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Maximum likelihood estimation of the stochastic frontier model with endogenous switching or sample selection

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  • Hung-pin Lai

Abstract

Heckman’s (Ann Econ Soc Meas 15:475–492, 1976 ; Econometrica 47(1):153–161, 1979 ) sample selection model has been employed in many applications of linear or nonlinear regression studies. It is well known that ignoring the sample selectivity may result in estimation bias of the estimator. Although the stochastic frontier (SF) model with sample selection has been investigated in Greene (J Product Anal 34:15–24, 2010 ), we intend to extend the model in several directions in this paper. First, we extend the distribution of the inefficiency from the half normal to truncated normal distribution. Second, we discuss the likelihood estimation method for the SF model with sample selection and also its most common incarnation, endogenous switching. Third, we suggest a simple framework to derive the closed form of the likelihood function using the closed skew-normal distribution. Fourth, we propose the estimator for the technical efficiency index due to Battese and Coelli (Empir Econ 20(2):325–332, 1995 ) based on the sample selection information. Finally, we also demonstrate the approach using the Taiwan hotel industry data. Copyright Springer Science+Business Media New York 2015

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  • Hung-pin Lai, 2015. "Maximum likelihood estimation of the stochastic frontier model with endogenous switching or sample selection," Journal of Productivity Analysis, Springer, vol. 43(1), pages 105-117, February.
    • Handle: RePEc:kap:jproda:v:43:y:2015:i:1:p:105-117
    DOI: 10.1007/s11123-014-0410-2
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    References listed on IDEAS

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    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    2. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    3. Hung-pin Lai & Cliff Huang, 2013. "Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions," Journal of Productivity Analysis, Springer, vol. 40(1), pages 1-14, August.
    4. Hung-pin Lai, 2013. "Estimation of the threshold stochastic frontier model in the presence of an endogenous sample split variable," Journal of Productivity Analysis, Springer, vol. 40(2), pages 227-237, October.
    5. Maddala, G.S., 1986. "Disequilibrium, self-selection, and switching models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 28, pages 1633-1688, Elsevier.
    6. William Greene, 2010. "A stochastic frontier model with correction for sample selection," Journal of Productivity Analysis, Springer, vol. 34(1), pages 15-24, August.
    7. Joseph Terza, 2009. "Parametric Nonlinear Regression with Endogenous Switching," Econometric Reviews, Taylor & Francis Journals, vol. 28(6), pages 555-580.
    8. Battese, G E & Coelli, T J, 1995. "A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data," Empirical Economics, Springer, vol. 20(2), pages 325-332.
    9. Subal Kumbhakar & Efthymios Tsionas & Timo Sipiläinen, 2009. "Joint estimation of technology choice and technical efficiency: an application to organic and conventional dairy farming," Journal of Productivity Analysis, Springer, vol. 31(3), pages 151-161, June.
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    Cited by:

    1. Boris E. Bravo‐Ureta & Mario González‐Flores & William Greene & Daniel Solís, 2021. "Technology and Technical Efficiency Change: Evidence from a Difference in Differences Selectivity Corrected Stochastic Production Frontier Model," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(1), pages 362-385, January.
    2. K Hervé Dakpo & Laure Latruffe & Yann Desjeux & Philippe Jeanneaux, 2022. "Modeling heterogeneous technologies in the presence of sample selection: The case of dairy farms and the adoption of agri‐environmental schemes in France," Agricultural Economics, International Association of Agricultural Economists, vol. 53(3), pages 422-438, May.
    3. Centorrino, Samuele & Pérez-Urdiales, María & Bravo-Ureta, Boris & Wall, Alan, 2022. "Binary endogenous treatment in stochastic frontier models with an application to soil conservation in El Salvador," Efficiency Series Papers 2022/02, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    4. Khalid Maman Waziri, 2017. "Generalized Glass Ceilings in the United States – A Stochastic Metafrontier Approach," Working Papers halshs-01569834, HAL.
    5. German Blanco, 2017. "Who benefits from job placement services? A two-sided analysis," Journal of Productivity Analysis, Springer, vol. 47(1), pages 33-47, February.
    6. Bazen, Stephen & Waziri, Khalid Maman, 2017. "The Assimilation of Young Workers into the Labour Market in France: A Stochastic Earnings Frontier Approach," IZA Discussion Papers 10841, Institute of Labor Economics (IZA).
    7. Centorrino, Samuele & Perez Urdiales, Mari­a & Bravo-Ureta, Boris & Wall, Alan, 2021. "Binary Endogenous Treatment in Stochastic Frontier Models with an Application to Soil Conservation in El Salvador," 95th Annual Conference, March 29-30, 2021, Warwick, UK (Hybrid) 312058, Agricultural Economics Society - AES.
    8. Won-Sik Hwang & Ho-Sung Kim, 2022. "Does the adoption of emerging technologies improve technical efficiency? Evidence from Korean manufacturing SMEs," Small Business Economics, Springer, vol. 59(2), pages 627-643, August.

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    More about this item

    Keywords

    Stochastic frontier model; Sample selection; Endogenous switching; Maximum likelihood estimation; Closed skew-normal distribution; C13; C34; D2;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • D2 - Microeconomics - - Production and Organizations

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