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Local Semi-Parametric Efficiency of the Poisson Fixed Effects Estimator

Author

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  • Verdier Valentin

    (Department of Economics, University of North Carolina, Chapel Hill, NC 27599, USA, Phone: +1 919-966-3962)

Abstract

Hausman, Hall, and Griliches [Hausman, J., H. B. Hall, and Z. Griliches. 1984. “Econometric Models for Count Data with an Application to the Patents-R & D Relationship.” Econometrica 52 (4): 909–938.] have defined the Poisson fixed effects (PFE) estimator to estimate models of panel data with count dependent variables under distributional assumptions conditional on covariates and unobserved heterogeneity, but without any restriction on the distribution of unobserved heterogeneity conditional on covariates. Wooldridge [Wooldridge, J. M. 1999. “Distribution-Free Estimation of some Nonlinear Panel Data Models.” Journal of Econometrics 90 (1): 77–97.] showed that the PFE estimator is actually consistent even if the distributional assumptions of the PFE model are violated, as long as the restrictions imposed on the conditional mean of the dependent variable are satisfied. In this note I study the efficiency of the PFE estimator in the absence of distributional assumptions. I show that the PFE estimator corresponds to the optimal estimator for random coefficients models of Chamberlain [Chamberlain, G. 1992. “Efficiency Bounds for Semiparametric Regression.” Econometrica 60 (3): 567–596.] in the particular case where the assumptions of equal conditional mean and variance and zero conditional serial correlation are satisfied, regardless of whether the distributional assumptions of the PFE model hold. For instance the dependent variable does not need to be a count variable. This local efficiency result, combined with the simplicity and robustness of the PFE estimator, should provide a useful additional justification for its use to estimate conditional mean models of panel data.

Suggested Citation

  • Verdier Valentin, 2018. "Local Semi-Parametric Efficiency of the Poisson Fixed Effects Estimator," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-10, January.
    • Handle: RePEc:bpj:jecome:v:7:y:2018:i:1:p:10:n:5
    DOI: 10.1515/jem-2015-0022
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    References listed on IDEAS

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    1. Daron Acemoglu & Joshua Linn, 2004. "Market Size in Innovation: Theory and Evidence from the Pharmaceutical Industry," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 1049-1090.
    2. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    3. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    4. Rose, Nancy L, 1990. "Profitability and Product Quality: Economic Determinants of Airline Safety Performance," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 944-964, October.
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    Cited by:

    1. Nicholas Brown & Jeffrey Wooldridge, 2023. "More Efficient Estimation of Multiplicative Panel Data Models in the Presence of Serial Correlation," Working Paper 1497, Economics Department, Queen's University.

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    More about this item

    Keywords

    non-linear models; optimal instruments; panel data; Poisson fixed effects estimator;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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