2022/14 | LEM Working Paper Series | ||||||||||||||||
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Approximations and Inference for Nonparametric Production Frontiers |
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Cinzia Daraio and Leopold Simar |
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Nonparametric production frontiers; DEA; FDH; partial frontiers; directional distances; linear
approximations; local linear approximations.
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JEL Classifications | |||||||||||||||||
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C1, C14, C13
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Abstract | |||||||||||||||||
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Nonparametric methods have been widely used for assessing the performance of organizations in
the private and public sector. The most popular ones are based on envelopment estimators, like the
FDH or DEA estimators, that estimate the attainable sets and its efficient boundary by enveloping
the cloud of observed units in the appropriate input-output space. The statistical properties of these
flexible estimators have been established. However these nonparametric techniques do not allow to make
sensitivity analysis of the production outputs to some particular inputs, or to infer about marginal
products and other coefficients of economic interest. On the contrary, parametric models for production
frontiers allow richer and easier economic interpretation but at a cost of restrictive assumptions on the
data generating process. In addition, the latter rely mostly on regression methods fitting the center
of the cloud of observed points. In this paper we offer a way to avoid these drawbacks and provide
approximations of these coefficients of economic interest by “smoothing” the popular nonparametric
estimators of the frontiers. Our approach allows to handle fully multivariate cases. We describe the
statistical properties for both the full and the partial (robust) frontiers. We consider parametric but
also flexible approximations based on local linear tools providing local estimates of all the desired partial
derivatives and we show how to deal with environmental factors. An illustration on real data from
European Higher Education Institutions (HEI) shows the usefulness of the proposed approach.
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