Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions

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 gand 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 Gthat is oracle efficient, achieving the same performance as an estimator based on local least squares when H is known. Copyright The Econometric Society 2007.