Econometric Models for Fractional Response Variables in the Presence of Sample Selectivity and Multiple Dependent Variables

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Fractional response variables are variables taking values in the [0,1]-interval. A specific example of a fractional response variable is the share of exports in total sales. However, not only true fractions in the literal sense will be considered as fractional response variables, but also other variables which are naturally restricted to the [0,1]-interval, e.g., the perceived probability that a certain event (like job loss) occurs. Fractional response variables appear quite often as dependent variables in applied economic research. For the econometric analysis of such variables, fractional logit and probit models have been proposed and applied. This project has four objectives. First, a sample selection model for fractional response variables shall be developed. Non-random sample selectivity often occurs in empirical research and leads to biased and inconsistent estimates of the parameters of interest when sample selectivity is not properly taken into account. Since a sample selection model has not been developed so far for fractional response variables, this gap shall be filled with this project. The second objective is to apply the sample selection model to relevant economic problems, in order to show the gains from an application of the proposed model in empirical practice. The third objective is to develop a multivariate fractional response model. Most models involving fractional response variables are univariate models in the sense that they consider a single fractional response variable only. This project aims at extending these univariate models to multivariate settings, i.e., to consider multiple fractional response variables. The main reason for using multivariate models is that efficiency gains can be realized from a joint modeling approach, i.e., estimated standard errors can be reduced by using a multivariate estimation approach. The fourth and final objective is to apply the multivariate fractional response model to relevant economic problems, again in order to show the gains from an application of this model in empirical practice.