Testing Positive Endogeneity in Inputs in Data Envelopment Analysis

Data envelopment analysis (DEA) has been widely applied to empirically measure the technical efficiency of a set of schools for benchmarking their performance. However, the endogeneity issue in the production of education, which plays a central role in education economics, has received minor attention in the DEA literature. Under a DEA framework, endogeneity arises when at least one input is correlated with the efficiency term. Cordero et al. (European Journal of Operational Research 244:511–518, 2015) highlighted that DEA performs well under negative and moderate positive endogeneity. However, when an input is highly and positively correlated with the efficiency term, DEA estimates are misleading. The aim of this work is to propose a new test, based on defining a grid of input flexible transformations, for detecting the presence of positive endogeneity in inputs. To show the potential ability of this test, we run a Monte Carlo analysis evaluating the performance of the new approach in finite samples. The results show that this test outperforms alternative statistical procedures for detecting positive high correlations between inputs and the efficiency term. Finally, to illustrate our theoretical findings, we perform an empirical application on the education sector.