Resumen de Bayesian analysis of heterogeneity in stochastic frontier models
Jorge Eduardo Galán Camacho
In this thesis, we put forward the modeling of heterogeneity in a Bayesian context by capturing both observed and unobserved heterogeneity in the inefficiency distribution under static and dynamic formulations. We propose several novel speciffications which permit the identiffication of heterogeneity in these contexts. The first of our proposed methods captures unobserved heterogeneity in the inefficiency by modeling a random parameter in the inefficiency distribution. Results suggest that this method is successful in identifying unobserved heterogeneity and that it also can be used as a way to test the relevancy of observed covariates. Also, the location of heterogeneity is found to have important effects on efficiency estimations which are more evident when unobserved heterogeneity is accounted for. The second proposal captures unobserved heterogeneity sources related to firm-specific effects of observed covariates in the inefficiency. This is performed by modeling random coefficients in the inefficiency. It is found that allowing random coefficients for the inefficiency covariates captures firm-speciffic effects which remain unidentiffied under the regular fixed coefficients models. This speciffication distinguishes properly firms in term of the effects of inefficiency drivers and separates unobserved heterogeneity related to these effects from efficiency. Our third proposal relies on the framework of dynamic SFA and speciffies a model that is able to capture unobserved heterogeneity in the inefficiency persistence and unobserved technological heterogeneity. Both unobserved effects are found to be very relevant in explaining inefficiency and its evolution over time. Finally, the implications of including observed covariates in dynamic models were studied by mean of an inefficiency speciffication that allows separating observed inefficiency heterogeneity from the dynamic process. The model allows identifying those firm characteristics that may have persistence effect in the inefficiency from those that can be rapidly adjusted. In general, location of observed covariates is found to have important implications in the identiffication of inefficiency drivers and posterior efficiency estimations. The proposed models are implemented in very different applications such as health performance, airlines, banking and electricity distribution and our results have important implications for companies, regulators and policy makers in these sectors. The inference of all the models is carried out using Bayesian methods and the Win-BUGS software package is used for the implementation throughout. We provide the codes used in each chapter of the thesis at the end of the corresponding chapters. This thesis has the following structure. Chapter 1 presents an introduction to the most important concepts on frontier efficiency, the measuring methods, SFA and its Bayesian approach, and a literature review on the treatment of observed and unobserved heterogeneity in SFA models. Chapter 2 presents the problem of observed heterogeneity in SFA by analyzing the effects of including observed covariates in the frontier, and in different parameters and distributions of the inefficiency. Chapter 3 presents the models proposed to identify unobserved heterogeneity in the inefficiency. Firstly, by modeling a random parameter in the inefficiency; and secondly, by allowing coefficients of inefficiency drivers to vary randomly across firms. Chapter 4 extends the analysis of heterogeneity in the dynamic framework by proposing two specifications: one that identifies unobserved heterogeneity in the inefficiency persistence and in the technology and another one that is able to separate observed heterogeneity from the dynamic behaviour of inefficiency. Finally, Chapter 5 discusses the main conclusions, contributions and further lines of research.
