a sufficient number of correct moment conditions to identify the unknown parameters of interest. The paper specifies moment selection criteria that are GMM analogues of the widely used BIC and AIC model selection criteria. (The latter is not consistent.) The paper also considers downward and upward testing procedures. All of the moment selection procedures discussed in this paper are based on the minimized values of the GMM criterion function for different vectors of moment conditions. The procedures are applicable in time-series and cross-sectional contexts. Application of the results of the paper to instrumental variables estimation problems yields consistent procedures for selecting instrumental variables.