Nonparametric estimation homothetic and homothetically separable functions - Arthur Lewbel; Oliver Bruce Linton (Centre for Microdata Methods and Practice (cemmap), 2003)
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.
Keywords: C14; C21; D24; 330; Cost Function; Economies of Scale; Homogeneous Function; Homothetic Function; Index Models; Nonparametric; Production Function; Separability; Schätzung; Nichtparametrisches Verfahren; Theorie