Collaborative Research: Applications of Asymptotic Statistical Decision Theory in Econometrics

这个项目将使用渐近统计决策理论来开发新的程序和最优性结果的两个领域目前感兴趣的计量经济学：估计和推断部分确定的参数;和最佳治疗分配规则。部分识别模型最近在经济学中受到了相当大的关注。在部分识别的统计经济模型中，即使使用理想化的数据集，也不是所有感兴趣的量都可以完全恢复，但是可以获得感兴趣的量的界限。虽然这些模型可以通过放松辅助假设来增加实证分析的稳健性，但从统计学的角度来看，它们是非标准的。通过使用渐近统计决策理论的工具来分析这些模型，我们可以得到对统计过程性质的严格限制，简单地比较备选过程，并得到最优性结果。本研究的结果将为经济学家进行边界分析提供新的工具和选择最佳工具的方法。该项目的第二个组成部分将发展治疗和政策分析的决策理论方法。在这一部分中，PI考虑最佳治疗分配问题。在社会和医学科学中，治疗评估的一个主要目标是为如何分配个人治疗提供指导。例如，一些研究已经研究了对个人进行分析以确定那些可能从社会计划中受益的人的问题。这些实证研究通常侧重于估计或推断治疗效果的大小。本研究采用决策理论方法，将数据的统计分析与正式的政策决策联系起来。在最近的工作中，PI已经展示了如何使用这种方法在广泛的二元静态情况下开发治疗分配的最佳程序。在他们研究计划的下一阶段，PI将把我们的分析扩展到一些具有实际意义的情况：多值或连续治疗的设置;以及动态治疗分配问题，其中可以根据中间结果顺序做出决策。更广泛的影响：具有部分识别的模型出现在整个社会和生命科学中。这项研究将为其他社会科学、调查分析、生物统计和其他领域的研究人员提供估计和推断工具。治疗分配问题和相关的动态规划问题也有广泛的应用。这项研究将为医学、生物统计学和许多其他领域的研究人员提供程序，以便根据过去的数据最佳地提出治疗和政策建议。

This project will use asymptotic statistical decision theory to develop new procedures and optimality results for two areas of current interest in econometrics: estimation and inference for partially identified parameters; and optimal treatment assignment rules. Partially identified models have received considerable recent attention in economics. In partially identified statistical economic models, not all quantities of interest can be perfectly recovered even with an idealized data set, but one can obtain bounds on the quantities of interest. Although such models can increase the robustness of empirical analysis by relaxing auxiliary assumptions, they are nonstandard from a statistical viewpoint. By using tools from asymptotic statistical decision theory to analyze these models, we can obtain sharp restrictions on the properties of statistical procedures, compare alternative procedures simply, and obtain optimality results. The results of this research will provide economists with new tools, and methods for selecting the best tools, for conducting bounds analyses. The second component of this project will develop decision-theoretic approaches to treatment and policy analysis. In this component, the PIs consider optimal treatment assignment problems. A major goal of treatment evaluation in the social and medical sciences is to provide guidance on how to assign individuals to treatments. For example, a number of studies have examined the problem of profiling individuals to identify those likely to benefit from a social program. These empirical studies typically focus on estimation, or inference on the size of the treatment effect. This research takes a decision-theoretic approach, which connects the statistical analysis of the data to a formal policy decision. In recent work, the PIs have shown how such an approach can be used to develop optimal procedures for treatment assignment in a wide range of binary, static cases. In the next phase of their research program, the PIs will broaden our analysis to a number of situations of practical relevance: settings with multi-valued or continuous treatments; and dynamic treatment assignment problems, where decisions can be made sequentially in response to intermediate outcomes. Broader Impact: Models with partial identification arise throughout the social and life sciences. This research will provide estimation and inference tools for researchers in other social sciences, survey analysis, biostatistics, and other fields. Treatment assignment problems and related dynamic programming problems also have broad application. The research will provide researchers in medicine, biostatistics, and many other fields with procedures to make treatment and policy recommendations optimally in light of past data.