Proportional Incremental Cost Probability Functions and their Frontiers

Frédérique Fève, Jean-Pierre Florens and Leopold Simar

No 2022016, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: The econometric analysis of cost functions is based on the analysis of the condi- tional distribution of the cost Y given the level of the outputs X ∈ Rp+ and given a set of environment variables Z ∈ Rd. The model basically describes the conditional distribution of Y given X ≥ x and Z = z. In many applications, the dimension of Z is naturally large and a fully nonparametric specification of the model is limited by the curse of the dimensionality. Most of the approaches so far are based on two-stage estimations when the frontier level does not depend on the value of Z. But even in the case of separability of the frontier, the estimation procedure suffers from several prob- lems, mainly due to the inherent bias of the estimated efficiency scores and the poor rates of convergence of the frontier estimates. In this paper we suggest an alternative semi-parametric model which avoids the drawbacks of the two-stage methods. It is based on a class of model called the Proportional Incremental Cost Functions (PICF), adapted to our setup from the Cox proportional hazard models extensively used in survival analysis for durations models. We define the PICF model, then we examine its properties and propose a semi-parametric estimation. By this way of modeling, we avoid the first stage nonparametric estimation of the frontier and avoid the curse of dimensionality keeping the parametric √n rates of convergence for the parameters of interest. We are also able to derive √n-consistent estimator of the conditional order-m robust frontiers (which, by contrast to the full frontier, may depend on Z) and we prove the Gaussian asymptotic properties of the resulting estimators. We illustrate the flexibility and the power of the procedure by some simulated examples and also with some real data sets.

Keywords: Cost efficiency; Nonparametric robust frontier; Proportional hazard model; Environmental variables (search for similar items in EconPapers)
JEL-codes: C10 C14 C51 D22 (search for similar items in EconPapers)
Pages: 35
Date: 2022-05-01
New Economics Papers: this item is included in nep-ecm, nep-eff and nep-env
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://dial.uclouvain.be/pr/boreal/en/object/bore ... tastream/PDF_01/view (application/pdf)

Related works:
Chapter: Proportional incremental cost probability functions and their frontiers (2024)
Journal Article: Proportional incremental cost probability functions and their frontiers (2023)
Working Paper: Proportional incremental cost probability functions and their frontiers (2023)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvad:2022016

Access Statistics for this paper

More papers in LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA) Voie du Roman Pays 20, 1348 Louvain-la-Neuve (Belgium). Contact information at EDIRC.
Bibliographic data for series maintained by Nadja Peiffer ().