Are for-profit hospitals more efficient than non-profit hospitals? A case study of Zimbabwe using data envelopment analysis and the Tobit model

This paper is a first attempt to examine efficiency in the Zimbabwean hospital sector using the nonparametric data envelopment analysis (DEA) methodology. The paper evaluates whether for-profit hospitals are significantly more efficient than non-profit hospitals in order to shed some light on the role of profit incentives as implied by the theory of property rights. DEA findings revealed that there was a marked deviation of efficiency scores from the best practice frontier with for-profit hospitals having the highest mean overall technical efficiency (OTE) score of 61.4%. The mean OTE scores for mission and public hospitals were 35% and 50.3% respectively. Evidence from the second stage, Tobit model suggested that while both for-profit hospitals and government hospitals were both important in influencing efficiency, for-profit hospitals had a higher marginal mean efficiency score than government hospitals.


INTRODUCTION
The World Bank's study conducted by Akin et al. (1987) indicated that apart from the problems of allocation and inequity in African health care systems, one of the major challenges in developing countries is inefficiency.Empirical evidence emerging from various studies in South Africa by Zere (2000), in Kenya (Kirigia et al., 2002), Ghana (Osei et al., 2005) and Namibia (Zere et al., 2006) also indicates the wide prevalence of technical inefficiency in hospital care provision.Health care facilities in most developing countries grapple with the challenge of scarce resources, which constrain their ability to provide good quality services to its citizens.Zere (2000) states that this acute shortage of health care resources is attributed to many factors, the most important of which include poor macroeconomic performance, cutbacks in public spending, increased population growth, and the prevalence of diseases such as the AIDS epidemic and malaria.This lack of adequate health resources in most African economies is also aggravated by the widespread inefficiency in the health care systems particularly within hospitals.Barnum and Kutzin (1993) in their study found that hospitals in developing countries utilise an average of 50 to 80% of public sector health resources.Hence, in view of these facts the need to examine the efficiency of hospitals in any economy cannot be overstated.
There is an increasing recognition that improved health status contribute significantly to economic growth and development.In 2000, member countries of the United Nations agreed towards a commitment to eradicate poverty and improve the welfare and health of the poorest countries by 2015 (WHO, 2005).Therefore improvement in health is central to the attainment of millennium development goals (MDGs).Good health is important because it is an intrinsic element of human well-being.As a component of human capital, health is a key factor in the creation of wealth.In a study of the connection between health and wealth, Pritchett and Summers (1996) concluded that wealthier nations are healthier nations.Given this nexus between health and wealth, its disruptions certainly dislocate all the essential links this sector has with the rest of the economy.
The hospital sector in Zimbabwe has been undergoing significant structural changes in the way in which hospital care is provided.One important structural change has been the growth of the private sector.The role of the private sector (for-profit and not for-profit) in health is becoming significant in Zimbabwe.Many health care analysts have suggested that a continual movement in the direction of profit incentives in the production of hospital care might significantly improve the sector's poor economic performance.This view argued from the theory of property rights maintain that the non-profit hospital is inherently inefficient because no individuals` income is tied to economic performance (Nyman and Bricker, 1989).Furthermore, it is believed that non-profit hospital managers may cause the hospital to pursue goals other than strict cost minimization.While the theoretical case to argue for for-profit hospitals is relatively strong, however, empirically the case in favour of for-profit hospital performance is unclear.The purpose of this study is therefore to evaluate the impact of profit incentives on technical efficiency in the production of hospital care services in Zimbabwe.

AN OVERVIEW OF THE HEALTH CARE SECTOR IN ZIMBABWE
Zimbabwe is facing a severe challenge of a nearly collapsing health care system.Against an environment of severe political instability and macroeconomic constraints such as increasing poverty levels, slow economic recovery and high unemployment.The brain drain crisis is currently one of the topical challenges in the country where deteriorating economic, social and political conditions are exacerbating the emigration tide.The health delivery sector was the worst affected by migration as health workers were emigrating in search of better livelihoods in emerging and developed economies (Chikanda, 2004).Hence, owing to the generally poor macroeconomic fundamentals coupled with declining donor support, the health sector delivery system in Zimbabwe has been deteriorating especially during the pre-dollarisation period.As a result, health indicators are showing that the country is digressing away from the targets for achieving the millennium development goals.However, while there are undeniable major shortfalls in resources within Zimbabwe's health care system, this paper argues that there is potential for improved efficiency in the use of the available resources.
Zimbabwe's health sector is diverse comprising the Maredza 11671 central government hospitals, municipal hospitals and clinics, private hospitals and clinics owned by mining and agricultural enterprises for their employees.Government hospitals are allocated budgets for salaries, supplies and other provisions.Non-profit private providers in the form of mission hospitals are also an integral part of the health delivery system in Zimbabwe.The government assists mission hospitals with financial grants and other technical skills in order to subsidize their activities.State-owned and mission hospitals are therefore resource intensive and as such require an efficient management system.A traditional health sector is also in existence whose conduct is regulated by Zimbabwe National Traditional Healers Association (ZINATHA).With the worsening of the HIV and AIDS epidemic, NGOs have since been playing an important role in the prevention and control of HIV as well as dealing with the social impact of the epidemic.
In the past, donor funding used to complement government support for the health sector.However, owing to the political instability, donor funding has since dwindled.Hence, one of the obstacles to achieving universal health care in Zimbabwe has been inadequate funding in the public health sector.Currently, public facilities are over-stretched by the demands of a growing population and the increase in the HIV and AIDS.There is little development of these facilities due to the severe shortage of resources.Hence the dire need to mobilize extra resources for the health sector.Private for profit providers, although concentrated in urban areas, have been instrumental in providing and financing health care in the country.After independence in the 1980s, the government had little confidence in the private for-profit hospital sector.However, today the for-profit hospital sector is acknowledged as an integral and complementary component in the health delivery system.Given the fact that health care resources are scarce in Zimbabwe, there is need for policy makers to encourage efficient utilizing in a way which maximizes their health benefits for the majority.

CONCEPTUALISING EFFICIENCY
This paper will review two frontier approaches to efficiency measurement: the cost and production approaches.Efficiency measurement is derived from the cost or production boundary.For instance, production can take place only below or on the frontier.Similarly, observed costs can be above the cost frontier but not below the frontier because it is impossible to achieve costs lower than the minimum input requirements implied by the production frontier.The amounts by which an organization lies below its production frontier or the amount by which it lies above its cost frontier can be regarded as a measure of relative efficiency.

The production function approach
The first empirical treatment of the production function as a frontier is found in the work of Farrell (1957).A production function is a process of physical transformation in which inputs are combined to generate output.Thus, a production function defines efficient transformation possibilities, given a set of feasible techniques.In the case of inefficiency, the production function may be written as an inequality: Where i y is observed output at hospital i, and i X is a vector of inputs and  is a vector of parameters which describe the transformation process.f (.) is the production function and has the interpretation of the efficiency frontier or .max y At inefficient operations, observed performance   i y is less than potential output ) ( max y .The residual ) ( i  can be regarded as the difference between observed and potential performance and can be treated as a residual in the production function.
The residual i  is strictly non-positive to guarantee that observed output is not greater than potential.In other words, max y y i  is not possible.Ideally, the efficiency residual should be equal to 0 for the production unit to be efficient since actual and potential outputs will be equal.
The cost function approach Ganley and Cubbin (1992) states that the theory of duality between cost and production implies that there exists a dual cost function to the product transformation function in (1) above.Since it is possible that observed costs can exceed the minimum cost possible, the cost function may be written as an inequality: ). ;

   
In the presence of inefficiency, observed costs are greater than potential and the efficiency residuals are positive.Since frontier costs are the minimum feasible, observed costs cannot fall below minimum costs.

Technical and allocative efficiency
According to Farrell (1957) who pioneered most of the work on efficiency measurement, the efficiency of a firm consists of technical efficiency and allocative efficiency.A production plan is said to be technically efficient if the inputs which are employed produce maximum output or if maximum output is produced using the least amount of inputs.Thus technical inefficiency is due to excessive input usage.Allocative efficiency on the other hand, reflects the ability of a hospital to use these inputs in optimal proportions given their respective prices and the production technology.Depending on whether one has control over inputs or outputs, an input or output orientation can be specified.An input orientation measures input reductions that are necessary for a production unit to become efficient without a reduction in output.Input inefficiencies show the degree to which inputs must be reduced for the inefficient hospital to lie on the best practice frontier.An output orientation measures the expansion of output that is necessary for efficiency improvement holding inputs constant.Thus output inefficiencies represent the needed increase in output for the inefficient hospital to become efficient.

DATA ENVELOPMENT ANALYSIS (DEA) MODELS
DEA is a linear programming technique originally developed by Farrell (1957) and later by Charnes et al. (1978) to evaluate the efficiency of public sector and non-profit organizations.However, since its introduction it has been developed and extended for a variety of uses including application in for-profit institutions.The original DEA model had an input orientation and assumed constant returns to scale (CRS).However, subsequent development of the model by Banker et al. (1984) gave origin to the variable returns to scale (VRS) model.DEA is a non-stochastic and non-parametric method that incorporates multiple inputs and multiple outputs and enables an overall evaluation of technical efficiency.It is nonstatistical in that it makes no assumption on the probability distribution of errors and non-parametric in the sense that it does not assume that the underlying technology belongs to a certain class of specific functional form.

The input-oriented constant returns to scale model
The input-oriented CRS model which was initially proposed by Charnes et al. (1978) had an input orientation and exhibited constant returns to scale.The mathematical formulation of DEA assumes data on K inputs and M outputs on a sample of N decision making units (DMU 1 s).The inputs and outputs for the i-th DMU can therefore be represented by the vectors xi and yi, respectively or more technically by an N K  input matrix and N M  output matrix.The purpose of DEA is to construct a non-parametric envelopment frontier over the data points such that all observed points lie on or below the production frontier (Coelli, 1996).For each i-th DMU there is need to obtain a measure of the ratio of all outputs over all inputs, such as According to Coelli (1996), the mathematical formulation for the input-oriented CRS DEA Model which will generate optimal weights is as follows: Equation 5 is used to select the optimal weights which are the values of u and v such that the efficiency measure of the i th DMU is maximized subject to the constraint that all efficiency measures must be less than or equal to one.The problem with this equation is that it has an infinite number of solutions, hence, to avoid this, a constraint ' i vx= 1 can be imposed thereby providing the following formulation: The notation change in u and v to  and  represent the transformation to a form which is known as the multiplier of the linear programming problem.An equivalent envelopment formulation can be obtained using duality linear programming as formulated in Equation ( 7).The duality of Equation ( 7) constructs a piecewise linear approximation to the true frontier by minimizing the quantities of x inputs required to meet stated levels of the y outputs (Ganley and Cubbin, 1992).The dual equivalent envelopment form will be: 1 Charnes et al. introduced the term "decision making units" (or DMU) which is now widely used in literature.A DMU is to be regarded as an entity for converting inputs into outputs.

Maredza 11673
Where  is a scalar and  is an N x 1 vector of constants.This envelopment form is more preferable than the equation 7 because it has got fewer constraints.It is equation 8 that is used to calculate the efficiency scores.The value of  will be the efficiency score for the i-th DMU and should satisfy 1   .A value of 1 indicates a point on the efficiency frontier and hence a technically efficient DMU.The linear programming problem is solved N times once for each DMU in the sample.

The input-oriented variable returns to scale (VRS) model
The CRS assumption is only appropriate when all DMU's are operating at an optimal scale.The prevalence of imperfect competition and financial constraints, for instance, may cause a DMU not to operate at an optimal scale.Banker et al. (1984) suggested an extension of the CRS DEA model to account for variable returns to scale (VRS) situations.Adopting the CRS specification when all the DMU under study are not operating at an optimal scale will result in measures of technical efficiency which are "mixed up" with scale efficiencies (SE).Thus the VRS specification will allow the generation of technical efficiency scores that are independent of these scale efficiencies.The CRS linear programming problem, Equation 8, is modified to account for VRS by adding the convexity constraint: N1` = 1 to give: Where N1 is an N × 1 vector of ones.This forms a convex hull which envelopes the data more tightly than the CRS hull, thus the technical efficiency scores of VRS will be greater or equal to the technical efficiency scores from the CRS model.Technical efficiency scores from a CRS DEA can be due to scale inefficiency or "pure" technical inefficiency.Scale inefficiency is the ratio of the CRSTE to the VRSTE.Therefore, if there is a difference between the CRS and VRS efficiency scores it indicates that the DMU is scale inefficiency (Coelli, 1996).

The calculation of DEA efficiency scores
DEA incorporates many inputs and outputs and calculates an overall efficiency assessment.The efficiency scores are calculated as the ratio of the weighted sum of outputs to the weighted sum of inputs.For all the hospitals in the sample, this ratio must be equal to or less than unity.The hospital that utilizes the least amounts of inputs to obtain a given level of output or the one that achieves maximum output with given level of inputs forms the efficient frontier (or boundary) and becomes the best practice.Other hospitals are then evaluated relative to this best practice.Less efficient ones are located inside the frontier.DEA uses linear programming techniques to construct a non-parametric piecewise surface or frontier over the data in order to calculate efficiencies relative to this surface (or frontier) (Coelli, 1996).Thus the DEA methodology calculates the efficiency scores by measuring the distance of each DMU from the efficiency frontier (best practice).The more a hospital deviates from this best-practice the less efficient it is.However, it is important to emphasise that DEA is a measure of relative efficiency as opposed to absolute efficiency.The particular hospital exhibiting "best practice" can be less efficient if it is placed in a different peer group with better performers.Oberholzer et al. (2010) in their study of bank efficiency state that DEA measures the efficiency of a bank relative to its peers, which are the other banks included in the study, and not in relation to a theoretical maximum.

The Censored Tobit model
The efficiency scores derived from the DEA technique are then regressed on a number of categorical factors to identify those factors influencing inefficiency.The second stage in the empirical analysis of this study therefore involves the use of Tobit regression.The dependent variable (efficiency scores) are regressed on proxy variables that are hypothesised to influence efficiency namely hospital size, ownership, average length of stay and bed occupancy rate.The Censored Tobit model also known as the limited dependant variable regression model has the strength of estimating equations whose dependent variable values are restricted within some range.Since efficiency scores are limited to the [0, 1] interval, there are no observations above the upper limit and below the lower limit, hence the need to take this fact into account.The standard Tobit regression will be censored between 0 and 1 as follows: The vector zi includes the variables that affect DMU efficiency and the vector  is a vector of coefficients to be estimated.It is critical that these regressors are not correlated among themselves.The idea is to be able to ascertain with reasonable accuracy the relationship between each of the independent variables and the dependent variable.A correlation matrix was computed to investigate the interrelationships among the sets of variables to be included in the model and Table 1 presents the results.
Table 1 show that the variables exhibit very low correlations and therefore do not suffer from the problem of multi-collinearity.Table 2 shows descriptive statistics for the variables to be employed in the model.Note that in order to avoid the dummy variable trap, an intercept term was omitted and dummy variables were assigned to each category of hospital ownership.The empirical model to be estimated therefore takes the following form; where:

EFFi
-Overall Technical Efficiency Score PROFi -Ownership dummy: 1 if for-profit hospital, 0 otherwise GOVi -Ownership dummy: 1 if state owned hospital, 0 otherwise MISSi -Ownership dummy: 1 if mission hospital, 0 otherwise BORi -Bed Occupancy Rate (%) ALSi -Average length of stay (days) BEDSi -Size variable reflecting number of beds i  -Error term to capture other possible factors not specified.

Data and justification of variables
This study uses data on hospitals from all the provinces in the country, covering the period 2006 to 2008, the years for which relatively reliable data are available.The data was obtained from the Health Department and the Zimbabwe National Health Profile (2007) published by the Ministry of Health and Child Welfare (MOH&CW) as well as from Zimbabwe Association of Churchrelated Hospitals (ZACH).However, like most developing countries most of the data on private for-profit hospitals in Zimbabwe is not published due to their reluctance to release information governing their activities which might place them at a disadvantaged position with their competitors.As a result the variable information pertaining to private for-profit hospitals was collected from individual hospitals.This is predominantly the reason why this category accounts for a small sample in the study.Nevertheless this constraint in data collection does not compromise the quality of this study since the sample size is above that of the rule of thumb 2 .The availability and completeness of the data determined the selection of the time period covered.The sample consists of 36 mission hospitals and 44 public hospitals (13 central hospitals and 31 district hospitals) and 20 private for profit hospitals making a total sample of 100 hospitals.

Input and output variables
Hospitals are multi-product firms treating a diversity of patients with a variety of inputs.There is no consensus as to how outputs of hospital production should be accurately measured.However, the input and output variables used in this paper comprise of variables that support the assumption of the DEA method and the analysis of efficiency described in the literature.This study used inpatient days and total discharges to constitute the major output variables for the hospitals.Among the input variables, the number of existing hospital beds is used as a proxy for capital while the number of doctors and number of nurses has been used to reflect labour.These inputs and outputs are measured in their physical units.The application of the DEA methodology does not need a homogeneous unit of measurement, the reason being that DEA is unit invariant.Coelli (1996) maintains that changing the unit of measurement will not change the value of the efficiency measure.The inputs and outputs variables used in this study and their description have been provided in Table 3.
However the author is aware that hospitals produce other service outputs not included in the analysis such as community engagement and research activities.The difficulty in defining good measures for these outputs constrained their inclusion.On the input side sophisticated and expensive equipment were not included.However, the input variables captured are sufficient to shed light to the question at hand.Finally, the quality of hospital services is an ideal concept that should have been captured in our analysis.Again a quality variable was not accounted for due to problems of measurement.

Hospital ownership
Of paramount importance to the present study is to investigate the significance of profit incentives on efficiency.There is a view that economic inefficiency in the hospital sector is more prevalent among non-profit hospitals and that it may be improved by relying more heavily on profit incentives (Register and Bruning., 1987).The expectation in this study is therefore that for-profit ownership will be associated with greater efficiency than non-profit ownership.

2
The discriminating power of DEA is limited when a small number of DMUs are considered.Ganley and Cubbin (1992) state that the sample size should be larger than the product of the number of inputs and outputs.

Inpatient days
The number of days of care charged to a beneficiary (patient) who is admitted to a hospital bed for inpatient care services or skilled nursing facility care services (always in units of full days).

Discharged patients
The number of patients who leaves the hospital and either returns home or are transferred to another facility.

Beds
The number of existing patient beds within the hospital ready for use.

Doctors
The number of medical doctors employed in the hospital (both specialists and general medical practitioners).

Nurses
The number of nurses employed in the hospital (plus nursing aides)

Average length of stay (ALS)
The average length of stay variable is also included as an explanatory variable.The assumption is that patients with longer lengths of stay require more resources because they represent persistent cases that do not improve.As a result hospitals with patients with longer length of stay may exhibit lower efficiency scores.

Bed size
In order to control for the impact of hospital size on the degree of hospital efficiency, a hospital size variable is entered into the model.This variable seeks to capture the influence of hospital size on efficiency.The number of beds will be used as a proxy for hospital size.There is need to ascertain the variation in efficiency as the hospital size varies.Ideally, a hospital should operate at an optimal scale which is at the lowest of its long run average cost curve.However, in reality most hospitals exhibit scale inefficiencies in the form of increasing or decreasing returns to scale.

Bed occupancy rate (BOR)
Finally another determinant of efficiency is the occupancy rate.The occupancy rate will be measured by the number of patients in the hospital on a certain day divided by the actual number of beds.High occupancy levels are associated with higher level of efficiency.

EMPIRICAL RESULTS
The aim of this section is to present empirical results obtained from the DEA model over a sample of 100 hospitals classified as private for-profit, private not-for profit (mission) and public or state owned hospitals.Efficiency scores were generated using DEAP version 2.1 software package developed by Coelli (1996).The rest of the section is organized as follows.After running the DEA results, a second stage analysis of environmental factors is performed using the Tobit model.Input orientation was chosen owing to the fact that the hospital managers can only influence input utilization rather than output which is basically the choice of consumers.Therefore any inefficiency realized would call for input reduction as opposed to output expansion.Recall that efficiency scores ranges from 0 to 1 (or 0 to 100%).A score below unity represents an inefficient hospital which is located below the production frontier while a score of one implies that the hospital is fully efficient and lies on the production frontier.The CRS technical efficiency scores reveal combined inefficiencies which are equivalent to overall technical efficiency (OTE) scores; inefficiency due to pure technical inefficiency and inefficiency that is due to inappropriate hospital size (scale inefficiency).Therefore further decomposition of OTE into pure technical efficiency (PTE) and scale efficiency (SE) enables an investigation of the sources of the inefficiencies of each hospital in the sample.DEA results for each of the 100 hospitals in the sample are in Appendix 1. Table 4 is a summary of DEA results obtained for each efficiency type and hospital category.The table shows the mean efficiency score, minimum efficiency score, maximum efficiency score, standard deviation of efficiency scores and the number of hospitals that achieved 100% efficiency.

First stage: Results from the DEA model
The mean efficient score for for-profit hospitals is the summation of efficient scores for each hospital in the forprofit category divided by the total number of for-profit hospitals.Three types of efficiency measures were calculated for each hospital category namely overall efficiency (OTE), pure efficiency (PTE) and scale efficiency (SE).DEA findings in Table 4 revealed that there was a marked deviation of efficiency scores from the best practice frontier with for-profit hospitals having the highest mean OTE score of 61.4%.The mean OTE scores for mission and public hospitals were 35 and 50.3% respectively.This implies that average inputs utilisation could be potentially reduced by 38.6, 65 and 49.7%, without affecting the level of the output produced.Under PTE measures, for-profit hospitals exhibited the highest score of 71.1% while mission and public hospitals scored 64.8 and 62.6% respectively.Lastly, SE for forprofit hospitals were the highest indicating a score of 85.6% compared to that mission and public hospitals of 54.9 and 82.9%.This means that for-profit, mission and public hospitals each had the potential to reduce their input usage by 14.4, 45.1 and 17.1% if they operate on their optimum scale.This essentially reflects inefficiency due to inappropriate hospital size.As shown in Appendix 1, the predominant form of scale inefficiency observed is increasing returns to scale.Hence even these first stage results have clearly demonstrated that the for-profit hospitals are more efficient than any hospital type/category.This is because in all the three types of efficiency measures for-profit hospitals exhibited the highest efficiency scores.
Table 5 shows the distribution of efficiency scores for each category of hospitals under the three types of efficiency measurements.That is, the percentage of (forprofit, mission and public) hospitals that exhibited (OTE, PTE, and SE) efficiency scores within a particular range say 0 to 50%, 50 to 70%, 70 to 90% and 90 to 100%.For example an analysis of OTE indicates that the percentage of for-profit, mission and public hospitals that scored efficiency scores within the range 50 to 70 were 50, 11 and 36% respectively.Therefore for the for-profit hospitals it means half of the hospitals had scores from 50 to 70%.The results also showed that 10, 3 and 5% of the for-profit, mission and public hospitals operated on the frontier of OTE, that is, had scores of 100%.As far as OTE is concerned, this also constitute the proportion of hospitals whose practice must be emulated by the inefficient hospitals as they represent best practice performance.Under each type of efficiency, Table 5 also shows that for-profit hospitals account for a small number of the least efficient hospitals than any other categories.Again this suggests that, if any conclusion may be drawn from this piece of information, for-profit hospitals are more efficient than their non-profit counterpart.

Second Stage: Results from the Tobit Model
In the second stage analysis, DEA efficiency scores were analyzed by regressing them against hospital characteristics such as ownership type, hospital size, length of stay and occupancy rate.Of particular interest to the present study is the impact of ownership type on efficiency.Dummy variables were therefore used to capture for-profit, mission and public ownership type.If one type of hospital ownership is better in terms of technical efficiency, then the coefficient associated with that ownership dummy will reveal significance.Tobit results in Table 6 indicate that for-profit and public ownership are significant factors in influencing efficiency.However, the dummy variable for mission hospitals proved to be insignificant.The results therefore suggest that, if a hospital is a for-profit type and public type it would be associated with an efficiency score of 9.59% and 7.01% respectively.Hence, the more profit oriented a hospital is the greater the efficiency.For-profit hospitals are associated with 2.58% (9.59 -7.01) more efficiency compared to public hospitals.This finding is in conformity with the expectation of this study as for-profit ownership proved to be associated with greater efficiency than nonprofit hospitals.Tobit analysis results also confirmed that higher bed occupancy is associated with greater efficiency.The other determinant factors of efficiency such as MISS, ALS and BEDS (hospital size) do not have a significant contribution to the efficiency of hospitals.Therefore the property rights hypothesis that supports the notion that for-profit institutions are significantly more efficient than non-profit institutions cannot be rejected.

DISCUSSION, CONCLUSION AND RECOMMENDATIONS
This paper employed DEA to generate efficiency indices for individual hospitals relative to a best-practice frontier.DEA results demonstrated that for-profit hospitals had higher mean levels of both OTE and PTE than both mission and government hospitals.The main idea that motivated this study was to investigate the impact of profit incentives on technical efficiency in the provision of health care in the Zimbabwean health sector with the intention to shed some light on the debate about the validity of the theory of property rights.The evidence in this study suggests that while both for-profit hospitals and government hospitals were both important in influencing efficiency, for-profit hospitals had a higher marginal mean efficiency score than the government hospitals.Thus this paper supports the notion that initiatives that are intended to improve the health sector in Zimbabwe that are based on profit incentives are likely to be of paramount value to the economy.There is therefore need by the Zimbabwean government to encourage the participation of individual private firms to establish health facilities to augment government efforts in providing health services of greater quality to the population.
The findings of this study also revealed that the majority of hospitals are operating at less than their optimal levels which raises a serious concern for planners and policy makers.It is important to highlight that hospitals are instrumental in efforts aimed at achieving the current Millennium Development Goals (MDGs) scheduled for 2015.Such poor levels of efficiency retards efforts designed to attain these MDGs.The main focus of policy makers should be more on Mission hospitals which had the lowest overall efficiency score.When compared with the results obtained from other SADC countries, the overall efficiency of Zimbabwean public hospitals of 50.3% is lower.For example, Zere et al. (2000) found technical inefficiency levels ranging between 35 to 47% (That is 53%  OTE  65%).Another efficiency evaluation study conducted by Zere et al. (2006) in Namibian district hospitals for the period 1997/98 to 2000/2001 indicated OTE scores ranging from 62.7 to 74.3%.However, one must exercise caution when making inter-country comparisons as DEA is sensitive to the variables included in the analysis.Furthermore the efficiency scores are time specific and they change over time making the results relevant only at the point in time when the study was conducted.Moreover, it is also important to recall that DEA is a measure of relative efficiency and not absolute efficiency.Overall these findings support the view that most African public health systems exhibit wide prevalence of technical inefficiency.

.
Where i c represents average cost at hospital i, i z are determinants of costs and  is a vector of parameters and g (.) has a frontier interpretation denoting minimum costs   min c The efficiency ratio is defined by the residuals   i  in the cost function.

Table 1 .
A matrix of correlation of independent variables.

Table 3 .
Definition and description of the variables.

Table 4 .
Summary of DEA results.

Table 5 .
Distribution of efficiency scores for each hospital category.