Abstract: Many behavior characteristics in the area of economics, finance and business management can be depicted by moment restriction models. Nevertheless, the parameters estimation in these models is sensitive to the selection of moments. How to choose the optimal moments, and then get more accurate parameter estimation and statistical inference is a crucial problem in empirical research. A method is proposed in this paper to select moments for two-step generalized method of moments (GMM) estimators in moment restriction models with many moments. The basic idea of this method is choosing moments such that the MSE of the GMM estimator is smallest. Firstly, iterative techniques are used to derive the higher order mean squared error (MSE) for two-step GMM, and obtain the approximate MSE for the estimators using Nagar decomposition. Then the optimal selection criterion is proposed and the asymptotic efficiency is shown. Monte Carlo simulations indicate that the proposed selection criterion could improve the finite sample properties of two-step GMM, and reduce the finite sample bias of two-step GMM, significantly. This research provides a theoretical basis for selection of moments in empirical studies.

Key words: moment restriction models, generalized method of moments, higher order MSE, approximate MSE, selection criterion