BLUP in the nested panel regression model with serially correlated errors

The best linear unbiased predictor for the panel data regression model with serially correlated nested error components is derived. Furthermore, performance of the predictor is compared with the other predictors using the study of productivity of public capital in private production based on a panel of 28 states over the period 1970-1986. The estimators whose predictions are compared include OLS, nested effects ML estimator ignoring serial correlation and nested effects ML estimator accounting for the serial correlation. Based on prediction mean square error (PMSE) forecast performance, it is crucial to take into account nested effects as well as serial correlation.