Bayesian analysis of extreme events with threshold estimation

The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.

Optimal auction with a general distribution: virtual valuation without densities

We characterize the optimal auction in an independent private values framework for a completely general distribution of valuations. We do this introducing a new concept: the generalized virtual valuation. To show the wider applicability of this concept we present two examples showing how to extend the classical models of Mussa and Rosen and Baron and Myerson for arbitrary distributions

Growth,distribution and school policy

This paper investigates the relationship between growth, income inequality, and educational policies. An endogenous growth model is built in which there are two types of labor, skilled and unskilled, and the quality of the labor force (measured by the fraction of skilled workers) will ultimately determine the economic growth rate. We show that multi pIe inequality and growth paths may arise. Countries will not necessarily converge to the same economic growth and income distribution. When the proportion of skilled workers is low, the economy grows slow, and the Gini coeflicient is high. Low expected growth rate inhibits investments in human capital and the quality of the labor force tomorrow turns out to be low again, keeping the economy in the bad equilibrium. We then analyze the effects on growth and inequality of two types of government intervention: introduction of public schools and vouchers. Both types can induce the economic agents to invest more in education. The consequence will be an increase in the quality of the labor force, leading to higher growth rates and less inequality. Finally, we examine the welfare consequences of these interventions and conclude that they may be Pareto improving.