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Categorical data in local maximum likelihood: theory and applications to productivity analysis

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  • Byeong Park
  • Léopold Simar
  • Valentin Zelenyuk

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Abstract

In this paper we consider estimation of models popular in efficiency and productivity analysis (such as the stochastic frontier model, truncated regression model, etc.) via the local maximum likelihood method, generalizing this method here to allow for not only continuous but also discrete regressors. We provide asymptotic theory, some evidence from simulations, and illustrate the method with an empirical example. Our methodology and theory can also be adapted for other models where a likelihood of the unknown functions can be used to identify and estimate the underlying model. Simulation results indicate flexibility of the approach and good performances in various complex scenarios, even with moderate sample sizes. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Byeong Park & Léopold Simar & Valentin Zelenyuk, 2015. "Categorical data in local maximum likelihood: theory and applications to productivity analysis," Journal of Productivity Analysis, Springer, vol. 43(2), pages 199-214, April.
  • Handle: RePEc:kap:jproda:v:43:y:2015:i:2:p:199-214 DOI: 10.1007/s11123-014-0394-y
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    References listed on IDEAS

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    1. Bădin, Luiza & Simar, Léopold, 2009. "A Bias-Corrected Nonparametric Envelopment Estimator Of Frontiers," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1289-1318, October.
    2. Leopold Simar & Valentin Zelenyuk, 2006. "On Testing Equality of Distributions of Technical Efficiency Scores," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 497-522.
    3. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
    4. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    5. Markus Frölich, 2006. "Non-parametric regression for binary dependent variables," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 511-540, November.
    6. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
    7. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2008. "Local likelihood estimation of truncated regression and its partial derivatives: Theory and application," Journal of Econometrics, Elsevier, vol. 146(1), pages 185-198, September.
    8. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
    9. Jeffery Racine & Jeffrey Hart & Qi Li, 2006. "Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 523-544.
    10. Léopold Simar & Valentin Zelenyuk, 2011. "Stochastic FDH/DEA estimators for frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(1), pages 1-20, August.
    11. Subodh Kumar & R. Robert Russell, 2002. "Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence," American Economic Review, American Economic Association, pages 527-548.
    12. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355, June.
    13. Daniel J. Henderson & Valentin Zelenyuk, 2007. "Testing for (Efficiency) Catching-up," Southern Economic Journal, Southern Economic Association, vol. 73(4), pages 1003-1019, April.
    14. Valentin Zelenyuk & Vitaliy Zheka, 2006. "Corporate Governance and Firm’s Efficiency: The Case of a Transitional Country, Ukraine," Journal of Productivity Analysis, Springer, pages 143-157.
    15. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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    Citations

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    Cited by:

    1. Christopher F. Parmeter & Valentin Zelenyuk, 2016. "A Bridge Too Far? The State of the Art in Combining the Virtues of Stochastic Frontier Analysis and Data Envelopement Analysis," Working Papers 2016-10, University of Miami, Department of Economics.
    2. Fan Zhang & Joshua Hall & Feng Yao, 2017. "Does Economic Freedom Affect The Production Frontier? A Semiparametric Approach With Panel Data," Working Papers 17-27, Department of Economics, West Virginia University.
    3. Kelly D.T.Trinh & Valentin Zelenyuk, 2015. "Productivity Growth and Convergence: Revisiting Kumar and Russell (2002)," CEPA Working Papers Series WP112015, School of Economics, University of Queensland, Australia.

    More about this item

    Keywords

    Stochastic frontier models; Truncated regression; Local maximum likelihood; Nonparametric smoothing; Categorical variables; C13; C14; C2;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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