Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective


105 Pages Posted: 25 Mar 2020

See all articles by Laura Liu

Laura Liu

Indiana University Bloomington - Department of Economics

Date Written: February 16, 2020


This paper constructs individual-specific density forecasts for a panel of firms or households using a dynamic linear model with common and heterogeneous coefficients and cross-sectional heteroskedasticity. The panel considered in this paper features a large cross-sectional dimension N but short time series T. Due to the 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, I assume that there is an underlying distribution of heterogeneous parameters, model this distribution nonparametrically allowing for correlation between heterogeneous parameters and initial conditions as well as individual-specific regressors, and then estimate this distribution by pooling the information from the whole cross-section together. Theoretically, 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. Methodologically, I develop a simulation-based posterior sampling algorithm specifically addressing the nonparametric density estimation of unobserved heterogeneous parameters. Monte Carlo simulations and an empirical application to young firm dynamics demonstrate improvements in density forecasts relative to alternative approaches.

Keywords: Bayesian, Semiparametric Methods, Panel Data, Density Forecasts, Posterior Consistency, Young Firm Dynamics

JEL Classification: C11, C14, C23, C53, L25

Suggested Citation

Liu, Laura, Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective (February 16, 2020). CAEPR WORKING PAPER 2020-003, Available at SSRN: or

Laura Liu (Contact Author)

Indiana University Bloomington - Department of Economics ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States

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