The Optimal Choice of Moments in Dynamic Panel

Empirical researchers frequently use dynamic panel data models and employ Generalized Method of Moments (GMM) estimators (Hansen, 1982) to estimate model parameters. An important practical problem in the estimation of a dynamic panel data model is the choice of moments as it provides a large number of moment conditions. Even though adding moment conditions leads to efficiency gain according to the conventional asymptotic theory, it has been observed that in finite samples the GMM estimator behaves poorly in the presence of a large number of moment conditions, mainly due to bias. This paper derives the Nagar (1959) approximation of the mean squared error of the GMM estimator in dynamic panel data models with lagged dependent variable and strictly exogenous covariates. It shows that additional instruments should be included on the basis of how well they approximate the unobserved fixed effects. Using this result, a procedure for choosing the number of instruments and a procedure for shrinking the effects of additional instruments are proposed. Both methods are based on minimization of the asymptotic mean squared error. Monte Carlo experiments are conducted to compare the performance of these procedures with that of the GMM estimator using all the available moment conditions and that of the GMM estimator using a minimal subset of moment conditions. The results from the Monte Carlo study suggest that applying these procedures improves the GMM estimator in terms of mean squared error and that the confidence intervals based on the new estimation procedures have good coverage rates. The proposed methods are then applied to estimate a model of income dynamics, using PSID data, and an employment equation, using Spanish firm data.