Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 https://doi.org/10.1186/s12962-020-0199-y Cost Effectiveness and Resource Allocation

RESEARCH Open Access Technical efciency of provincial public healthcare in South Africa Victor Ngobeni* , Marthinus C. Breitenbach and Goodness C. Aye

Abstract Background: Forty-nine million people or 83 per cent of the entire population of 59 million rely on the public healthcare system in South Africa. Coupled with a shortage of medical professionals, high migration, inequality and unemployment; healthcare provision is under extreme pressure. Due to negligence by the health professionals, pro- vincial health departments had medical-legal claims estimated at R80 billion in 2017/18. In the same period, provin- cial health spending accounted for 33 per cent of total provincial expenditure of R570.3 billion or 6 per cent of South Africa’s Gross Domestic Product. Despite this, healthcare outcomes are poor and provinces are inefcient in the use of the allocated funds. This warrants a scientifc investigation into the technical efciency of the public health system. Methods: The study uses data envelopment analysis (DEA) to assess the technical efciency of the nine South African provinces in the provision of healthcare. This is achieved by determining, assessing and comparing ways that individual provinces can benchmark their performance against peers to improve efciency scores. DEA compares frms operating in homogenous conditions in the usage of multiple inputs to produce multiple outputs. Therefore, DEA is ideal for measuring the technical efciency of provinces in the provision of public healthcare. In DEA method- ology, the frms with scores of 100 per cent are technically efcient and those with scores lower than 100 per cent are technically inefcient. This study considers six DEA models using the 2017/18 total health spending and health staf as inputs and the infant mortality rate as an output. The frst three models assume the constant returns to scale (CRS) while the last three use the variable return to scale (VRS) both with an input-minimisation objective. Results: The study found the mean technical efciency scores ranging from 35.7 to 87.2 per cent between the health models 1 and 6. Therefore, inefcient provinces could improve the use of inputs within a range of 64.3 and 20.8 per cent. The Gauteng province defnes the technical efciency frontiers in all the six models. The second-best performing province is the North West province. Other provinces like KwaZulu-Natal, Limpopo and the Eastern Cape only perform well under the VRS. The other three provinces are inefcient. Conclusions: Based on the VRS models 4 to 6, the study presents three policy options. Policy option 1 (model 4): the efciency gains from addressing health expenditure wastage in four inefcient provinces amounts to R17 billion. Pol- icy option 2 (model 5): the potential savings from the same provinces could be obtained from reducing 17,000 health personnel, advisably, in non-core areas. In terms of Policy option 3 (model 6), three inefcient provinces should reduce 6940 health workers while the same provinces, inclusive of KwaZulu-Natal could realise health expenditure savings of R61 million. The potential resource savings from improving the efciency of the inefcient provinces could be used to refurbish and build more hospitals to alleviate pressure on the public health system. This could also reduce the per capita numbers per public hospital and perhaps their performance as overcrowding is reportedly negatively afect- ing their performance and health outcomes. The potential savings could also be used to appoint and train medical

*Correspondence: [email protected] Department of Economics, University of Pretoria, Lynnwood Rd, Hatfeld, Pretoria 0002, South Africa

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practitioners, specialists and researchers to reduce the alarming numbers of medical legal claims. Given the existing challenges, South Africa is not ready to implement the National Health Insurance (NHI) Scheme, as it requires addi- tional fnancial and human resources. Instead, huge improvements in public healthcare provision could be achieved by re-allocating the resources ‘saved’ through efciency measures by increasing the quality of public healthcare and extending healthcare to more recipients. Keywords: Expenditure, Data envelopment analysis, Healthcare, Inefciency, Technical efciency JEL Classifcation: C6-Mathematical programming models, D2-Production and organisations, Fiscal policies and behaviour of economic agents, I1-Health

Introduction healthcare insurance. According to the Government of According to Statistics South Africa [57], South Africa is the Republic of South Africa [23], there is a substantial a Southern African country with a population of 55.6 mil- diference in resource availability between the public and lion, estimated at 59 million in 2018. Coovadia et al. [15] private health sectors with more than half of fnancial and Mayosi and Benatar [39] indicate that South Africa and human resources allocated to the private sector. is a middle-income country with health outcomes worse Marten et al. [36] indicate that, aside from the institu- than in many low-income countries. Tis is exacerbated tional structure of the healthcare system and inadequate by inadequate human resources to cater for a growing public health infrastructure, another Achilles heel is the population coupled with a rising number of refugees and absolute and chronic defcit of healthcare workers in the economic migrants. As a result, there is growing concern country. Table 1 shows that the existing healthcare work- about the state of the public health system, its efciency ers are unevenly distributed along the health qualifcation and capability to provide sustainable services. Te South categories and geographical areas. Tis uneven distribu- African health care sector is comprised of public and tion of staf and skills according to Coovadia et al. [15] private segments that are deep-rooted in the past unjust has compromised the ability to deliver key programmes, policies of Apartheid, which caused disparities in health- notably for Human Immunodefciency Virus (HIV), care access between black and white citizens that there tuberculosis (TB), child health, mental health, and mater- is inequitable access to health services between the poor nal health. Mayosi and Benatar [39] mention that nurses majority and the rich minority in South Africa. Tis situ- are central to healthcare, especially in rural areas where ation still persists. However, the current divides are gen- physicians are reluctant to practice. Table 1 also shows erally between the rich and the poor irrespective of race. that the nursing personnel accounts for 143,264 or 63 per Te Government of the Republic of South Africa [23] cent of total health personnel while medical practitioners, states that, overall, the health sector has 813 hospitals specialists and researchers account for 19,988 or 9 per with 133,387 beds for acute health care. Te public sec- cent. Despite a small component of medical doctors as tor accounts for 49.7 per cent or 404 of these hospitals a proportion of total healthcare workers, 70 per cent are with 69 per cent of total bed allocation. Te private sec- employed in the private sector, implying shortages in the tor comprises 409 hospitals (50.3 per cent) with 31 per public sector. Moreover, government’s increased invest- cent of the total bed allocation. Tese numbers clearly ment in the medical profession produced more doctors point to inequality between the private and public hos- over the years, but a brain drain has since reversed these pitals and may further hint at a shortage of public health gains. South Africa incurs the highest costs for medical infrastructure as these numbers translate into 81,188 doctor education but, in turn, loses returns on invest- people per public hospital with an average of 228 beds ment as doctors migrate to Europe. Tirty per cent of per public facility. Mayosi and Benatar [39] add that South African doctors have emigrated and 58 per cent many state hospitals are in a dire state with much of pub- are intending to emigrate to Western countries. Commu- lic healthcare infrastructure run down and dysfunctional nity health workers account for 23.7 per cent or 54,180 of due to underfunding, mismanagement, and neglect. Tis health personnel and 4.3 per cent to other health person- compromises the quality of healthcare and leads to ear- nel categories. lier than required patient discharges. Te Competition Another major challenge in the healthcare sector is Commission [14] states that, in 2018, the vulnerable the high cost of providing medical care in South Africa. and poorly resourced public healthcare facilities served Te Health Systems Trust [25] indicates that this cost approximately 83 per cent of the population who were is already high and has been increasing rapidly over the largely without medical insurance. Te private health- last three decades. Moreover, the high public sector sala- care facilities served 17 per cent of the population private ries and excessive administration costs; duplication of Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 3 of 19 4 8 3 7 9 12 22 22 14 % of total 100 9198 6287 28,163 49,750 51,319 32,468 18,444 15,920 20,991 Total 228,217 6210 2954 7687 3070 6842 5622 Other 12,034 12,480 12,389 64,965 60 78 21 177 293 808 116 Medical specialists 1929 1345 4827 Medical researchers 1 5 13 120 12 1 2 – 6 160 664 457 934 1903 3614 3383 1248 1079 1719 Medical practitioners 15,001 2295 9409 5471 1520 4511 5314 Professional Professional nurses 10,993 14,223 17,163 70,899 864 5260 1972 6518 5976 4731 1431 2489 4152 Nursing assistants 33,393 939 237 958 3263 7694 9926 4085 1881 2608 Enrolled nurses Enrolled 31,591 Student nurses Student – – 2902 951 470 749 – 21 – 5093 76 64 67 49 356 823 512 116 225 Pupil Pupil auxiliary nurses 2288 Practicing health personnel by sector April 2018. Source: Author’s own Table based on Health Systems Trust [ 24 ] Trust Systems based on Health Table own Author’s 2018. Source: health personnel by sectorPracticing April 1 Table psychologists, physiotherapists, pharmacists, therapists, occupational health workers, environmental and specialists, therapists practitioners, dental community health workers, clinical associates, to refers “Other” of the other category 83 per cent comprise health workers Community personnel. national exclude fgures The and audiologists. and speech therapists radiographers Province Eastern Cape Free State Free Gauteng KwaZulu-Natal Limpopo Mpumalanga Northern Cape North West Western Cape Western Total Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 4 of 19

services and inefciencies are a serious problem. Table 2 sector where competition for resources is greater, creat- shows that the provincial health sector accounted for ing a gap between available and required resources for R186.9 billion of the total provincial budget in 2017/18, healthcare delivery. Moreover, the National Treasury [47] which was a 6 per cent contribution to the country’s GDP reports that provincial health departments also face con- by all provinces for the same period. Te total health tingent liability risks associated with medical-legal claims spending of R186.9 billion was also equivalent to 33 per due to negligence by health professionals. In 2017/18, cent of total provincial expenditure of R570.3 billion in this liability was estimated at R80 billion, up 32 per cent the same year. Te compensation of employees’ budget from 2016/17. Pay-outs against these claims amounted accounted for 61 per cent of total health expenditure. to R1.5 billion in 2017/18 and are projected to exceed Coovadia et al. [15] report that the health sector is also R2 billion in 2018/19. negatively afected by weak political and management Te Health Systems Trust [25] states that, while it is leadership. Tere is insufcient political and manage- important to improve the efciency of existing resources, ment leadership to manage underperformance, especially there is limited available information for efciency deter- in the public health sector. Tis negatively impacts on mination. Moreover, scientifc economic analysis is not the efcient administration of the sector and on the pro- usually used when allocating resources. Given the limited vision of quality healthcare services. Tese challenges funding of the public healthcare sector and increasing have to be resolved urgently, as the Government of the healthcare expenditure requirements, the use of scien- Republic of South Africa [23] reports that South Africa tifc methods to evaluate and compare public healthcare is currently working towards the provision of free quality efciency spending is inevitable and critical in reshap- universal healthcare (UHC) by 2030 which will be pub- ing healthcare policy. Te present study flls this gap by licly funded. Terefore, UHC could require additional using DEA to determine the technical efciency of pro- fnancial and human resources prompting the efcient vincial healthcare in South Africa. Coelli et al. [13] state use of existing funding resources. Given the substan- that DEA is widely used to measure technical efciency tial health budgets and their impact on macroeconomic in the public sector, including in the healthcare sector. indicators and human development, Verhoeven et al. Despite this, studies measuring technical efciency of [60] maintain that there is a general concern about the provincial healthcare sector in South Africa are lack- rapid rise in costs and the trade-ofs between efciency ing. Most international studies capturing South Africa and equity. Te Health Systems Trust [25] states that compare the national health system with that of other the vision of UHC and the current inefcient delivery of countries without outlining specifc provincial health health services are mutually exclusive. As a result, cost efciency or inefciency levels. Tis is despite the pro- containment is an important consideration in the deliv- vincial health spending accounting for 33 per cent of ery of healthcare as fnancial and human resources avail- provincial annual budgets. A survey of the health sector able for healthcare are limited, especially in the public DEA efciency assessment literature that was conducted in the current study refects that the study is the frst to assess and quantify in-depth, the technical efciency of the provincial healthcare sector in South Africa. Tere- Table 2 Provincial health contributions to Gross Domestic fore, the study generates new knowledge for efciency Product. Sources: Statistics South Africa [56]. National benchmarking and improvement. Given the background Treasury [42–46, 48–51] of the health sector, the rest of the paper is set out as fol- Province GDP Health spending Health lows: in “Literature review” section, the study conducts a spending % review of literature using DEA to assess healthcare ef- GDP ciency in the public sector, “Methodology and data” sec- Eastern Cape 247,040,000 22,771,139 9 tion outlines methodology and data, “Efciency results” Free State 154,400,000 9,795,191 6 section discusses the efciency results and “Conclusion” Gauteng 1,080,800,000 44,132,368 4 section summarises the fndings of the study and details KwaZulu-Natal 494,080,000 40,430,163 8 its recommendations. Limpopo 216,160,000 19,522,743 9 Mpumalanga 216,160,000 12,445,693 6 Literature review Northern Cape 61,760,000 4,722,157 8 In terms of DEA literature, in Europe, DEA was used by North West 185,280,000 11,420,212 6 Campanella et al. [11] to assess the technical efciency Western Cape 432,320,000 21,671,137 5 of 50 Italian hospitals. Te results revealed an aver- Total 3,088,000,000 186,910,803 6 age efciency score of 77 per cent amongst the DMUs, GDP Gross Domestic Product in R’000 in 2017 terms with a requirement for the inefcient DMUs to reduce Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 5 of 19

their input usage by 23 per cent to achieve efciency. Lo thereby requiring inefcient DMUs to curb input wastage Storto and Goncharuk [34] employed DEA to measure by 4 per cent. the technical efciency of 32 European (EU) countries. Other international DEA studies that involved Africa Te results for model 1 showed that inefcient countries and, in particular, South Africa, are also presented in this should reduce input usage by 36 and 34 per cent in 2011 section. Alhassan et al. [3] used DEA to assess the techni- and 2014, respectively. Te mean efciency score for cal efciency of 64 health facilities in Ghana. Te results model 2 indicated that inefcient DMUs should increase showed an average technical efciency score of 65 per outputs by 68 and 56 per cent for the same years. Asan- cent, meaning a reduction in the use of inputs by 35 per dului et al. [6] also used DEA to analyse the efciency cent. DEA was also used by Jarjue et al. [26] to determine of healthcare systems of 30 EU countries. Te model 1 the technical efciency of 41 secondary healthcare cen- results respectively showed an average efciency score tres in the Gambia. Te mean efciency score was 65 per of 74 and 75 per cent under the assumptions of CRS and cent, meaning that inefcient DMUs could still increase VRS. Te model 2 results yielded slightly diferent aver- output by 35 per cent. 10 per cent of the DMUs were age technical efciency scores of 81 and 77 per cent scale efcient while 90 per cent were scale inefcient with respectively for the CRS and VRS perspectives. Asandu- a mean efciency score of 87 per cent. Kim and Kang [27] lui and Fatulescu [7] used DEA to evaluate the technical applied DEA to analyse the technical efciency of health- efciency of the healthcare systems of 27 EU countries. care systems of 170 countries, including South Africa. Te study identifed fve countries on the efciency fron- Te research found that only 17 per cent of the studied tier. 14 countries had efciency scores below 50 per cent, countries used inputs efciently. Asian countries were needing to reduce their input usage by more than 50 per the most efcient and South Africa was amongst the inef- cent to be efcient. Te remaining countries had ef- fcient countries, with an efciency score of 84 per cent ciency levels of above 50 per cent. Another technical ef- wasting about 16 per cent of inputs. High and upper mid- ciency analytical study in the EU region was conducted dle-income countries had efciency scores of over 70 per by Baciu and Bolezat [9] who assessed the technical cent and lower-middle income and lower-income coun- efciency of healthcare of 27 EU countries. Te average tries recorded the average efciency scores of 67 per cent technical efciency score of all the DMUs was 60 per and 66 per cent respectively. Additional research by Pra- cent, showing more room by the inefcient DMUs to setyo and Zuhdi [54] investigated the technical efciency reduce the overall input usage by 40 per cent while main- of healthcare provision in 81 countries, including South taining the same output levels. Anton [4] measured the Africa. Te study observed that 17 countries were ef- technical efciency of 20 healthcare systems in Eastern cient in using government expenditure and South Africa and Central Europe. Te study obtained an overall mean had an efciency score of 94 per cent. DEA was also used efciency score of 98 per cent for life expectancy and 82 by Marschall and Flessa [35] to compute the technical per cent for the infant mortality of all the DMUs in the efciency of 20 healthcare centres in Burkina Faso. Te studied healthcare systems. Varabyova and Schreyögg CRS approach found an average mean efciency score of [59] assessed the technical efciency of healthcare in 31 91 per cent and the VRS approach yielded a mean ef- Organisation for Economic Co-operation and Develop- ciency score of 94 per cent; refecting a potential increase ment (OECD) countries using DEA. Te mean efciency in outputs by 9 and 6 per cent respectively. Akazili et al. score was 70 per cent, indicating possible input contrac- [2] applied DEA to calculate the technical efciency of tion by 30 per cent and possible output expansions by 89 randomly sampled healthcare centres in Ghana. Tey the same proportions. Afonso and St. Aubyn [1] applied found that 65 per cent of healthcare centres were techni- DEA to compare the output efciency of healthcare sys- cally inefcient as they used the resources they did not tems of 30 OECD countries. Tey ascertained that seven need. Tey had an average technical efciency score of countries were on average technically efcient and inef- 57 per cent, implying that on average, they could reduce fcient countries could on average increase their output input utilisation by 43 per cent without reducing the pre- efciency by 40 per cent. Chowdhury et al. [12] analysed vailing output levels. the technical efciency of 113 acute healthcare hospitals In another case, DEA was adopted by Benneyan et al. in Canada, a North American country, revealing that [10] to compare the technical efciency of healthcare most Ontario hospitals were not technically efcient, systems of 180 countries. Tey found that 115 countries, 65 per cent were subject to decreasing returns to scale including South Africa were not efcient. Masiye [38] (DRS), 10 per cent to increasing return to scale (IRS) and used DEA to evaluate the technical efciency of 30 hospi- 25 per cent were CRS efcient. Gannon [20] assessed the tals in Zambia. Te overall results showed that Zambian technical efciency of 60 Irish hospitals using DEA. Te hospitals operated at a 67 per cent level of technical ef- results showed a mean efciency score of 96 per cent, ciency, implying that 33 per cent of input resources were Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 6 of 19

being wasted. Zere et al. [65] adopted an input-minimi- frontier to tightly enclose the production technology sation objective to analyse the technical efciency of 30 (input and output variables). Cooper et al. [16] and McWil- district hospitals in Namibia. Te CRS results yielded liams et al. [40] state that DEA was developed in a microe- the average efciency scores ranging between 63 and conomic setting and applied to frms to convert inputs into 74 per cent over the study period. Te mean VRS ef- outputs. However, in efciency determination, the term ciency scores ranged from 67 to 72 per cent. Te study “frm” is often replaced by the more encompassing DMU. also revealed that IRS were a predominant form of scale DEA is an appropriate method of computing and analysing inefciency. Kirigia et al. [28] analysed the technical ef- the efciency of public sector institutions as they employ ciency of 155 public clinics in KwaZulu-Natal in South multiple inputs to produce multiple outputs. DEA esti- Africa. Tey ascertained that only 47 clinics were tech- mated frontiers do not make any assumptions upfront or nically efcient and 108 were not. Te inefcient clinics specify the functional form related to the production tech- had room to be efcient by reducing inputs and increas- nology. Aristovnik [5] and Martić et al. [37] state that there ing outputs. Tey could reduce the number of nurses are input-minimisation and output-maximisation DEA by 417 and general staf by 457. Tese reductions repre- orientation models. Te former determines the quantity sented 31 and 32 per cent inefciency rates. Te outputs of inputs that could be curtailed without reducing the pre- could be increased by 115,534 antenatal care visits, 1010 vailing level of outputs to make the DMUs efcient and baby deliveries, 179,075 child health care visits, 5702 the latter expands outputs of the DMUs until a combina- dental care visits, 121,658 family planning visits, 56,068 tion of inputs and outputs reach the production possibility psychiatry visits, 34,270 sexually transmitted infections frontier while holding the levels of inputs constant. How- related care visits and 34,270 TB related visits. Lastly, ever, the selection of each orientation is dependent on the Kirigia et al. [29] assessed the technical efciency of 55 objectives of a particular study. provincial hospitals in KwaZulu-Natal using DEA. Te According to Taylor and Harris [58], DEA is a com- average technical efciency score was 90.6 per cent. 22 parative efciency measurement tool that evaluates the DMUs were inefcient needing to reduce inputs as fol- efciency of homogeneous DMUs operating in similar lows, 117 doctors, 295 administration staf, 2709 nurses, environmental conditions and where there is no known 835 general staf, 1191 provisioning staf, 61 paramedics, relationship between the conversion of inputs and out- 58 technicians, 38 other staf members and 1752 beds. puts. Wang and Alvi [61] report that DEA only uses the In terms of the 21 health sector studies reviewed in information used in a particular study to determine ef- this paper, only fve related to South Africa. Tree of the ciency and does not take into consideration other factors studies were comparative cross-country efciency bench- that are exogenous to the study. DEA measures the dis- marking studies than relative provincial efciency ana- tance or derivatives of production functions to determine lytical studies. Tese studies used diferent variables to the extent of DMU’s efciency deviation from the opti- those applied in the present study. Te other two studies mal position. It classifes the DMUs into extremely ef- compared the efciency of clinics and hospitals in one of cient performers versus inefcient performers. In terms the nine South African province, however, they did not of the DEA methodology, the current study uses both the use expenditure as a variable of analysis. Te current CCR and the BCC models to test for stability, variability study focuses on the efciency of all the provinces, it is and robustness of the obtained efciency results. Tese specifc and explicit in terms of which provinces should models are described in the following paragraphs. be prioritised for reforms, therefore, enabling bench- Under the CCR model, suppose there are M diferent marking and improvement. number of inputs and P diferent number of outputs for N DMUs. Tese quantities are represented by column Methodology and data vectors xij (i = 1, 2, 3, ...M, j = 1, 2, 3 ...N ) and qrj In this paper, we follow the DEA approach developed by (r = 1, 2, 3, ...P, j = 1, 2, 3 ...N ) Te M × N input Farrell in 1957 and enhanced in 1978 by Charnes, Cooper matrix, X and P × N output matrix, Q represents the and Rhodes (also called the CCR model) to convert the production technology for all the N number of DMUs. fractional linear efciency estimates into linear mathemat- For each DMU, the ratio of all the output variables over ′ ′ ical efciency programmes under the CRS. We also use all the input variables is represented by u qrj/v xi . Where the VRS approach reported by Gavurova et al. [22] to have u = P × 1 vector output weights and v = M × 1 vector been developed in 1984 by Banker, Charnes and Cooper input weights. Te optimal weights or the efciency esti- to transform the CCR model to allow for consideration of mates are obtained by solving a mathematical problem. scale efciency analysis. Tis is called the Banker, Charnes In the context of the CRS, an efcient DMU operates at and Cooper (BCC) model. Te terminology “envelopment” most productive scale size (MPSS) or technically optimal in DEA refers to the ability of the efciency production production scale (TOPS). Hence, the optimal weights or Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 7 of 19

efciency estimates are obtained by solving a mathematical Avkiran [8] states that the CRS postulates no signifcant problem that is refected in Eq. 1. relationship between DMU’s operational size and their ′ ′ efciency. Tat is, under the CRS assumption, the large Tops = max(u q /v xij) u,v rj DMUs are deemed to attain the same levels of efciency as small DMUs in transforming inputs to outputs. Tere- St. fore, the CRS assumption implies that the size of a DMU is not relevant when assessing technical efciency. How- ′ ′ ever, in most cases, DMUs have varying sizes and this u qrj/v xij ≤ 1 (1) becomes a factor when determining their efciency. As a result, Gavurova et al. [22] mention that in 1984, the CCR ≥ u, v 0 formulation was generalised to allow for the VRS. Lavado and Domingo [31] argued that, in practice, there is pleth- Equation 1 shows the original linear programme, called ora of factors such as fnancial constraints that may result the primal. It aims to maximise the efciency score, which in the DMUs not operating at optimal scale. Aristovnik is represented by the ratio of all the weights of outputs to [5] adds that, if one cannot assume the existence of the inputs, subject to the efciency score not exceeding 1, with CRS, then a VRS type of DEA is an appropriate choice for all inputs and outputs being positive. Equation 1, has an computing efciency. Gannon [20] advises that the VRS infnite number of solutions, if (u, v) is a solution, so is αv, ′ should be used if it is likely that the size of a DMU will αv. To avoid this, one can impose a constraint v xij = 1, have a bearing on efciency. As such, Yawe [63] cautions which produces Eq. 2. that the use of the CRS specifcation when the DMUs are ′ max(u q ) not operating at an optimal scale results in a measure of u,v rj technical efciency which is confounded by scale efects. Te solution is to use the VRS as it permits for the calcu- St. lation of scale inefciency. Te CRS linear programming problem can be modifed to account for the VRS by add- ′ = ′ v xij 1 (2) ing the convexity constraint: N1 = 1 to Eq. 3, where N1 is an N × 1 vector of ones to formulate Eq. 4. Equation 4 ′ ′ u qrj − v xij ≤ 0 represents the BBC-VRS model with an input-minimisa- tion orientation. Terefore, Eqs. 1 to 3 represent the CRS models while Eqs. 4 to 5 represents the VRS models. u, v ≥ 0 Minθ, θ An equivalent envelopment problem can be developed for the problem in Eq. 2, using duality in linear program- St. ′ ming. Te dual for maxu,v(u qrj) is minθ, θ . Te value of θ is the efciency score; it satisfes the condition θ ≤ 1 ; it −qrj + Q ≥ 0 is the scalar measure. Lauro et al. [32] report that λ is an (4) N × 1 vector of all constants representing intensity vari- − ≥ ables indicating necessary combinations of efcient entities θxij X 0 or reference units (peers) for every inefcient DMU, it lim- its the efciency of each DMU to be greater than 1. Tis N1′ = 1 results in Eq. 3, which represents the CCR-CRS model with an input minimisation orientation. ≥ 0 Minθ, θ Lauro et al. [32] and Yuan and Shan [64] report that the CCR and the BCC models only difer in the man- St. ner the latter includes convexity constraints. Since −q + Q ≥ 0 the current model considers the VRS, the restriction rj (3) n i=1 n = 1 is introduced. Ramírez Hassan [55] cau- tions that, if this restriction is not there, it would imply θx − X ≥ 0 i the application of the CRS model. Te same analogy ≥ 0. applies to all the inefcient provinces in the sample. Tat is, the slacks and the radial movements are cal- culated for all inefcient provinces using Eq. 5. Te Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 8 of 19

BCC is adept to calculate pure technical efciency and relevant for this study as the technical efciency of provin- inefciency and when applied with the CCR model, it cial healthcare considers total health spending and total I also measures scale inefciency. Where, i=1 I = 1 , a health staf as inputs. Te DMUs have control over these I DMU is on a CRS frontier, if i=1 I < 1 , the DMU is variables, especially on expenditure as opposed to heath I I > 1 located on the IRS frontier and if i=1 , there is outputs. Te selected output variable for this study is the DRS. Given that this study has adopted both the CCR IMR. A longitudinal approach was not adopted since the and the VRS with an input-minimisation orientation. composition of provincial health expenditure remains the Te DEA models used in this study also consider the same throughout. Table 3 summarises the efciency ana- slack movements for the inefcient DMUs. As a result, lytical data. Te literature review presented in this paper the models account for the slacks in Eq. 5. shows that total health spending, health staf and the IMRs − are commonly used variables to analyse health sector ef- Minθ, j, S+, S r i ciency. Terefore, this paper considers various health pro- duction technologies with a maximum three-variables. M P Data for the IMR and total health staf are actual fgures − − + + θ ε Si Si obtained from the audited annual reports of provinces for = =  i 1 r 1 2017/18. Data for total health spending is obtained from the National Treasury’s 2017/18 provincial revenue and N N expenditure data. Tere are high variations refected by θx − x − − = 0, x = i0 ij j Si ij j X (5) high standard deviations from the mean with respect to = = j 1 j 1 health expenditure across all the provinces. Te minimum expenditure of R4.7 billion was recorded in the Northern N N Cape, with Gauteng spending the sample maximum of + θqr0 = qrj j − Sr = 0, qrj j = Q = = j 1 j 1 Table 3 Input and output variables. Sources: Eastern Cape N Department of Health [17], Free State Department of j = 1 Health [18], Gauteng Department of Health [21], KwaZulu- Natal Department of Health [30], Limpopo Department j=1 of Health [33], Mpumalanga Department of Health [41], Northern Cape Department of Health [52], North West + − j, Sr , Si > 0 Department of Health [53], Western Cape Government Health [62]. National Treasury [42–46, 48–51] Coelli et al. [13] defne slacks as input excesses and output Provinces Health inputs Health output shortfalls that are required over and above the initial radial movements to push DMUs to efciency levels. Both the x1 (THE) x2 (THS) y1 (IMR) slack and radial movements are characterised only with the Eastern Cape 22,771,139 40,424 14 inefcient DMUs. Te radial movements are initial input Free State 9,795,191 17,301 11.8 contractions or output expansions+ − that are required for a Gauteng 44,132,368 66,124 10.1 frm to become efcient. Si and Si in Eq. 5 are the output KwaZulu-Natal 40,430,163 68,125 12.4 and input slacks respectively to be calculated with θ, and n . Limpopo 19,522,743 33,848 12.4 ε , is the non-Archimedean constant. Gavurova et al. [22] Mpumalanga 12,445,693 20,421 9.7 hint that if the slack variables of a DMU are not equal to Northern Cape 4,722,157 6924 11.6 zero and the technical efciency score is lower than one, it is North West 11,420,212 17,536 8.1 necessary to perform a non-radial shift that is expressed by Western Cape 21,671,137 31,549 9.3 the slack variables to achieve technical efciency. In Eq. 5, Observations 9 9 9 the slack variables determine the optimum level of inputs Mean 20,767,867 33,584 11 that DMUs would have to utilise and the outputs that they Minimum 4,722,157 6924 8 would have to produce to become efcient, provided that Maximum 44,132,368 68,125 14 these DMUs are inefcient. Terefore, the slacks depict the Median 19,522,743 31,549 12 under-produced outputs or overused inputs. Standard deviation 12,794,907 20,302 2 Given the specifed model, it is clear that this paper uses THE is the actual total health expenditure or spending measured in R’000 the CCR and BCC models with input-minimisation objec- THS is the total number of people or workers employed in the health sector tives to analyse technical efciency of provincial health- IMR refers to the number of deaths per 1000 live births of children under 1 year care in South Africa for the 2017/18 fnancial year. Tis is of age Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 9 of 19

R44.1 billion. Tere were also major variations in the num- the worst performing DMU with an efciency score of 3.5 ber of total health staf per province. per cent. Table 5 reveals an average efciency score of 63.9 Te six health models considered in this study are sum- per cent for health model 3 when total health expenditure marised in Table 4, of which three are based on the CRS and total health staf were used together as inputs of the and three on the VRS. Te shapes of the frontiers of these health production frontier while maintaining the same rate models are illustrated graphically by Figs. 1, 2, 3, 4, 5 and of IMR. Tese variables complemented each other; the use 6 in Appendix. of one without the other decreased the efciency scores. In this model, Gauteng, the Northern Cape and the North Efciency results West Provinces were technically efcient. Te Free State, Avrikan [8] reports that the CRS efciency scores repre- Limpopo, Mpumalanga and the Western Cape’s efciency sent technical efciency. On the other hand, the VRS ef- scores surpassed 50 per cent. KwaZulu-Natal and the ciency scores represent pure technical efciency. Fried et al. Eastern Cape were below 50 per cent with the latter as an [19] provide intuition that the efciency results calculated extreme inefcient outlier. through the VRS are always higher than those calculated When only total health spending was used as an input using the CRS. Tis is because the best VRS efciency under the VRS in health model 4, the mean efciency score frontier is only formed by convex efcient combinations of was 69 per cent. Tis was 33.3 per cent higher than the ef- inputs and outputs. As a result, the BCC model envelops ciency results that are obtained in health model 1 for the data tighter than the CCR model. Moreover, the VRS is same variable. Tis implied that the size of provinces mat- comprehensive as it captures DMUs that are efcient in the ters in determining the technical efciency of their health CRS and VRS dispensations. Terefore, it contains a smaller spending. Five provinces, the Eastern Cape, Gauteng, Kwa- number of inefcient DMUs. Table 5 shows the provincial Zulu-Natal, Limpopo and the North West Provinces were health technical and scale efciency scores for all the six purely technically efcient. Tis means that four provinces health models. Te health model 1 yielded an average health had to reduce total health expenditure inefciency by 31 technical efciency score of 35.7 per cent, implying that all per cent. Tis model also showed that the Eastern Cape, the inefcient provinces should reduce total health spend- KwaZulu-Natal, North West and Limpopo were largely dis- ing by 64.3 per cent while maintaining the same levels of the advantaged when scale was disregarded, as they were only IMR. Gauteng defned the health efciency frontier and the efcient under the VRS while they were inefcient under North West province was very close to optimality with an the CRS. Te Mpumalanga Province was the least efcient efciency score of 80 per cent. Te other seven DMUs had DMU in this scenario with an inefciency score of 85.7 per the efciency scores ranging between 6.4 and 30 per cent, cent. It was followed by the Free State, Western Cape and implying inefciency range of between 70 and 93.6 per cent. the Northern Cape Provinces with inefciency rates of 68.7, Te Eastern Cape was the least efcient province with 66.7 and 58.3 per cent respectively. an efciency score of 6.4 per cent. Mpumalanga records Te frontier for total health staf in health model 5 was an efciency score of 12.9 per cent, the Free State 13.7 per exactly similar to the one for total health spending in cent, the Northern Cape 18.3 per cent, KwaZulu-Natal, health model 4, meaning that the efciency scores for the Limpopo and the Western Cape had efciency scores of DMUs were similar when individually assessing these two 30 per cent each. As it relates to health model 2, the mean variables. As a result, the shapes of the efciency frontiers efciency score was 35.4 per cent. Te efciency scores of health models 4 and 5 were also similar. Tis implied for all the DMUs, except for the Eastern Cape were simi- that either one of these variables was appropriate to lar to those in health model 1. Te Eastern Cape was still assess the technical efciency of the health sector under

Table 4 Health efciency DEA models Models DEA model Number of variables Variable description

Health model 1 CRS 2 Total health expenditure and infant mortality rate Health model 1 CRS 2 Total health staf and infant mortality rate Health model 1 CRS 3 Total health expenditure, total health staf and infant mortality rate Health model 1 VRS 2 Total health expenditure and infant mortality rate Health model 1 VRS 2 Total health staf and infant mortality rate Health model 1 VRS 3 Total health expenditure, total health staf and infant mortality rate

CRS constant returns to scale and VRS Variable returns to scale = Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 10 of 19 DRS DRS – DRS DRS IRS – – DRS 0.063 0.906 1000 0.375 0.648 0.930 1.000 1.000 0.870 0.755 DRS DRS – DRS DRS IRS DRS IRS IRS 0.035 0.440 1000 0.300 0.300 0.900 0.440 0.800 0.900 0.568 DRS DRS – DRS DRS IRS DRS IRS IRS Scale efciency 0.064 0.440 1000 0.300 0.300 0.900 0.440 0.800 0.900 0.572 Health model 6 1000 0.670 1000 1000 1000 0.542 1.000 1000 0.635 0.872 Health model 5 1000 0.313 1000 1000 1000 0.143 0.417 1000 0.333 0.690 Health model 4 1000 0.313 1000 1000 1000 0.143 0.417 1000 0.333 0.690 Health model 3 0.063 0.607 1000 0.375 0.648 0.504 1000 1000 0.552 0.639 Health model 2 0.035 0.137 1000 0.300 0.300 0.129 0.183 0.800 0.300 0.354 Health model 1 0.064 0.137 1.000 0.300 0.300 0.129 0.183 0.800 0.300 0.357 Health technical and scale efciency scores. Source: Author’s graph based on DEAP 2.1 efciency graph results Author’s Source: and scale technical efciencyHealth scores. 5 Table Province scale to return VRS variable scale, to returns CRS constant Eastern Cape Free State Free Gauteng KwaZulu-Natal Limpopo Mpumalanga Northern Cape North West Western Cape Western Mean Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 11 of 19

the VRS. Te results of the health model 6 also show that per cent. Te Northern Cape had overall health spending when both these input variables were considered under radial movement of R4.9 billion (81.7 per cent inefciency the VRS, the average pure technical efciency score of score), accounting for 10.6 per cent of the consolidated the DMUs increased by 23.3 per cent compared to health provincial health spending inefciency with an IMR of 11 model 3 results. Te health model 6 mean efciency score per cent. KwaZulu-Natal, Limpopo, Western Cape and the was 87.2 per cent, denoting that inefcient DMUs should North West Provinces collectively accounted for 17 per reduce total health expenditure and total health person- cent or R7.9 billion (associated with their respective 70, 70, nel by 12.8 per cent. Six provinces were purely technically 70 and 80 per cent inefciency rates) of the overall health efcient in health model 6. Tese were the Eastern Cape, expenditure inefciency at the prevailing IMR. In health Gauteng, KwaZulu-Natal, Limpopo, Northern Cape and model 2, all the provinces had a mean health staf inef- the North-West. Te inefcient DMUs are the Free State, ciency score of 64.6 per cent, equivalent to 64,400 more Mpumalanga and the Western Cape. health personnel than required. Te Eastern Cape had to Table 5 also shows the scale efciency scores for the reduce health workers by 38,600 (96.5 inefciency weight) DMUs under consideration. Te frst column under the while still maintaining the IMR at 14 per cent. Te Free heading “scale efciency” in Table 5 shows the scale ef- State had 6900 (86.3 per cent inefciency weight) more ciency scores derived by dividing the efciency results of personnel than it should, Mpumalanga 6100 (87.1 per cent health model 1 by health model 4 results. Te second col- inefciency score) and the Northern Cape 4900 (81.7 per umn shows the type of scale efciency. Terefore, the aver- cent inefciency score) at the prevailing IMRs. KwaZulu- age scale efciency score of all the DMUs when total health Natal and Limpopo were each supposed to reduce their spending was used as a single variable was 57.2 per cent, total health workers by 2800 (30 per cent efciency rate) depicting high levels of scale inefciency. Te scale inef- and the Western Cape by 2100 (30 per cent efciency fcient DMUs need to improve scale efciency by 42.8 per score). Te North West was closest to the efciency fron- cent. Only Gauteng was CRS scale efcient, providing a tier defned by Gauteng, it only had 200 (20 per cent inef- benchmark for all the scale inefcient DMUs. Te Western fciency rate) more health personnel than required. In Cape, Mpumalanga and the North West Provinces were terms of health model 3, when total health spending and very close to scale efciency. Tey were the only DMUs on total health staf were simultaneously applied as inputs, the the IRS frontier while the other fve scale inefcient DMUs overall health expenditure mean inefciency score of 36.1 were on a DRS curve. Te third column in Table 5 indicates per cent was equal to R481.8 million total health spending an average scale inefciency score of 56.8 per cent when and 49,337 total health personnel in line with an improve- total health personnel was used as a single input, result- ment in the efciency scores from 35 per cent to 63.9 per ing in 8 DMUs being scale inefcient. Te Western Cape, cent. Te Eastern Cape had R397.2 million overall health Mpumalanga and the North West Provinces are very close expenditure inefciency faced with a daunting task of to scale efciency. Tey were the only DMUs on IRS fron- reducing health sector employees by 37,470 (93.7 per cent tier while the other fve scale inefcient DMUs were on inefciency rate). KwaZulu-Natal was required to curtail DRS. Te last two columns in Table 5 show that when both total health spending by 42.5 million and total health staf inputs were employed, the average scale efciency was 75.5 by 2500 in line with a 62.5 per cent inefciency score to per cent. Gauteng, Northern Cape and the North West were become efcient. All inefcient provinces had to reduce scale efcient, Mpumalanga was the only DMU on the IRS the average technical inefciency score of 36.1 per cent for while the other scale inefcient provinces were on DRS. both health spending and staf. Te Free State used R6.7 Table 6 indicates the radial and slack movements for all million more than it should and could reduce the overall the health DEA models. In the health model 1, the mean health personnel by 3148 to address its inefciency rate of efciency score of 35.7 per cent translated into an average 39.3 per cent. Te Limpopo province had health expendi- inefciency score of 64.3 per cent. Tis inefciency score ture and staf radial movements of R11.6 million and 1407 was equivalent to eight inefcient provinces overusing total respectively, associated with its inefciency rate of 35.2 health expenditure by R46.4 billion. In other words, total per cent. Te Mpumalanga Province had an inefciency health spending could be reduced by R46.4 billion, while score of 49.6 per cent; it overused total health spending of still producing the same output levels. Te Eastern Cape R9.9 million and should reduce total health staf by 3469 to could reduce total health spending by R20.6 billion (93.6 become efcient. Te Western Cape should reduce health per cent inefciency rate) given the IMR of 14 per cent. expenditure by R13.9 million and health staf by 1343 (44.8 Te Free State’s and Mpumalanga’s respective inefcient per cent inefciency score). Te peers for the Eastern total health spending levels were R6.9 billion (86.3 per cent Cape, Free State, Limpopo, Mpumalanga and the Western inefciency score) and R6.1 billion (87.1 per cent rate of Cape are the North West and the Northern Cape and for inefciency) given their current levels of IMR of 11 and 9 KwaZulu-Natal is Gauteng. Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 12 of 19 Total 56,000,000 (46,400,000) – 9,600,000 96 – 96 74,000 (64,400) – 9600 96 – 96 74,000 49,337 – 24,663 682,000 481,764 – 200,236 96 – 96 Western Cape Western 3,000,000 (2,100,000) – 900,000 9 – 9 3 3000 (2100) – 900 9 – 9 3 3000 (1343) – 1657 31,000 (13,875) – 17,125 9 – 9 7;8 North West 1,000,000 (2000) – 800,000 8 – 8 3 1000 (200) – 800 8 – 8 3 1000 – – 1000 17,000 – – 17,000 8 – 8 8 Northern Cape 6,000,000 (4,900,000) – 1,100,000 11 – 11 3 6000 (4900) – 1100 11 – 11 3 6000 – – 6000 6,000 – – 6000 11 – 11 7 Mpumalanga 7,000,000 (6,100,000) – 900,000 9 – 9 3 7000 (6100) – 900 9 – 9 3 7000 (3469) – 3531 20,000 (9912) – 10,088 9 – 9 7;8 Limpopo 4,000,000 (2,800,000) – 1,200,000 12 – 12 3 4000 (2800) – 1200 12 – 12 3 4000 (1407) – 2593 33,000 (11,607) – 21,393 12 – 12 7;8 KwaZulu-Natal 4,000,000 (2,800,000) – 1,200,000 12 – 12 3 4000 (2800) – 1200 12 – 12 3 4000 (2500) – 1500 68,000 (42,500) – 25,500 12 – 12 8 Gauteng 1,000,000 – – 1,000,000 10 – 10 3 1000 – – 1000 10 – 10 3 1000 – – 1000 66,000 – – 66,000 10 – 10 3 Free State Free 8,000,000 (6,900,000) – 1,100,000 11 – 11 3 8000 (6900) – 1100 11 – 11 3 8000 (3148) – 4852 17,000 (6689) – 10,311 11 – 11 7;8 Eastern Cape Eastern 22,000,000 (20,600,000) – 1,400,000 14 – 14 3 40,000 (38,600) – 1400 14 – 14 3 40,000 (37,470) – 2530 424,000 (397,181) – 26,819 14 – 14 7;8 Total health expenditure and health staf radial and slack movements: CRS. Source: Author’s graph based on DEAP 2.1 efciency graph results Author’s CRS. Source: and slack movements: and health staf radial health expenditure Total THS original input THS original THS radial movement THS slack movement THE original input THE original THE radial movement THE slack movement Original input Original Input radial movement Input slack movement Input target Original output Original Output radial movement Output target DMU peers Original input Original Input radial movement Input slack movement Input target Original output Original Output radial movement Output target DMU peers

THS target

THE target Original output Original Output radial movement Output target DMU peers 6 Table Provinces THE is in R’000 scale to return CRS constant health staf, THS total DMU decision-making health expenditure, THE total unit, Model 1: CRS THE only Model 1: CRS Model 2: CRS THS only Model 2: CRS Model 3: CRS THS and THE THS and Model 3: CRS Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 13 of 19

Table 7 shows that in terms of the health model 4, only and reintroducing it in the last models under the same fve DMUs were purely technically inefcient with an over- assumptions. Tis exercise showed that the efciency all inefciency score of 31 per cent, translating into total results improved when the two variables were used simul- health spending inefciency of R17 billion. Mpumalanga taneously and decreased when they were used individu- accounted for R6 billion (85.7 per cent inefciency score) ally under the CRS and the VRS. Tis further refects that of this amount, the Free State for R5.5 billion (68.7 per cent the health efciency results are sensitive to the number inefciency weight), Northern Cape for R3.5 billion (58.3 of inputs used in efciency analysis. Using a single health per cent inefciency score) and the Western Cape for R2 input generated lower efciency results in both assump- billion (66.7 per cent inefciency score). Tis overspend- tions. Figure 7 in Appendix illustrates the individual pro- ing could be curtailed while maintaining the same IMRs. vincial scores within the broader DMUs’ performance. Te Free State and the Northern Cape should draw lessons Gauteng was the best performing DMU defning the ef- from Gauteng and KwaZulu-Natal while Mpumalanga, ciency frontier in all the six health models. Te second- North West and the Western Cape should learn from best performing province was the North West. Other Gauteng. Te model showed output slacks of 1, 2 and 1 per provinces like KwaZulu-Natal, Limpopo and the Eastern cent for Mpumalanga, North West and the Western Cape Cape only perform well under the VRS. Mpumalanga, respectively. Given the nature of the IMR, it is not ideal to Western Cape and the Free State are poorly performing increase this measure. Te same fve provinces were inef- provinces with respect to health sector efciency. fcient in health model 5. Teir mean inefciency score of Te efciency scores of the VRS model (models 4, 5 31 per cent was equivalent to 17,000 more health workers and 6) are used to formulate the recommendations for than required. Te Free State accounted for 32.4 per cent this study since this method is comprehensive. Te fol- or 5500 of this amount (68.7 per cent inefciency score), lowing policy options and recommendations are made. Mpumalanga 35.3 per cent or 6000 (85.7 per cent inef- ciency score), Northern Cape 20.6 per cent or 3500 (58.3 • Policy option 1 (health model 4): Target minimising per cent) and the Western Cape for 11.8 per cent or 2000 total health expenditure in four inefcient provinces, (66.7 per cent inefciency score) of excess health staf. Te the Free State, Mpumalanga, Northern Cape and the model showed the output slacks of 1, 2 and 1 per cent for Western Cape. Teir collective healthcare expendi- Mpumalanga, North West and the Western Cape respec- ture inefciencies amounted to R17 billion. Te Free tively. Te Free State’s peers were Gauteng and KwaZulu- State should curtail overspending by R5.5 billion Natal and the rest of the DMUs could draw lessons from and the Northern Cape’s is R3.5 billion. Tey could Gauteng. In terms of health model 6, only three provinces draw lessons from Gauteng and KwaZulu-Natal. had a mean inefciency score of 12.8 per cent, equivalent Mpumalanga was spending R6 billion on healthcare to inefcient total health spending of R26.1 million and more than it should while the Western Cape should 6940 excess health staf. Te Northern Cape reached the reduce its inefciency by R2 billion. All the interven- efciency point. Te Free State had excess staf of 2644 tions to realise these levels of spending should be and R5.6 million of health expenditure (33 per cent inef- implemented while maintaining the prevailing levels fciency rate), Mpumalanga 3202 and R9.2 million (45.8 of IMRs. Tese two provinces can benchmark their per cent inefciency score) and the Western Cape of 1094 health operations with Gauteng for pure technical and R11.3 million (36.5 per cent inefciency weight). Te efciency improvements. model showed an output slack of 0.7 per cent for Mpuma- • Policy option 2 (health model 5): Target reducing the langa. Te Free State and the Western Cape could improve overusage of the health staf in the four inefcient their performance by benchmarking with Limpopo, provinces. In terms of minimising total health staf, Northern Cape and North West while Mpumalanga’s there was overstafng in the Free State, Mpuma- peers are the Northern Cape and the North West. langa, Northern Cape and the Western Cape. Teir consolidated health staf inefciency was 17,000 peo- Conclusion ple. Te Free State should reduce health staf comple- Tis study determined the average technical efciency ment by 5500 benchmarking with Gauteng and Kwa- scores of the six health models. Te mean efciency scores Zulu-Natal, Mpumalanga by 7000, Northern Cape by ranged from 35.7 per cent to 87.2 per cent between health 6000 and the Western Cape by 2000 with all of them model 1 and health model 6. Tis illustrates that, in line benchmarking with Gauteng while maintaining the with theoretical postulates, the DEA results under the same rates infant mortality. VRS were higher than under the CRS. Te sensitivity • Policy option 3 (health model 6): In cases where the analysis was conducted by dropping one input variable interest of policy makers was to improve health staf in the frst two models both under the CRS and the VRS and expenditure at the same time, the Free State, Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 14 of 19 97 0.678 – 96 620,924 (35,000) (26,076) 682,000 67,060 – (6940) 74,000 100 4 – 96 57,000 – (17,000) 74,000 4 – 96 39,000,000 – (17,000,000) 56,000,000 Total 7;5;8 9 – – 9 19,695 – (11,305) 31,000 1906 – (1094) 3000 3 10 1 – 9 1000 – (2000) 3000 3 10 1 – 9 1,000,000 – (2,000,000) 3,000,000 Western Cape Western 8 8 – – 8 17,000 – – 17,000 1000 – – 1000 3 10 2 – 8 1000 – – 1000 3 10 2 – 8 1,000,000 – – 1,000,000 North West 7 11 – – 11 6000 – – 6000 6000 – – 6000 3 11 – – 11 2500 – (3500) 6000 4;3 11 – – 11 2,500,000 – (3,500,000) 6,000,000 Northern Cape 7;8 9.7 0.678 – 9 10,847 – (9153) 20,000 3798 – (3202) 7000 3 10 1 – 9 1000 – (6000) 7000 3 10 1 – 9 1,000,000 – (6,000,000) 7,000,000 Mpumalanga 5 12 – – 12 33,000 – – 33,000 4000 – – 4000 4 12 – – 12 4000 – – 4000 5 12 – – 12 4,000,000 – – 4,000,000 Limpopo 5 12 – – 12 33,000 (35,000) – 68,000 4000 – – 4000 4 12 – – 12 4000 – – 4000 4 12 – – 12 4,000,000 – – 4,000,000 KwaZulu-Natal 3 10 – – 10 66,000 – – 66,000 1000 – – 1000 3 10 – – 10 1000 – – 1000 3 10 – – 10 1,000,000 – – 1,000,000 Gauteng 5;8;7 11 – – 11 11,382 – (5618) 17,000 5356 – (2644) 8000 3;4 11 – – 11 2500 – (5500) 8000 4;3 11 – – 11 2,500,000 – (5,500,000) 8,000,000 Free State Free 1 14 – – 14 424,000 – – 424,000 40,000 – – 40,000 1 14 – – 14 40,000 – – 40,000 1 14 – – 14 22,000,000 – – 22,000,000 Eastern Cape Eastern Total health expenditure and health staf radial and slack movements: VRS. Source: DEAP 2.1 efciencyVRS. Source: results and slack movements: and health staf radial health expenditure Total THE slack movement THE radial movement THE original input THE original THS slack movement THS radial movement THS original input THS original DMU peers Output target Output slack movement Output radial movement Original output Original THE target

THS target

DMU peers Output target Output slack movement Output radial movement Original output Original Input target Input slack movement Input radial movement Original input Original DMU peers Output target Output slack movement Output radial movement Original output Original Input target Input slack movement Input radial movement Original input Original Model 6: VRS THS and THE Model 5: VRS THS only VRS Model 5: Model 4: VRS THE only VRS Model 4: 7 Table Provinces scale to VRS variable returns health staf, THS total DMU decision-making health expenditure, THE total unit, Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 15 of 19

Mpumalanga and the Western Cape should respec- only determines the inefciency levels of health spending tively reduce staf by 2644, 3202 and 1094 while and health personnel without methodologically explain- maintaining the same levels of IMR. Te same prov- ing the factors resulting in these inefciencies. As a inces should be assisted to cut their spending inef- result, it is difcult to understand why such inefcien- ciencies by R26.1 million. Te Free State by R5.6 mil- cies exist. Te study also sufers from a small sample size lion, Mpumalanga by R9.2 million and the Western problem by just analysing nine provinces. However, this Cape by R11.3 million while KwaZulu-Natal should limitation is structural given that South Africa has only curtail THE by R35 million. Te Free State and the nine provinces. Western Cape should learn from Limpopo, the Acknowledgements Northern Cape and the North West to improve their I hereby acknowledge the assistance and guidance of Professor Marthinus efciency while Mpumalanga should benchmark Breitenbach and Dr. Goodness Aye for their contributions to the study. with the last two provinces. Authors’ contributions VN is the main author as a Doctorate students under the supervision of Te potential savings from improving the efciency of MB and GA. MB and GA suggested the appropriate analytical model while VN inputted the data and interpreted the results. MB and GA checked the the inefcient provinces could also be used to refurbish and accuracy of the model results, their interpretation and also contributed on the build more hospitals to alleviate the pressure on the public recommendations. All authors read and approved the fnal manuscript. health system. Tis could also reduce the per capita num- Funding bers per public hospital and perhaps their performance as The authors hereby acknowledges the fnancial assistance of the National overcrowding is reportedly negatively afecting their perfor- Research Foundation and the University of Pretoria. Opinions expressed and mance and health outcomes. Moreover, overcrowded hospi- conclusions arrived at, are those of the authors and are not necessarily attrib- uted to the National Research Foundation. tals amid low professional health workers place pressure on the few appointed core health staf complement. Tis war- Availability of data and materials rants the use of potential savings to appoint more personnel, The datasets analysed during the current study are available from the cor- responding author on reasonable request. This particularly relates to the DEA especially medical practitioners, specialists and researchers model inputs and results. Most of data sources are listed in the reference list. while reducing personnel expenditure in non-core areas, as there is a general shortage of healthcare practitioners in Ethics approval and consent to participate Not applicable. South Africa. Tis implies the improvement of the ratio of practitioners and nursing assistants to attended patients. Consent for publication Moreover, it is essential to retrain health professionals using Not applicable. the realised efciency gains to reduce the alarming numbers Competing interests of medical-legal claims. Tis could also free up additional The authors declare that they have no competing interests. resources to enhance service delivery. Te study also cautions that, given healthcare per- Appendix: Health efciency frontiers sonnel and infrastructure challenges, South Africa is See Figs. 1, 2, 3, 4, 5, 6, 7. not ready to implement the National Health Insurance (NHI) scheme. Te scheme requires additional fnan- cial and human resources amidst the existing inef- ciencies. Instead of taking on the NHI at this juncture, which would be very costly, South Africa can make huge improvements in public healthcare provision by improv- ing efciency and re-allocating those resources ‘saved’ through efciency measures, to improving the quality of healthcare and extending healthcare to more recipi- ents. Implementing the NHI without implementing the efciency measures will set up the health sector for cer- tain failure. In general, provinces should also review the high spending levels on goods and services to ensure value-for-money. Inefcient provinces should continuously monitor the efciency of health spending and health personnel and publish their efciency performance periodically for pub- lic scrutiny. Tis could promote efcient and evidence- Fig. 1 Health model 1 DEA efciency frontier (Source: Author’s graph based budgeting. In terms of study limitations, this study based DEAP version 2.1 efciency results) Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 16 of 19

Fig. 5 Health model 5 DEA efciency frontier (Source: Author’s graph Fig. 2 Health model 2 DEA efciency frontier (Source: Author’s graph based DEAP version 2.1 efciency results) based DEAP version 2.1 efciency results)

Fig. 3 Health model 3 DEA efciency frontier (Source: Author’s graph based DEAP Version 2.1 efciency results)

Fig. 6 Health model 6 DEA efciency frontier (Source: Author’s graph based DEAP version 2.1 efciency results)

Fig. 4 Health model 4 DEA efciency frontier (Source: Author’s graph based DEAP version 2.1 efciency results) Ngobeni et al. Cost Ef Resour Alloc (2020) 18:3 Page 17 of 19

1,200

1,000

0,800

0,600

0,400

0,200

- Eastern Cape Free State GautengKwaZulu-Natal Limpopo Mpumalanga Northern Cape North West Western Cape

Health Model 1 Health Model 2 Health Model 3 Health Model 4 Health Model 5 Health Model 6 Fig. 7 Summary of provincial health technical efciency model results. Author’s graph based on DEAP 2.1 efciency results

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