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A Post-Truncation Parameterization of Truncated Normal Technical Inefficiency

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In this paper we consider a stochastic frontier model in which the distribution of technical inefficiency is truncated normal. In standard notation, technical inefficiency u is distributed as N^+ (μ,σ^2). This distribution is affected by some environmental variables z that may or may not affect the level of the frontier but that do affect the shortfall of output from the frontier. We will distinguish the pre-truncation mean (μ) and variance (σ^2) from the post-truncation mean μ_*=E(u) and variance σ_*^2=var(u). Existing models parameterize the pre-truncation mean and/or variance in terms of the environmental variables and some parameters. Changes in the environmental variables cause changes in the pre-truncation mean and/or variance, and imply changes in both the post-truncation mean and variance. The expressions for the changes in the post-truncation mean and variance are quite complicated. In this paper, we suggest parameterizing the post-truncation mean and variance instead. This leads to simple expressions for the effects of changes in the environmental variables on the mean and variance of u, and it allows the environmental variables to affect the mean of u only, or the variance of u only, or both.

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  • Christine Amsler & Peter Schmidt & Wen-Jen Tsay, 2013. "A Post-Truncation Parameterization of Truncated Normal Technical Inefficiency," IEAS Working Paper : academic research 13-A002, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    • Handle: RePEc:sin:wpaper:13-a002
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    1. Anil Bera & Subhash Sharma, 1999. "Estimating Production Uncertainty in Stochastic Frontier Production Function Models," Journal of Productivity Analysis, Springer, vol. 12(3), pages 187-210, November.
    2. Rulon D. Pope, 2003. "Agricultural Risk Analysis: Adequacy of Models, Data, and Issues," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(5), pages 1249-1256.
    3. Caudill, Steven B. & Ford, Jon M., 1993. "Biases in frontier estimation due to heteroscedasticity," Economics Letters, Elsevier, vol. 41(1), pages 17-20.
    4. Reifschneider, David & Stevenson, Rodney, 1991. "Systematic Departures from the Frontier: A Framework for the Analysis of Firm Inefficiency," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 715-723, August.
    5. Kumbhakar, Subal C. & Sun, Kai, 2013. "Derivation of marginal effects of determinants of technical inefficiency," Economics Letters, Elsevier, vol. 120(2), pages 249-253.
    6. Richard E. Just & Rulon D. Pope, 1979. "Production Function Estimation and Related Risk Considerations," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 61(2), pages 276-284.
    7. Hung-jen Wang & Peter Schmidt, 2002. "One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels," Journal of Productivity Analysis, Springer, vol. 18(2), pages 129-144, September.
    8. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
    9. Antonio Alvarez & Christine Amsler & Luis Orea & Peter Schmidt, 2006. "Interpreting and Testing the Scaling Property in Models where Inefficiency Depends on Firm Characteristics," Journal of Productivity Analysis, Springer, vol. 25(3), pages 201-212, June.
    10. Kumbhakar, Subal C & Ghosh, Soumendra & McGuckin, J Thomas, 1991. "A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 279-286, July.
    11. Caudill, Steven B & Ford, Jon M & Gropper, Daniel M, 1995. "Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 105-111, January.
    12. Hung-Jen Wang, 2002. "Heteroscedasticity and Non-Monotonic Efficiency Effects of a Stochastic Frontier Model," Journal of Productivity Analysis, Springer, vol. 18(3), pages 241-253, November.
    13. Richard E. Just, 1975. "Risk Aversion under Profit Maximization," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 57(2), pages 347-352.
    14. 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.
    15. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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    Cited by:

    1. Christopher F. Parmeter & Hung-Jen Wang & Subal C. Kumbhakar, 2017. "Nonparametric estimation of the determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 47(3), pages 205-221, June.
    2. Namonje-Kapembwa, Thelma & Black, Roy & Jayne, Thomas S., 2015. "Does Late Delivery of Subsidized Fertilizer Affect Smallholder Maize Productivity and Production?," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205288, Agricultural and Applied Economics Association.
    3. Cheol-Keun Cho & Peter Schmidt, 2020. "The wrong skew problem in stochastic frontier models when inefficiency depends on environmental variables," Empirical Economics, Springer, vol. 58(5), pages 2031-2047, May.
    4. Hampf, Benjamin, 2015. "Estimating the materials balance condition: A stochastic frontier approach," Darmstadt Discussion Papers in Economics 226, Darmstadt University of Technology, Department of Law and Economics.

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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