Forecasting with panel data: estimation uncertainty versus parameter heterogeneity
We develop novel forecasting methods for panel data with heterogeneous parameters and examine them together with existing approaches. We conduct a systematic comparison of their predictive accuracy in settings with different cross-sectional (N) and time (T) dimensions and varying degrees of parameter heterogeneity. We investigate conditions under which panel forecasting methods can perform better than forecasts based on individual estimates and demonstrate how gains in predictive accuracy depend on the degree of parameter heterogeneity, whether heterogeneity is correlated with the regressors, the goodness of fit of the model, and, particularly, the time dimension of the data set. We propose optimal combination weights for forecasts based on pooled and individual estimates and develop a novel forecast poolability test that can be used as a pretesting tool. Through a set of Monte Carlo simulations and three empirical applications to house prices, CPI inflation, and stock returns, we show that no single forecasting approach dominates uniformly. However, forecast combination and shrinkage methods provide better overall forecasting performance and offer more attractive risk profiles compared to individual, pooled, and random effects methods.