Hypothesis testing in nonparametric models of production using multiple sample splits

Several tests of model structure developed by Kneip et al. (J Bus Econ Stat 34:435–456, 2016) and Daraio et al. (Econ J 21:170–191, 2018) rely on comparing sample means of two different efficiency estimators, one appropriate under the conditions of the null hypothesis and the other appropriate under the conditions of the alternative hypothesis. These tests rely on central limit theorems developed by Kneip et al. (Econ Theory 31:394–422, 2015) and Daraio et al. (Econ J 21:170–191, 2018), but require that the original sample be split randomly into two independent subsamples. This introduces some ambiguity surrounding the sample-split, which may be determined by choice of a seed for a random number generator. We develop a method that eliminates much of this ambiguity by repeating the random splits a large number of times. We use a bootstrap algorithm to exploit the information from the multiple sample-splits. Our simulation results show that in many cases, eliminating this ambiguity results in tests with better size and power than tests that employ a single sample-split.