This paper proposes consistent moment selection procedures for generalized method of moments estimation based on the J test of over-identifying restrictions [Hansen, L.P., 1982. Large sample properties of generalized method of moments estimators. Econometrica 50, 1029-1054] and on the Eichenbaum, Hansen and Singleton test of the validity of a subset of moment conditions [Eichenbaum, M.S., Hansen, L.P., Singleton, K.J., 1988. A Time Series Analysis of Representative Agents Models of Consumption and Leisure Choice Under Uncertainty. Quarterly Journal of Economics 103, 51-78]. (c) 2006 Elsevier B.V. All rights reserved.