Journal of Productivity Analysis

, Volume 34, Issue 1, pp 15–24 | Cite as

A stochastic frontier model with correction for sample selection

  • William GreeneEmail author


Heckman’s (Ann Econ Soc Meas 4(5), 475–492, 1976; Econometrica 47, 153–161, 1979) sample selection model has been employed in three decades of applications of linear regression studies. This paper builds on this framework to obtain a sample selection correction for the stochastic frontier model. We first show a surprisingly simple way to estimate the familiar normal-half normal stochastic frontier model using maximum simulated likelihood. We then extend the technique to a stochastic frontier model with sample selection. In an application that seems superficially obvious, the method is used to revisit the World Health Organization data (WHO in The World Health Report, WHO, Geneva 2000; Tandon et al. in Measuring the overall health system performance for 191 countries, World Health Organization, 2000) where the sample partitioning is based on OECD membership. The original study pooled all 191 countries. The OECD members appear to be discretely different from the rest of the sample. We examine the difference in a sample selection framework.


Stochastic frontier Sample selection Simulation Efficiency 

JEL Classification

C13 C15 C21 


  1. Aigner D, Lovell K, Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. J Econ 6:21–37Google Scholar
  2. Battese G, Coelli T (1995) A model for technical inefficiency effects in a stochastic frontier production for panel data. Empir Econ 20:325–332CrossRefGoogle Scholar
  3. Boyes W, Hoffman S, Low S (1989) An econometric analysis of the bank credit scoring problem. J Econ 40:3–14Google Scholar
  4. Bradford D, Kleit A, Krousel-Wood M, Re R (2001) Stochastic frontier estimation of cost models within the hospital. Rev Econ Stat 83(2):302–309CrossRefGoogle Scholar
  5. Collins A, Harris R (2005) The impact of foreign ownership and efficiency on pollution abatement expenditures by chemical plants: Some UK evidence. Scott J Political Econ 52(5):757–768Google Scholar
  6. Econometric Software, Inc. (2007) LIMDEP version 9.0. Plainview, New YorkGoogle Scholar
  7. Gourieroux C, Monfort A (1996) Simulation based econometric methods. Oxford University Press, OxfordGoogle Scholar
  8. Gravelle H, Jacobs R, Street JA (2002a) Comparing the efficiency of national health systems: Econometric analysis should be handled with care. University of York, Health Economics Unit, UK ManuscriptGoogle Scholar
  9. Gravelle H, Jacobs R, Street JA (2002b) Comparing the efficiency of national health systems: A sensitivity approach. University of York, Health Economics Unit, UK ManuscriptGoogle Scholar
  10. Greene W (1994) Accounting for excess zeros and sample selection in poisson and negative binomial regression models. Stern School of Business, NYU, Working Paper EC-94-10Google Scholar
  11. Greene W (2004) Distinguishing between heterogeneity and inefficiency: Stochastic frontier analysis of the World Health Organization’s panel data on national health care systems. Health Econ 13:959–980CrossRefGoogle Scholar
  12. Greene W (2008a) The econometric approach to efficiency analysis. In: Lovell K, Schmidt S (eds) The measurement of efficiency. H Fried Oxford University Press, OxfordGoogle Scholar
  13. Greene W (2008b) Econometric analysis, 6th edn. Prentice Hall, Englewood CliffsGoogle Scholar
  14. Greene W, Misra S (2004) Simulated maximum likelihood estimation of the stochastic frontier model. Manuscript, Department of Marketing, University of RochesterGoogle Scholar
  15. Heckman J (1976) Discrete, qualitative and limited dependent variables. Ann Econ Soc Meas 4(5):475–492Google Scholar
  16. Heckman J (1979) Sample selection bias as a specification error. Econometrica 47:153–161CrossRefGoogle Scholar
  17. Hollingsworth J, Wildman B (2002) The efficiency of health production: Re-estimating the WHO panel data using parametric and nonparametric approaches to provide additional information. Health Econ 11:1–11CrossRefGoogle Scholar
  18. Jondrow J, Lovell K, Materov I, Schmidt P (1982) On the estimation of technical inefficiency in the stochastic frontier production function model. J Econ 19:233–238Google Scholar
  19. Kaparakis E, Miller S, Noulas A (1994) Short run cost inefficiency of commercial banks: A flexible stochastic frontier approach. J Money Credit Bank 26:21–28CrossRefGoogle Scholar
  20. Koop G, Steel M (2001) Bayesian analysis of stochastic frontier models. In: Baltagi B (ed) Companion to theoretical econometrics. Blackwell, OxfordGoogle Scholar
  21. Kopp R, Mullahy J (1990) Moment-based estimation and testing of stochastic frontier models. J Econ 46(1/2):165–184Google Scholar
  22. Kumbhakar S, Tsionas M, Sipilainen T (2009) Joint estimation of technology choice and technical efficiency: An application to organic and conventional dairy farming. J Prod Anal 31(3):151–162CrossRefGoogle Scholar
  23. Lai H, Polachek S, Wang H (2009) Estimation of a stochastic frontier model with a sample selection problem. Working Paper, Department of Economics, National Chung Cheng University, TaiwanGoogle Scholar
  24. Maddala G (1983) Limited dependent and qualitative variables in econometrics. Cambridge University Press, CambridgeGoogle Scholar
  25. Murphy K, Topel R (2002) Estimation and inference in two stem econometric models. J Bus Econ Stat 20:88–97CrossRefGoogle Scholar
  26. New York Times, Editorial: “World’s Best Medical Care?” August 12, 2007Google Scholar
  27. Newhouse J (1994) Frontier estimation: How useful a tool for health economics? J Health Econ 13:317–322CrossRefGoogle Scholar
  28. Pitt M, Lee L (1981) The measurement and sources of technical inefficiency in the indonesian weaving industry. J Dev Econ 9:43–64CrossRefGoogle Scholar
  29. Rahman S, Wiboonpongse A, Sriboonchitta S, Chaovanapoonphol Y (2009) Production efficiency of jasmine rice producers in Northern and North-eastern Thailand. J Agric Econ, online, pp 1–17 (forthcoming)Google Scholar
  30. Sipiläinen T, Oude Lansink A (2005) Learning in switching to organic farming, Nordic Association of Agricultural Scientists, NJF Report, Vol 1, Number 1, 2005.
  31. Smith M (2003) Modeling sample selection using archimedean copulas. Econ J 6:99–123Google Scholar
  32. Stevenson R (1980) Likelihood functions for generalized stochastic frontier estimation. J Econ 13:58–66Google Scholar
  33. Tandon A, Murray C, Lauer J, Evans D (2000) Measuring the overall health system performance for 191 countries, World Health Organization, GPE Discussion Paper, EIP/GPE/EQC Number 30, 2000.
  34. Terza J (1994) Dummy endogenous variables and endogenous switching in exponential conditional mean regression models, Manuscript, Department of Economics, Penn State UniversityGoogle Scholar
  35. Terza J (1996) FIML, method of moments and two stage method of moments estimators for nonlinear regression models with endogenous switching and sample selection, Working Paper, Department of Economics, Penn State UniversityGoogle Scholar
  36. Terza J (1998) Estimating count data models with endogenous switching: Sample selection and endogenous treatment effects. J Econ 84(1):129–154Google Scholar
  37. Terza JV (2009) Parametric nonlinear regression with endogenous switching. Econ Rev 28:555–580CrossRefGoogle Scholar
  38. Train K (2003) Discrete choice methods with simulation. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  39. Tsionas E, Kumbhakar S, Greene W (2008) Non-Gaussian stochastic frontier models. Manuscript, Department of Economics, University of BinghamtonGoogle Scholar
  40. Weinstein M (1964) The sum of values from a normal and a truncated normal distribution. Technometrics 6:104–105 469–470CrossRefGoogle Scholar
  41. Winkelmann R (1998) Count data models with selectivity. Econ Rev 4(17):339–359CrossRefGoogle Scholar
  42. World Health Organization (2000) The World Health Report. WHO, GenevaGoogle Scholar
  43. Wynand P, van Praag B (1981) The demand for deductibles in private health insurance: A probit model with sample selection. J Econ 17:229–252Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Economics, Stern School of BusinessNew York UniversityNew YorkUSA

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