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A Stochastic Frontier Model for Discrete Ordinal Outcomes: A Health Production Function

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Listed:
  • William Griffiths
  • Xiaohui Zhang

    ()

  • Xueyan Zhao

    ()

Abstract

The stochastic frontier model used for continuous dependent variables is extended to accommodate output measured as a discrete ordinal outcome variable. Conditional on the inefficiency error, the assumptions of the ordered probit model are adopted for the log of output. Bayesian estimation utilizing a Gibbs sampler with data augmentation is applied to a convenient re-parameterisation of the model. Using panel data from an Australian longitudinal survey, demographic and socioeconomic characteristics are specified as inputs to health production, whereas production efficiency is made dependent on lifestyle factors. Posterior summary statistics are obtained for selected health status probabilities, efficiencies, and marginal effects.

Suggested Citation

  • William Griffiths & Xiaohui Zhang & Xueyan Zhao, 2010. "A Stochastic Frontier Model for Discrete Ordinal Outcomes: A Health Production Function," Monash Econometrics and Business Statistics Working Papers 3/10, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2010-3
    as

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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2010/wp3-10.pdf
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    References listed on IDEAS

    as
    1. van den Broeck, Julien & Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1994. "Stochastic frontier models : A Bayesian perspective," Journal of Econometrics, Elsevier, pages 273-303.
    2. repec:aph:ajpbhl:10.2105/ajph.2004.050914_7 is not listed on IDEAS
    3. William Greene, 2004. "Distinguishing between heterogeneity and inefficiency: stochastic frontier analysis of the World Health Organization's panel data on national health care systems," Health Economics, John Wiley & Sons, Ltd., vol. 13(10), pages 959-980.
    4. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
    5. Battese, George E. & Coelli, Tim J., 1988. "Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data," Journal of Econometrics, Elsevier, vol. 38(3), pages 387-399, July.
    6. Li, Mingliang & Tobias, Justin, 2005. "Bayesian Analysis of Structural Effects in an Ordered Equation System," Staff General Research Papers Archive 12247, Iowa State University, Department of Economics.
    7. Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian efficiency analysis through individual effects: Hospital cost frontiers," Journal of Econometrics, Elsevier, pages 77-105.
    8. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    9. Fernandez, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 1997. "On the use of panel data in stochastic frontier models with improper priors," Journal of Econometrics, Elsevier, vol. 79(1), pages 169-193, July.
    10. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
    11. Willam Greene, 2005. "Fixed and Random Effects in Stochastic Frontier Models," Journal of Productivity Analysis, Springer, vol. 23(1), pages 7-32, January.
    12. Atkinson, Scott E. & Crocker, Thomas D., 1992. "Econometric health production functions: Relative bias from omitted variables and measurement error," Journal of Environmental Economics and Management, Elsevier, vol. 22(1), pages 12-24, January.
    13. Jaume Puig-Junoy, 1998. "Measuring health production performance in the OECD," Applied Economics Letters, Taylor & Francis Journals, vol. 5(4), pages 255-259.
    14. H. Shelton Brown, 2003. "Managed care and technical efficiency," Health Economics, John Wiley & Sons, Ltd., vol. 12(2), pages 149-158.
    15. Benjamins, Maureen Reindl & Hummer, Robert A. & Eberstein, Isaac W. & Nam, Charles B., 2004. "Self-reported health and adult mortality risk: An analysis of cause-specific mortality," Social Science & Medicine, Elsevier, vol. 59(6), pages 1297-1306, September.
    16. Unto Häkkinen & Marjo-Riitta Järvelin & Gunnar Rosenqvist & Jaana Laitinen, 2006. "Health, schooling and lifestyle among young adults in Finland," Health Economics, John Wiley & Sons, Ltd., vol. 15(11), pages 1201-1216.
    17. Kumbhakar, Subal C & Ghosh, Soumendra & McGuckin, J Thomas, 1991. "A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 279-286, July.
    18. Baron-Epel, Orna & Kaplan, Giora & Haviv-Messika, Amalia & Tarabeia, Jalal & Green, Manfred S. & Nitzan Kaluski, Dorit, 2005. "Self-reported health as a cultural health determinant in Arab and Jewish Israelis: MABAT--National Health and Nutrition Survey 1999-2001," Social Science & Medicine, Elsevier, vol. 61(6), pages 1256-1266, September.
    19. Bruce Hollingsworth & John Wildman, 2003. "The efficiency of health production: re-estimating the WHO panel data using parametric and non-parametric approaches to provide additional information," Health Economics, John Wiley & Sons, Ltd., vol. 12(6), pages 493-504.
    20. Cebu Study Team, 1992. "A child health production function estimated from longitudinal data," Journal of Development Economics, Elsevier, vol. 38(2), pages 323-351, April.
    21. Jaume Puig-Junoy & Vicente Ortún, 2004. "Cost efficiency in primary care contracting: a stochastic frontier cost function approach," Health Economics, John Wiley & Sons, Ltd., vol. 13(12), pages 1149-1165.
    22. Jylhä, Marja, 1994. "Self-rated health revisited: Exploring survey interview episodes with elderly respondents," Social Science & Medicine, Elsevier, vol. 39(7), pages 983-990, October.
    23. Contoyannis, Paul & Jones, Andrew M., 2004. "Socio-economic status, health and lifestyle," Journal of Health Economics, Elsevier, vol. 23(5), pages 965-995, September.
    24. U.-G. Gerdtham & M. Löthgren & M. Tambour & C. Rehnberg, 1999. "Internal markets and health care efficiency: a multiple-output stochastic frontier analysis," Health Economics, John Wiley & Sons, Ltd., vol. 8(2), pages 151-164.
    25. Andrew Street, 2003. "How much confidence should we place in efficiency estimates?," Health Economics, John Wiley & Sons, Ltd., vol. 12(11), pages 895-907.
    26. repec:aph:ajpbhl:1982:72:8:800-808_7 is not listed on IDEAS
    27. Li Mingliang & Tobias Justin L, 2006. "Bayesian Analysis of Structural Effects in an Ordered Equation System," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(4), pages 1-24, December.
    28. Gary Koop & Mark F J Steel, 1999. "Bayesian Analysis of Stochastic Frontier Models," ESE Discussion Papers 19, Edinburgh School of Economics, University of Edinburgh.
    29. 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.
    30. Bauer, Paul W., 1990. "Recent developments in the econometric estimation of frontiers," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 39-56.
    31. 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.
    32. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June.
    33. Michael D. Rosko, 2001. "Cost efficiency of US hospitals: a stochastic frontier approach," Health Economics, John Wiley & Sons, Ltd., vol. 10(6), pages 539-551.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Bayesian estimation; Gibbs sampling; ordered probit; production efficiency.;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior

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