Forward Orthogonal Deviations GMM and the Absence of Large Sample Bias

2022/12/28 by Robert F. Phillips, Phillips, Robert F.
Economics, Econometrics and Finance · #Econometrics (econ.EM) #Economic Growth and Productivity #FOS: Economics and business #Fiscal Policy and Economic Growth #Spatial and Panel Data Analysis

paper · pdf · doi:10.48550/arxiv.2212.14075

openalex publication_date 2022/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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