Efficiency in Two-stage Data Envelopment Analysis: An Application to Insurance Companies

The paper is focused on the application of the two-stage DEA in assessing the efficiency of Slovak and Czech commercial insurance companies. DEA models are non parametric methods for assessing the efficiency, which use linear programming. The efficiency score is expressed for each subject analyzed and used to compare the transformation of multiple inputs into multiple outputs. Two-stage models allow comparing the efficiency of subprocesses, into which the whole process is divided. By adding the sequence of steps consisting of the application of various statistical methods, two-stage models allow to assess the efficiency of the subprocesses and thereby to determine the strengths and weaknesses of the analyzed subjects, respectively of individual subgroups of subjects. The aim of this paper was to compare the efficiency of Slovak and Czech insurance companies using the two-stage models. At the same time, efficiency score values from the classical DEA model and the two-stage model are compared. Methods of analysis, synthesis, comparison and mathematical-statistical methods are used in this paper. A part of the analysis is the traditional DEA model and the two-stage model. There was no statistically significant difference in the probability distribution of the efficiency score for both subprocesses in the traditional and two-stage model. There was a statistically significant difference in the probability distribution of the efficiency score of the second subprocess for insurance companies in Slovakia and the Czech Republic in the two-stage model.