Conventional statistical methods for panel data are based on the assumption that unobserved heterogeneity is time constant. Despite the central importance of this assumption for panel data methods, few studies have developed statistical methods for testing this assumption and modeling time-varying unobserved heterogeneity. In this article, I introduce a formal test to check the assumption of time-constant unobserved heterogeneity using Bayesian model comparison. Then, I present two panel data methods that account for time-varying unobserved heterogeneity in the context of the random-effects model and the fixed-effects model, respectively. I illustrate the utility of the introduced methods using both simulated data and examples drawn from two important debates in the political economy literature: (1) the identification of shifting relationships between income inequality and economic development in capitalist countries and (2) the effects of the GATT/WTO on bilateral trade volumes.