Forward Orthogonal Deviations GMM and the Absence of Large Sample Bias

TL;DR

This paper demonstrates that forward orthogonal deviations GMM estimators are asymptotically unbiased under certain conditions on the number of instrumental variables, contrasting with other transformations that may induce bias.

Contribution

It establishes that FOD-based GMM estimators avoid large sample bias when the number of instruments grows slower than the square root of T, a novel result specific to FOD.

Findings

FOD GMM estimators are asymptotically unbiased under certain growth conditions.

Bias is linked to the number of instruments and transformation used.

Monte Carlo simulations support the theoretical findings.

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.