Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective. Issue 2 (3rd April 2023)

• Record Type: Journal Article
• Authors: Liu, Laura
• Is Part Of: Journal of business & economic statistics. Volume 41:Issue 2(2023)
• Page Start: 349
• Page End: 363
• Publication Date: 2023-04-03
• Subjects: Bayesian -- Density forecasts -- Panel data -- Posterior consistency -- Semiparametric methods -- Young firm dynamics; Economics -- Statistical methods -- Periodicals; Commercial statistics -- Periodicals; Économie politique -- Méthodes statistiques -- Périodiques; Statistique commerciale -- Périodiques; 330.015195
• DOI: 10.1080/07350015.2021.2021922
• Languages: English
• ISSNs: 0735-0015

Abstract

Abstract: This article constructs individual-specific density forecasts for a panel of firms or households using a dynamic linear model with common and heterogeneous coefficients as well as cross-sectional heteroscedasticity. The panel considered in this article 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 combining information from the whole panel. Theoretically, I prove that in cross-sectional homoscedastic cases, 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.