Optimal toll rates accounting for traffic accidents: A productive efficiency approach
研究西班牙收费高速公路部门2003-2018年的生产效率，将交通事故作为非期望产出纳入分析，发现可通过调整费率同时提高行驶里程并减少事故。
This study analyzes the productive efficiency of the toll motorway sector in Spain over the 2003–2018 period by applying a stochastic frontier analysis with the particularity of including an undesirable output (traffic accidents with victims). Given the multioutput nature of the study and the presence of negative externalities, the method used is based on hyperbolic distance functions. The results obtained reveal that i) the average efficiency in the sector suggests that it is possible to increase the total number of vehicle-kilometers traveled by 29% and simultaneously reduce recorded accidents with victims by 23%, ii) there was technical progress of 16.5% during the study period, iii) reducing by one unit the number of accidents with victims would be equivalent to a monetary value of over 491 thousand euros in terms of the loss of toll revenue paid by light or heavy vehicles, and iv) the shadow price of accidents with victims allows us to determine that the optimal toll rate for heavy vehicles should be 1.62 times that of light vehicles.