Results
Table 1 summarizes the results of the stochastic frontier cost function estimation in Frontier 4.1. Since the index of the likelihood ratio (LR) test was high in this estimate for the Cobb-Douglas function, there was no need to estimate the translog function. In order to calculate the economic efficiency, it is necessary to estimate the cost function through the cost of inputs and the total cost of the laboratory unit. In this study, the total costs of construction, consumables, property, equipment, and staff salaries of the relevant laboratory were used to calculate the total cost of the hospitals’ laboratory units.
Table 1 : Estimation of Frontier Cost Function Parameters (SFA) from the Maximum Likelihood Method (ML)
In Column 2 of Table 2, the amount of economic efficiency obtained from the cost function estimation is greater than one, because Frontier 4.1 does not consider a constraint in cost function estimation such as the economic efficiency range between zero and one. In order to compare the calculated SFA efficiencies, the economic efficiency figures obtained from the SFA method were divided into the highest cost efficiency figure in Table 2 (1.124) until the numerical values of economic efficiency fall between zero and one (Column 3 in Table 1). In this method, the average economic efficiency of the laboratory units of hospitals affiliated with the UUMS was 0.931 (SD=0.034). Also, the lowest cost-efficiency belonged to Hospital Laboratory 9 (value=0.89), and the highest cost efficiency was related to Hospital 13 (value=1).
Table 2 : Economic efficiency of clinical laboratories of hospitals affiliated with the UUMS through the SFA method
In Table 3, no significant relationship is observed between output, i.e. the number of admissions, with expert, ELISA, cell counters, incubators, centrifuges, microscopes, and microbial culture medium inputs. In other words, these inputs do not have a considerable impact on the output level, which may be due to the high similarity of data collected from hospitals’ laboratories and, therefore, a reduced fluctuation between data and their low variance. Also, in Table 3, the sum of the partial elasticity coefficients of the inputs was 1.94, so the return to scale among the laboratory units of the studied hospitals was ascending. The negative production elasticity of some production factors indicated that the laboratories under study were in the third and non-economic stages of production in terms of applying these factors. Also, the production elasticity relative to specialist input was 3.82, which was greater than the other elasticities. This means that a 1% increase in this production factor leads to the highest increase in the return of laboratories by 3.82%. According to the final results of the maximum likelihood estimation regarding the accuracy of using the Cobb-Douglas function, since the LR value was 7.93, the Cobb-Douglas function form was chosen. In other words, due to the high LR value of the Cob-Douglas function rather than the translog function, this form was suitable for the SFA for the studied laboratory units. The gamma variable that shows the contribution of inefficiency variance in the production function also equaled 1 with a standard error of 0.0000006. That is, the share of random factors in the inefficiency of clinical laboratories in hospitals affiliated with the UUMS was equal to zero, and the observed inefficiency component had the major contribution. The significance of the γ parameter confirms that inefficiency plays an important role in the model.
Table 3 : Estimation of stochastic frontier production function (SFA) parameters from the maximum likelihood method (ML)
According to the results of Table 4, the average technical efficiency of medical diagnostic laboratories affiliated with the UUMS was 0.519 (SD=0.33). According to the SFA model, the lowest technical efficiency belonged to Hospital 17 (value=0.049) and the highest technical efficiency belonged to Hospitals 2 and 3 (value=0.999).
Table 4 : Technical efficiency of the clinical laboratories of hospitals affiliated with the UUMS through the SFA method