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Non Parametric Instrumental Variables Estimation for Efficiency Frontier

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  • Cazals, Catherine
  • Feve, Frederique
  • Florens, Jean-Pierre
  • Simar, Leopold

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.
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Suggested Citation

  • Cazals, Catherine & Feve, Frederique & Florens, Jean-Pierre & Simar, Leopold, 2016. "Non Parametric Instrumental Variables Estimation for Efficiency Frontier," LIDAM Reprints ISBA 2016014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2016014
    Note: In : Journal of Econometrics, vol. 190, p. 349-359 (2016)
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    2. Kenneth Løvold Rødseth & Rasmus Bøgh Holmen & Timo Kuosmanen & Halvor Schøyen, 2023. "Market access and seaport efficiency: the case of container handling in Norway," Journal of Shipping and Trade, Springer, vol. 8(1), pages 1-25, December.
    3. D’Inverno, Giovanna & Smet, Mike & De Witte, Kristof, 2021. "Impact evaluation in a multi-input multi-output setting: Evidence on the effect of additional resources for schools," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1111-1124.
    4. Jean-Pierre Florens & Léopold Simar & Ingrid Van Keilegom, 2020. "Estimation of the Boundary of a Variable Observed With Symmetric Error," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 425-441, January.
    5. 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.
    6. Mastromarco, Camilla & Simar, Léopold, 2018. "Globalization and productivity: A robust nonparametric world frontier analysis," Economic Modelling, Elsevier, vol. 69(C), pages 134-149.
    7. Frédérique Fève & Jean-Pierre Florens & Léopold Simar, 2023. "Proportional incremental cost probability functions and their frontiers," Empirical Economics, Springer, vol. 64(6), pages 2721-2756, June.
    8. Jad Beyhum & Jean-Pierre FLorens & Ingrid Van Keilegom, 2020. "Nonparametric instrumental regression with right censored duration outcomes," Papers 2011.10423, arXiv.org.
    9. Beyhum, Jad & Florens, Jean-Pierre & Van Keilegom, Ingrid, 2020. "Nonparametric Instrumental Regression with Right Censored Duration Outcomes," TSE Working Papers 20-1164, Toulouse School of Economics (TSE).
    10. Centorrino, Samuele & Pérez-Urdiales, María, 2023. "Maximum likelihood estimation of stochastic frontier models with endogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 82-105.
    11. Laurens Cherchye & Bram De Rock & Dieter Saelens & Marijn Verschelde & Bart Roets, 2022. "Performance Analysis with Unobserved Inputs: An Application to Endogenous Automation in Railway Traffic Management," Working Papers ECARES 2022-06, ULB -- Universite Libre de Bruxelles.
    12. Cordero, Jose Manuel & Polo, Cristina & Simancas, Rosa, 2022. "Assessing the efficiency of secondary schools: Evidence from OECD countries participating in PISA 2015," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    13. Jad Beyhum & Jean-Pierre Florens & Ingrid Van Keilegom, 2021. "A nonparametric instrumental approach to endogeneity in competing risks models," Papers 2105.00946, arXiv.org.
    14. Camilla Mastromarco & Léopold Simar, 2021. "Latent heterogeneity to evaluate the effect of human capital on world technology frontier," Journal of Productivity Analysis, Springer, vol. 55(2), pages 71-89, April.
    15. Juan Aparicio & Jose Manuel Cordero & Carlos Díaz-Caro, 2020. "Efficiency and productivity change of regional tax offices in Spain: an empirical study using Malmquist–Luenberger and Luenberger indices," Empirical Economics, Springer, vol. 59(3), pages 1403-1434, September.
    16. Mastromarco, Camilla & Simar, Leopold, 2017. "Cross-Section Dependence and Latent Heterogeneity to Evaluate the Impact of Human Capital on Country Performance," LIDAM Discussion Papers ISBA 2017030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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    More about this item

    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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