Quantile regression and frontier analysis

In chapter 3, quantile regression is used to estimate probabilistic frontiers, i.e. frontiers based on the probability of being dominated. The results from the empirical application using an Italian hotel dataset show rejections of a parametric functional form and a location shift effect, large uncertainty of the estimates of the frontier and wide confidence intervals for the estimates of efficiency. Quantile regression is further developed to estimate thick probabilistic frontiers, i.e. frontiers based on a group of efficient firms. The empirical results show that the differences between the inefficient and efficient firms at lower quantiles of the conditional distribution function are from the coefficient (85 percent of the total effect) and the residual effects (25 percent) and at higher quantiles from the coefficient (68 percent) and the regressor effects (22 percent). The results from the Monte Carlo simulations in chapter 4 show that under the correctly assumed stochastic frontier models, the probabilistic frontiers can have the lowest bias and mean squared error of the efficiency estimates. When outliers or location-scale shift effects are included, more preference is towards the probabilistic frontiers. The nonparametric probabilistic frontiers are nearly always preferable to Data Envelopment Analysis and Free Disposable Hull. In chapter 5, a fixed effects quantile regression estimator is used to estimate a cost frontier and efficiency levels for a panel dataset of English NHS Trusts. Waiting times elasticities are estimated from -0.14 to 0.17 in the cross-sectional models and -0.008 to 0.03 in the panel models. Cost minimisation ranged from 33 to 60 days in the cross-sectional model and from 37 to 54 days in the panel model. The results show that the effects of the inputs and control variables vary depending on the efficiency of the Trusts. The efficiency estimates reveal very different conclusions depending on the model choice