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Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective

Laura Liu

No 2018-036, Finance and Economics Discussion Series from Board of Governors of the Federal Reserve System (US)

Abstract: 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 application to young firm dynamics demonstrate improvements in density forecasts relative to alternative approaches.

Keywords: Bayesian nonparametric methods; Density forecasts; Panel data; Posterior consistency; Young firm dynamics (search for similar items in EconPapers)
JEL-codes: C11 C14 C23 C53 L25 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-for and nep-ore
Date: 2018-05-22
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DOI: 10.17016/FEDS.2018.036

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