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Testing procedures for detection of linear dependencies in efficiency models

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Abstract
The validity of many efficiency measurement methods rely upon the assumption that variables such as input quantities and output mixes are independent of (or uncorrelated with) technical efficiency, however few studies have attempted to test these assumptions. In a recent paper, Wilson (2003) investigates a number of independence tests and finds that they have poor size properties and low power in moderate sample sizes. In this study we discuss the implications of these assumptions in three situations: (i) bootstrapping non-parametric efficiency models; (ii) estimating stochastic frontier models and (iii) obtaining aggregate measures of industry efficiency. We propose a semi-parametric Hausmann-type asymptotic test for linear independence (uncorrelation), and use a Monte Carlo experiment to show that it has good size and power properties in finite samples. We also describe how the test can be generalized in order to detect higher order dependencies, such as heteroscedasticity, so that the test can be used to test for (full) independence when the efficiency distribution has a finite number of moments. Finally, an empirical illustration is provided using data on US electric power generation.
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  • Antonio Peyrache & Tim Coelli, 2008. "Testing procedures for detection of linear dependencies in efficiency models," CEPA Working Papers Series WP022008, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:30
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    File URL: https://economics.uq.edu.au/files/5295/WP022008.pdf
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    1. Léopold Simar & Paul Wilson, 2000. "Statistical Inference in Nonparametric Frontier Models: The State of the Art," Journal of Productivity Analysis, Springer, vol. 13(1), pages 49-78, January.
    2. Charles Blackorby & R. Russell, 1999. "Aggregation of Efficiency Indices," Journal of Productivity Analysis, Springer, vol. 12(1), pages 5-20, August.
    3. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    4. 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.
    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    6. Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, vol. 46(4), pages 883-900, July.
    7. Paul Wilson, 2003. "Testing Independence in Models of Productive Efficiency," Journal of Productivity Analysis, Springer, vol. 20(3), pages 361-390, November.
    8. Zelenyuk, Valentin, 2006. "Aggregation of Malmquist productivity indexes," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1076-1086, October.
    9. Schmidt, Peter & Sickles, Robin C, 1984. "Production Frontiers and Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 367-374, October.
    10. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-676, August.
    11. Battese, G E & Coelli, T J, 1995. "A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data," Empirical Economics, Springer, vol. 20(2), pages 325-332.
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    2. Jose M. Cordero & Cristina Polo & Nickolaos G. Tzeremes, 2020. "Evaluating the efficiency of municipalities in the presence of unobserved heterogeneity," Journal of Productivity Analysis, Springer, vol. 53(3), pages 377-390, June.
    3. Karagiannis, Giannis, 2012. "More on the Fox paradox," Economics Letters, Elsevier, vol. 116(3), pages 333-334.
    4. Bigerna, Simona & D’Errico, Maria Chiara & Polinori, Paolo, 2021. "Energy security and RES penetration in a growing decarbonized economy in the era of the 4th industrial revolution," Technological Forecasting and Social Change, Elsevier, vol. 166(C).
    5. Cordero, José Manuel & Santín, Daniel & Sicilia, Gabriela, 2015. "Testing the accuracy of DEA estimates under endogeneity through a Monte Carlo simulation," European Journal of Operational Research, Elsevier, vol. 244(2), pages 511-518.
    6. Daniel Santín & Gabriela Sicilia, 2018. "Using DEA for measuring teachers’ performance and the impact on students’ outcomes: evidence for Spain," Journal of Productivity Analysis, Springer, vol. 49(1), pages 1-15, February.
    7. Vittadini, Giorgio & Sturaro, Caterina & Folloni, Giuseppe, 2022. "Non-Cognitive Skills and Cognitive Skills to measure school efficiency," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    8. Bigerna, Simona & D'Errico, Maria Chiara & Polinori, Paolo, 2022. "Environmental variables and power firms' productivity: micro panel estimation with time-Invariant variables," MPRA Paper 114157, University Library of Munich, Germany.
    9. Ari Hyytinen & Pekka Ilmakunnas & Mika Maliranta, 2016. "Olley–Pakes productivity decomposition: computation and inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(3), pages 749-761, June.

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