This paper considers a linear panel data model with time varying heterogeneity. Bayesian inference techniques organized around Markov chain Monte Carlo (MCMC) are applied to implement new estimators that combine smoothness priors on unobserved heterogeneity and priors on the factor structure of unobserved effects. The latter have been addressed in a non-Bayesian framework by Bai (2009) and Kneip et al. (2012), among others. Monte Carlo experiments are used to examine the finite-sample performance of our estimators. An empirical study of efficiency trends in the largest banks operating in the U.S. from 1990 to 2009 illustrates our new estimators. The study concludes that scale economies in intermediation services have been largely exploited by these large U.S. banks.