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Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions

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  • Arthur Lewbel
  • Oliver Linton

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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Bibliographic 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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Citations

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Cited by:
  1. David Jacho-Chavez & Arthur Lewbel & Oliver Linton, 2006. "Identification and Nonparametric Estimation of a Transformed Additively Separable Model," Boston College Working Papers in Economics 652, Boston College Department of Economics, revised 26 Nov 2008.
  2. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
  3. 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.
  4. 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.
  5. Henderson, Daniel J., 2008. "A Nonparametric Examination of Capital-Skill Complementarity," IZA Discussion Papers 3865, Institute for the Study of Labor (IZA).
  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. 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.

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