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.
Authors
![Arthur Lewbel](/sites/default/files/styles/square_desktop/public/2022-07/Arthur%20Lewbel.png?itok=MXnJtTf7)
Research Associate Boston College
Arthur is a Research Associate of the IFS and holds the Barbara A. and Patrick E. Roche chair in economics at Boston College.
![Person graphic](/sites/default/files/styles/square_desktop/public/2022-06/IFS-person-graphic.png?itok=hWCtTSrz)
Oliver Linton
Working Paper details
- DOI
- 10.1920/wp.cem.2003.1403
- Publisher
- IFS
Suggested citation
Lewbel, A and Linton, O. (2003). Nonparametric estimation of homothetic and homothetically separable functions. London: IFS. Available at: https://ifs.org.uk/publications/nonparametric-estimation-homothetic-and-homothetically-separable-functions (accessed: 30 June 2024).
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