Advancing Universal Health Coverage in the COVID-19 Era: An Assessment of Public Health Services Technical Efficiency and Applied Cost Allocation in Cambodia

Keywords: health service efficiency, social health protection, costing, cost allocation, Universal Health Coverage, Cambodia JEL classification codes: Health Care Financing, Public Health Insurance, Input Output Models, Policy Making, Frontier Estimation, Developing Countries

COVID-19 is causing serious impacts on tax revenue and consequentially on public health budgets. This study assesses Cambodia's public health services technical efficiency, unit costs, and utilization rates to quantify the extent to which current health financing can accommodate the expansion of social health protection coverage. Overall, for the public health system to be fully efficient output would need to increase by 34 and 73 percent for hospitals and health centers, respectively. We find public sector service quality, private sector providers, and non-discretionary financing to be statistically significant factors affecting technical efficiency. This study pioneers the application of Data Envelopment Analysis-Aumann-Shapley applied cost allocation to the health sector, enabling unit cost estimation for the major social health insurance payment categories. We estimate there is potential supply-side 'service space' to expand population coverage to an additional 4.69 million social health insurance beneficiaries with existing financing if the public health system were fully efficient.

Introduction 1.1 Overview

Cambodia has committed to advancing Universal Health Coverage which requires expanding population coverage under its social health protection schemes. However, the near-term potential for new government investment is unlikely as tax revenues fall due to pandemic related economic disruption. Most government ministries and institutions, exempting the Ministry of Health, are required to reduce their expenditures by at least 50 percent of the approved national budget figures for the current year [START_REF] Star | Cambodia's economy projected to return to positive growth in 2021 as Covid-19 new cases continues to soar, total now above 17[END_REF]. However, austerity exacerbates health inequities in countries with weak social protection policies [START_REF] Ruckert | Health inequities in the age of austerity: the need for social protection policies[END_REF].

And, countries with higher levels of inequity in income, education, and health are the least efficient in relation to health outcomes [START_REF] Schenkman | From income inequality to social inequity: impact on health levels in an international efficiency comparison panel[END_REF].

Context

Health Services Efficiency

Increasing health sector expenditure may not significantly affect health outcomes when efficiency is low [START_REF] Grigoli | Waste not, want not: the efficiency of health expenditure in emerging and developing economies[END_REF]. Thus, performance measurement of public services is essential to ensure quality services and value for money [START_REF] Pidd | Measuring the performance of public services: Principles and practice[END_REF]. Inefficiencies in the public health sector are well documented [START_REF] Banzon | Overcoming public sector inefficiencies toward universal health coverage: the case for national health insurance systems in Asia and the Pacific[END_REF]. The 2010 World Health Report asserts that all countries can achieve more with the same resources, conservatively estimating that 20-40 percent of all healthcare expenditure is wasted [START_REF] Chisholm | Improving health system efficiency as a means of moving towards universal coverage[END_REF]. A study assessing overall health system technical efficiency in Asia found Cambodia to be among the countries that can improve use of the current resources [START_REF] Ahmed | Measuring the efficiency of health systems in Asia: a data envelopment analysis[END_REF].

Public sector health expenditure is 47 percent of Cambodia's total health expenditure (WHO, 2019); however, only about 20 percent of people with an illness or injury first seek care in the public sector [START_REF] Jithitikulchai | Health equity funds as the pathway to universal coverage in Cambodia: care seeking and financial risk protection[END_REF]. A district level efficiency analysis of public health services in five Cambodian provinces found evidence of sub-optimal performance [START_REF] Ensor | Exploring the influence of context and policy on health district productivity in Cambodia[END_REF]. Another study concluded that increasing health service utilization and quality could improve public health center efficiency [START_REF] Beiter | Technical efficiency of public health centers. A two-stage Data Envelopment Analysis (DEA) from Cambodia[END_REF]. Finally, a recent healthcare costing study found considerable differences in workload which was inversely correlated with total and unit costs within each facility level which suggests that cost-efficiency could be improved by increasing service volume [START_REF] Jacobs | Costing for Universal Health Coverage: Insight into essential economic data from three provinces in Cambodia[END_REF].

Improved efficiency is a central tenant of Cambodia's high-level policy and strategy documents. The Rectangular Strategy for Growth, Employment, Equity and Efficiency calls for "ensuring efficiency and effectiveness of the public institutions and management of all the resources" as a means towards medium and long-term sustainable development [START_REF] Rgc | Progress Report of Public Financial Management Reform Program Implementation[END_REF]. The National Strategic Development Plan aims to increase public sector efficiency for sustainable development and poverty reduction to achieve the Sustainable Development Goals (RGC, 2019a). And, the National Social Protection Policy Framework calls for enhancing the efficiency, equity, transparency and consistency of the social protection system (Council of Ministers, 2017). The pandemic's disproportionate impacts on poor and vulnerable communities present opportunities for policy makers to tackle deep-rooted system performance issues with long-term implications for health financing and health systems performance [START_REF] Kurowski | From Double Shock to Double Recovery-Implications and Options for Health Financing in the Time of COVID-19[END_REF].

Health Services Costing

Healthcare service cost information is needed to support evidence-based, effective and efficient health care reforms [START_REF] Flessa | Basing care reforms on evidence: the Kenya health sector costing model[END_REF]. Regularly updated costing data for each facility level can be used to strengthen strategic purchasing and cost containment [START_REF] Tangcharoensathien | Achieving universal health coverage goals in Thailand: the vital role of strategic purchasing[END_REF]. For example, cost data can be used to determine social health insurance reimbursement rates as the system shifts from supply to demand-side financing. Increasing the social health insurance reimbursement would incentivize increased service volume, thereby increasing efficiency [START_REF] Kolesar | Decision time: Cost estimations and policy implications to advance Universal Health Coverage in Cambodia[END_REF]. In addition, cost data can inform budget planning and efficient resource allocation. However, costing exercises are resource intensive and can require significant expense and effort [START_REF] Jacobs | Costing for Universal Health Coverage: Insight into essential economic data from three provinces in Cambodia[END_REF]. Therefore, they are infrequent and often limited to a few facilities and health services, particularly in lowand middle-income countries [START_REF] Adam | Variability in costs across hospital wards. A study of Chinese hospitals[END_REF][START_REF] Jacobs | Costing for Universal Health Coverage: Insight into essential economic data from three provinces in Cambodia[END_REF].

Social Health Protection

Cambodia's largest social health protection scheme, the Health Equity Fund (HEF), was established to provide free access to health care for the poorest. The scheme reimburses public health facilities user-fees normally paid by the patient. Since 2017, approximately 2.6 million household members have been covered under the HEF, representing about 16.1 per cent of the total population. Free benefits under the HEF have been extended to some informal workers and selected populations (about 93,500 enrollees). In addition, the roll-out of the On-demand ID Poor system in 2020 has increased eligibility to approximately 468,000 new beneficiaries. Currently, the National Social Security Fund (NSSF) members are approximately 2,314,000 including 1,884,000 private sector employees and 430,000 civil servants, retirees, and veterans. Total effective social health protection coverage equates to about one-third of the total population. Cambodia's high-level strategy and policy documents including the National Strategic Development Plan 2019-2023 call to advance Universal Health Coverage (UHC) by increasing population coverage of social health protection to 65 percent by 2023. Expanding population coverage under the social health protection schemes is expected to increase public health service utilization. However, user-fee reimbursements paid to public health facilities are allocated to pay for staff incentives (60 percent) and quality improvement (~40 percent). Thus, social health protection scheme reimbursements are likely insufficient to cover the increased costs related to personnel, medications, and commodities associated with increased utilization when population coverage is expanded (Kolesar et al., 2021).

This study assesses the technical efficiency of Cambodian public health services to quantify the extent to which current health sector supply-side resources can accommodate social health protection expansion. In addition, we examine explanatory factors associated with technical efficiency; and, estimate the unit cost of service provision for the major social health insurance reimbursement categories to inform the policy discussion on strategic purchasing and demand-side health financing.

Impact of COVID-19

The global impacts of COVID-19 are unprecedented. The pandemic affects medium-term economic growth, poverty, government revenues, and government spending; even countries with relatively low case counts are facing substantial reductions in national revenue [START_REF] Imf | A crisis like no other, an uncertain recovery[END_REF][START_REF] Kurowski | From Double Shock to Double Recovery-Implications and Options for Health Financing in the Time of COVID-19[END_REF]. Forecasts project that near-term per capita government health spending could slow and even decrease, particularly among low and lower-middle income countries [START_REF] Kurowski | From Double Shock to Double Recovery-Implications and Options for Health Financing in the Time of COVID-19[END_REF]. In Cambodia, the pandemic has caused sharp deceleration in most of the country's main growth engines including tourism, manufacturing export, and construction. In 2019, these sectors accounted for more than 70 percent of growth. In 2020, the Cambodian economy registered negative growth of -3.1 percent (World Bank, 2021). This has serious impacts on tax revenue and consequentially on government budgets in general, and the public health budget in particular [START_REF] Thmey | Hun Sen announces up to 50 pct budget cut amid COVID-19. Cambodianess. Cambodianess[END_REF]. At the same time, unemployment is increasing financial vulnerability to health shocks with out-of-pocket healthcare expenditure comprising an excessive share of income [START_REF] Kolesar | Expanding social health protection in Cambodia: An assessment of the current coverage potential and gaps, and social equity considerations[END_REF].

Decreased economic output can be expected to lead to decreased utilization of health services that require payment. A 1 percent decrease in GDP per capita is expected to result in a decline in out-of-pocket healthcare expenditure per capita of nearly 1 percent [START_REF] Ke | The determinants of health expenditure: a country-level panel data analysis[END_REF]. Despite the Cambodian government's emergency cash transfer program to mitigate the effects of the COVID-19 economic shock among the poor, poverty is likely to have increased [START_REF] Star | Cambodia's economy projected to return to positive growth in 2021 as Covid-19 new cases continues to soar, total now above 17[END_REF]World Bank, 2020). For most lower-middle income countries government revenue is not expected to rebound to pre-pandemic levels until 2024-2025 [START_REF] Kurowski | From Double Shock to Double Recovery-Implications and Options for Health Financing in the Time of COVID-19[END_REF].

Public Health System Structure

Cambodia's public health system consists of a network of 34 national and provincial-municipal level hospitals, 92 Operational District (OD) referral hospitals, 1,221 health centers, and 127 health posts.

Hospitals are sub-categorized into four levels: national hospitals and complimentary package of activities (CPA) hospitals levels 1-3 [START_REF] Ministry | Health Care Efficiency In Transition Economies: An Application of Data Envelopment Analysis[END_REF]. Health centers provide a minimum package of activities (MPA) and operate health posts which extend services to hard-to-reach areas. The MPA focuses on preventative and basic curative services; each health center serves approximately 10,000-20,000 people.

Health Operational Districts (ODs), responsible for health center oversight, are typically comprised of 10-15 health centers covering about 100,000-200,000 people and a district referral hospital. A summary of services provided by facility level is presented in appendix 1.

Decentralization and De-concentration

There is empirical evidence demonstrating that good governance and strengthened public financial management systems can positively impact health system performance and service delivery as well as efficiency of government spending on health [START_REF] Goryakin | Public financial management and health service delivery: a literature review[END_REF][START_REF] Kurowski | From Double Shock to Double Recovery-Implications and Options for Health Financing in the Time of COVID-19[END_REF]. In 2001, the Cambodian central government began introducing decentralization reforms [START_REF] Khoun | Fiscal decentralisation and good governance: convergence or divergence? The experience of commune councils in Cambodia[END_REF] with the Public Financial Management Reform Program following in 2004. This program focuses on four areas to improve:

(1) budget credibility; (2) financial accountability; (3) budget policy linkages; and (4) performance accountability [START_REF] Rgc | Progress Report of Public Financial Management Reform Program Implementation[END_REF]. The commitment to these reforms was renewed in the government's highlevel strategy and policy documents. The Rectangular Strategy Phase IV sets out to deepen "reforms to achieve good governance, particularly public administration reform, public financial management reform, decentralization and de-concentration reform" (RGC, 2018b). The National Strategic Development Plan 2019-2023 aims to strengthen the implementation of the Decentralization and De-concentration (D&D) Reform Program by delegating power and transfer of functions, resources and technology to administrative units to obtain appropriate autonomy, including decision-making, management and resource allocation (RGC, 2019a). This focus aligns with the National Social Protection Policy Framework's cross-cutting principles of good governance and effective spending (Council of Ministers, 2017).

Until 2020, the Ministry of Health was solely responsible for the organization and delivery of government health services. The Directorate General for Health oversaw health service delivery through 24 Ministry of Health Provincial Health Departments (PHDs) and the municipality of Phnom Penh. Each PHD operated the provincial hospital and governed the Health Operational Districts [START_REF] Annear | The Kingdom of Cambodia Health System Review[END_REF]. In December 2019, the government issued Sub-Decree No. 193 ANKr. BK to delegate health management functions and service provision to the 25 provincial-municipal administrations. This directive transfers decision-making and responsibility for health service management including financial resources, properties, and human resources to the provincial-municipal administrations as of January 1, 2020. In turn, the administrations are "accountable and responsible to Minister of Health for management, organization, and performance of the delegated health functions" in line with the national health policy, strategic plan, clinical guidelines, protocols, and technical standards [START_REF] Rgc | Progress Report of Public Financial Management Reform Program Implementation[END_REF]. In 2019, 38.6 percent of the approved Ministry of Health budget (~USD $444 million) was allocated to the provincial-municipal level.

Methods

Data

Data was compiled from multiple sources including: the Cambodia Demographic and Health Survey, 2019 Cambodian Census, 2019-2020 Cambodia Socio-economic Survey (CSES), Ministry of Health Achievement Reports, administrative data, and budget/expenditure reports. The study focuses on 2019 as 2020 data is not likely to fairly represent the efficiency of the public health system due to pandemic-related changes in health care-seeking behavior. In addition, 2019 provides a baseline to enable the future performance evaluations of the impact of the D&D policy change.

This analysis aligns, to the degree possible, with the major social health insurance reimbursement categories at the hospital and health center levels (see Appendix 1).

Due to administrative data limitations, expenditures by facility type are estimated using National Health Accounts data weighted according to the number of each facility type by province (WHO, 2019). To avoid double counting, maternity services (i.e.

delivery and abortion care) are subtracted out from outpatient cases for health centers and inpatient cases for hospitals by province. We convert Khmer Riel (KHR) to United States dollars (US$) using the standard rate 4,100 KHR = 1US$.

Analytical methods

Data Envelopment Analysis

Technical efficiency can be assessed in terms of the amount or mix of service outputs that can be produced within a given budget [START_REF] Chisholm | Improving health system efficiency as a means of moving towards universal coverage[END_REF]. Data Envelopment Analysis (DEA) is a performance benchmarking method in operations management based on a systems view of production according to which resources/inputs are processed into products/outputs. The resulting metric is a measure of technical efficiency relative to the most efficient decision-making units or unit of analysis which form the best practice or efficiency frontier. A fundamental assumption behind this method is that if a given producer is capable of producing X units of output with Y inputs, then other producers should also be able to do the same if they were to operate efficiently [START_REF] Bogetoft | Performance benchmarking: Measuring and managing performance[END_REF]. DEA is an established performance measurement method and has been used to evaluate the technical efficiency of health systems [START_REF] Ahmed | Measuring the efficiency of health systems in Asia: a data envelopment analysis[END_REF][START_REF] Alexander | Implementing and interpreting a data envelopment analysis model to assess the efficiency of health systems in developing countries[END_REF][START_REF] Cheng | Estimating the technical efficiency of health care systems: A crosscountry comparison using the directional distance function[END_REF][START_REF] Evans | The Comparative Efficiency of National Health Systems in Producing Health: An Analysis of 191 Countries[END_REF]Mirmirani & Ilacqua, 2008;[START_REF] Ozcan | Health care benchmarking and performance evaluation[END_REF][START_REF] Radojicic | Going beyond health efficiency: What really matters?[END_REF]. The approach can use the radial projection to the efficiency frontier to calculate target outputs levels for each inefficient decision-making unit [START_REF] Boussofiane | Applied data envelopment analysis[END_REF][START_REF] Jain | Manufacturing performance measurement and target setting: A data envelopment analysis approach[END_REF][START_REF] Thanassoulis | Estimating preferred target input-output levels using data envelopment analysis[END_REF].

This study used STATA 17 to calculate all efficiency metrics and associated Simar-Wilson regression modeling [START_REF] Badunenko | Nonparametric frontier analysis using Stata[END_REF][START_REF] Statacorp | Stata Statistical Software: Release 17[END_REF]. Technical efficiency measures are overly optimistic under standard underlying DEA assumptions [START_REF] Badunenko | Nonparametric frontier analysis using Stata[END_REF]. Therefore, we use bootstrapping (2000 times of repeated sampling, with α = .05) to estimate bias-corrected technical efficiency scores. This approach uses Debreu-Farrell output distance functions and enables the calculation of lower and upper bounds [START_REF] Li | Measuring and benchmarking technical efficiency of public hospitals in Tianjin, China: A Bootstrap-Data envelopment analysis approach[END_REF][START_REF] Shephard | Theory of cost and production functions[END_REF]. Given the Royal Government of Cambodia's (RCG) current Decentralization and De-concentration (D&D) reform program discussed above, the unit of analysis or decision-making unit (DMU) is the provincial-municipal administration.

We fit two DEA output-oriented models: (1) hospital services, and (2) health center services. The nonparametric test of returns to scale indicated variable returns to scale (VRS) for the hospital model and constant returns to scale (CRS) for the health center model. The input for each model is the summed total of expended financial resources including staff salaries, pharmaceuticals and consumables, equipment and supplies, other operating costs, social health insurance service payments (from the Health Equity Funds and the National Social Security Fund), and performance-based service delivery grants. Service delivery grants provide public health facilities with additional, flexible budget for delivering quality health services while incentivizing quality improvement [START_REF] Pheakdey | Improving Health Service Quality in the Kingdom of Cambodia: A Policy Perspective[END_REF]. Outputs focus on the major social health insurance payment categories (i.e. outpatient cases, inpatient cases, major and minor surgeries, and maternity care). We limited the input and output factors to the essential components of the service production process to improve the discriminatory power of the analysis given the number of DMUs (N=25) [START_REF] Cooper | Efficiency aggregation with enhanced Russell measures in data envelopment analysis[END_REF]. The hospital model excludes national level hospitals from the municipality of Phnom Penh as they provide specialized services which are not comparable with services provided by CPA1-3 hospitals (see Appendix 1). Table 1 presents descriptive statistics for all variables used in the DEA models.

Regression Analysis

The second stage analysis employs truncated regression using the Simar and Wilson approach to assess explanatory factors of the bias-corrected technical efficiency scores [START_REF] Simar | Estimation and inference in two-stage, semi-parametric models of production processes[END_REF]. The results for both models were separately regressed on population size, hospital and health center quality scores (and their respective quadratic terms), number of large and small private providers (and the quadratic term for the health center model) as well as hospital and health center non-discretionary resources. The quality score is a facility-level index based on the three healthcare quality dimensions of structure, process, and outcome; scores are collected every three months through a national monitoring system [START_REF] Pheakdey | Improving Health Service Quality in the Kingdom of Cambodia: A Policy Perspective[END_REF]. Nondiscretionary resources are defined as the summed total of staff salaries, pharmaceuticals and consumables, equipment and supplies, and other operating costs. The health center regression model also included hospital and health center utilization rates. The hospital and health center regression models are shown in equations 1 and 2, respectively. Descriptive statistics for explanatory variables used in the models are presented in Table 2. 1) The exploratory analysis tested other variables that could potentially explain technical efficiency including population density, proportion of urban/rural population, poverty density, mean days of productively loss due to illness or injury, distance from the capital city Phnom Penh, education completion rate, literacy rate, and the proportion of women citing distance as a barrier to accessing healthcare. Quadratic and logarithmic transformations for each variable were also tested; these variables were excluded from the final regression models as they did not improve the fit as evaluated using the log ratio test (Deb, Norton, & Manning, 2017). 1 0

Hospital_Technical_Efficiency i = B 0 + B 1 Population i + B 2 Hospital_quality i + + B 3 Hospital_quality_squared i B 4 Large_private_providers i + B 5 Nondiscretionary_resources (logged) i + ε i (
Health_Center_Technical_Efficiency i =B 0 + B 1 Population i +

Applied Cost Allocation

Finally, we use RStudio 4.1.0 (R Core Team, 2021) to estimate the unit cost for each of the major insurance reimbursement categories by using the DEA-Aumann-Shapley applied cost allocation approach. The Aumann-Shapley prices associated with a given output vector are estimated by weighting the sum of gradients of the linear facets of the estimated cost function along a radial contraction path of the observed output vector. The weights are proportional to the length of the projected line segments [START_REF] Bogetoft | Applied cost allocation: The DEA-Aumann-Shapley approach[END_REF].

Calculations are proportionally weighted and restricted (+/-50 percent) from updated Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ) Social Health Protection Programme costing data that was compiled using a standard step-down micro-costing methodology for public health centers and referral hospitals CPA1-3 [START_REF] Flessa | Costing of Health Care Services in Three Provinces of Cambodia[END_REF][START_REF] Jacobs | Costing for Universal Health Coverage: Insight into essential economic data from three provinces in Cambodia[END_REF]. Hence, we use the GIZ weights as a reference, but allow for deviations of the relative GIZ price 50 percent up and down. We estimate a VRS (hospitals) and CRS (health centers) cost functions C(.) with restrictions on the dual weight.

Equation 3 expresses the assumption of the ratio of the dual weights for k outputs.

(3)

Using the estimation technology, we calculate the fixed costs C(0). The efficient variable costs can now be allocated using Aumann Shapley (A-S) prices. The theoretical literature has shown this method (and A-S prices) possesses a number of desirable properties, and it has essentially been the unanimous recommendation of economists for decades when sharing the costs of joint production [START_REF] Friedman | Three methods to share joint costs or surplus[END_REF]. The AS price of product j is the average marginal cost as shown in equation 4.

(4)

Here S is the number of steps we use in the approximation and is the marginal costs of product j at the point . Using these prices, we can allocate a large share of the cost of a DMU. What is left is the fixed costs and the possible inefficiency (see equation 5).

(5)

1 1

We allocate the non-allocated, remaining costs proportional to the allocated cost shares. Hereby the final costs assigned to product j is calculated following equation 6.

(6)

As hospital data was aggregated by province-municipality, hospital level (i.e. CPA1-3) specific rates are estimated using weights calculated by averaging the social health insurance payment rates and costing data described above. We consider this to be a rational approach as there is evidence that total and unit costs of different hospital levels are not significantly different [START_REF] Flessa | Costing of Health Care Services in Three Provinces of Cambodia[END_REF].

Service Space Potential

Finally, we use service-specific facility level utilization rates, output production targets calculated from the bias-corrected technical efficiency scores, and unit costs calculated from the applied cost allocation to estimate the potential additional social health insurance beneficiaries that could be enrolled and served by the public health system with existing supply-side financial resources (i.e. exempting user fee reimbursement payments) if the system were operating efficiently. We account for new beneficiary enrolment in 2020 under the On-demand identification system, and assume a five (5) percent service utilization increase for both current and the potential newly enrolled beneficiaries.

1 2

Results

Health Service Utilization and Technical Efficiency

Figure 1 compares hospital and health center service utilization for each output-payment category. With the exception of hospital inpatient cases, HEF beneficiaries generally used public health services at a higher rate compared to the rest of the population (i.e. non-inclusive of HEF beneficiaries) for each major service category. However, inpatient cases at the health center level among HEF beneficiaries are substantially higher: more than 34 times higher (0.137/0.004) compared to the rest of the population. Outpatient cases are 1.63 and 1.37 times higher compared to the rest of the population, at hospitals and health centers, respectively. In addition, minor surgeries at the hospital level are 7.3 times higher than for non-HEF beneficiaries.

Figure Figure 2 shows the total hospital and health center inpatient and outpatient to financing ratios for each province-municipality. Lower ratio values indicate lower inpatient and outpatient outputs relative to the inputs. The variation among provinces highlights the different output levels given their respective inputs.

Provinces L and W are outliers in both their relative output to financing ratios and their population sizes.

However, provinces X and K are similar in size to W and have notably higher outpatient to financing ratios.

Smaller population provinces tend to have lower inpatient to financing ratios, but are comparable to other provinces in relation to outpatient to financing ratios.

Figure 2. Scatterplot of inpatient days and outpatient services to total financing ratios by provincemunicipality, circle size weighted by population size Table 3 summarizes the technical efficiency (TE) results. The mean population weighted efficiency scores are 1.12 (hospitals) and 1.41 (health centers); the mean bias-corrected, population weighted scores are 1.34 (hospitals) and 1.73 (health centers). This suggests that, overall, if the public health system were fully efficient, hospital service output could increase by 34 percent, and health center service output could increase by 73 percent with current financing. Kep was found to be an outlier with three times the ratio of bias squared to variance for its radial measure less than 1. Thus, bias-corrected scores were not calculable for this province. A scatterplot of hospital and health center TE scores by province-municipality is presented in appendix 2. The correlation coefficient of the bias-corrected hospital and health center scores is 0.16. This suggests a positive, but minimal relationship between hospital and health center efficiency.

1 5 In relation to health facility quality scores, there are statistically significant, non-linear effects on technical efficiency both at the hospital and health center levels. Figure 3 shows the predicted marginal effects of healthcare quality scores on technical efficiency after controlling for population size and other model covariates. The result shows that provinces with the lowest and highest quality scores have higher technical efficiency. However, technical efficiency increases with quality scores once quality scores reach a critical threshold of about 65 percent for hospitals and 75 percent for health centers.

Explanatory Factors

Figure 3. Predicted marginal effects of provincial-municipal level mean quality scores on hospital and health center technical efficiency with 95 percent confidence intervals In addition, the number of private sector providers has a statistically significant effect on public health facility technical efficiency, both at the hospital and health center levels. Figure 4 shows the predicted marginal effects of private healthcare providers on public hospital and health center technical efficiency after controlling for population size and other covariates. For hospitals, there is a small (-0.001), but statistically significant (p<0.01) negative effect on technical efficiency as the number of large-scale private healthcare increases. For health centers, there is a non-linear effect with small (0.001), but statistically significant (p<0.01) positive effect on technical efficiency when the number of small-scale private providers is limitedup to about 700. However, beyond this threshold additional private providers have a small, but highly statistically significant (p<.001) negative effect on health center technical efficiency. Cambodia 1 7 Figure 4. Predicted marginal effects of provincial-municipal level private providers on public hospital and health center technical efficiency with 95 percent confidence intervals In addition, the analysis shows that a US$ 100,000 increase in hospital non-discretionary resources decreases hospital technical efficiency by 0.011 points (p-value<0.05). The same effect is observed for health centers: a US$100,000 increase in non-discretionary resources decreases technical efficiency by 0.01 points (p-value<0.01). Finally, the hospital utilization rate has a large (-3.946) and statistically significant (p<0.01) negative effect on health center technical efficiency.

Health Services Technical Efficiency and Applied Cost Allocation in

Unit Costing

Table 5 compares the social health insurance public health facility payment rates (columns 1-2), Jacobs et al.

costing study results and results from the continued data collection from the GIZ study (columns 3-4).

Column 5 shows the adjusted GIZ costing data; the adjustment was done to account for the difference between the total cost in the study data (i.e. US$ 105,203,311 for hospitals and US$102,028,845 for health centers) and the estimated cost assuming the GIZ service specific unit costs multiplied by total service outputs. 1 For the hospital model the total cost in the data only accounted for 67.2 percent of the projected (GIZ) costs (i.e. US$156,608,043). For the health center model the total cost in the data was 209 percent of the projected (GIZ) costs (i.e. US$48,828,997) indicating that the GIZ costs can only explain about half of 1 GIZ costs were adjusted using the ratio of cost inputs in this study to projected total costs using GIZ unit cost data. Cambodia 1 8 the actual costs. The Aumann-Shapley estimates from this study (column 6) are presented for each facility level and major service category. Column 7 shows the relative difference between the Aumann-Shapley estimates and the adjusted GIZ costing data estimates, i.e. the difference expressed as a ratio of the GIZ costing data estimates. Service costs at CPA1 hospitals are higher compared to CPA2 hospitals and to a lesser degree CPA3 hospitals. This is attributed to low service volume [START_REF] Jacobs | Costing for Universal Health Coverage: Insight into essential economic data from three provinces in Cambodia[END_REF]. corresponding adjusted rates are $211.23 for maternity care at health centers and $34.92, $30.18, and $26.32 at hospitals CPA1-3 respectively.

Health Services Technical Efficiency and Applied Cost Allocation in

Aumann-Shapley maternity service costs are substantially higher ($322.91) compared to GIZ costing data.

This can be attributed to the fact that there are additional service categories such as chronic patient care which were excluded from the DEA model as utilization data and case count data was not available.

Therefore, costs for these unaccounted-for services are redistributed to other service categories which increases the health center cost estimates for maternity services and makes them higher compared to the GIZ costing estimates.

Health Equity Fund payments cover between 6 percent and 255 percent of the estimated unit costs, corresponding to health center maternity care and CPA3 hospital minor surgery respectively. Most notably, minor and major surgery payments exceed the estimated unit costs for these services. HEF payments as a proportion of the Aumann-Shapley costs by facility level and service category are presented in appendix 3.

Health Service Space Potential

Figure 5 shows the current coverage of the four social health insurance schemes in relation to the expansion potential and national target. Using facility-level efficiency scores, unit costs, and service utilization data, we estimate the potential supply-side 'service space' to expand population coverage with existing supplyside financing if the public health system were fully efficient. This equates to an additional 4.69 million new social health insurance beneficiaries or about 28.7 percent of the population. The potential expansion would make a substantial contribution towards reducing the population coverage gap towards Cambodia's National Strategic Development Plan coverage target of 65 percent of the population by 2023. Notes: NSSF= National Social Security Fund, C=civil servants, F= formal employees, HEF=Health Equity Funds, Ex= extensions to special populations 1

Discussion

Limitations

There are several limitations to this study. First, the potential population coverage expansion estimates and associated increased service utilization related to increased technical efficiency assume that public facility user-fees will be paid under a social health insurance scheme. The projected cost of additional user-fee payments to expand the Health Equity Fund to the uncovered 1st-3rd wealth quintile people (approximately 3.5 million people) are modeled to range from US$ 23.0 (using current HEF payment rates) to 36.5 million (using NSSF payment rates), assuming the adoption of several complimentary policy options (Kolesar et al., 2021).

Second, the study does not assess performance relating to high-level health outcomes such as morbidity, mortality or life-expectancy. However, given the overall low utilization of public health services and the plethora of factors which impact on such outcomes, the public health system's contribution is likely limited and very difficult to measure. In addition, there is very limited data available that measure such outcomes at the provincial-municipal level.

Third, this study does not evaluate the efficiency of private sector services which are the predominant provider as comparable data is not available. However, the study does assess the impact of private providers on public health service efficiency by including several related variables in the second stage analysis. In addition, this study does not assess technical efficiency among individual public health facilities. Although this approach is possible if the data is available our focus is on the provincial-municipal level where management responsibility has recently been delegated. The study estimates grouped hospital and grouped health center technical efficiency at the provincial-municipal level. With the exception of specialized national hospitals, this approach captures the full range of public health services and aims to provide a better understanding of where to focus efficiency improvement efforts within each province.

Fourth, comparative service-type unit costs do not exactly align with the social health insurance payment categories. We address this issue by generalizing unit costs which include the specific reimbursement category. In addition, published unit cost data is limited to health facilities in three provinces. To increase the reliability of the estimates we also compare unit cost estimates with updated data from ongoing data collection from a high-quality costing study. In addition, the model outputs are limited to the major service categories. Two additional service payment categories (i.e. emergency services and long-acting family planning methods) were initially included in the models as these services have different payment rates (with utilization/claims data recorded by the social health insurance mechanisms). However, the Ministry of Health does not separate these services in the provincial-municipal aggregated data and the assumptions 2 required to model utilization for these services among the general population yielded inconsistent results. In addition, the discriminatory power of DEA is constrained when there is a large number of inputs and outputs and a small number of decision-making units. Limiting the model to the essential components of the service production process is considered a best practice [START_REF] Cooper | Efficiency aggregation with enhanced Russell measures in data envelopment analysis[END_REF].

Finally, this study does not assess system-wide reforms that could further improve input efficiency or financial savings such as pooling health insurance funds and merging schemes, improving procurement to lower the purchase cost of pharmaceuticals, consumables, equipment and supplies, and reducing overhead [START_REF] Banzon | Overcoming public sector inefficiencies toward universal health coverage: the case for national health insurance systems in Asia and the Pacific[END_REF][START_REF] Thomson | Economic crisis, health systems and health in Europe: impact and implications for policy[END_REF]. Such measures could increase budgetary space for health providing that they are well-defined and public financial management systems enable such gains to be repurposed toward prioritized health needs [START_REF] Barroy | Do efficiency gains really translate into more budget for health? An assessment framework and country applications[END_REF]. This topic is further discussed below.

Interpretation

Health Service Utilization and Efficiency

This study assesses public health service technical efficiency at the provincial-municipal level. The results reconfirm under-utilization of public health services and quantify the potential to improve efficiency by expanding social health insurance population coverage with the current supply-side financing. These findings are consistent with other empirical studies. Ensor et al. found HEF to be associated with higher public health facility efficiency [START_REF] Ensor | Exploring the influence of context and policy on health district productivity in Cambodia[END_REF]. A recent costing study found that most health facilities make a minor surplus suggesting that they could increase the number of patients without running a loss [START_REF] Flessa | Costing of Health Care Services in Three Provinces of Cambodia[END_REF]. Jacobs et al. note that service volume along with contextual factors such as poverty incidence, population density and accessibility affect unit costs [START_REF] Jacobs | Costing for Universal Health Coverage: Insight into essential economic data from three provinces in Cambodia[END_REF].

There is mixed evidence as to if the HEF increases public health service utilization due to issues with gaps in financial risk protection, general low utilization of public providers, and deficient eligibility targeting [START_REF] Jithitikulchai | Health equity funds as the pathway to universal coverage in Cambodia: care seeking and financial risk protection[END_REF]. However, a direct comparison of utilization rates by service level and type demonstrates that public health service utilization among HEF beneficiaries is generally higher compared to the rest of the population. This provides evidence that Cambodia's largest social health protection scheme improves access. Notwithstanding, it is important to note that utilization data does not capture efficacy or quality of the service provided [START_REF] Xu | Health financing and access to effective interventions[END_REF].

There is some evidence that fee-for-service reimbursements, the system used by Cambodia's social health protection schemes, may contribute to oversupply as it incentivizes service provision [START_REF] Aboubacar | Health Financing and Budgeting Reforms in Gabon: Progress and Challenges on the Road to Universal Health Coverage[END_REF][START_REF] Gosden | Capitation, salary, fee-for-service and mixed systems of payment: effects on the behaviour of primary care physicians[END_REF][START_REF] Patcharanarumol | Strategic purchasing and health system efficiency: a comparison of two financing schemes in Thailand[END_REF][START_REF] Saleh | Health financing in the Republic of Gabon: The World Bank[END_REF]. However, provider remuneration is complex and there is also evidence that the risk of Health Services Technical Efficiency and Applied Cost Allocation in Cambodia 2 3 overprovision is contextual [START_REF] Bertone | The complex remuneration of human resources for health in lowincome settings: policy implications and a research agenda for designing effective financial incentives[END_REF][START_REF] Di Guida | Testing the myth of fee-for-service and overprovision in health care[END_REF].

Moreover, health service utilization rates in Cambodia are considered low compared with other Asian countries (OECD/ WHO, 2018).

This study estimates the potential supply-side 'service space' for 4.69 million additional social health protection beneficiaries in a fully efficient public health system. This could raise total population coverage of social health insurance to 60 percent while leveraging the unutilized service capacity of the public health system. However, this still leaves a population coverage gap of 40 percent. The gap is worrisome given the expected decline in out-of-pocket spending on healthcare due to pandemic-related economic hardship which will need to be offset with public financing [START_REF] Tandon | Economic Impact of COVID-19[END_REF]. Additional investments in the health system can ensure access to needed health services, particularly among the financially vulnerable [START_REF] Kurowski | From Double Shock to Double Recovery-Implications and Options for Health Financing in the Time of COVID-19[END_REF]. For Cambodia this would imply an increase in government health expenditure of 0.6 percent of GDP [START_REF] Tandon | Economic Impact of COVID-19[END_REF]. Although policymakers may raise concerns about adding budget to an inefficient system, there are several smart investments to promote continuous health system efficiency improvement.

These include the prioritization of primary health care, strategic purchasing, alignment of financing and delivery, better accountability through results-based outcome and output contracts and related provider incentives, decentralization, moving care out of hospitals, and independent regulatory agencies [START_REF] Barroy | Do efficiency gains really translate into more budget for health? An assessment framework and country applications[END_REF][START_REF] Gertler | Do microfinance programs help families insure consumption against illness?[END_REF][START_REF] Mathauer | Strategic purchasing for universal health coverage: key policy issues and questions: a summary from expert and practitioners[END_REF][START_REF] Thomson | Economic crisis, health systems and health in Europe: impact and implications for policy[END_REF][START_REF] Yip | Improving Health System Efficiency: Reforms for improving the efficiency of health systems: lessons from 10 country cases[END_REF]. For example, one simple measure would be to link all social health insurance provider payments to both service provision and health facility quality scores [START_REF] Pheakdey | Improving Health Service Quality in the Kingdom of Cambodia: A Policy Perspective[END_REF].

Evidence shows that government health expenditure as a percentage of total health expenditure (i.e. inclusive of out-of-pocket expenditure) is positively associated with efficiency [START_REF] González | Value efficiency analysis of health systems: does public financing play a role[END_REF].

The expansion of social health protection, particularly to the financially vulnerable, can support economic recovery by enabling households to maintain productivity, thereby stabilizing household income and expenditure.

Finally, efficiency gains need to be reinvested to provide an incentive for continuous health system performance improvement [START_REF] Barroy | Do efficiency gains really translate into more budget for health? An assessment framework and country applications[END_REF]. To effectively address public health service inefficiency, provincial-municipal administrations need to be given adequate flexibility to reallocate resources to increase the volume or quality of the most efficiently delivered services [START_REF] Barroy | Do efficiency gains really translate into more budget for health? An assessment framework and country applications[END_REF]. In addition, predictable financing to sub-national governments is imperative to improve health service performance (Gertler, Giovagnoli and Martinez 2014).

Explanatory Factors

Health Services Technical Efficiency and Applied Cost Allocation in Cambodia 2 4

The second stage analysis identifies several factors which explain the variation in technical efficiency among the provinces. The finding that provinces with the lowest and highest quality scores have higher technical efficiency suggests that among provinces with lower health facility quality scores, some improvements in health center quality may decrease technical efficiency, potentially indicating that the initial investments in quality such as training and facility upgrades increase costs and/or decrease service output. Similarly, it could also indicate that facilities with the lowest quality scores are underfinanced and therefore do not invest in quality improvement measures but have high patient volume which yields high technical efficiency scores. This suggests that provincial-municipal level public health facilities need to attain a quality score critical threshold of about 65 percent-75 percent before quality improvement can contribute to technical efficiency. A study of Portuguese public hospitals found that good clinical safety practices tend to be associated with low technical efficiency, concluding that there are trade-offs between efficiency and quality [START_REF] Ferreira | Do quality and access to hospital services impact on their technical efficiency[END_REF].

The nonlinear relationship between small-scale private providers and public health centers suggests that there may be service complementarity between the sectors when the number of private providers is limited.

However, the overall marginal negative effect of private sector providers on public health service technical efficiency is likely due to competition which reduces the number of patients seeking public sector care.

Moreover, the dominance of the largely unregulated, pro-rich private sector accounts for a significant proportion (57.5 percent) of out-of-pocket spending [START_REF] Asante | Who benefits from healthcare spending in Cambodia? Evidence for a universal health coverage policy[END_REF]World Bank, 2019). As private health services and health insurers can exacerbate health inequity, it is essential for countries to determine the appropriate level of privatization in their systems which necessitates transparent and responsible regulation alongside efforts to improve public system efficiency [START_REF] Schenkman | Alterity or austerity: a review on the value of health equity in times of international economic crises[END_REF].

The marginal negative effect of supply-side resources/financing on technical efficiency suggests that increased financial autonomy and demand-side financing may yield better value for money. Health financing should focus on smart investments discussed above such as increasing social health insurance payments.

The finding that the hospital utilization has a large, statistically significant negative effect on health center technical efficiency suggests that patients bypassing health centers and going directly to hospitals is an issue. This is consistent with other research in Cambodia which found that primary care facilities are regularly bypassed due to a lack of key personnel, stock-outs of essential drugs and substandard quality of care [START_REF] Flessa | Costing of Health Care Services in Three Provinces of Cambodia[END_REF]. This may be redressed by correcting the underlying causes and incentivizing health center referrals such as prioritizing service provision at hospitals for patients with a formal health center referral.

There are likely additional or secondary factors which contribute to public health system underutilization. including competency and attitude of providers (Nagpal, 2019). Another factor is limited service availability, particularly for non-communicable diseases [START_REF] Jithitikulchai | Health equity funds as the pathway to universal coverage in Cambodia: care seeking and financial risk protection[END_REF]. Moreover, it is also possible that patients may avoid public care-seeking due to unofficial fees or face substantial indirect financial shocks relating to needed medical care and/or lost productivity (Kolesar, 2021).

Unit Costing

We calculate unit costs using the DEA-Aumann-Shapley applied cost allocation approach. To the best of our knowledge, this study is the first time this method has been used for health services costing. The results are comparable with recent, high-quality public health facility costing data, and we believe this approach to be a good alternative to traditional costing studies which can be labor intensive, time consuming, and expensive.

The approach is not without limitations however. First, the number of costing categories is limited as a function of the DEA model. This issue could be mitigated to a degree by increasing the number of decisionmaking units. For example, if data is available, more robust results would be expected by using hospitals and health centers as the primary unit of analysis (as opposed to grouping them by province-municipality).

Second, this Aumann-Shapley analysis used previous costing study results for weighting. Although it is common to rely on existing data to parameterize cost models, it requires that such data exist.

Health provider payments can incentivize or de-incentivize particular services. The Health Equity Fund payment rates are inconsistent with the estimated cost of service provision across the major payment categories. The wide variability (6 percent -255 percent) of payments as a proportion of the estimated unit costs suggests that payment rates should be realigned. In particular, the higher than cost reimbursements for hospital surgeries is notable. Given minor surgeries at the hospital level are 7.3 times higher among HEF beneficiaries compared with the rest of the population, the overpayment may be creating a perverse incentive and service overutilization. In fact, there is evidence of both public and private healthcare facilities providing surgeries for commercial interest [START_REF] Gryseels | When 'substandard'is the standard, who decides what is appropriate? Exploring healthcare provision in Cambodia[END_REF].

Conclusion

Public health service efficiency can be improved by increasing utilization. This can be achieved by enrolling more beneficiaries into the social health insurance schemes with current supply-side financing levels. Other factors that can lead to increased efficiency are improving health service quality, regulating private sector providers, focusing on discretionary financing, and incentivizing a referral system. In addition, the current social health insurance payment rates are not well aligned with the service unit costs. Moreover, shifting financial resources to smart investments, especially demand-side financing including increasing the MPA outpatient consultations: New and follow-up outpatient consultations at a health center. The consultation services include: interrogation, physical exam, medical education, counseling, consultation booklet, para-clinic services (malaria rapid test and TB smear), treatment and prescribed medicines, follow-up treatment of TB, DOTS, or leprosy.

Figure 5 .

 5 Figure 5. Effective Social Health Insurance Coverage, Expansion Potential, and Target Coverage

  For example, systematic factors can lead to patient avoidance of public facilities due to quality perceptions Health Services Technical Efficiency and Applied Cost Allocation in Cambodia 2 5

Table 1 .

 1 Descriptive statistics for inputs and outputs for the hospital and health center services models

		Sum	Mean	Median	SD	Min	Max
		(1)	(2)	(3)	(4)	(5)	(4)
	Hospital Services Model
	Inputs (US$)
	Staff salaries	46,859,986 1,874,399 1,768,218	852,593	566,232 3,530,746
	Pharmaceuticals and consumables	739,853	29,594	12,961	32,150	0	112,171
	Equipment and supplies	609,012	24,360	17,381	26,978	0	104,544
	Other operating costs	27,081,818 1,083,273	996,914	437,520	521,485 1,953,461
	SHI Service Payments	19,349,376	773,975	381,258 1,699,779	21,727 8,823,583
	Service Delivery Grants	10,563,269	422,531	368,828	245,809	100,841	954,413
	Total Hospital Inputs	105,203,314 4,208,133 3,444,580 2,712,180 1,455,698 14,810,350
	Outputs
	Outpatient cases	1,762,958	70,518	38,434	73,304	933	319,679
	Inpatient cases	577,938	23,118	21,045	13,422	2,094	48,930
	Major surgeries	51,840	2,074	1,375	2,135	0	8,827
	Minor surgeries	38,880	1,555	1,125	1,524	0	6,597
	Maternity services	123,747	4,950	4,556	2,978	309	10,536
	Health Center Services Model
	Inputs (US$)
	Staff salaries	46,919,583 1,876,783 1,673,185 1,218,450	90,173 3,959,417
	Pharmaceuticals and consumables	695,758	27,830	13,397	35,701	0	137,128
	Equipment and supplies	475,329	19,013	12,780	20,258	0	69,390
	Other operating costs	26,363,296 1,054,532	904,118	718,193	98,746 2,594,306
	SHI Service Payments	16,701,444	668,058	324,696 1,075,967	3,287 5,508,723
	Service Delivery Grants	10,873,438	434,938	382,482	333,136	15,257 1,162,660
	Total Health Center Inputs	102,028,848 4,081,154 3,519,662 2,774,032	220,243 9,246,370
	Outputs
	Outpatient cases	9,001,900	360,076	267,371	302,626	19,092 1,058,099
	Inpatient cases	57,694	2,308	519	3,220	0	11,457
	Maternity services	140,979	5,639	5,911	3,518	198	12,816

SD= Standard Deviation, US$= United States dollars, SHI= Social Health Insurance

  B 2 HC_quality i + B 3 HC_quality_squared i + B 4 Small_private_providers i + B 5 Small_private_providers_squared i + B 6 Nondiscretionary_resources i + B 7 Hospital_utilization i + B 8 Health_center_utilization i + ε i (2)

Table 2 .

 2 Descriptive statistics of explanatory variables used in the second stage analysis

		Sum	Mean	Median	SD	Min	Max
		(1)	(2)	(3)	(4)	(5)	(6)
	Population (both models)	16,341,870	653,675	634,448	477,239	42,516 1,861,611
	Hospital Services Model
	Hospital quality scores (mean, weighted)	-	65.8	67.1	12.6	40.6	85.0
	Large private health providers	841	34	11	86	1	439
	Nondiscretionary resources (US$)	75,290,669 301,1627 2,764,244 1,220,138 1,173,043 5,374,128
	Health Center Services Model
	Health center quality scores (mean)	-	69.1	70.3	10.9	44.7	92.0
	Small private health providers	13,734	549	482	499	47	2,272
	Nondiscretionary resources (US$)	74,453,966 2,978,159 2,596,936 1,906,678	201,699 6,025,001
	Hospital utilization rate	-	0.060	0.057	0.026	0.010	0.113
	Health center utilization rate	-	0.553	0.518	0.208	0.141	0.880
	Note: SD= Standard Deviation

  1. Comparison of hospital and health center utilization rates among Health Equity Fund (HEF) beneficiaries and the general population

		Outpatient cases	0.082 0.134
	Health Centers Hospitals	Maternity care Inpatient cases Outpatient cases Maternity care Minor surgery Major surgery Inpatient cases	0.008 0.004 0.006 0.004 0.005 0.060 0.008 0.137 0.007 0.032 0.007 0.028			0.663		0.906
		0.0	0.1	0.2 0.3	0.4 0.5	0.6	0.7	0.8 0.9	1.0
			HEF Utilization	Population Utilization
									1
									3

Table 3 .

 3 Hospital and health center services output-oriented Debreu-Farrell efficiency scores with 95 percent confidence limits for 25 provincial-municipal administrations

			Hospital Services Model		Health Center Services Model
	DMU	Province-	TE	Bias-	TE	TE	TE	Bias-	TE	TE
	code	Municipality		corrected	Lower	Upper		corrected	Lower	Upper
				TE	Limit	Limit		TE	Limit	Limit
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
	A	Banteay Meanchey	1.28	1.52	1.36	2.00	1	1.08	1.00	1.29
	B	Battambang	1.01	1.19	1.05	1.65	1.15	1.20	1.16	1.27
	C	Kampong Cham	1	1.36	1.10	2.43	1.57	1.63	1.58	1.78
	D	Kampong Chnang	1	1.63	1.42	5.19	1.01	1.05	1.01	1.18
	E	Kampong Speu	1.20	1.33	1.24	1.51	1.18	1.21	1.18	1.32
	F	Kampong Thom	1.05	1.16	1.09	1.43	1.09	1.13	1.09	1.22
	G	Kampot	1	1.14	1.04	1.31	1.34	1.38	1.34	1.50
	H	Kandal	1	1.14	1.05	1.37	1.23	1.29	1.24	1.46
	I	Koh Kong	1.84	2.14	1.95	2.96	2.06	2.14	2.08	2.26
	J	Kratie	1.27	1.38	1.30	1.58	1.45	1.50	1.45	1.68
	K	Mondulkiri	1.69	2.10	1.81	3.44	1.04	1.12	1.05	2.12
	L	Phnom Penh	1.31	1.44	1.32	1.81	2.90	3.01	2.93	3.24
	M	Preah Vihear	1	1.35	1.11	2.15	1	1.22	1.01	4.15
	N	Prey Veng	1.09	1.21	1.12	1.39	1.06	1.12	1.07	1.30
	O	Pursat	1.09	1.19	1.11	1.41	1	1.06	1.01	1.13
	P	Rattanakiri	1.01	1.19	1.06	1.94	1.38	1.48	1.40	2.53
	Q	Siem Reap	1	1.44	1.19	2.77	1.18	1.24	1.19	1.42
	R	Sihanoukville	1	1.24	1.08	2.00	1.11	1.14	1.12	1.24
	S	Stung Treng	2.41	2.65	2.47	3.32	1.29	1.34	1.29	1.45
	T	Svay Rieng	1	1.11	1.05	1.26	1.30	1.36	1.31	1.47
	U	Takeo	1	1.37	1.15	2.41	1.43	1.49	1.44	1.65
	V	Oddor Meanchey	1	1.26	1.07	2.66	1.66	1.73	1.68	1.87
	W	Kep	1	.	.	.	1.64	1.71	1.64	1.99
	X	Pailin	1	1.68	1.72	7.99	1.06	1.09	1.06	1.18
	Y	Tbaung Khmoum	1.27	1.44	1.29	1.80	1.07	1.11	1.07	1.23
		Min	1	1.11	1.03	1.26	1	1.05	1	1.13
		Max	2.41	2.65	2.47	7.99	2.90	3.01	2.92	4.15
		Mean	1.18	1.45	1.30	2.41	1.32	1.39	1.34	1.72
		Weighted Mean*	1.12	1.34	1.19	1.36	1.41	1.73	1.66	2.13
		Median	1.01	1.35	1.14	1.97	1.18	1.24	1.19	1.46

Notes: DMU= Decision Making Unit, TE= Technical Efficiency, *weighted by population,

  Table 4 presents results from the Simar Wilson regressions of the bias-corrected, Shephard distance technical efficiency scores. Population size has a positive, highly statistically significant effect on hospital efficiency, but not health center efficiency. Both the hospital and health center models reveal health service quality,

	private providers, and non-discretionary health resources/financing to be statistically significant factors
	affecting technical efficiency.
	Table 4. Explanatory factors for hospital and health center technical efficiency
		Hospital	Health
		Services	Center
	VARIABLES	Model	Services
		(1)	Model
			(2)
	Population (per 100,000)	0.049***	0.024
		(0.014)	(0.017)
	Hospital quality scores	-0.047*
		(0.019)
	Hospital quality scores (squared)	0.000*
		(0.000)
	Large-scale private healthcare providers	-0.001**
		(0.000)
	Hospital non-discretionary resources (per US$100,000)	-0.011*
		(0.005)
	Health center quality scores		-0.088***
			(0.021)
	Health center quality scores (squared)		0.001***
			(0.000)
	Small-scale private healthcare providers		0.001**
			(0.000)
	Small-scale private healthcare providers (squared)		-0.000***
			(0.000)
	Health center non-discretionary resources (per US$100,000)		-0.010**
			(0.003)
	Hospital utilization rate		-3.946**
			(1.492)
	Health center utilization rate		0.525***
			(0.137)
	sigma	0.101***	0.075***
		(0.015)	(0.011)
	Constant	2.278***	3.946***
		(2.094)	(0.816)
	Observations	24	25
	Wald Chi2	22.84***	76.51***
	Standard errors in parentheses
	*** p<0.001, ** p<0.01, * p<0.05
			1
			6

Table 5 .

 5 Social health insurance public health facility payment rates and costing study results by facility level and major service category in US$

						GIZ costing		Relative
		HEF	NSSF	Jacobs et	GIZ costing	data, 2019	Current	difference
		Payments	Payments	al., 2019	data, 2019	adjusted	study
	CPA3 Hospital	(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Outpatient cases	7.80	7.80	41.53	19.51	13.11	20.15	0.54
	Inpatient cases	29.27	40.73	158.21	169.48	113.85	157.32	0.38
	Maternity care	19.51	37.80	46.57	39.18	26.32	64.31	1.44
	Major Surgery	243.90	243.90	29.79	43.88	29.48	149.90	4.09
	Minor Surgery	97.56	48.78	34.04	38.78	26.05	38.26	0.47
	CPA2 Hospital
	Outpatient cases	3.90	3.90	5.87	7.76	5.21	5.63	0.08
	Inpatient cases	24.39	28.78	86.53	100.99	67.84	95.21	0.40
	Maternity care	19.51	29.27	27.75	44.93	30.18	54.60	0.81
	Major Surgery	78.05	97.56	24.87	87.80	58.98	76.96	0.30
	Minor Surgery	48.78	48.78	25.87	31.57	21.21	27.06	0.28
	CPA1 Hospital
	Outpatient cases	2.44	2.93	9.65	16.17	10.86	8.20	-0.25
	Inpatient cases	19.51	31.71	291.45	129.74	87.15	186.88	1.14
	Maternity care	19.51	24.39	66.72	51.98	34.92	73.09	1.09
	Major Surgery	n.a.	n.a.	n.a.	n.a.	n.a.	n.a.	n.a
	Minor Surgery	39.02	24.39	40.39	39.24	26.36	37.45	0.42
	Health Center
	Outpatient cases	0.98	1.46	3.88	3.74	7.81	6.51	-0.17
	Inpatient cases	19.51	19.51	12.46	15.78	32.97	32.98	-0.05
	Maternity care	19.51	19.51	107.29	101.09	211.23	344.00	0.63
	HEF = Health Equity Funds; NSSF = National Social Security Funds
	Aumann-Shapley applied cost allocation estimates for each major social health insurance payment category
	are comparable to the updated GIZ costing data with a few notable exceptions. GIZ data shows major
	surgery at CPA3 hospitals to be about half the cost of major surgery at CPA2 hospitals, $43.88 and $87.80
	respectively, (unadjusted) and $29.48 and $58.98 (adjusted) respectively. Aumann-Shapley estimates show

major surgery at CPA3 hospitals to be about double the cost of major surgery at CPA2 hospitals, $149.90 and $76.96 respectively. Likewise, GIZ data shows health center maternity service cost to be higher ($101.09) than CPA1-3 hospital maternity costs, $51.

98, $44.93, and $31.98

respectively. The Health Services Technical Efficiency and Applied Cost Allocation in Cambodia 1 9

Technical Efficiency and Applied Cost Allocation in Cambodia Hospital-level No. Health services Case Categories Referral hospital, level 1 Referral hospital, level 2 Referral hospital, level 3

														National hospital/
														national center
			HEF (a)	NSSF (b)	GIZ costing (c)	HEF	NSSF	GIZ costing	HEF	NSSF GIZ costing	HEF	NSSF	GIZ costing	HEF	NSSF
			Outpatient Services
	1		Outpatient checkup and consultation (including small surgical cases that refer to suturing, wound dressing, excision....)	Outpatient consultations Non-hospitalized minor surgical procedures Short-acting birth control	Outpatient / patient	10,000	12,000 20,000 10,000	33,500	16,000	Prevention contact OPD services patient contact Per inpatient day Chronic patients contact 16,000* 32,000 40,000 31,000	4,000 24,000 40,000	6,000 100,000	27,000 14,000 14,500 120,000 60,000 40,000 100,000
	2 3	2	MPA short-term birth control service MPA long-term birth control 20,000 20,000 Surgery per Long-term contraceptive methods using Contraceptive Non-hospitalized method using minor surgical IUD or Implant activities IUD or Implant (IUD / Implant) Screening for cervical cancer Permanent methods inpatient day 128,000 100,000 20,000 40,000 (Vasectomy and Emergency (whether to refer or not) First Aid interventions for patients or victims who are at risk of life threatening with vital/danger signs; emergency acts include: Check, monitor and record regular life signs and treatment according MPA emergency and referral or non-referral OPD services patient contact 20,000 123,000 100,000 400,000 20,000 40,000 20,000 (hospitalization) inpatient day 20,000 tubal ligation) Per inpatient day Inpatient care MPA minor surgical activities Adult general General medicine medicine per 100,000 130,000 120,000 118,000 160,000	10,000 30,000 163,000 100,000 600,000 20,000 100,000 20,000 14,000 14,500 12,000 167,000 400,000
	4	3	to medical conditions as well as arrangements to refer to the referral hospital as necessary. and pediatrics Delivery and abortion/miscarriage Hospitalization for gynecology Inpatient treatments Hospitalization for general child	MPA delivery Per inpatient day 80,000 Paediatrics per inpatient day	100,000 92,000	157,000 122,000	100,000	150,000 108,000	121,000 123,000	Maternity 120,000	80,000 200,000 128,000	80,000 172,000 150,000	400,000 934,000 140,000 350,000
		4	Inpatient department (IPD) TB	TB inpatient day		160,000	221,000		180,000	322,000		80,000* 200,000	182,000	300,000

*For health centers with inpatient beds (former district hospitals)

Health Services *corrected from 160,000 in the Prakas

Health Services

Technical Efficiency and Applied Cost Allocation in Cambodia Hospital-level continued

  Ministry of Economy and Finance. Inter-ministerial Prakas on Price of Service Benefit Packages of Health Equity Fund and Cash Transfer to Female Laborers for Delivery, and Procedures for Expense Implementation, No. 497 SHV. BrK, May 8, 2018 (b) Ministry of Labor and Vocational Training, Ministry of Health. Inter-Ministrial Prakas No. 327 LV/PrK on Revision of Annex 1 of Inter-Ministerial Prakas No. 173 LV/PrK., dated 05 May 2016, on Provider Payment Methods for Health Care (c) Steffen Flessa S, Jacobs B, Hui K, Thiede M, Appelt B. Costing of Health Care Services in Three Provinces of Cambodia Final Report, April 2018, Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ) Social Health Protection Programme

	No. Health services Case Categories		Referral hospital, level 1	Referral hospital, level 2	Referral hospital, level 3		National hospital/
														national center
		HEF (a)	NSSF (b)	GIZ costing	HEF	NSSF	GIZ	HEF	NSSF	GIZ	HEF	NSSF	GIZ	HEF	NSSF
				(c)			costing			costing			costing
		Emergency, surgery, and delivery related services
		Emergency	Emergency		250,000 120,000		250,000 240,000		300,000	320,000		320,000	800,000
	5	services
		Small surgeries Moderate surgical	Surgery per	160,000		128,000 200,000 200,000 123,000	400,000	200,000	163,000	400,000	600,000
	6		activity	inpatient day
	7	interventions Major surgeries Major surgical					320,000 400,000		1,000,000 1,000,000		1,200,000 1,500,000
		Birth delivery, abortion /	Delivery	Maternity per inpatient day		100,000			120,000			160,000			400,000
	8	miscarriage /			80,000		249,000 80,000		126,000	80,000		173,000	80,000
		post-abortion / miscarriage care	Miscarriage/abortion			100,000			120,000			150,000			400,000
	Sources:
		(a)

Hospital CPA-3

(2)

Hospital CPA-2

(3) [START_REF] Bogetoft | Performance benchmarking: Measuring and managing performance[END_REF][START_REF] Emrouznejad | DEAzone and Management Science and Operational Research[END_REF]. Figure 3 shows the hospital and health center Shephard efficiency scores. Provinces L, I and S are outliers in terms of population size and technical efficiency. Notably, there are provinces with population sizes similar to I and S that are more efficient such as K and P.