Forward Orthogonal Deviations GMM and the Absence of Large Sample Bias

Abstract: It is well known that generalized method of moments (GMM) estimators of dynamic panel data regressions can have significant bias when the number of time periods ($T$) is not small compared to the number of cross-sectional units ($n$). The bias is attributed to the use of many instrumental variables. This paper shows that if the maximum number of instrumental variables used in a period increases with $T$ at a rate slower than $T^{1/2}$, then GMM estimators that exploit the forward orthogonal deviations (FOD) transformation do not have asymptotic bias, regardless of how fast $T$ increases relative to $n$. This conclusion is specific to using the FOD transformation. A similar conclusion does not necessarily apply when other transformations are used to remove fixed effects. Monte Carlo evidence illustrating the analytical results is provided.