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Econometrics Paper
Nonparametric Estimation of Homothetic and Homothetically Separable Functions
Arthur Lewbel and Oliver Linton
October 2003
Paper No' EM/2003/461:
Full Paper (pdf)

Tags: cost function; economic scale; homogeneous function; homothetic function; index models; nonparametric; production function; separability.

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.