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Frontier estimation in nonparametric location-scale models

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  • Florens , Mark
  • Simar, Leopold
  • Van Keilegom, Ingrid

Abstract

Conditional efficiency captures efficiency of firms facing heterogeneous environmental conditions. Traditional approaches estimate nonparametrically conditional distribution requiring smoothing techniques. We rather use a flexible nonparametric location-scale model to eliminate the dependence of inputs/outputs on these factors. These “pre-whitened” inputs/outputs define the optimal frontier function and a “pure” measure of efficiency more reliable to produce rankings, since the influence of external factors has been eliminated. Both full and order-m frontiers are used. The asymptotic properties are established. We can also derive the frontiers in the original units with their asymptotic properties. The approach is illustrated with some simulated and real data.
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Suggested Citation

  • Florens , Mark & Simar, Leopold & Van Keilegom, Ingrid, 2011. "Frontier estimation in nonparametric location-scale models," LIDAM Discussion Papers ISBA 2011030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2011030
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    8. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2012. "How to measure the impact of environmental factors in a nonparametric production model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 818-833.
    9. Badin, Luiza & Daraio, Cinzia & Simar, Léopold, 2010. "Optimal bandwidth selection for conditional efficiency measures: A data-driven approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 633-640, March.
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    20. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
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    23. Müller Ursula U. & Schick Anton & Wefelmeyer Wolfgang, 2007. "Estimating the error distribution function in semiparametric regression," Statistics & Risk Modeling, De Gruyter, vol. 25(1/2007), pages 1-18, January.
    24. Cinzia Daraio & Léopold Simar, 2005. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," Journal of Productivity Analysis, Springer, vol. 24(1), pages 93-121, September.
    25. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
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    Cited by:

    1. Mastromarco, Camilla & Simar, Leopold, 2014. "Global Dependence and Productivity: A Robust Nonparametric World Frontier Analysis," LIDAM Discussion Papers ISBA 2014049, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Mastromarco, Camilla & Simar, Léopold, 2018. "Globalization and productivity: A robust nonparametric world frontier analysis," Economic Modelling, Elsevier, vol. 69(C), pages 134-149.
    3. Cinzia Daraio & Leopold Simar & Paul W. Wilson, 2019. "Quality and its Impact on Efficiency," LEM Papers Series 2019/06, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    4. 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.
    5. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    6. Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2016. "Nonparametric Estimation of Efficiency in the Presence of Environmental Variables," LIDAM Discussion Papers ISBA 2016027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. 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.
    8. Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2015. "Testing the "Separability" Condition in Two-Stage Nonparametric Models of Production," LIDAM Discussion Papers ISBA 2015018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Daraio, Cinzia & Simar, Léopold & Wilson, Paul W., 2021. "Quality as a latent heterogeneity factor in the efficiency of universities," Economic Modelling, Elsevier, vol. 99(C).
    10. Camilla Mastromarco & Léopold Simar & Valentin Zelenyuk, 2021. "Predicting recessions with a frontier measure of output gap: an application to Italian economy," Empirical Economics, Springer, vol. 60(6), pages 2701-2740, June.
    11. Jose M. Cordero & Cristina Polo & Daniel Santín, 2020. "Assessment of new methods for incorporating contextual variables into efficiency measures: a Monte Carlo simulation," Operational Research, Springer, vol. 20(4), pages 2245-2265, December.
    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. 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).
    14. Camilla Mastromarco & Léopold Simar & Valentin Zelenyuk, 2019. "Predicting Recessions: A New Measure of Output Gap as Predictor," CEPA Working Papers Series WP112019, School of Economics, University of Queensland, Australia.
    15. Zheng Li & Roderick M. Rejesus & Xiaoyong Zheng, 2021. "Nonparametric Estimation and Inference of Production Risk," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(5), pages 1857-1877, October.
    16. Wilson, Paul W., 2018. "Dimension reduction in nonparametric models of production," European Journal of Operational Research, Elsevier, vol. 267(1), pages 349-367.
    17. Fusco, Elisa & Vidoli, Francesco & Sahoo, Biresh K., 2018. "Spatial heterogeneity in composite indicator: A methodological proposal," Omega, Elsevier, vol. 77(C), pages 1-14.
    18. Mastromarco, Camilla & Simar, Léopold & Van Keilegom, Ingrid, 2022. "Estimating Nonparametric Conditional Frontiers and Efficiencies: A New Approach," LIDAM Discussion Papers ISBA 2022035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2020. "Fast and efficient computation of directional distance estimators," Annals of Operations Research, Springer, vol. 288(2), pages 805-835, May.
    20. Vidoli, Francesco & Canello, Jacopo, 2016. "Controlling for spatial heterogeneity in nonparametric efficiency models: An empirical proposal," European Journal of Operational Research, Elsevier, vol. 249(2), pages 771-783.
    21. Ferrara, Giancarlo & Vidoli, Francesco, 2017. "Semiparametric stochastic frontier models: A generalized additive model approach," European Journal of Operational Research, Elsevier, vol. 258(2), pages 761-777.
    22. Simar, Léopold & Vanhems, Anne & Van Keilegom, Ingrid, 2016. "Unobserved heterogeneity and endogeneity in nonparametric frontier estimation," Journal of Econometrics, Elsevier, vol. 190(2), pages 360-373.
    23. Leonardo Andrade Rocha & Ahmad Saeed Khan & Patrícia Verônica Pinheiro Sales Lima & Maria Ester Dal Poz & Fernando Porfirio Soares De Oliveira, 2016. "Corrupção, Burocracia E Outras Falhas Institucionais: O “Câncer” Da Inovação E Do Desenvolvimento," Anais do XLIII Encontro Nacional de Economia [Proceedings of the 43rd Brazilian Economics Meeting] 090, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    24. Leonardo Rocha Andrade & Leonardo Q. Cardenas & Fernando Dias Lopes & Fernando P. S. Oliveira & Kaio Cesar Fernandes, 2018. "The Impact of R&D Investments on Performance of Firms in Different Degrees of Proximity to the Technological Frontier," Economics Bulletin, AccessEcon, vol. 38(2), pages 1156-1170.
    25. José Solana‐Ibáñez & Manuel Caravaca‐Garratón, 2021. "Stakeholder engagement and corporate social reputation: The influence of exogenous factors on efficiency performance (stakeholder engagement and exogenous factors): Stakeholder engagement and exogenou," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 28(6), pages 1891-1905, November.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

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