A Fast Method for Implementing Hypothesis Tests with Multiple Sample Splits in Nonparametric Models of Production

Kneip et al. (Journal of Business and Economic Statistics, 34, 435–456, 2016) and Daraio et al. (The Econometrics Journal, 21, 170–191, 2018) provide non-parametric tests of (i) convexity versus non-convexity of the production set, (ii) constant versus non-constant returns-to-scale of the frontier, and (iii) separability versus non-separability of the frontier with respect to environmental variables. Among other uses, these tests are essential for deciding which non-parametric efficiency estimator should be used to estimate technical efficiency. Each test requires randomly splitting the sample. Although theory establishes that the tests are valid for any random split, results can vary with different splits. This paper provides a computationally efficient method to aggregate test outcomes across multiple sample-splits using a simple decision rule, and we prove that our rule yields tests with asymptotic size no greater than the nominal size. We provide tests using multiple sample-splits to remove the ambiguity resulting from a single sample-split and give extensive Monte Carlo evidence on the size and power of our tests. The computational time required by the new tests is about 0.001 times that required by the bootstrap method proposed by Simar and Wilson (Journal of Productivity Analysis, 53, 287–303, 2020). The reduction in computational burden makes the tests useful in a practical sense for empirical researchers using inexpensive desktop or laptop computers.