Conical FDH Estimators of General Technologies, with Applications to Returns to Scale and Malmquist Productivity Indices
(2022) , 63 pages
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- Abstract
- Nonparametric envelopment estimators are often used to estimate the attainable sets and its efficient boundary and to assess efficiency and changes in productivity. Kneip et al. (2015, 2016) provide asymptotic theory enabling inference about expected efficiency and testing constant versus variable returns to scale using these estimators, and Kneip et al. (2021) provide asymptotic results that can be used to make inference about expected changes in productivity measured by Malmquist indices. All of these results require convexity of the attainable set, but in a number of situations this assumption is questionable. Kneip et al. (2016) also provide a test of convexity versus non-convexity of a production set, and convexity is rejected in several recent studies. This paper extends the results mentioned above to allow for possibly nonconvex technologies. Properties of a nonparametric envelopment estimator of distance to the boundary of the cone spanned by a possibly non-convex attainable set are derived. These new results are then extended to make inference about geometric means of Malmquist indices and to test constant versus non-constant returns to scale when the production set is not convex.
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Kneip, A., Simar, L., & Wilson, P. W. (2022). Conical FDH Estimators of General Technologies, with Applications to Returns to Scale and Malmquist Productivity Indices (LIDAM Discussion Paper ISBA 2022/24). https://hdl.handle.net/2078.5/102812