Robust Estimators in Generalized Pareto Models

This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT.Comment: 26pages, 6 figure

Technology and Firm Size Distribution:Evidence from Italian Manufacturing

This paper explores the relationship between firm size distribution and technology. Similarly to Crosato and Ganugi (2006), we focus on six industries from the Micro1 survey by the Italian Statistical National Office (ISTAT). Firm technology is analysed across selected industries by means of a non-parametric production analysis, the Free Disposal Hull approach (Deprins et al., 1984; Kerstens and Vanden Eeckaut, 1999). The existence of a link between technical efficiency and size on the one hand, and between scale elasticity and size on the other is investigated. Graphical analyses show the absence of a clear-cut relation in the first case, while an inverse relation is found in the second one. Building on this relation, we inquire whether the shape of the firm size-distribution is related to a particular pattern of returns to scale. This problem is studied through the Zipf Plot (Stanley et al., 1995) of the Pareto IV distribution, which is concave for firms up to a given threshold, and then becomes linear. Results show that firms in the concave part of the plot experience increasing returns to scale. On the contrary, firms in the linear part are mainly characterised by constant returns to scale.Italian manufacturing; Free Disposal Hull; Pareto distributions; Returns to scale;