Nonparametric Estimation of Efficiency in the Presence of Environmental Variables

This paper demonstrates that standard central limit theorem (CLT) results do not hold for means of nonparametric conditional efficiency estimators, and provides new CLTs that do hold, permitting applied researchers to estimate confidence intervals for mean conditional efficiency or to compare mean efficiency across groups of producers along the lines of the test developed by Kneip et al. (JBES, 2015b). The new CLTs are used to develop a test of the "separability" condition that is necessary for second-stage regressions of efficiency estimates on environmental variables. We show that if this condition is violated, not only are second-stage regressions meaningless,but also first-stage, unconditional efficiency estimates are without meaning. As such,the test developed here is of fundamental importance to applied researchers using non-parametric methods for efficiency estimation. Our simulation results indicate that our tests perform well both in terms of size and power. We present a real-world empirical example by updating the analysis performed by Aly et al. (R. E. Stat., 1990) on U.S. commercial banks; our tests easily reject the assumption required for two-stage estimation, calling into question results that appear in hundreds of papers that have been published in recent years.