We provide a comprehensive examination of the predictive accuracy of panel forecasting methods based on individual, pooling, fixed effects, and Bayesian estimation, and propose optimal weights for forecast combination schemes. We consider linear panel data models, allowing for weakly exogenous regressors and correlated heterogeneity. We quantify the gains from exploiting panel data and demonstrate how forecasting performance depends on the degree of parameter heterogeneity, whether such heterogeneity is correlated with the regressors, the goodness of fit of the model, and the cross-sectional (N) and time (T) dimensions. Monte Carlo simulations and empirical applications to house prices and CPI inflation show that forecast combination and Bayesian forecasting methods perform best overall and rarely produce the least accurate forecasts for individual series.