Feasible Generalized Least Squares for Panel Data with Cross-sectional and Serial Correlations

TL;DR

This paper introduces a feasible GLS estimator for panel data that efficiently accounts for heteroskedasticity, serial, and cross-sectional correlations by estimating the error covariance matrix with banding and thresholding methods.

Contribution

It develops a consistent estimation approach for the error covariance matrix in panel data, improving efficiency over OLS under complex correlation structures.

Findings

The estimator is more efficient than OLS in simulations.

The limiting distribution of the estimator is established.

The method performs well in empirical application.

Abstract

This paper considers generalized least squares (GLS) estimation for linear panel data models. By estimating the large error covariance matrix consistently, the proposed feasible GLS (FGLS) estimator is more efficient than the ordinary least squares (OLS) in the presence of heteroskedasticity, serial, and cross-sectional correlations. To take into account the serial correlations, we employ the banding method. To take into account the cross-sectional correlations, we suggest to use the thresholding method. We establish the limiting distribution of the proposed estimator. A Monte Carlo study is considered. The proposed method is applied to an empirical application.