Autocorrelated Errors in Panel Linear Regression: A New Objective Bayesian Perspective

A challenge to the estimation and inference of panel linear regression models consists in the uncertainty associated with the unknown autocovariance of errors. For an improved quantification of this uncertainty particularly in the context of wide panels, the study derives an objective Bayesian posterior of the interested coefficients where the unknown autocovariance of errors is marginalized out. Due to the intractability of the posterior's normalizing constant, estimation and inference rely on the Monte Carlo samples generated from the No-U-Turn Sampler algorithm. Theoretic works show that the proposed Bayesian method approaches the properties of generalized least squares (GLS) asymptotically. Simulation tests reveal that the Bayesian method performs closer to GLS compared to other frequentist methods, achieving a relatively reasonable balance between robustness and efficiency. For a real application, the Bayesian method is extended to the case of unbalanced panel and then compared with other methods in examining the ambiguous relation between CEO duality and financial performance. Finally, limitations of the current study and recommendations for the future research are discussed.