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Nonparametric Estimation of Homothetic and Homothetically Separable Functions

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Author Info
Arthur Lewbel
Oliver Linton

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Abstract

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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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2003/461.

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Date of creation: Oct 2003
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Handle: RePEc:cep:stiecm:/2003/461

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Keywords: Cost function economic scale homogeneous function homothetic function index models nonparametric production function separability.

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  6. 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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  8. 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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  21. Chen, Heng Z. & Randall, Alan, 1997. "Semi-nonparametric estimation of binary response models with an application to natural resource valuation," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 323-340. [Downloadable!] (restricted)
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