Efficient Shrinkage Estimation in Heterogeneous Panel Data Models Under Fixed or High-Dimensional Restrictions

This paper develops a Stein-like shrinkage estimator for heterogeneous panel data models with cross-sectional heteroskedasticity and contemporaneous error dependence, where the cross-section dimension is fixed and the time dimension increases. The estimator combines unrestricted and restricted feasible generalized least squares (FGLS) estimators, with a weight determined by a Wald statistic assessing the imposed linear restrictions. Under independence over time and suitable regularity conditions, we derive analytical expressions for the asymptotic bias, mean squared error matrix, and risk of the standard shrinkage estimator. We establish sufficient conditions for asymptotic risk dominance over the unrestricted FGLS estimator and characterize the limiting relative asymptotic risk under sequential limits with increasing regressor and restriction dimensions. Monte Carlo simulations examine the finite-sample performance of positive-part shrinkage under homogeneity and exclusion restrictions. An application to forecasting output growth in 19 countries illustrates modest improvements in forecast accuracy.