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.
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Length: 18 pages Date of creation: 29 Oct 2003 Date of revision:
04 Sep 2006 Handle: RePEc:boc:bocoec:585
Note: Previously circulated as "Nonparametric Estimation of Homothetic and Homothetically Separable Functions" Contact details of provider: Postal: Boston College, 140 Commonwealth Avenue, Chestnut Hill MA 02467 USA Phone: 617-552-3670 Fax: +1-617-552-2308 Email: Web page: http://fmwww.bc.edu/EC/ More information through EDIRC
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Find related papers by JEL classification: C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models D24 - Microeconomics - - Production and Organizations - - - Production; Capital and Total Factor Productivity; Capacity
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