Estimation Uncertainty in Credit Risk Assessment: Comparison of Credit Risk Using Bootstrapping and an Asymptotic Approach
IWH Discussion Papers,
For credit risk assessment, probability of default and correlation have to be estimated simultaneously. However, these estimates are uncertain. To assess this uncertainty the literature has discussed the use of asymptotic confidence regions. This kind of region though needs a long credit history for exact assessment. An alternative method to generate a confidence region for a short credit history is bootstrapping. Hence, it could be more appropriate to assess estimation uncertainty with bootstrapping than with asymptotic methods if only a short credit history is available. Based on a simulation study, it is analyzed how many periods should be available for assessing credit risk – taking account of estimation uncertainty – if bootstrapping and a Wald confidence region shall achieve similar results. This article shows that more than 100 cycles have to be available for similar results.
Economies of Scope in European Railways: An Efficiency Analysis
IWH Discussion Papers,
In the course of railway reforms in the end of the last century, national European governments, as well the EU Commission, decided to open markets and to separate railway networks from train operations. Vertically integrated railway companies – companies owning a network and providing transport services – argue that such a separation of infrastructure and operations would diminish the advantages of vertical integration and would therefore not be suitable to raise economic welfare. In this paper, we conduct a pan-European analysis to investigate the performance of European railways with a particular focus on economies of vertical integration. We test the hypothesis that integrated railways realise economies of joint production and, thus, produce railway services on a higher level of efficiency. To determine whether joint or separate production is more efficient we apply a Data Envelopment Analysis super-efficiency bootstrapping model which relates the efficiency for integrated production to a virtual reference set consisting of the separated production technology. Our findings are that in a majority of European Railway companies exist economies of scope.