Dummy Endogenous Variables in Threshold Crossing Models, with Applications to Health Economics

阈值交叉模型是分析微观经济学、医学和其他领域中的二进制数据的标准框架。例如，分析师经常通过想象潜在的健康状况低于某个门槛来对死亡率进行建模。当其中一个回归变量是一个虚拟的内生变量时，就会出现一个常见的问题，例如对健康状况最差的人进行的医疗程序。恢复内生变量平均效应的标准方法要么取决于参数分布假设的有效性，要么要求工具具有很强的性质。工具变量分析可以恢复“局部平均处理效应”，但不能恢复平均效应。PIS建议开发一种新的非参数方法，用于在有工具的阈值跨越模型中评估虚拟内生变量的平均效应。使用这种方法的早期版本，PI构建了明确的界限。当所有的回归变量都是离散的时，PI已经开发出以给定的指定概率渐进地包含边界中的每个点的置信度集。PI将扩展他们的推理程序，包括允许连续回归，并考虑渐近包含具有所需概率的整个识别集的置信度集。PI将开发其他类别的阈值交叉模型和有限因变量模型的界限，而不是二元选择模型，例如有序选择模型。PI将扩展他们的分析，以考虑离散时间动态结果模型中的虚拟内生回归变量。该分析应用于一个重要的医学问题。放置Swan-Ganz导尿管是一种非常常见的手术，北美每年有200多万患者接受导尿。医生们争论，接受Swan-Ganz导尿术的患者中观察到的更高的死亡率是否可以归因于导尿术本身，还是由于导尿术患者的健康状况没有观察到的恶化。在初步分析中，PI考虑了Swan-Ganz导尿术对后期死亡率的影响。拟议的理论工作将允许PI应用统计推断程序来解释这种情况下结果变量的动态性质。该项目具有广泛的智力意义，因为它提出了关于非参数、不可分离模型中的内生变量的理论文献。以前的方法需要连续的内生回归变量，连续的结果变量，或者特别强烈的统计识别要求。这项研究引入了一种新的方法，而不需要这些对象中的任何一个，而这些对象在经验环境中往往是不可用的。这个研究项目也将在理论计量经济学之外产生更广泛的影响。建议的经验性项目本身就很重要，结果将为医生提供关于棘手的患者护理决策的指导。二元内生变量对有限因变量的影响分析是经验经济学、社会学、政治学、医学等领域的一个普遍问题，因此理论工作具有广泛的适用性。

Threshold crossing models are a standard framework for analyzing binary data in microeconomics, medicine, and elsewhere. For example, analysts often model mortality by imagining latent health status falling below a threshold. A common problem arises when one of the regressors is a dummy endogenous variable, such as a medical procedure that is performed on individuals with the worst unobserved health. Standard methodologies for recovering the average effect of the endogenous variable either depend on the validity of parametric distributional assumptions or require strong properties on an instrument. Instrumental variables analysis recovers the 'Local Average Treatment Effect' but not the average effect.The PIs propose developing a new non-parametric methodology for evaluating the average effect of a dummy endogenous variable in a threshold crossing model where there is an instrument. Using an early version of this methodology, the PI's have constructed sharp bounds. When all regressors are discrete, the PI's have developed confidence sets that asymptotically contain each point in the bounds with a given specified probability. The PI's will extend their procedures for inference, including to allow for continuous regressors and to consider confidence sets that asymptotically contain the entire identified set with the desired probability. The PI's will develop bounds for other classes of threshold crossing models and limited dependent variable models beyond binary choice models, for example, ordered choice models. The PI's will extend their analysis to consider dummy endogenous regressors in discrete-time, dynamic outcome models.The analysis is applied to an important medical problem. The placement of Swan-Ganz catheters is an extremely common procedure with over 2 million patients in North America catheterized each year. Doctors debate whether the greater observed mortality of patients receiving Swan-Ganz catheterization can be attributed to catheterization itself, or are due to the unobserved worse health of catheterized patients. In preliminary analysis, the PI's have considered the effect of Swan-Ganz catheterization on later mortality. The proposed theoretical work will allow the PI's to apply statistical inference procedures to account for the dynamic nature of the outcome variable to this situation.The project is of broad intellectual significance because it advances the theoretical literature on endogenous variables in nonparametric, nonseparable models. Previous approaches require a continuous endogenous regressor, a continuous outcome variable, or particularly strong statistical identification requirements. The research introduces a new approach without the need for any of these objects, which are often not available in empirical settings.This research program will also have broader impacts outside of theoretical econometrics. The empirical project proposed is important in its own right, and the results will provide doctors with guidance on thorny patient care decisions. The analysis of the effect of binary endogenous variables on limited dependent variables is a common problem in empirical economics, sociology, political science, and medicine; hence, the theoretical work will have wide applicablity.