In a recent paper, Yoon and Lee (2019) (YL hereafter) propose a weighted Fama and MacBeth (FMB hereafter) two-step panel regression procedure and provide evidence that their weighted FMB procedure produces more efficient coefficient estimators than the usual unweighted FMB procedure. The purpose of this study is to supplement and improve their weighted FMB procedure, as they provide neither asymptotic results (i.e. consistency and asymptotic distribution) nor evidence on how close their standard error estimator is to the true standard error.
First, asymptotic results for the weighted FMB coefficient estimator are provided. Second, a finite-sample-adjusted standard error estimator is provided. Finally, the performance of the adjusted standard error estimator compared to the true standard error is assessed.
It is found that the standard error estimator proposed by Yoon and Lee (2019) is asymptotically consistent, although the finite-sample-adjusted standard error estimator proposed in this study works better and helps to reduce bias. The findings of Yoon and Lee (2019) are confirmed even when the average R2 over time is very small with about 1% or 0.1%.
The findings of this study strongly suggest that the weighted FMB regression procedure, in particular the finite-sample-adjusted procedure proposed here, is a computationally simple but more powerful alternative to the usual unweighted FMB procedure. In addition, to the best of the authors’ knowledge, this is the first study that presents a formal proof of the asymptotic distribution for the FMB coefficient estimator.
