An Augmented Anderson-Hsiao Estimator for Dynamic Short-T Panels

This paper introduces the idea of self-instrumenting endogenous regressors in settings when the correlation between these regressors and the errors can be derived and used to bias-correct the moment conditions. The resulting bias-corrected moment conditions are less likely to be subject to the weak instrument problem and can be used on their own or in conjunction with other available moment conditions to obtain more efficient estimators. This approach can be applied to estimation of a variety of models such as spatial and dynamic panel data models. This paper focuses on the latter, and proposes a new estimator for short T dynamic panels by augmenting Anderson and Hsiao (AAH) estimator with bias-corrected quadratic moment conditions in first differences which substantially improve the small sample performance of the AH estimator without sacrificing on the generality of its underlying assumptions regarding the fixed effects, initial values and heteroskedasticity of error terms. Using Monte Carlo experiments it is shown that AAH estimator represents a substantial improvement over the AH estimator and more importantly it performs well even when compared to Arellano and Bond and Blundell and Bond (BB) estimators that are based on more restrictive assumptions, and continues to have satisfactory performance in cases where the standard GMM estimators are inconsistent. Finally, to decide between AAH and BB estimators we also propose a Hausman type test which is shown to work well when T is small and n sufficiently large.