Journal of Productivity Analysis

, Volume 39, Issue 2, pp 101–110 | Cite as

Investigating the impact of endogeneity on inefficiency estimates in the application of stochastic frontier analysis to nursing homes

  • Ryan L. Mutter
  • William H. Greene
  • William Spector
  • Michael D. Rosko
  • Dana B. Mukamel


This paper examines the impact of an endogenous cost function variable on the inefficiency estimates generated by stochastic frontier analysis (SFA). The specific variable of interest in this application is endogenous quality in nursing homes. We simulate a dataset based on the characteristics of for-profit nursing homes in California, which we use to assess the impact on SFA-generated inefficiency estimates of an endogenous regressor under a variety of scenarios, including variations in the strength and direction of the endogeneity and whether the correlation is with the random noise or the inefficiency residual component of the error term. We compare each of these cases when quality is included and excluded from the cost equation. We provide evidence of the impact of endogeneity on inefficiency estimates yielded by SFA under these various scenarios and when the endogenous regressor is included and excluded from the model.


Stochastic frontier analysis Endogeneity Efficiency Quality Nursing homes 

JEL Classification

C13 C15 I12 



This paper does not represent the policy of either the Agency for Healthcare Research and Quality (AHRQ) or the U.S. Department of Health and Human Services (DHHS). The views expressed herein are those of the authors and no official endorsement by AHRQ or DHHS is intended or should be inferred. This research was partially funded by contracts from AHRQ: AHRQ Contract Number HHSP233200900285P (Michael Rosko, Dana Mukamel) and HHSN263200500063293 (William Greene).


  1. Anderson RI, Lewis D, Webb JR (1999) The efficiency of nursing home chains and the implications of non-profit status. J Real Estate Portfolio Manage 5(3):235–245Google Scholar
  2. Chirikos T (1998) Identifying efficiently and economically operated hospitals: the prospects and pitfalls of applying frontier regression techniques. J Health Polit Policy Law 23(December):879–904Google Scholar
  3. Deming W (1982) Out of the Crisis. Massachusetts Institute of Technology, CambridgeGoogle Scholar
  4. Farsi M, Filippini M (2004) An empirical analysis of cost efficiency in non-profit and public nursing homes. Ann Public Cooper Econ 75:339–365CrossRefGoogle Scholar
  5. Gertler P, Waldman D (1992) Quality-adjusted cost functions and policy evaluation in the nursing home industry. J Polit Econ 100(6):1232–1256CrossRefGoogle Scholar
  6. Greene W (2011) Econometric Analysis, 7th edn. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  7. Hollingsworth B (2008) The measurement of efficiency and productivity of health care delivery. Health Econ 17:1107–1128CrossRefGoogle Scholar
  8. Hussey P, de Vries H, Romley J, Wang M, Chen S, Shekell P, McGlynn E (2009) A systematic review of health care efficiency measures. Health Serv Res 44(3):784–805CrossRefGoogle Scholar
  9. Jondrow J, Lovell CK, Materov I, Schmidt P (1982) On the estimation of technical efficiency in the stochastic frontier production function model. J Econ 19:233–238Google Scholar
  10. Li T, Rosenman R (2001) Cost efficiency in Washington hospitals: a stochastic frontier approach using panel data. Health Care Man Sci 4(2):73–81CrossRefGoogle Scholar
  11. Li Y, Harrington C, Spector W, Mukamel D (2010) State regulatory enforcement and nursing home termination from the Medicare and Medicaid programs. Health Serv Res 45(6):1796–1814CrossRefGoogle Scholar
  12. Lovell CK (1994) Production frontiers and productive efficiency. In: Fried H, Lovell C, Schmidt S (eds) The Measurement of Productive Efficiency. Oxford University Press, New York, pp 1–67Google Scholar
  13. Mukamel D, Li Y, Harrington C, Spector W, Weimer D, Bailey L (2011) Does state regulation of quality impose costs on nursing homes? Med Care 49(6):529–534CrossRefGoogle Scholar
  14. Mutter R, Rosko M, Wong H (2008) Measuring hospital inefficiency: the effects of controlling for quality and patient burden of illness. Health Serv Res 43(6):1992–2013CrossRefGoogle Scholar
  15. Nyman J (1988) The marginal cost of nursing home care: New York, 1983. J Health Econ 7:393–412CrossRefGoogle Scholar
  16. Rosko M, Mutter R (2008) Assessing the robustness of hospital inefficiency estimates: an assessment of stochastic frontier regression. Med Care Res Rev 65:131–166CrossRefGoogle Scholar
  17. Stock JH, Wright JH, Yogo M (2002) A survey of weak instruments and weak identification in generalized method of moments. J Bus Econ Stat 20(4): 518–529CrossRefGoogle Scholar
  18. Vitaliano D, Toren M (1991) Cost and efficiency in nursing homes: a stochastic frontier approach. J Health Econ 13:281–300CrossRefGoogle Scholar
  19. Vitaliano D, Toren M (1996) Hospital cost and efficiency in a regime of stringent regulation. East Econ J 22:161–173Google Scholar

Copyright information

© Springer Science+Business Media, LLC (outside the USA) 2012

Authors and Affiliations

  • Ryan L. Mutter
    • 1
  • William H. Greene
    • 2
  • William Spector
    • 1
  • Michael D. Rosko
    • 3
  • Dana B. Mukamel
    • 4
  1. 1.Center for Delivery, Organization and MarketsAgency for Healthcare Research and QualityRockvilleUSA
  2. 2.Stern School of BusinessNew York UniversityNew YorkUSA
  3. 3.School of Business AdministrationWidener UniversityChesterUSA
  4. 4.Department of Medicine, Health Policy Research InstituteUniversity of California, IrvineIrvineUSA

Personalised recommendations