Forecasting with Dynamic Panel Data Models

TL;DR

This paper develops a novel forecasting method for short panel data using Tweedie's formula, leveraging cross-sectional information to improve prediction accuracy and demonstrating its effectiveness through simulations and real-world bank revenue forecasts.

Contribution

It introduces an empirical Bayes predictor based on Tweedie's formula for heterogeneous coefficients, achieving asymptotic optimality and improved forecasting performance.

Findings

The predictor is asymptotically ratio-optimal compared to known distribution benchmarks.

Empirical results show superior forecast accuracy in Monte Carlo simulations.

Application to bank revenue data demonstrates practical forecasting improvements.

Abstract

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.