Efficiency Score Research Based On Bootstrap-DEA Model

Data Envelopment Analysis (DEA) was proposed by Charnes, Cooper and Rhodes (1978), which is based on the mathematical programming model to evaluate relative efficiency between the production units with multiple inputs and multiple outputs. However, through the traditional DEA method, we can get the efficiency score of each production unit, judge and compare the relative effectiveness among the production units, but we cannot determine whether differences between these estimators are statistically significant. So this method is lack of statistical significance. In order to overcome it, Simar and Wilsion (1998) applied Bootstrap method, proposed by Efron (1979), to DEA method, such that Bootstrap samples can be constructed by mimicking the data-generating process (DGP), large numbers of the efficiency score estimates can be resulted, which can be used to construct empirical distribution. Hence one can obtain the confidence interval of efficiency score and test its statistical significance. However, when using the Bootstrap-DEA method, for some production units which are DEA-efficient (efficiency score equals 1) and have a very high super-efficiency score, the bias between the estimates and the efficiency score is relatively too large. And this may result in efficiency scores of these production units are significantly lower than that of some inefficient (efficiency score is lower than 1) production units, which is inconsistent with the facts. The reasons is that the model used to compute the efficiency estimates is unstable and is changing, and this changing model has a big effect on DEA-efficient production units. This paper proposes an improved Bootstrap-DEA method, here the super-efficiency DEA model is applied to compute the efficiency scores, and this model can guarantee not to be changed. So we can obtain large numbers of super-efficiency score estimates, furthermore the confidence interval and empirical distribution of super efficiency score can also be established. Noting that the empirical distribution function is skewed, so it is better to use the median to illustrate the overall level. Then we can inspect the median and illustrate the significance between super-efficiency scores by using Wilcoxon rank sum test. To illustrate the two methods, Bootstrap-DEA and improved Bootstrap-DEA, we conduct numerical analysis by using the data of the public library of the national 31 provinces in 2014.