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Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 585.

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Length: 18 pages
Date of creation: 29 Oct 2003
Date of revision: 04 Sep 2006
Handle: RePEc:boc:bocoec:585

Note: Previously circulated as "Nonparametric Estimation of Homothetic and Homothetically Separable Functions"
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Related research

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

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References

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  1. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-70, March.
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  3. Ahn, Hyungtaik, 1995. "Nonparametric two-stage estimation of conditional choice probabilities in a binary choice model under uncertainty," Journal of Econometrics, Elsevier, vol. 67(2), pages 337-378, June.
  4. Chesher, A, 2001. "Quantile driven identification of structural derivatives," Open Access publications from University College London http://discovery.ucl.ac.u, University College London.
  5. Pedro Gozalo & Oliver Linton, 1994. "Local Nonlinear Least Squares Estimation: Using Parametric Information Nonparametrically," Cowles Foundation Discussion Papers 1075, Cowles Foundation for Research in Economics, Yale University.
  6. 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.
  7. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  8. Rosa L. Matzkin, 1999. "Nonparametric Estimation of Nonadditive Random Functions," Working Papers 38, Universidad de San Andres, Departamento de Economia, revised Sep 2001.
  9. Lewbel, Arthur & McFadden, Daniel & Linton, Oliver, 2011. "Estimating features of a distribution from binomial data," Journal of Econometrics, Elsevier, vol. 162(2), pages 170-188, June.
  10. 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.
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  13. 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.
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  15. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 655-679.
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  19. Joel Horowitz & Enno Mammen, 2002. "Nonparametric estimation of an additive model with a link function," CeMMAP working papers CWP19/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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  21. repec:wop:humbsf:2002-63 is not listed on IDEAS
  22. Horowitz, Joel L, 2001. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Econometrica, Econometric Society, vol. 69(2), pages 499-513, March.
  23. 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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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. Yingyong Dong & Arthur Lewbel, 2009. "Nonparametric identification of a binary random factor in cross section data," CeMMAP working papers CWP16/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  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.
  4. Linton, Oliver, 2008. "Estimation of a semiparametric transformation model. Ann. Stat," Open Access publications from Université catholique de Louvain info:hdl:2078.1/36983, Université catholique de Louvain.
  5. Henderson, Daniel J., 2008. "A Nonparametric Examination of Capital-Skill Complementarity," IZA Discussion Papers 3865, Institute for the Study of Labor (IZA).
  6. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/15031, Universidad Carlos III de Madrid.

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