Technical and scale efficiency in public and private Irish nursing homes – a bootstrap DEA approach

Abstract

This article provides methodological and empirical insights into the estimation of technical efficiency in the nursing home sector. Focusing on long-stay care and using primary data, we examine technical and scale efficiency in 39 public and 73 private Irish nursing homes by applying an input-oriented data envelopment analysis (DEA). We employ robust bootstrap methods to validate our nonparametric DEA scores and to integrate the effects of potential determinants in estimating the efficiencies. Both the homogenous and two-stage double bootstrap procedures are used to obtain confidence intervals for the bias-corrected DEA scores. Importantly, the application of the double bootstrap approach affords true DEA technical efficiency scores after adjusting for the effects of ownership, size, case-mix, and other determinants such as location, and quality. Based on our DEA results for variable returns to scale technology, the average technical efficiency score is 62 %, and the mean scale efficiency is 88 %, with nearly all units operating on the increasing returns to scale part of the production frontier. Moreover, based on the double bootstrap results, Irish nursing homes are less technically efficient, and more scale efficient than the conventional DEA estimates suggest. Regarding the efficiency determinants, in terms of ownership, we find that private facilities are less efficient than the public units. Furthermore, the size of the nursing home has a positive effect, and this reinforces our finding that Irish homes produce at increasing returns to scale. Also, notably, we find that a tendency towards quality improvements can lead to poorer technical efficiency performance.

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Notes

  1. 1.

    Appendix Table 12 details the most important studies which estimate efficiency models for the nursing home sector. See also sections 3 and 5 for further details on those studies.

  2. 2.

    The NHSS has been in existence since 1993. It had been known previously as the Nursing Home Subvention Scheme before it was transformed, and re-launched as the Nursing Home Support Scheme – “A Fair Deal” in October 2009.

  3. 3.

    It should be noted that under the assumption of CRS, both the input-oriented and output-oriented technical efficiency will be the same.

  4. 4.

    The efficiency score is a point estimate without a probability distribution around it as required by the Tobit method or any other parametric regression technique. Using the DEA point estimates in a second stage analysis may cause biased and inconsistent estimates of the parameters of the explanatory/ determining variables.

  5. 5.

    It should be noted that the method developed by Simar and Wilson [43] is relatively robust with regard to the chosen bandwidth of the confidence intervals.

  6. 6.

    In order to test the sensitivity of our results in relation to the labour measures used, we substitute for the number of staff with the salaries of full-time nurses and the salaries of health care attendants for the primary and secondary inputs respectively. Here, our findings are robust across the number of staff employed and salaries variables. Results for the latter are available on request.

  7. 7.

    In many industries, firms respond to increases in wage rates by substituting more capital for labour. However, this is difficult to achieve in the labour intensive nursing home industry. Thus, the effect of higher input prices points to fewer labour inputs being demanded.

  8. 8.

    Activities of daily living (ADLs).

  9. 9.

    The final number of observations reported in Table 4 is lower than reported earlier (see Table 2) due to missing observations for medical staff, and for some efficiency determining variables (see Table 5 below).

  10. 10.

    The total number of observations for Models 2 and 3 is further reduced to 110, as there are two observations missing for the number of medical staff.

  11. 11.

    The estimations were performed using the FEAR software package (see e.g. [48]). As the results obtained for Models 2 and 3, using the bootstrap procedure, are very similar to those provided for Model 1, they are not presented but are available on request.

  12. 12.

    The bias-corrected efficiency scores for Models 2 and 3 are 0.53 and 0.55 respectively.

  13. 13.

    The estimations for the double bootstrap DEA were performed using the rDEA package within the R platform.

References

  1. 1.

    Aaronson WE, Zinn JS, Rosko MD (1994) Do For-Profit and Not-for-Profit Nursing Homes Behave Differently? Gerontologist 34(6):775–786

  2. 2.

    Aigner DJ, Lovell CAK, Schmidt P (1977) Formulation and estimation of stochastic frontier production functions. J Econ 6(1):21–37

    Article  Google Scholar 

  3. 3.

    Anderson RL, Lewis D, Webb JR (1999) The efficiency of nursing home chains and the implications of non-profit status. J Real Estate Portfol Manag 5(3):235–245

    Google Scholar 

  4. 4.

    Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag Sci 30(9):1078–1092

    Article  Google Scholar 

  5. 5.

    BDO Ireland (2014) Health’s ageing crisis: time for action - a future strategy for Ireland’s long-term residential care sector. BDO Report. http://www.nhi.ie/?p=publications_BDO_report. Accessed 18 Oct 2016

  6. 6.

    Björkgren MA, Häkkinen U, Linna M (2001) Measuring efficiency of long-term care units in Finland. Health Care Manag Sci 4(3):193–200

    Article  Google Scholar 

  7. 7.

    Blegen MA, Goode CJ, Reed L (1998) Nurse staffing and patient outcomes. Nurs Res 47(1):43–50

    Article  Google Scholar 

  8. 8.

    Borge L-E, Haraldsvik M (2009) Efficiency potential and determinants of efficiency: an analysis of the care for the elderly sector in Norway. Int Tax Public Financ 16(4):468–486

    Article  Google Scholar 

  9. 9.

    Canniffe M (1999) One answer to age-old problem. The Irish Times 24th September (http://www.irishtimes.com/business/one-answer-to-age-old-problem-1.231138, accessed 18 October 2016)

  10. 10.

    Central Statistics Office (2013) Population and labour force projections 2016–2046. CSO, Dublin

    Google Scholar 

  11. 11.

    Chang SJ, Cheng MA (2013) The impact of nursing quality on nursing home efficiency: evidence from Taiwan. Review of Accounting and Finance 12(4):369–386

    Article  Google Scholar 

  12. 12.

    Charnes A, Cooper E, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2(6):429–444

    Article  Google Scholar 

  13. 13.

    Chattopadhyay S, Heffley D (1994) Are for-profit nursing homes more efficient? Data envelopment analysis with a case-mix constraint. East Econ J 20(2):171–186

    Google Scholar 

  14. 14.

    Chattopadhyay S, Ray SC (1996) Technical, scale and size efficiency in nursing home care: a non-parametric analysis of Connecticut homes. Health Econ 5(4):363–373

    Article  Google Scholar 

  15. 15.

    Crivelli L, Filippini M, Lunati D (2002) Regulation, ownership and efficiency in the Swiss nursing home industry. Int J Health Care Finance Econ 2(2):79–97

    Article  Google Scholar 

  16. 16.

    Delellis NO, Ozcan YA (2013) Quality outcomes among efficient and inefficient nursing homes: a national study. Health Care Manag Rev 38(2):156–165

    Article  Google Scholar 

  17. 17.

    DG ECFIN (2012) The 2012 ageing report: Economic and budgetary projections for the EU27 member states 2010–2060, joint report prepared by the European Commission (DG ECFIN) and the economic policy committee (AWG), European Union

  18. 18.

    Färe R, Grosskopf S, Logan J (1983) The relative efficiency of Illinois electric utilities. Resources and Energy 5(4):349–367

  19. 19.

    Färe R, Grosskopf S, Logan J (1985) The relative performance of publicly-owned and privately-owned electric utilities. Journal of Public Economics 26 (1):89–106

  20. 20.

    Farrell M (1957) The measurement of productive efficiency. J R Stat Soc 120A(3):253–281

    Google Scholar 

  21. 21.

    Farsi M, Filippini M, Lunati D (2008) Economies of scale and efficiency measurement in Switzerland’s nursing homes. Swiss J Econ Statist 144(3):359–378

    Article  Google Scholar 

  22. 22.

    Filippini, M (1999) Economies of scale in the Swiss nursing home industry. Working Paper (https://ideas.repec.org/p/soz/wpaper/9901.html, accessed 30 June 2016)

  23. 23.

    Fizel JL, Nunnikhoven TS (1992) Technical efficiency of for-profit and non-profit nursing homes. Manag Decis Econ 13(5):429–439

    Article  Google Scholar 

  24. 24.

    Fizel JL, Nunnikhoven TS (1993) The efficiency of nursing home chains. Applied Economics 25(1):49–55

  25. 25.

    Garavaglia G, Lettieri E, Agasisti T, Lopez S (2011) Efficiency and quality of care in nursing homes: an Italian case study. Health Care Manag Sci 14(1):22–35

    Article  Google Scholar 

  26. 26.

    Gertler P, Waldman D (1994). Why are not-for-profit nursing homes more costly, RAND Corporation

  27. 27.

    Harrington C, Olney B, Carrillo H, Kang T (2012) Nurse staffing and deficiencies in the largest for-profit nursing home chains and chains owned by private equity companies. Health Serv Res 47:106–128

    Article  Google Scholar 

  28. 28.

    Hoffler RA, Rungeling B (1994) US nursing homes: are they cost efficient? Econ Lett 44(3):301–305

    Article  Google Scholar 

  29. 29.

    Hollingsworth B (2003) Non-parametric and parametric applications measuring efficiency in health care. Health Care Manag Sci 6(4):203–218

    Article  Google Scholar 

  30. 30.

    Hollingsworth B (2008) The measurement of efficiency and productivity of health care delivery. Health Econ 17(10):1107–1128

    Article  Google Scholar 

  31. 31.

    Hollingsworth B, Peacock SJ (2008) Efficiency measurement in health and health care, Routledge

  32. 32.

    Iparraguirre JL, Ma R (2015) Efficiency in the provision of social care for older people. A three-stage data envelopment analysis using self-reported quality of life. Socio Econ Plan Sci 49(1):33–46

    Article  Google Scholar 

  33. 33.

    Kalseth J (2003) Political determinants of efficiency variation in municipal service production: an analysis of long-term care in Norway, Norwegian University of Science and Technology

  34. 34.

    Kleinsorge IK, Karney DF (1992) Management of nursing homes using data envelopment analysis. Socio Econ Plan Sci 26(1):57–71

    Article  Google Scholar 

  35. 35.

    Knox KJ, Blankmeyer EC, Stutzman JR (2007) Technical efficiency in Texas nursing facilities: a stochastic production frontier approach. J Econ Financ 31(1):75–86

    Article  Google Scholar 

  36. 36.

    Kooreman P (1994) Nursing home care in the Netherlands: a nonparametric efficiency analysis. J Health Econ 13(3):301–316

    Article  Google Scholar 

  37. 37.

    Laine J, Finne-Soveri U, Björkgren M, Linna M, Noro A, Häkkinen U (2005) The association between quality of care and technical efficiency in long-term care. Int J Qual Health Care 17(3):259–267

    Article  Google Scholar 

  38. 38.

    Nyman JA, Bricker DL (1989) Profit incentives and technical efficiency in the production of nursing home care. Rev Econ Stat 71(4):586–594

    Article  Google Scholar 

  39. 39.

    Nyman JA, Bricker DL, Link D (1990) Technical efficiency in nursing homes. Med Care 28(6):541–551

    Article  Google Scholar 

  40. 40.

    Ozcan YA, Wogen SE, Mau LW (1998) Efficiency evaluation of skilled nursing facilities. J Med Syst 22(4):211–224

    Article  Google Scholar 

  41. 41.

    Rosko MD, Chilingerian JA, Zinn JS, Aaronson WE (1995) The effects of ownership, operating environment, and strategic choices on nursing-home efficiency. Med Care 33(10):1001–1021

    Article  Google Scholar 

  42. 42.

    Simar L, Wilson PW (1998) Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models. Manag Sci 44(1):49–61

    Article  Google Scholar 

  43. 43.

    Simar L, Wilson PW (2000) Statistical inference in nonparametric frontier models: the state of the art. J Prod Anal 13(1):49–78

    Article  Google Scholar 

  44. 44.

    Simar L, Wilson PW (2007) Estimation and inference in two-stage, semi-parametric models of production processes. J Econ 136(1):31–64

    Article  Google Scholar 

  45. 45.

    Simar L, Wilson PW (2011) Two-stage DEA: caveat emptor. J Prod Anal 36(2):205–218

    Article  Google Scholar 

  46. 46.

    Vitaliano DF, Toren M (1994) Cost and efficiency in nursing homes: a stochastic frontier approach. J Health Econ 13(3):281–300

    Article  Google Scholar 

  47. 47.

    Wang YH, Chou LF (2005) The efficiency of nursing homes in Taiwan: an empirical study using data envelopment analysis. Manag Rev 12(1):167–194

    Google Scholar 

  48. 48.

    Wilson P (2008) FEAR: a software package for frontier efficiency analysis with R. Socio Econ Plan Sci 42(4):247–254

    Article  Google Scholar 

  49. 49.

    Worthington C (2004) Frontier efficiency measurement in health care: a review of empirical techniques and selected applications. Med Care Res Rev 61(2):135–170

    Article  Google Scholar 

  50. 50.

    Zinn JS (1993) The influence of nurse wage differentials on nursing home staffing and resident care decisions. Gerontologist 33(6):721–729

    Article  Google Scholar 

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Correspondence to Marta Zieba.

Appendix

Appendix

Table 12 Previous evaluations of efficiency in the nursing home sector
Table 13 Mean comparison tests on the differences in DEA TE and SE between public and private nursing homes

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Ni Luasa, S., Dineen, D. & Zieba, M. Technical and scale efficiency in public and private Irish nursing homes – a bootstrap DEA approach. Health Care Manag Sci 21, 326–347 (2018). https://doi.org/10.1007/s10729-016-9389-8

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Keywords

  • DEA
  • Bootstrapping
  • Technical efficiency
  • Nursing homes
  • Long-term care
  • Public versus private
  • Ireland

JEL codes

  • I19
  • L33
  • D24
  • H51