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