Two-way random effects model with serial correlation

This paper derives a feasible GLS estimator for a two-way error component model with serial correlation on both the time effects as well as the remainder disturbances. This estimator is based on two methods, one proposed by De Porres and Krishnaku mar(2013) for deriving the spectral decomposition of a general error component structure and the other based on an inversion trick for the variance-covariance matrix of this model suggested by Skoglund and Karlsson (2001). While the last paper used maximum likelihood methods under the normality assumption, we use method of moments estimators following Baltagi and Li (1991) for the one-way error component model with serially correlated remainder disturbances and its extension by Brou et al. (2011) for the two-way model with serially correlated time effects as well as remainder disturbances. Monte Carlo simulations are performed to compare the performance of these two estimators as well as a bias correction version based on Nobach (2023). Our results find that the method based on the (Skoglund and Karlsson 2001) inverse that is bias corrected a la (Nobach 2023) performs the best in root mean square error (RMSE) as well as mean absolute percentage error (MAPE) and is recommended.