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Nonparametric estimation of homothetic and homothetically separable functions

Authors: Arthur Lewbel and Oliver Linton
Date: 01 July 2007
Type: Journal article, Econometrica, Vol. 75, No. 4, pp. 1209-1227


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.

Previous version:
Arthur Lewbel and Oliver Linton October 2003, Nonparametric estimation of homothetic and homothetically separable functions, cemmap Working Paper, CWP14/03

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