Many economic and econometric applications require the integration of functions lacking a closed form antiderivative, which is therefore a task that can only be solved by numerical methods. We propose a new family of probability densities that can be used as substitutes and have the property of closed form integrability. This is especially advantageous in cases where either the complexity of a problem makes numerical function evaluations very costly, or fast information extraction is required for time-varying environments. Our approach allows generally for nonparametric maximum likelihood density estimation and may thus find a variety of applications, two of which are illustrated briefly:

Estimation of Value at Risk based on approximations to the density of stock returns.

Recovering risk neutral densities for the valuation of options from the option price - strike price relation

We propose a new family of density function that posses both flexibility and closed form expressions for moments and anti-derivatives, making them particularly appealing for applications. We illustrate its usefulness by applying our new family to obtain density forecasts of U.S. inflation. Our methods generate forecasts that improve on standard methods based on AR-ARCH models relying on normal or Student's t-distributional assumptions.

This paper explains the divergent behavior of European and US unemployment rates using a job market model of the labor market with an interaction between shocks and institutions. It shows that a reduction in TFP growth rates, an increase in real interest rates, and an increase in tax rates leads to a permanent increase in unemployment rates when the replacement rates or initial tax rates are high, while no increase in unemployment occurs when institutions are "employment friendly." The paper also shows that an increase in turbulence, modelled as an increased probability of skill loss, is not a robust explanation for the European unemployment puzzle in the context of a matching model with both endogenous job creation and job destruction.

In this paper we propose a subsampling estimator for the distribution of statistics diverging at either known or unknown rates when the underlying time series is strictly stationary and strong mixing. Based on our results we provide a detailed discussion how to estimate extreme order statistics with dependent data and present two applications to assessing financial market risk. Our method performs well in estimating Value at Risk and provides a superior alternative to Hill's estimator in operationalizing Safety First portfolio selection.