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Unobserved Heterogeneity in Income Dynamics: An Empirical Bayes Perspective

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  • Jiaying Gu
  • Roger Koenker

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 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, ρ^≈0.48$\hat{\rho }\approx 0.48$, 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.

Suggested Citation

  • Jiaying Gu & Roger Koenker, 2017. "Unobserved Heterogeneity in Income Dynamics: An Empirical Bayes Perspective," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 1-16, January.
  • Handle: RePEc:taf:jnlbes:v:35:y:2017:i:1:p:1-16
    DOI: 10.1080/07350015.2015.1052457
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    Cited by:

    1. Feng, Long & Dicker, Lee H., 2018. "Approximate nonparametric maximum likelihood for mixture models: A convex optimization approach to fitting arbitrary multivariate mixing distributions," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 80-91.
    2. Oguzhan Cepni & Riza Demirer & Rangan Gupta & Ahmet Sensoy, 2022. "Interest rate uncertainty and the predictability of bank revenues," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(8), pages 1559-1569, December.
    3. John Carter Braxton & Kyle F. Herkenhoff & Jonathan Rothbaum & Lawrence Schmidt, 2021. "Changing Income Risk across the US Skill Distribution: Evidence from a Generalized Kalman Filter," Opportunity and Inclusive Growth Institute Working Papers 55, Federal Reserve Bank of Minneapolis.
    4. Antonio Pacifico, 2023. "Obesity and labour market outcomes in Italy: a dynamic panel data evidence with correlated random effects," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 24(4), pages 557-574, June.
    5. Li, Jing & Stock, James H., 2019. "Cost pass-through to higher ethanol blends at the pump: Evidence from Minnesota gas station data," Journal of Environmental Economics and Management, Elsevier, vol. 93(C), pages 1-19.
    6. Federico Bassetti & Roberto Casarin & Marco Del Negro, 2022. "A Bayesian Approach to Inference on Probabilistic Surveys," Staff Reports 1025, Federal Reserve Bank of New York.
    7. Amaresh K Tiwari, 2021. "A Control Function Approach to Estimate Panel Data Binary Response Model," Papers 2102.12927, arXiv.org, revised Sep 2021.
    8. Li Tan & Cory Koedel, 2019. "The Effects of Differential Income Replacement and Mortality on U.S. Social Security Redistribution," Southern Economic Journal, John Wiley & Sons, vol. 86(2), pages 613-637, October.
    9. Liu, Laura & Moon, Hyungsik Roger & Schorfheide, Frank, 2021. "Panel forecasts of country-level Covid-19 infections," Journal of Econometrics, Elsevier, vol. 220(1), pages 2-22.
    10. Botosaru, Irene, 2023. "Time-varying unobserved heterogeneity in earnings shocks," Journal of Econometrics, Elsevier, vol. 235(2), pages 1378-1393.
    11. Fernández-Val, Iván & Gao, Wayne Yuan & Liao, Yuan & Vella, Francis, 2022. "Dynamic Heterogeneous Distribution Regression Panel Models, with an Application to Labor Income Processes," IZA Discussion Papers 15236, Institute of Labor Economics (IZA).
    12. Chaoran Chen & Zhigang Feng & Jiaying Gu, 2022. "Health, Health Insurance, and Inequality," Working Papers tecipa-730, University of Toronto, Department of Economics.
    13. Raffaella Giacomini & Sokbae Lee & Silvia Sarpietro, 2023. "A Robust Method for Microforecasting and Estimation of Random Effects," Papers 2308.01596, arXiv.org.
    14. Li Tan, 2021. "Imputing Top‐Coded Income Data in Longitudinal Surveys," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(1), pages 66-87, February.

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