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

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

  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. 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. 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. 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. Activities of daily living (ADLs).

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

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

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Authors and Affiliations

  1. Department of Economics, Kemmy Business School, University of Limerick, Limerick, Ireland

    Shiovan Ni Luasa, Declan Dineen & Marta Zieba

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  1. Shiovan Ni Luasa
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  2. Declan Dineen
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  3. Marta Zieba
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Correspondence to Marta Zieba.

Appendix

Appendix

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

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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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