The outcome in a randomized experiment is sometimes nonnegative with a clump of observations at zero and continuously distributed positive values. One widely used model for a nonnegative outcome with a clump at zero is the Tobit model, which assumes that the treatment has a shift effect on the distribution of a normally distributed latent variable and the observed outcome is the maximum of the latent variable and zero. We develop a class of semiparametric models and inference procedures that extend the Tobit model in two useful directions. First, we consider more flexible models for the treatment effect than the shift effect of the Tobit model; for example, our models allow for the treatment to have a larger in magnitude effect for upper quantiles. Second, we make semiparametric inferences using empirical likelihood that allow the underlying latent variable to have any distribution, unlike the original Tobit model that assumes the latent variable is normally distributed. We apply our approach to data from the RAND Health Insurance Experiment. We also extend our approach to observational studies in which treatment assignment is strongly ignorable.

中文翻译：

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当结块为零且结果为非负时，半参数模型和治疗效果的推断

随机实验的结果有时是非负的，观察结果为零且连续分布正值。一种广泛使用的非负结果模型是 Tobit 模型，该模型假设治疗对正态分布的潜在变量的分布有偏移效应，并且观察到的结果是潜在变量和零的最大值。我们开发了一类半参数模型和推理程序，它们在两个有用的方向上扩展了 Tobit 模型。首先，我们考虑比 Tobit 模型的转移效应更灵活的治疗效果模型；例如，我们的模型允许治疗对上分位数产生更大的影响。第二，我们使用允许潜在潜在变量具有任何分布的经验似然性进行半参数推断，这与假设潜在变量呈正态分布的原始 Tobit 模型不同。我们将我们的方法应用于兰德健康保险实验的数据。我们还将我们的方法扩展到观察性研究，在这些研究中，治疗分配是强烈可忽略的。