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This paper constructs individual-specific density forecasts for a panel offirms or households using a dynamic linear model with common and heterogeneouscoefficients as well as cross-sectional heteroskedasticity. The panelconsidered in this paper features a large cross-sectional dimension N but shorttime series T. Due to the short T, traditional methods have difficulty indisentangling the heterogeneous parameters from the shocks, which contaminatesthe estimates of the heterogeneous parameters. To tackle this problem, I assumethat there is an underlying distribution of heterogeneous parameters, modelthis distribution nonparametrically allowing for correlation betweenheterogeneous parameters and initial conditions as well as individual-specificregressors, and then estimate this distribution by combining information fromthe whole panel. Theoretically, I prove that in cross-sectional homoskedasticcases, both the estimated common parameters and the estimated distribution ofthe heterogeneous parameters achieve posterior consistency, and that thedensity forecasts asymptotically converge to the oracle forecast.Methodologically, I develop a simulation-based posterior sampling algorithmspecifically addressing the nonparametric density estimation of unobservedheterogeneous parameters. Monte Carlo simulations and an empirical applicationto young firm dynamics demonstrate improvements in density forecasts relativeto alternative approaches.

Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective