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Nonparametric estimation of homothetic and homothetically separable functions

  • Arthur Lewbel

    (Institute for Fiscal Studies and Boston College)

  • Oliver Linton

    ()

    (Institute for Fiscal Studies and London School of Economics)

For vectors x and w, let r(x,w) be a function that can be nonparametrically estimated consistently and asymptotically normally. We provide consistent, asymptotically normal estimators for the functions g and h, where r(x,w) = h[g(x),w], g is linearly homogeneous and h is monotonic in g. This framework encompasses homothetic and homothetically separable functions. 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. Extensions to related functional forms include a generalized partly linear model with unknown link function. We provide simulation evidence on the small sample performance of our estimator, and we apply our method to a Chinese production dataset.

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File URL: http://cemmap.ifs.org.uk/wps/cwp0314.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP14/03.

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Length: 17 pp.
Date of creation: Oct 2003
Date of revision:
Handle: RePEc:ifs:cemmap:14/03
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  5. Arthur Lewbel & Oliver Linton & D. L. McFadden, 2006. "Estimating features of a distribution from binomial data," LSE Research Online Documents on Economics 4418, London School of Economics and Political Science, LSE Library.
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  20. 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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  22. Andrew Chesher, 2001. "Quantile driven identification of structural derivatives," CeMMAP working papers CWP08/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  23. Primont, Daniel & Primont, Diane, 1994. "Homothetic non-parametric production models," Economics Letters, Elsevier, vol. 45(2), pages 191-195, June.
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  25. 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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