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Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions

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Author Info
Arthur Lewbel
Oliver Linton

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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 gand 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 Gthat is oracle efficient, achieving the same performance as an estimator based on local least squares when H is known. Copyright The Econometric Society 2007.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2007.00787.x
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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 75 (2007)
Issue (Month): 4 (07)
Pages: 1209-1227
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Handle: RePEc:ecm:emetrp:v:75:y:2007:i:4:p:1209-1227

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  7. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November. [Downloadable!] (restricted)
  8. Pedro Gozalo & Oliver Linton, 1994. "Local Nonlinear Least Squares Estimation: Using Parametric Information Nonparametrically," Cowles Foundation Discussion Papers 1075, Cowles Foundation, Yale University. [Downloadable!]
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  10. Andrew Chesher, 2001. "Quantile driven identification of structural derivatives," CeMMAP working papers CWP08/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  13. Richard Blundell & James Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  14. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-45, March. [Downloadable!] (restricted)
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  15. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, 09. [Downloadable!] (restricted)
  16. Daniel McFadden, 1996. "Computing Willingness-to-Pay in Random Utility Models," Working Papers _011, University of California at Berkeley, Econometrics Laboratory Software Archive.
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  18. Jefferson, Gary & Hu, Albert G. Z. & Guan, Xiaojing & Yu, Xiaoyun, 2003. "Ownership, performance, and innovation in China's large- and medium-size industrial enterprise sector," China Economic Review, Elsevier, vol. 14(1), pages 89-113. [Downloadable!] (restricted)
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  20. Hanoch, Giora & Rothschild, Michael, 1972. "Testing the Assumptions of Production Theory: A Nonparametric Approach," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 256-75, March-Apr. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Yingying Dong & Arthur Lewbel, 2009. "Nonparametric Identification of a Binary Random Factor in Cross Section Data," Boston College Working Papers in Economics 707, Boston College Department of Economics. [Downloadable!]
    Other versions:
  2. Henderson, Daniel J., 2008. "A Nonparametric Examination of Capital-Skill Complementarity," IZA Discussion Papers 3865, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  3. 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. [Downloadable!]
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