Nonparametric Shape-Constrained Models For Production Economics

Abstract

In production economics, the cost function is a critical tool used to infer productivity and efficiency measures to describe the key features of an industry. This dissertation investigates nonparametric estimators with shape constraints. The goals are to improve researchers’ understanding and illustrate the advantages of this set of estimators over other commonly used estimators. First, the dissertation studies the direction selection for stochastic directional distance functions. Unlike much of the published literature on directional distance functions, the analysis is performed in stochastic settings. Applying a recently developed non-parametric shape-constrained estimator on a set of simulations, user guidelines about selecting the direction, a key tuning parameter for such estimators, are given. The estimator is tested and compared to other estimators by applying it to a cost function estimation. An application of stochastic directional distance function estimator to the US hospitals industry gives insights into the industry such as most productive scale size and output trade-off information. Second, several approximations of shape-constrained non-parametric estimators are analyzed. The approximations consist of piece-wise linear versus smooth (at least of class C^2 ) estimated functions and coordinate-wise versus global constraints. The fitting performance and the shape constraints violations percentages are the main criteria established for the comparison. New estimators are developed for the analysis, in particular a B-spline based shape-constrained estimator for smooth cases. Based on the results obtained on a range of simulations, guidelines are determined to help users pick the best estimator, among the ones considered in the study, depending on the characteristics of the data. Finally additional insights on the US hospital industry are provided while showcasing the implementation of some of the introduced estimators on real data.