Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective
CAEPR WORKING PAPER 2020-003
105 Pages Posted: 25 Mar 2020
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
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