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)
Date: 2003-10-29, Revised 2006-09-04
New Economics Papers: this item is included in nep-cmp, nep-ecm, nep-eff and nep-mfd
Note: Previously circulated as "Nonparametric Estimation of Homothetic and Homothetically Separable Functions"
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Related works:
Journal Article: Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions (2007)
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