Panel Data Inference in Finance: Least-Squares vs Fama-Macbeth

Abstract

Empirical research in finance frequently involves analysis of panel data sets. In corporate finance, we typically encounter panels with large cross sections (large N), while in asset pricing, panels with long time series (large T) are more common. For each case, we examine four estimators: the Least-Squares (LS) and Fama-MacBeth (FM) estimators and their generalized versions. In particular, we offer a rigorous econometric analysis of the FM estimation procedure in the context of panel data. This covers the traditional FM method that is suitable for the large T case, as well as a novel modification of the method appropriate for the large N case. The generalized versions are more efficient, but the corresponding standard errors may be poorly estimated resulting in unreliable t-statistics. An extensive simulation study demonstrates that the estimators under consideration perform remarkably well in moderately small samples. In particular, we provide evidence that both estimation procedures (LS and FM), when properly applied, have comparable performance in the sense that they produce equally reliable t-statistics. Since the two approaches are justified under very similar assumptions, researchers are encouraged to use both approaches in their empirical work to ensure the validity of their results.

Keywords: Panel data, Fama-MacBeth, Standard errors

JEL Classification: C33