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Empirical Economics

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01-01-2021

Aggregate efficiency of industry and its groups: the case of Queensland public hospitals

Authors: Bao Hoang Nguyen, Valentin Zelenyuk

Published in: Empirical Economics | Issue 6/2021

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Abstract

In this paper, we explore the efficiency of different groups of hospitals in Queensland, Australia, focusing on teaching and non-teaching hospitals, by adapting the most recent developments on statistical analysis of aggregate efficiency. We focus on the two approaches: the bootstrap approach proposed by Simar and Zelenyuk (J Appl Econ 22(7):1367–1394, 2007) and the central limit theorems recently developed by Simar and Zelenyuk (Oper Res 66(1):137–149, 2018), (Eur J Oper Res, 2020). To adapt these developments, we extend the central limit theorems to the context where there are several sub-groups in the population. Using real data on Queensland public hospitals, we found that teaching hospitals are significantly less efficient than non-teaching hospitals when benchmarking is done with respect to the constant returns to scale frontier, but are significantly more efficient when benchmarking with respect to the variable returns to scale frontier.

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See Sickles and Zelenyuk (2019) for more details and related discussion.

In principle, for hospitals, labour can be viewed to some extent as a variable input since some nurses and doctors can be hired per diem, rather than having them salaried throughout a year. This might potentially lead to the endogeneity of labour input since a productivity shock might alter a hospitals’ choice of the number and the composition of employees (see similar discussions in Zuckerman et al. 1994; Thornton 1998, and references therein). The issue, however, might not be serious in the context of our analysis, where in Australia casual employees only account for around 10% of the hospital labour force (Gilfillan 2020). Moreover, the ability of hospitals to change their labour input in response to a productivity shock is also constrained by the shortage of health workforce in the country, especially doctors and nurses (see discussions about the shortage of Australian health workforce in Mason 2013).

We use \(\lambda \left( X^\ell _i, Y^\ell _i\right) \) and \({\hat{\lambda }}\left( X^\ell _i,Y^\ell _i ~\big |~{\mathcal {X}}_{n}\right) \) (will be discussed later) to denote, respectively, the true and the estimate of true technical efficiency of a random point \(\left( X^\ell _i, Y^\ell _i\right) \) in sub-group \(\ell \), and we replace \(\left( X^\ell _i, Y^\ell _i\right) \) with \(\left( x^\ell , y^\ell \right) \) to denote the true and estimated efficiencies of a fixed point \(\left( x^\ell , y^\ell \right) \).

This approach was largely initiated by Farrell (1957) and then generalized and popularized by Charnes et al. (1978), with many developments after.

See details in Kneip et al. (1998, 2008); Park et al. (2000, 2010).

Here, we change notations to emphasize that estimates are obtained at fixed points.

We have \(2^L\) different ways to construct 2 subsets of the entire group from 2 subsets of L sub-groups.

For the entire group confidence intervals, one can directly apply the relevant formulas in KSW, SZ2018 and SZ2020.

FY stands for Financial Year, which in Australia starts on 1 July and ends on 30 June of the next calendar year.

Public hospitals in Queensland include acute hospitals, women’s and children’s hospitals, and psychiatric hospitals. Women’s and children’s hospitals and psychiatric hospitals can be viewed as specialized hospitals (i.e. providing healthcare services to a specific target population or group of conditions).

In 2013, the Gold Coast Hospital closed, and the Gold Coast University Hospital subsequently opened to replace it (all patients treated at the Gold Coast Hospital were transferred to the Gold Coast University Hospital).

A hospital is defined as a teaching hospital if it affiliates with universities to provide undergraduate medical education as advised by the relevant state health authority.

There are some hospitals changing their teaching status during the studied period.

The five peer groups are listed in descending order of service diversification and their volume of activities as follows: principal referral, acute group A, acute group B, acute group C, and acute group D. As indicated in Australian Institute of Health and Welfare (2015), the last two are usually smaller than the first three.

An alternative is to use price-based aggregation [e.g. see discussion in Zelenyuk (2020) and Nguyen and Zelenyuk (2020a)].

We use the constant inlier cost weights of the year 2013/14 obtained from the Independent Hospital Pricing Authority (2013).

The NEP is determined by the Independent Hospital Pricing Authority for public hospital services through the analysis of data on actual activity and costs in public hospitals.

All computations were done in Matlab with codes programmed by the authors, which involve standard Matlab library and some adopted Matlab codes from Simar and Zelenyuk (2006) (for the density estimation and the adapted Li test).

The trimming is based on the distribution of estimated efficiency scores using the CRS-DEA estimator, but it is very similar to the case of VRS-DEA in terms of the number of and the composition of trimmed observations.

The p-values of the adapted Li test for the null hypotheses of equality of distributions of efficiency scores before and after trimming the data for CRS-DEA and VRS-DEA cases are 0.16 and 0.35, respectively, thus we do not reject the null hypotheses.

Simar and Wilson (2011) adapted the data-driven approach proposed in Politis et al. (2001) and Bickel and Sakov (2008) to select a subsample size in subsampling bootstrap for envelopment estimators and demonstrated its good performance by Monte Carlo evidence (see more discussions in Sickles and Zelenyuk 2019).

The optimal \(\gamma \) is tuned using a CRS-DEA model and will also be used for the sub-group analysis in the next section.

The scale efficiency score is computed as a ratio of the CRS-DEA technical efficiency score to the VRS-DEA technical efficiency score. The scale inefficiency level is obtained by subtracting the reciprocal of the scale efficiency score from one.

Results for sub-group efficiencies based on hospital size and geographical location are provided in “Appendix B”.

It is worth mentioning here that the use of Tobit regression in a two-stage DEA context is not appropriate (see more discussion in Simar and Wilson 2007).

In our sample, \(81\%\) of teaching hospitals are large hospitals.

See an example here at ABC NEWS (2017).

A work in progress using this approach is currently being done by Grosskopf et al. (2020).

A work in progress using this approach is currently being done by Nguyen and Zelenyuk (2020b).

It is important to note here that the joint density \(f^\ell \) can be different across subgroups (e.g. due to the difference in the distributions of efficiency scores), but the support \({\mathcal {D}}\) and the technology set \(\Psi \) are assumed to be the same across all subgroups.

ABC NEWS (2017) Ramping issue continues to plague Adelaide hospitals’ emergency departments. https://www.abc.net.au/news/2017-09-12/how-ramping-affecting-adelaide-hospitals-emergency-departments/8896018 (2020-11-05)

Australian Institute of Health and Welfare (2015) Australian hospital peer groups. Technical report 66, Australian Institute of Health and Welfare, Canberra, ACT

Ayanian JZ, Weissman JS (2002) Teaching hospitals and quality of care: a review of the literature. Milbank Q 80(3):569–593CrossRef

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

Berta P, Callea G, Martini G, Vittadini G (2010) The effects of upcoding, cream skimming and readmissions on the Italian hospitals efficiency: a population-based investigation. Econ Modell 27(4):812–821CrossRef

Besstremyannaya G (2013) The impact of Japanese hospital financing reform on hospital efficiency: a difference-in-difference approach. Jpn Econ Rev 64(3):337–362CrossRef

Bickel PJ, Sakov A (2008) On the choice of \(m\) in the \(m\) out of \(n\) bootstrap and confidence bounds for extrema. Stat Sin 18:967–985

Biørn E, Hagen TP, Iversen T, Magnussen J (2003) The effect of activity-based financing on hospital efficiency: a panel data analysis of DEA efficiency scores 1992–2000. Health Care Manag Sci 6(4):271–283CrossRef

Burgess JF, Wilson PW (1996) Hospital ownership and technical inefficiency. Manag Sci 42(1):110–123CrossRef

Burgess JF, Wilson PW (1998) Variation in inefficiency among US hospitals. INFOR Inf Syst Oper Res 36(3):84–102

Cameron JM (1985) The indirect costs of graduate medical education. N Engl J Med 312(19):1233–1238CrossRef

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

Chowdhury H, Zelenyuk V (2016) Performance of hospital services in Ontario: DEA with truncated regression approach. Omega 63:111–122CrossRef

Chua CL, Palangkaraya A, Yong J (2011) Hospital competition, technical efficiency and quality. Econ Rec 87(277):252–268CrossRef

Clement JP, Valdmanis VG, Bazzoli GJ, Zhao M, Chukmaitov A (2008) Is more better? an analysis of hospital outcomes and efficiency with a DEA model of output congestion. Health Care Manag Sci 11(1):67–77CrossRef

Daraio C, Simar L (2007) Economies of scale, scope and experience in the italian motor-vehicle sector. In: Daraio C, Simar L (eds) Advanced robust and nonparametric methods in efficiency analysis: methodology and applications. Springer Science and Business Media, Berlin, pp 135–165

Deprins D, Simar L, Tulkens H (1984) Measuring labor efficiency in post offices. In: Marchand MG, Pestieau P, Tulkens H (eds) The performance of public enterprises: concepts and measurements. Amsterdam, North-Holland, pp 243–267

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

Färe R, He X, Li S, Zelenyuk V (2019) A unifying framework for farrell profit efficiency measurement. Oper Res 67(1):183–197CrossRef

Färe R, Primont D (1995) Multi-output production and duality: theory and applications. Kluwer Academic Publishers, New YorkCrossRef

Färe R, Zelenyuk V (2003) On aggregate Farrell efficiencies. Eur J Oper Res 146(3):615–620CrossRef

Farrell MJ (1957) The measurement of productive efficiency. J R Stat Soc Ser A (Gen) 120(3):253–290CrossRef

Ferrier GD, Trivitt JS (2013) Incorporating quality into the measurement of hospital efficiency: a double DEA approach. J Prod Anal 40(3):337–355CrossRef

Gilfillan G (2020) COVID-19: Impacts on casual workers in Australia—a statistical snapshot. Technical report, Parliament of Australia, Canberra, ACT

Grosskopf S, Margaritis D, Valdmanis V (2001) Comparing teaching and non-teaching hospitals: a frontier approach (teaching vs. non-teaching hospitals). Health Care Manag Sci 4(2):83–90CrossRef

Grosskopf S, Margaritis D, Valdmanis V (2004) Competitive effects on teaching hospitals. Eur J Oper Res 154(2):515–525CrossRef

Grosskopf S, Nguyen BH, Yong J, Zelenyuk V (2020) Healthcare structural reform and the performance of public hospitals: the case of Queensland, Australia. In Progress

Hao SS, Pegels CC (1994) Evaluating relative efficiencies of Veterans affairs medical centers using data envelopment, ratio, and multiple regression analysis. J Med Syst 18(2):55–67CrossRef

Harris J, Ozgen H, Ozcan Y (2000) Do mergers enhance the performance of hospital efficiency? J Oper Res Soc 51(7):801–811CrossRef

Hofmarcher MM, Paterson I, Riedel M (2002) Measuring hospital efficiency in Austria—a DEA approach. Health Care Manag Sci 5(1):7–14CrossRef

Independent Hospital Pricing Authority (2013) National efficient price determination 2013-2014. Technical report, Independent Hospital Pricing Authority

Indik BP (1963) Some effects of organization size on member attitudes and behavior. Human Relat 16(4):369–384CrossRef

Ingham GK (1967) Organizational size, orientation to work and industrial behaviour. Sociology 1(3):239–258CrossRef

Jensen GA, Morrisey MA (1986) The role of physicians in hospital production. Rev Econ Stat 68:432–442CrossRef

Kneip A, Park BU, Simar L (1998) A note on the convergence of nonparametric DEA estimators for production efficiency scores. Econ Theory 14:783–793CrossRef

Kneip A, Simar L, Wilson PW (2008) Asymptotics and consistent bootstraps for DEA estimators in nonparametric frontier models. Econ Theory 24(6):1663–1697CrossRef

Kneip A, Simar L, Wilson PW (2015) When bias kills the variance: central limit theorems for DEA and FDH efficiency scores. Econ Theory 31(2):394–422CrossRef

Kneip A, Simar L, Wilson PW (2016) Testing hypotheses in nonparametric models of production. J Bus Econ Stat 34(3):435–456CrossRef

Lehner LA, Burgess JF (1995) Teaching and hospital production: the use of regression estimates. Health Econ 4(2):113–125CrossRef

Magnussen J (1996) Efficiency measurement and the operationalization of hospital production. Health Serv Res 31(1):21–37

Mason J (2013) Review of Australian government health workforce programs. Department of Health and Ageing Canberra

Nayar P, Ozcan YA (2008) Data envelopment analysis comparison of hospital efficiency and quality. J Med Syst 32(3):193–199CrossRef

Nayar P, Ozcan YA, Yu F, Nguyen AT (2013) Benchmarking urban acute care hospitals: efficiency and quality perspectives. Health Care Manag Rev 38(2):137–145CrossRef

Nguyen BH, Zelenyuk V (2020a) Output and input aggregation in hospital efficiency analysis. In Progress

Nguyen BH, Zelenyuk V (2020b) Robust efficiency analysis of public hospitals in Queensland, Australia, CEPA Working Paper Series, (WP05/2020)

O’Neill L, Rauner M, Heidenberger K, Kraus M (2008) A cross-national comparison and taxonomy of DEA-based hospital efficiency studies. Socio-Econ Plan Sci 42(3):158–189CrossRef

Park BU, Jeong S-O, Simar L (2010) Asymptotic distribution of conical-hull estimators of directional edges. Ann Stat 38(3):1320–1340CrossRef

Park BU, Simar L, Weiner C (2000) FDH efficiency scores from a stochastic point of view. Econ Theory 16:855–877CrossRef

Politis DN, Romano JP, Wolf M (2001) On the asymptotic theory of subsampling. Stat Sin 11:1105–1124

Productivity Commission (2010) Public and private hospital: multivariate analysis. Technical report supplement to research report, Productivity Commission, Canberra, ACT66

Rich EC, Gifford G, Luxenberg M, Dowd B (1990) The relationship of house staff experience to the cost and quality of inpatient care. J Am Med Assoc 263(7):953–957CrossRef

Shahian DM, Nordberg P, Meyer GS, Blanchfield BB, Mort EA, Torchiana DF, Normand S-LT (2012) Contemporary performance of us teaching and nonteaching hospitals. Acad Med 87(6):701–708CrossRef

Sheather SJ, Jones MC (1991) A reliable data-based bandwidth selection method for kernel density estimation. J R Stat Soc Ser B (Methodol) 53(3):683–690

Shephard RW (1953) Cost and production functions. Princeton University Press, Princeton

Shephard RW (1970) Theory of cost and production functions. Princeton University Press, Princeton

Sickles R, Zelenyuk V (2019) Measurement of productivity and efficiency. Cambridge University Press, CambridgeCrossRef

Silverman BW (1986) Density estimation for statistics and data analysis. Chapman and Hall, London, New YorkCrossRef

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

Simar L, Wilson PW (2011) Inference by the \(m\) out of \(n\) bootstrap in nonparametric frontier models. J Prod Anal 36(1):33–53CrossRef

Simar L, Wilson PW (2020) Hypothesis testing in nonparametric models of production using multiple sample splits. J Prod Anal 53(3):287–303CrossRef

Simar L, Zelenyuk V (2006) On testing equality of distributions of technical efficiency scores. Econ Rev 25(4):497–522CrossRef

Simar L, Zelenyuk V (2007) Statistical inference for aggregates of Farrell-type efficiencies. J Appl Econ 22(7):1367–1394CrossRef

Simar L, Zelenyuk V (2018) Central limit theorems for aggregate efficiency. Oper Res 66(1):137–149CrossRef

Simar L, Zelenyuk V (2020) Improving finite sample approximation by central limit theorems for estimates from data envelopment analysis. Eur J Oper Res 284(3):1002–1015CrossRef

Thornton J (1998) Do physicians employ aides efficiently?: Some new evidence on solo practitioners. J Econ Finance 22(2–3):85–96CrossRef

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

Zelenyuk V (2020) Aggregation of inputs and outputs prior to data envelopment analysis under big data. Eur J Oper Res 282(1):172–187CrossRef

Zelenyuk V, Zheka V (2006) Corporate governance and firm’s efficiency: the case of a transitional country, Ukraine. J Prod Anal 25(1–2):143–157CrossRef

Zuckerman S, Hadley J, Lezzoni L (1994) Measuring hospital efficiency with frontier cost functions. J Health Econ 13(3):255–280CrossRef

Title: Aggregate efficiency of industry and its groups: the case of Queensland public hospitals
Authors: Bao Hoang Nguyen
Valentin Zelenyuk
Publication date: 01-01-2021
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 6/2021
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-020-01994-1

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