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Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions

Arthur Lewbel () and Oliver Linton ()

No 585, Boston College Working Papers in Economics from Boston College Department 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.

Keywords: Cost Function; Economies of Scale; Homogeneous Function; Homothetic Function; Index Models; Nonparametric; Oracle Efficiency; Production Function; Separability. (search for similar items in EconPapers)
JEL-codes: C14 C21 D24 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cmp, nep-ecm, nep-eff and nep-mfd
Date: 2003-10-29, Revised 2006-09-04
Note: Previously circulated as "Nonparametric Estimation of Homothetic and Homothetically Separable Functions"
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Journal Article: Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions (2007) Downloads
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