A Subset-Continuous-Updating Transformation on GMM Estimators for Dynamic Panel Data Models

The two-step GMM estimators of Arellano and Bond (1991) and Blundell and Bond (1998) for dynamic panel data models have been widely used in empirical work; however, neither of them performs well in small samples with weak instruments. The continuous-updating GMM estimator proposed by Hansen, Heaton and Yaron (1996) is in principle able to reduce the small-sample bias but it involves high-dimensional optimizations when the number of regressors is large. This paper proposes a computationally feasible variation on the standard two-step GMM estimators by applying the idea of continuous-updating on the autoregressive parameter only, given the fact that the absolute value of the autoregressive parameter is less than unity for a dynamic panel data model to be stationary. We show that our subset-continuous-updating transformation does not alter the asymptotic distribution of the two-step GMM estimators and it therefore retains consistency. Our simulation results indicate that the transformed GMM estimators significantly outperform their standard two-step counterparts in small samples