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Single Index Models for nonparametric conditional frontiers

Author

Listed:
  • Cazals, Catherine

    (Toulouse School of Economics)

  • Florens, Jean-Pierre

    (Toulouse School of Economics)

  • Simar, Léopold

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

In production theory, attention has been paid to the analysis of the impact of environmental variables on the efficiency of firms. The standard approach to this problem is to use conditional frontier models. For nonparametric approaches, this may create serious problems if the number of environmental factors increases, exacerbating the curse of dimensionality inherent in such models. In order to address this issue, it is investigated whether Single Index Models (SIM) could be used for modeling the effect of these variables on the production process. A test is proposed for the SIM hypothesis and the asymptotic properties are analyzed. If the SIM model is not rejected, better rates of convergence of the conditional efficiency estimates are obtained. The finite sample properties of the proposed test and the properties of the resulting estimates of the SIM, when it is not rejected, are investigated through Monte Carlo experiments. The method is illustrated with a real data set from the French national postal operator in charge of universal service.

Suggested Citation

  • Cazals, Catherine & Florens, Jean-Pierre & Simar, Léopold, 2026. "Single Index Models for nonparametric conditional frontiers," LIDAM Reprints ISBA 2026015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2026015
    DOI: https://doi.org/10.1016/j.ecosta.2026.04.001
    Note: In: Econometrics and Statistics, 2026
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    Keywords

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D22 - Microeconomics - - Production and Organizations - - - Firm Behavior: Empirical Analysis

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