Unobserved Heterogeneity in Income Dynamics: An Empirical Bayes Perspective

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Abstract. Empirical Bayes methods for Gaussian compound decision problems involving longitudinal data are considered. The new convex optimization formulation of the nonparametric (Kiefer-Wolfowitz) maximum likelihood estimator for mixture models is employed to construct nonparametric Bayes rules for compound decisions. The methods are first illustrated with some simulation examples and then with an application to models of income dynamics. Using PSID data we estimate a simple dynamic model of earnings that incorporates bivariate heterogeneity in intercept and variance of the innovation process. Profile likelihood is employed to estimate an AR(1) parameter controlling the persistence of the innovations. We find that persistence is relatively modest,ρ ≈ 0.48, when we permit heterogeneity in variances. Evidence of negative dependence between individual intercepts and variances is revealed by the nonparametric estimation of the mixing distribution, and has important consequences for forecasting future income trajectories.Version: October 4, 2014. This research was partially supported by NSF grant SES-11-53548. All computational results of this paper can be reproduced with the aid of the R packages REBayes, Koenker (2012), and Rmosek, Friberg (2012), and code available from the authors on request. The Rmosek package provides a convenient R interface to the Mosek optimization language of Andersen (2010). We would like to express our appreciation to referees, Associate Editor, Editor and participants in the CeMMaP-UCL, Harvard-MIT, Georgetown, Rutgers, Cornell and University of Maryland econometrics workshops for valuable comments while retaining full responsibility for all errors of omission and commission.

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