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Interpreting and Testing the Scaling Property in Models where Inefficiency Depends on Firm Characteristics

Author

Listed:
  • Antonio Alvarez
  • Christine Amsler
  • Luis Orea
  • Peter Schmidt

Abstract

Let u ≥ 0 be technical inefficiency, let z be a set of variables that affect u, and let δ be the parameters of this relationship. The model satisfies the scaling property if u(z, δ) can be written as a scaling function h(z, δ) times a random variable u* that does not depend on z. This property implies that changes in z affect the scale but not the shape of u(z,δ). This paper reviews the existing literature and identifies models that do and do not have the scaling property. It also discusses practical advantages of the scaling property. The paper shows how to test the hypothesis of scaling, and other interesting hypotheses, in the context of the model of Wang, Journal of Productivity Analysis, 2002. Finally, two empirical examples are given. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jproda:v:25:y:2006:i:3:p:201-212
    DOI: 10.1007/s11123-006-7639-3
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    References listed on IDEAS

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    2. Cuesta, Rafael A. & Orea, Luis, 2002. "Mergers and technical efficiency in Spanish savings banks: A stochastic distance function approach," Journal of Banking & Finance, Elsevier, vol. 26(12), pages 2231-2247.
    3. 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.
    4. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
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    7. 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.
    8. Han, Chirok & Orea, Luis & Schmidt, Peter, 2005. "Estimation of a panel data model with parametric temporal variation in individual effects," Journal of Econometrics, Elsevier, vol. 126(2), pages 241-267, June.
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    More about this item

    Keywords

    Stochastic frontier model; Scaling property; Technical inefficiency; C12; C31; C52;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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