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Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions

Author

Listed:
  • Arthur Lewbel

    () (Boston College)

  • Oliver Linton

    () (London School of Economics)

Abstract

For vectors z and w and scalar v, let r(v,z,w) be a function that can be nonparametrically estimated consistently and asymptotically normally, such as a distribution, density, or conditional mean regression function. We provide consistent, asymptotically normal nonparametric estimators for the functions G and H, where r(v,z,w)=H[vG(z),w], and some related models. This framework encompasses homothetic and homothetically separable functions, and transformed partly additive models r(v,z,w)=h[v+g(z),w] for unknown functions g and h. Such models reduce the curse of dimensionality, provide a natural generalization of linear index models, and are widely used in utility, production, and cost function applications. We also provide an estimator of G that is oracle efficient, achieving the same performance as an estimator based on local least squares knowing H.

Suggested Citation

  • Arthur Lewbel & Oliver Linton, 2003. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Boston College Working Papers in Economics 585, Boston College Department of Economics, revised 04 Sep 2006.
  • Handle: RePEc:boc:bocoec:585
    Note: Previously circulated as "Nonparametric Estimation of Homothetic and Homothetically Separable Functions"
    as

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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Jacho-Chávez, David & Lewbel, Arthur & Linton, Oliver, 2010. "Identification and nonparametric estimation of a transformed additively separable model," Journal of Econometrics, Elsevier, vol. 156(2), pages 392-407, June.
    2. Juan M. Rodríguez-Póo & Stefan Sperlich & Philippe Vieu, 2012. "A Practical Test for Misspecification in Regression: Functional Form, Separability and Distribution," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 12093, Institut d'Economie et Econométrie, Université de Genève.
    3. Dong, Yingying & Lewbel, Arthur, 2011. "Nonparametric identification of a binary random factor in cross section data," Journal of Econometrics, Elsevier, vol. 163(2), pages 163-171, August.
    4. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    5. Daniel J. Henderson, 2009. "A Non-parametric Examination of Capital-Skill Complementarity," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(4), pages 519-538, August.
    6. Le-Yu Chen, 2009. "Identification of structural dynamic discrete choice models," CeMMAP working papers CWP08/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.

    More about this item

    Keywords

    Cost Function; Economies of Scale; Homogeneous Function; Homothetic Function; Index Models; Nonparametric; Oracle Efficiency; Production Function; Separability.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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