This study proposes $p$-th Tobit quantile regression models with endogenousvariables. In the first stage regression of the endogenous variable on theexogenous variables, the assumption that the $\alpha$-th quantile of the errorterm is zero is introduced. Then, the residual of this regression model isincluded in the $p$-th quantile regression model in such a way that the $p$-thconditional quantile of the new error term is zero. The error distribution ofthe first stage regression is modelled around the zero $\alpha$-th quantileassumption by using parametric and semiparametric approaches. Since the valueof $\alpha$ is a priori unknown, it is treated as an additional parameter andis estimated from the data. The proposed models are then demonstrated by usingsimulated data and real data on the labour supply of married women.
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机译：这项研究提出了具有内生变量的第$ p $个Tobit分位数回归模型。在内生变量对外生变量的第一阶段回归中，引入了误差项的第\ alpha $分位数为零的假设。然后，该回归模型的残差以新误差项的$ p $个条件分位数为零的方式包含在第$ p $个分位数回归模型中。通过使用参数和半参数方法，围绕第零个\ alpha $假设假设对第一阶段回归的误差分布进行建模。由于$ \ alpha $的值是先验未知的，因此将其视为附加参数并根据数据进行估算。然后通过使用已婚妇女劳动力供应的模拟数据和真实数据来证明所提议的模型。
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