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

分数响应变量是取值在[0,1]区间内的变量。分数响应变量的一个具体例子是出口在总销售额中的份额。然而，不仅字面意义上的真分数将被视为分数响应变量，而且其他自然限于[0,1]区间的变量也将被视为分数响应变量，例如，某一事件（如失业）发生的感知概率。分数响应变量在应用经济学研究中经常作为因变量出现。对于这些变量的计量分析，分数logit和probit模型已经被提出并应用。这个项目有四个目标。首先，建立分数阶响应变量的样本选择模型。非随机样本选择性经常出现在实证研究中，当样本选择性没有得到适当考虑时，会导致对感兴趣的参数的估计有偏差和不一致。由于目前尚未建立分数响应变量的样本选择模型，本项目将填补这一空白。第二个目标是将样本选择模型应用于相关的经济问题，以显示在实证实践中应用所提出的模型的收益。第三个目标是建立一个多元分数响应模型。大多数涉及分数级响应变量的模型都是单变量模型，因为它们只考虑单个分数级响应变量。本项目旨在将这些单变量模型扩展到多变量设置，即考虑多个分数响应变量。使用多变量模型的主要原因是可以通过联合建模方法实现效率提升，即通过使用多变量估计方法可以减少估计的标准误差。第四个也是最后一个目标是将多元分数响应模型应用于相关的经济问题，再次展示该模型在实证实践中的应用所带来的收益。

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.