Parametric approximations of nonparametric frontiers.

A large amount of literature has been developed on how to estimate frontier functions. The idea is to analyze how firms combine their inputs to produce in an efficient way, the output. The maximal achievable level of output for a given level of inputs defines the production frontier. The efficiency of a particular firm is then characterized by the distance between its level of output and this optimal level it should obtain if it were efficient. From a nonparametric perspective, envelopment estimators have been mostly used, like the Free Disposal Hull (FDH) or the Data Envelopment Analysis (DEA). The statistical theory of these estimators is now available. Nonparametric estimators are very appealing because they rely on very few assumptions, on the other hand, a parametric form for the production function allows for a richer economic interpretation of the production process under analysis. Here, in a deterministic frontiers framework, most of the approaches rely on “ad hoc” procedures based on standard regression methods (shifted OLS, corrected OLS, and MLE) and are based on strong distributional assumptions on the production process. Also they characterizes rather properties of the center of the cloud of points rather than its boundary. In this paper, we investigated a new approach, which tries to capture the shape of the cloud points near its boundary. It combines the nonparametric and the parametric approaches, by offering parametric approximations of nonparametric frontiers. For the nonparametric part, we use the FDH estimator or expected frontier of order-m, introduced by Cazals, Florens and Simar (2002). We provide the statistical theory for the obtained estimators (consistency and asymptotic distribution). We illustrate with some simulated examples, showing the advantages of our method compared with the regression-type estimators.

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Document type	Document de travail (Working Paper)
Access type	Accès libre
Publication date	2002
Language	Anglais
Number of pages	28 pages
Collection	STAT Discussion Papers - 0222
Affiliations	Université de Toulouse - IDEI/GREMAQ UCL - EUEN/STAT - Institut de statistique
Keywords	production function ; frontier ; nonparametric estimation
Links	http://sites.uclouvain.be/IAP-Stat-Phase-V-VI/ISBApub/ISBAdp.html#2002 http://hdl.handle.net/2078.1/122461[Handle]

See also
	[boreal:39709]	Parametric approximations of nonparametric frontiers