Point And Density Forecasts In Panel Data Models

This dissertation develops econometric methods that facilitate estimation and improve forecasting performance in panel data models. The panel considered in this paper features large cross-sectional dimension (N) but short time series (T). It is modeled by a dynamic linear model with common and heterogeneous coefficients and cross-sectional heteroskedasticity. Due to short T, traditional methods have difficulty in disentangling the heterogeneous parameters from the shocks, which contaminates the estimates of the heterogeneous parameters. To tackle this problem, the methods developed in this dissertation assume that there is an underlying distribution of the heterogeneous parameters and pool the information from the whole cross-section together via this distribution. Chapter 2, coauthored with Hyungsik Roger Moon and Frank Schorfheide, constructs point forecasts using an empirical Bayes method that builds on Tweedie's formula to obtain the posterior mean of the heterogeneous coefficients under a correlated random effects distribution. We show that the risk of a predictor based on a non-parametric estimate of the Tweedie correction is asymptotically equivalent to the risk of a predictor that treats the correlated-random-effects distribution as known (ratio-optimality). Our empirical Bayes predictor performs well compared to various competitors in a Monte Carlo study. In an empirical application, we use the predictor to forecast revenues for a large panel of bank holding companies and compare forecasts that condition on actual and severely adverse macroeconomic conditions. In Chapter 3, I focus on density forecasts and use a full Bayes approach, where the distribution of the heterogeneous coefficients is modeled nonparametrically allowing for correlation between heterogeneous parameters and initial conditions as well as individual-specific regressors. I develop a simulation-based posterior sampling algorithm specifically addressing the nonparametric density estimation of unobserved heterogeneous parameters. I prove that both the estimated common parameters and the estimated distribution of the heterogeneous parameters achieve posterior consistency, and that the density forecasts asymptotically converge to the oracle forecast. Monte Carlo simulations and an application to young firm dynamics demonstrate improvements in density forecasts relative to alternative approaches.