Unobserved Heterogeneity in Income Dynamics: An Empirical Bayes Perspective

Jiaying Gu, Roger Koenker

Research output: Contribution to journalArticlepeer-review


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 panel 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, (Formula presented.), 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.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalJournal of Business and Economic Statistics
Issue number1
StatePublished - Jan 2 2017


  • Mixture experiments
  • Nonparametric methods
  • Regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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