No abstract

Efficiency scores of production units are generally measured relative to an estimated production frontier. Nonparametric estimators (DEA, FDH, \cdots ) are based on a finite sample of observed production units. The bootstrap is one easy way to analyze the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier. The main point in order to validate the bootstrap is to define a reasonable data-generating process in this complex framework and to propose a reasonable estimator of it. This paper provides a general methodology of bootstrapping in nonparametric frontier models. Some adapted methods are illustrated in analyzing the bootstrap sampling variations of input efficiency measures of electricity plants.Data Envelopment Analysis, Bootstrap, Resampling Methods, Frontier Efficiency Models

A large amount of literature has been developed on how to specify and to estimate production frontiers or cost functions. Two different approaches have been mainly developed: the deterministic frontier model which relies on the assumption that all the observations are on a unique side of the frontier, and the stochastic frontier models where observational errors or random noise allows some observations to be outside of the frontier. In a deterministic frontier framework, nonparametric methods are based on envelopment techniques known as FDH (Free Disposal Hull) and DEA (Data Envelopment Analysis). Today, statistical inference based on DEA/FDH type of estimators is available but, by construction, they are very sensitive to extreme values and to outliers. In this paper, we build an original nonparametric estimator of the "efficient frontier" which is more robust to extreme values, noise or outliers than the standard DEA/FDH nonparametric estimators. It is based on a concept of expected minimum input function (or expected maximal output function). We show how these functions are related to the efficient frontier itself. The resulting estimator is also related to the FDH estimator but our estimator will not envelop all the data. The asymptotic theory is also provided. Our approach includes the multiple inputs and multiple outputs cases. As an illustration, the methodology is applied to estimate the expected minimum cost function for french post offices.

This paper proposes a general formulation of a nonparametric frontier model introducing external environmental factors that might influence the production process but are neither inputs nor outputs under the control of the producer. A representation is proposed in terms of a probabilistic model which defines the data generating process. Our approach extends the basic ideas from Cazals, Florens and Simar (2002) to the full multivariate case. We introduce the concepts of conditional efficiency measure and of conditional efficiency measure of order-m. Afterwards we suggest a practical way for computing the nonparametric estimators. Finally, a simple methodology to investigate the influence of these external factors on the production process is proposed. Numerical illustrations through some simulated examples and through a real data set on Mutual Funds show the usefulness of the approach.

No abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Non-parametric data envelopment analysis (DEA) estimators based on linear programming methods have been widely applied in analyses of productive efficiency. The distributions of these estimators remain unknown except in the simple case of one input and one output, and previous bootstrap methods proposed for inference have not been proven consistent, making inference doubtful. This paper derives the asymptotic distribution of DEA estimators under variable returns-to-scale. This result is then used to prove that two different bootstrap procedures (one based on sub-sampling, the other based on smoothing) provide consistent inference. The smooth bootstrap requires smoothing the irregularly-bounded density of inputs and outputs as well as smoothing of the DEA frontier estimate. Both bootstrap procedures allow for dependence of the inefficiency process on output levels and the mix of inputs in the case of input-oriented measures, or on inputs levels and the mix of outputs in the case of output-oriented measures. Terms of use: Documents in

No abstract

No abstract