Skip to main content
SpringerLink
Log in

A stochastic frontier model with correction for sample selection

  • Published:
Journal of Productivity Analysis Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. See Greene (2008a) for further development of the model and a survey of extensions and applications.

  2. Details on maximum likelihood estimation of the model can be found in ALS and elsewhere, e.g., Greene (Greene 2008b, Ch. 16).

  3. See Weinstein (1964).

  4. See Gourieroux and Monfort (1996), Train (2003), Econometric Software, Inc. (2007), Greene (2008b) and Greene and Misra (2004).

  5. See, also, Winkelmann (1998).

  6. The authors opt for a GMM estimator based on Kopp and Mullahy’s (1990) (KM) relaxation of the distributional assumptions in the standard frontier model. It is suggested, that KM “find that the traditional maximum likelihood estimators tend to overestimate the average inefficiency.” (Page 304) KM did not, in fact, make the latter argument, and we can find no evidence to support it in the since received literature. KM’s support for the GMM estimator is based on its more general, distribution free specification. We do note Newhouse (1994), whom Bradford et al. cite, has stridently argued against the stochastic frontier model as well, but not based on the properties of the MLE.

  7. See Battese and Coelli (1995).

References

  • Aigner D, Lovell K, Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. J Econ 6:21–37

    Google Scholar 

  • Battese G, Coelli T (1995) A model for technical inefficiency effects in a stochastic frontier production for panel data. Empir Econ 20:325–332

    Article  Google Scholar 

  • Boyes W, Hoffman S, Low S (1989) An econometric analysis of the bank credit scoring problem. J Econ 40:3–14

    Google Scholar 

  • Bradford D, Kleit A, Krousel-Wood M, Re R (2001) Stochastic frontier estimation of cost models within the hospital. Rev Econ Stat 83(2):302–309

    Article  Google Scholar 

  • 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):757–768

    Google Scholar 

  • Econometric Software, Inc. (2007) LIMDEP version 9.0. Plainview, New York

    Google Scholar 

  • Gourieroux C, Monfort A (1996) Simulation based econometric methods. Oxford University Press, Oxford

    Google Scholar 

  • 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 Manuscript

    Google Scholar 

  • Gravelle H, Jacobs R, Street JA (2002b) Comparing the efficiency of national health systems: A sensitivity approach. University of York, Health Economics Unit, UK Manuscript

    Google Scholar 

  • 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-94-10

  • 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 13:959–980

    Article  Google Scholar 

  • Greene W (2008a) The econometric approach to efficiency analysis. In: Lovell K, Schmidt S (eds) The measurement of efficiency. H Fried Oxford University Press, Oxford

    Google Scholar 

  • Greene W (2008b) Econometric analysis, 6th edn. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Greene W, Misra S (2004) Simulated maximum likelihood estimation of the stochastic frontier model. Manuscript, Department of Marketing, University of Rochester

  • Heckman J (1976) Discrete, qualitative and limited dependent variables. Ann Econ Soc Meas 4(5):475–492

    Google Scholar 

  • Heckman J (1979) Sample selection bias as a specification error. Econometrica 47:153–161

    Article  Google Scholar 

  • 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 11:1–11

    Article  Google Scholar 

  • Jondrow J, Lovell K, Materov I, Schmidt P (1982) On the estimation of technical inefficiency in the stochastic frontier production function model. J Econ 19:233–238

    Google Scholar 

  • Kaparakis E, Miller S, Noulas A (1994) Short run cost inefficiency of commercial banks: A flexible stochastic frontier approach. J Money Credit Bank 26:21–28

    Article  Google Scholar 

  • Koop G, Steel M (2001) Bayesian analysis of stochastic frontier models. In: Baltagi B (ed) Companion to theoretical econometrics. Blackwell, Oxford

    Google Scholar 

  • Kopp R, Mullahy J (1990) Moment-based estimation and testing of stochastic frontier models. J Econ 46(1/2):165–184

    Google Scholar 

  • 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):151–162

    Article  Google Scholar 

  • 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, Taiwan

  • Maddala G (1983) Limited dependent and qualitative variables in econometrics. Cambridge University Press, Cambridge

    Google Scholar 

  • Murphy K, Topel R (2002) Estimation and inference in two stem econometric models. J Bus Econ Stat 20:88–97

    Article  Google Scholar 

  • New York Times, Editorial: “World’s Best Medical Care?” August 12, 2007

  • Newhouse J (1994) Frontier estimation: How useful a tool for health economics? J Health Econ 13:317–322

    Article  Google Scholar 

  • Pitt M, Lee L (1981) The measurement and sources of technical inefficiency in the indonesian weaving industry. J Dev Econ 9:43–64

    Article  Google Scholar 

  • 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)

  • Sipiläinen T, Oude Lansink A (2005) Learning in switching to organic farming, Nordic Association of Agricultural Scientists, NJF Report, Vol 1, Number 1, 2005. http://orgprints.org/5767/01/N369.pdf

  • Smith M (2003) Modeling sample selection using archimedean copulas. Econ J 6:99–123

    Google Scholar 

  • Stevenson R (1980) Likelihood functions for generalized stochastic frontier estimation. J Econ 13:58–66

    Google Scholar 

  • 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. http://www.who.int/entity/healthinfo/paper30.pdf

  • Terza J (1994) Dummy endogenous variables and endogenous switching in exponential conditional mean regression models, Manuscript, Department of Economics, Penn State University

  • 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 University

  • Terza J (1998) Estimating count data models with endogenous switching: Sample selection and endogenous treatment effects. J Econ 84(1):129–154

    Google Scholar 

  • Terza JV (2009) Parametric nonlinear regression with endogenous switching. Econ Rev 28:555–580

    Article  Google Scholar 

  • Train K (2003) Discrete choice methods with simulation. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Tsionas E, Kumbhakar S, Greene W (2008) Non-Gaussian stochastic frontier models. Manuscript, Department of Economics, University of Binghamton

  • Weinstein M (1964) The sum of values from a normal and a truncated normal distribution. Technometrics 6:104–105 469–470

    Article  Google Scholar 

  • Winkelmann R (1998) Count data models with selectivity. Econ Rev 4(17):339–359

    Article  Google Scholar 

  • World Health Organization (2000) The World Health Report. WHO, Geneva

    Google Scholar 

  • Wynand P, van Praag B (1981) The demand for deductibles in private health insurance: A probit model with sample selection. J Econ 17:229–252

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Stern School of Business, New York University, 44 West 4th St., Rm. 7-78, New York, NY, 10012, USA

    William Greene

Authors
  1. William Greene
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to William Greene.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Greene, W. A stochastic frontier model with correction for sample selection. J Prod Anal 34, 15–24 (2010). https://doi.org/10.1007/s11123-009-0159-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11123-009-0159-1

Keywords

JEL Classification

Search

Navigation