Estimation Production Function of Inpatient Services and Input Productivity : A Cross-Sectional Study of Iran Selected Public Hospitals

Hamid Mohammadi, Mohammad Meskarpour-Amiri 3, * 1 Allameh Tabataba’i University, Tehran, IR Iran 2 Health Management Research Center, Baqiyatallah University of Medical Sciences, Tehran, IR Iran 3 Tarbiat Modares University, Tehran, IR Iran Corresponding Author: Mohammad Meskarpour-Amiri, Ph.D. Student of Health Economics, Tarbiat Modares University, Tehran, IR Iran. Tel: +98-21-82482476, Fax: +98-21-82482476, Email: mailer.amiri@gmail.com


Background
The health-care sector has been one of the most important sub-sectors of the services sector whose performance is an indicator of development and social welfare of a country.In most developing countries, 5 to 10% of government expenditure is allocated to this sector [1,2].Among the various components of the health-care sector, hospital services are the most common cause of cost growth in many countries and in the public sector, this growth has been much faster when compared to other sectors [3].According to an extensive study of the World Bank on public hospitals, hospitals' consumption share of public sector health resources in developing countries is between 50 to 80% [4].In Iran, more than 6.4% of GDP belongs to health costs and about 40% of government health spending is associated with hospital cares, at least half of which is financed directly by households out-of-pocket [4].Despite the importance role of hospitals in health care costs, few studies have been carried out on the economics of hospitals in developing countries [5].
One of the interesting topics in most developing countries including Iran is the utilization of healthcare resources and proper allocation of resources in the health sector.According to the Iran National Health Accounts, in 2007, total healthcare costs (as a part of GDP) were 145 trillion Rials in current prices [4,6].Generally, in the hospitals, the medical personnel and physical facilities and equipment, are the key factors of service production [6].Combination of these inputs according to the average level of technology utilized by them has remarkable changes during the last ten years.The hospital should employ economic analysis to ensure optimum utilization of resources and its production facilities.Using economic principles and subsequently, evaluation of the economic performance of the service provider organizations, shall cause the correction of process and the continuity of measures and provides economic management of hospital industry -as the most costly sector [7,8].One of the economic tools is production function of hospitals that actually shows the optimal combination of production resources for hospital services [9].
To calculate the marginal production of specialized manpower and capital of active beds in each hospital, Cobb-Douglas production function was employed.Cobb-Douglas production function in this study is illustrated in the following equation: Where Qinpatient =number of inpatients during a year as hospital production level of inpatient services K=number of beds as input of capital L=sum of doctors and assistants as specialized human resources A= constant coefficient or technology coefficient α and β are considered as technical coefficients for the production factors of capital (beds) and specialized human resources in public hospitals.The sum of the coefficients α and β are considered to be equal to 1, which therefore was a first order homogeneous production function.To estimate the production function with OLS method, the general shape of the production function was logarithmic and it was estimated using the Eviews7 software.
Where Qinpatient = hospital service production level K = number of beds as input of capital L=sum of doctors and assistants as specialized human resources A= constant coefficient or technology coefficient

Results
The result of estimation of production function for public hospitals demonstrated a significant relationship between the hospital service production level (number of inpatients per year), and production factors of human resources (L) and capital of bed (K) (P<0.05).The elasticity of inpatient service level in the public hospitals to specialized human resources and beds were 0.882 and 0.118 respectively.Based on this, 10% increase in net working hours of specialized human resources in public hospitals can causes 8.8% increase in average production levels of inpatient services.Also, 10% increase in the use of active beds would cause 1.1% increase in average production level of inpatient services in public hospitals.Table 1 shows the results of production function of inpatient services in the country's public hospital.In the above equation, 0.118 and 0.882 are considered as technical coefficients of capital of the beds and specialized human resources respectively.In this equation, 70.437 is defined as the anti-log of = 4.255, while  4.255 = 70.437.
Given the number of human resources (  ) and beds (  ) in each hospital, comparison of the actual product of each hospital with expected production level for that hospital revealed that 26 of studied hospitals have had inpatient services less than the average expected production level, and did not have full performance.
Results of the comparison of marginal production or marginal input productivity as well as the comparison of elasticity or standard marginal productivity of these factors with their average levels are shown in Table 2.

Discussion
The results revealed that in Iranian public hospitals, the elasticity of inpatient service level in terms of specialized human resources (0.88) is higher than beds (0.18).Based on this, the production of selected public hospitals in the country is most affected by the specialized manpower and reacts with more sensitivity to decrease and increase in specialized human resources rather than beds.The 10% increase in net working hours of specialized human resources (doctors and nurses), will increase the service production in country's public hospitals by 9%.Previous studies have also emphasized the importance of skilled manpower in the inpatient services production.The investigation of economic behavior of Tehran's publiceducational hospitals by Rezapour and Khalaj also revealed that elasticity of inpatient service in terms of specialized human resources of doctors (0.58) and nurses (0.37) is higher than beds (0.36) [10].Studying the production function of educational hospitals in Mashhad province, Mahboobi et al. also stated that the inputs of doctors, nurses, and beds with impact factors of 0.57, 0.36 and 0.24 respectively have the greatest impact on inpatient services production [6].In addition, investigation of the production function of hospitals affiliated to Qazvin University of Medical Sciences by Rezapour and Asefzadeh also revealed that the inputs of doctors, nurses and active beds have the most impact on inpatients service delivery in the hospitals [11].
Based on the results obtained for the production function of the public hospitals, the marginal productivity of human resources in 26 hospitals and the marginal productivity of beds in 21 hospitals were less than the average marginal productivity of input.In addition, 15 hospitals were faced with marginal productivity less than average for both inputs.Thus, it can be concluded that 26 hospitals were faced with surplus specialized human resources, and 21 hospitals were faced with a number of inactive hospital beds, and 15 hospitals were faced with both the problem of excess human resources, and the inactivation of inpatient beds.Moreover, the comparison of actual production level of each hospital with expected production-based on the inputs used showed that 26 public hospitals in the country's hospitals have had inpatient services less than the average expected production level, and did not have full efficiency.
The evaluation of the productivity and efficiency of hospitals based on the ratio of the output data have been considered in past studies.The researches carried out by Ghaderi et al. [12] and Sajadi et al. [13] can be noted in which using data envelopment analysis (DEA), the efficiency of educational-medical centers and hospitals were assessed.Afzali et al. [14] in their study which was conducted using two techniques of simple ratio analysis and comprehensive data envelopment analysis, technical efficiency of Social Security hospitals was measured, results revealed that 22 of the 53 hospitals were efficient and inefficient hospitals had an average efficiency score of 78%.Azar et al. in their study evaluated the efficacy of Tehran University of Medical Sciences hospitals using DEA.Results of the study revealed that only 8 of the 22 hospitals had full performance and 33 and 41% of excess beds and human sources exist in inefficient hospitals respectively [15].

Conclusion
Inpatient services in public hospitals are more sensitive to the input of specialized human resources than active beds.In addition, many of the studied public hospitals did not have full efficiency.It can be concluded that with the proper use of human resources and active beds, production levels in a significant number of hospitals can be increased.

Table 1 .
Results of estimating the production function of public hospital inpatient services

Table 2 .
Hospitals status in productivity and efficiency