  This paper considers the problem of forecasting a collection of short time
series using cross sectional information in panel data. We construct point
predictors using Tweedie's formula for the posterior mean of heterogeneous
coefficients under a correlated random effects distribution. This formula
utilizes cross-sectional information to transform the unit-specific (quasi)
maximum likelihood estimator into an approximation of the posterior mean under
a prior distribution that equals the population distribution of the random
coefficients. 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.
