Abstract:
Recently, in an attempt to produce robust production frontier estimators, Aragon et al. [2005, Nonparametric frontier estimation: a conditional quantile-based approach. Econometric Theory 21, 358-389] and Martins-Filho and Yao [2008, A smooth nonparametric conditional quantile frontier estimator. Journal of Econometrics 143, 317-333] considered the estimation of nonparametric α- frontier models based on conditional quantiles with α ∈ (0,1). There exist, however, a large and growing literature in economics devoted to the estimation of profit functions. In this paper, we first define an α-profit function based on the quantile of the suitably defined conditional distribution for profits. Second we propose a smooth nonparametric conditional quantile estimator for the α-profit function model. Our estimator is computationally simple, resistant to outliers and extreme values, and smooth. In addition, the estimator is shown to be consistent and asymptotically normal under mild regularity conditions. A small simulation study provides evidence of the finite sample properties for the estimator.
