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Panel Data Models with Nonadditive Unobserved Heterogeneity: Estimation and Inference


  • Iván Fernández-Val

    () (Boston University, Department of Economics)

  • Joonhwan Lee

    () (MIT)


The main purpose of this paper is to estimate panel data models with endogenous regressors and nonadditive unobserved individual heterogeneity including, for example, linear and nonlinear models where all the parameters can vary across individuals. The quantities of interest are means, variances, and other moments of the individual parameters. Since estimates of these quantities based on individual by individual GMM estimation can be severely biased due to the incidental parameter problem, we develop bias corrections that give more accurate estimates in moderately long panels. These corrections, derived from large-T expansions of the finite-sample bias of fixed effects GMM estimators, reduce the order of the bias from O(T¡1) to O(T¡2) and center the asymptotic distributions at the true values in moderately long panels under asymptotic sequences where n = o(T3). An empirical example on cigarette demand based on Becker, Grossman and Murphy (1994) shows significant heterogeneity in the price effect across U.S. states.

Suggested Citation

  • Iván Fernández-Val & Joonhwan Lee, "undated". "Panel Data Models with Nonadditive Unobserved Heterogeneity: Estimation and Inference," Boston University - Department of Economics - Working Papers Series wp2010-001, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2010-001

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    Cited by:

    1. Ryo Okui & Takahide Yanagi, 2014. "Panel Data Analysis with Heterogeneous Dynamics," KIER Working Papers 906, Kyoto University, Institute of Economic Research.
    2. Galvao, Antonio F. & Kato, Kengo, 2016. "Smoothed quantile regression for panel data," Journal of Econometrics, Elsevier, vol. 193(1), pages 92-112.
    3. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    4. Santiago Pereda Fernández, 2016. "Copula-based random effects models for clustered data," Temi di discussione (Economic working papers) 1092, Bank of Italy, Economic Research and International Relations Area.
    5. Koen Jochmans & Martin Weidner, 2018. "Inference on a Distribution from Noisy Draws," Papers 1803.04991,, revised Jun 2018.
    6. Koen Jochmans, 2017. "Two-Way Models for Gravity," The Review of Economics and Statistics, MIT Press, vol. 99(3), pages 478-485, July.
    7. Ryo Okui & Takahide Yanagi, 2018. "Kernel Estimation for Panel Data with Heterogeneous Dynamics," Papers 1802.08825,, revised Mar 2018.
    8. Koen Jochmans, 2017. "Two-Way Models for Gravity," The Review of Economics and Statistics, MIT Press, vol. 99(3), pages 478-485, July.
    9. Irene Botosaru & Chris Muris, 2017. "Binarization for panel models with fixed effects," CeMMAP working papers CWP31/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item


    Correlated Random Coefficient Model; Panel Data; Instrumental Variables; GMM; Fixed Effects; Bias; Cigarette demand;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • J51 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - Trade Unions: Objectives, Structure, and Effects


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