254 research outputs found
Some evidence about the evolution of the size distribution of Italian firms by age
In this short note we are interested in the distribution of Italian firm size by age. In the wake of other recent work, such as Cabral and Mata (2003) [On the evolution of firm size distribution: facts and theory. American Economic Review 93, 1075-1090] for Portuguese companies, we aim to verify if the size distribution of young firms (less than 5 years old) is sensibly different from that of older firms (more than 30 years old). To perform our analysis we use a very comprehensive industrial panel, with about 25k firms for twenty years of observations. As far as the results are concerned, it is possible to verify a clear difference in the size distribution of firms by age, for which we give a good fit using the generalized beta distribution of the second kind.firms' size distribution, generalized beta of the second kind, firms' age, empirical laws
Generalized extreme shock models with a possibly increasing threshold
We propose a generalized extreme shock model with a possibly increasing
failure threshold. While standard models assume that the crucial threshold for
the system may only decrease over time, because of weakening shocks and
obsolescence, we assume that, especially at the beginning of the system's life,
some strengthening shocks may increase the system tolerance to large shock.
This is for example the case of turbines' running-in in the field of
engineering. On the basis of parametric assumptions, we provide theoretical
results and derive some exact and asymptotic univariate and multivariate
distributions for the model. In the last part of the paper we show how to link
this new model to some nonparametric approaches proposed in the literature
Gini estimation under infinite variance
We study the problems related to the estimation of the Gini index in presence
of a fat-tailed data generating process, i.e. one in the stable distribution
class with finite mean but infinite variance (i.e. with tail index
). We show that, in such a case, the Gini coefficient cannot be
reliably estimated using conventional nonparametric methods, because of a
downward bias that emerges under fat tails. This has important implications for
the ongoing discussion about economic inequality.
We start by discussing how the nonparametric estimator of the Gini index
undergoes a phase transition in the symmetry structure of its asymptotic
distribution, as the data distribution shifts from the domain of attraction of
a light-tailed distribution to that of a fat-tailed one, especially in the case
of infinite variance. We also show how the nonparametric Gini bias increases
with lower values of . We then prove that maximum likelihood estimation
outperforms nonparametric methods, requiring a much smaller sample size to
reach efficiency.
Finally, for fat-tailed data, we provide a simple correction mechanism to the
small sample bias of the nonparametric estimator based on the distance between
the mode and the mean of its asymptotic distribution
An urn-based Bayesian block bootstrap
Block bootstrap has been introduced in the literature for resampling dependent data, i.e. stationary processes. One of the main assumptions in block bootstrapping is that the blocks of observations are exchangeable, i.e. their joint distribution is immune to permutations. In this paper we propose a new Bayesian approach to block bootstrapping, starting from the construction of exchangeable blocks. Our sampling mechanism is based on a particular class of reinforced urn processe
GENERALIZED EXTREME SHOCK MODELS WITH A POSSIBLY INCREASING THRESHOLD
We propose a generalized extreme shock model with a possibly increasing failure threshold. Although standard models assume that the crucial threshold for the system might only decrease over time, because of weakening shocks and obsolescence, we assume that, especially at the beginning of the system's life, some strengthening shocks might increase the system tolerance to large shock. This is, for example, the case of turbines' running-in in the field of engineering. On the basis of parametric assumptions, we provide theoretical results and derive some exact and asymptotic univariate and multivariate distributions for the model. In the last part of the article we show how to link this new model to some nonparametric approaches proposed in the literatur
AN URN MODEL FOR CASCADING FAILURES ON A LATTICE
A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial network
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