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Nonparametric instrumental variables estimation for efficiency frontier

Author

Listed:
  • Cazals, Catherine
  • Fève, Frédérique
  • Florens, Jean-Pierre
  • Simar, Léopold

Abstract

The paper investigates endogeneity issues in nonparametric frontier models. It considers a nonseparable model for a cost function C=φ(Y,U) where C and Y are the cost and the output, U is uniform in [0,1] and φ is increasing with respect to U. The cost frontier corresponds to U=0 and U can be interpreted as a normalized level of inefficiency. The endogeneity issue arises when Y is dependent of U. For identification and estimation, we use a nonparametric instrumental variables estimator of the model for fixed value U=α, and obtain an estimate of the α-quantile cost frontier φ(Y,α). This involves the solution of a non linear integral equation. If the true frontier φ(Y,0) is wanted, it is then estimated by estimating the bias correction φ(Y,0)−φ(Y,α) under additional regularity conditions. The procedure is illustrated through a simulated sample and with an empirical application to the efficiency of post offices.

Suggested Citation

  • Cazals, Catherine & Fève, Frédérique & Florens, Jean-Pierre & Simar, Léopold, 2016. "Nonparametric instrumental variables estimation for efficiency frontier," Journal of Econometrics, Elsevier, vol. 190(2), pages 349-359.
  • Handle: RePEc:eee:econom:v:190:y:2016:i:2:p:349-359
    DOI: 10.1016/j.jeconom.2015.06.010
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    References listed on IDEAS

    as
    1. Frédérique Fève & Jean-Pierre Florens, 2010. "The practice of non-parametric estimation by solving inverse problems: the example of transformation models," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 1-27, October.
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    Cited by:

    1. repec:eee:ecmode:v:69:y:2018:i:c:p:134-149 is not listed on IDEAS
    2. Guillermo Díaz & Vincent Charles, 2016. "Regulatory design and technical efficiency: public transport in France," Journal of Regulatory Economics, Springer, vol. 50(3), pages 328-350, December.
    3. repec:kap:enreec:v:69:y:2018:i:1:d:10.1007_s10640-016-0071-x is not listed on IDEAS
    4. Florens, Jean-Pierre & Simar, Léopold & Van Keilegom, Ingrid, 2019. "Estimation of the Boundary of a Variable Observed with A Symmetric Error," TSE Working Papers 19-990, Toulouse School of Economics (TSE).

    More about this item

    Keywords

    Endogeneity in frontier models; Instrumental variable quantile; Non linear integral equation; Landweber iteration; Tail index estimation;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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