The system GMM estimator developed by Blundell and Bond (1998) for dynamic panel data models has been widely used in empirical work; however, it does not perform well with weak instruments. This paper proposes a variation on the system GMM estimator, based on a simple transformation of the dependent variable. Simulation results indicate that, infinite samples, this transformed system GMM estimator greatly outperforms its conventional counterpart in estimating the coefficient of the lagged dependent variable, especially when the variation in the fixed effects is large relative to that in the idiosyncratic shocks and when the dependent variable is highly persistent. Applying this transformation also substantially strengthens the reliability of inferences on the overall model specification based upon the Sargan/Hansen test. As illustrations, the transformed system GMM estimator is applied to two empirical examples from the literature: a production function and an employment equation.

In this paper, we investigate the weak instruments problem of the generalized method of moments (GMM) estimator for dynamic panel data models. Specifically, we complement Bun and Windmeijer (2010) by considering the alternative first-difference and level models transformed by the forward GLS transformation. We demonstrate that this transformation yields a higher concentration parameter compared with the original models. This indicates that the proposed transformation yields stronger instruments even though the instruments used are identical. The Monte Carlo simulation results show that the system GMM estimator for the transformed model, called the forward system GMM estimator, performs better than the conventional system GMM estimator.

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.

Written by one of the world's leading experts on dynamic panel data reviews, this volume reviews most of the important topics in the subject. It deals with static models, dynamic models, discrete choice and related models.

This paper considers GMM based estimation and testing procedures for two versions of the AR(1) model with Fixed Effects, henceforth abbreviated as ARFE(1): the conditional ARFE(1) model, and the inclusive ARFE(1) model, which contains the stationary ARFE(1) models and the ARFE(1) model with a unit root. First, the paper presents a two-step Optimal Linear GMM (OLGMM) estimator for the inclusive model, which is asymptotically equivalent to the optimal nonlinear GMM estimator of Ahn and Schmidt (1997). Then the paper examines the properties of the GMM estimators for both versions of the model when the data are persistent. Among other things, we find that the OLGMM estimator is superefficient in the unit root case. Furthermore, under stationarity the covariances of the instruments of the Arellano-Bond estimator and the first differences of the dependent variable are not weak. We also derive new approximations to the finite sample distributions of the Arellano-Bond estimator (for both versions of the model), the Arellano-Bover estimator, and the System estimator. We employ local-to-zero asymptotics (cf Staiger and Stock (1997)) for the Arellano-Bond estimator for the conditional model, because its instruments are weak in this context, and we employ local-to-unity asymptotics, which is developed in this paper, for the estimators for the stationary model. The new approximations agree well with the Monte Carlo evidence in terms of bias and variance. Finally, various GMM based unit root tests against stationary and conditional alternatives are proposed.