This paper develops consistent model and moment selection criteria for GMM estimation. The criteria select the correct model speciﬁcation and all correct moment conditions asymptotically. The selection criteria resemble the widely used likelihood-based selection criteria BIC, HQIC, and AIC. (The latter is not consistent.) The GMM selection criteria are based on the J statistic for testing over-identifying restrictions. Bonus terms reward the use of fewer parameters for a given number of moment conditions and the use of more moment conditions for a given number of parameters. The paper applies the model and moment selection criteria to dynamic panel data models with unobserved individual eﬀects. The paper shows how to apply the selection criteria to select the lag length for lagged dependent variables, to detect the number and locations of structural breaks, to determine the exogeneity of regressors, and/or to determine the existence of correlation between some regressors and the individual eﬀect. To illustrate the ﬁnite sample performance of the selection criteria and their impact on parameter estimation, the paper reports the results of a Monte Carlo experiment on a dynamic panel data model.
Andrews, Donald W.K. and Lu, Biao, "Consistent Model and Moment Selection Criteria for GMM Estimation with Application to Dynamic Panel Data Models" (1999). Cowles Foundation Discussion Papers. 1482.