Collaborative Research: Applications of Asymptotic Statistical Decision Theory in Econometrics

该项目将使用渐近统计决策理论为计量经济学中当前感兴趣的两个领域开发新的程序和最优结果：部分识别参数的估计和推断；以及最优处理分配规则。部分确定的模型最近在经济学中受到了相当大的关注。在部分确定的统计经济模型中，即使使用理想化的数据集，也不是所有的利息量都可以完全恢复，但人们可以获得利息量的界限。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。利用渐近统计决策理论的工具对这些模型进行分析，我们可以得到统计过程性质的尖锐限制，简单地比较备选过程，并得到最优性结果。这项研究的结果将为经济学家提供新的工具，以及选择最佳工具进行边界分析的方法。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。在此组件中，pi考虑最优处理分配问题。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体治疗提供指导。例如，许多研究都研究了分析个人的问题，以确定那些可能从社会项目中受益的人。这些实证研究通常侧重于对治疗效果大小的估计或推断。本研究采用决策理论的方法，将数据的统计分析与正式的政策决定联系起来。在最近的工作中，pi已经展示了如何使用这种方法在大范围的二进制静态病例中开发最佳的治疗分配程序。在他们的研究计划的下一阶段，pi将把我们的分析扩展到一些实际相关的情况：多值或连续治疗的设置；以及动态处理分配问题，其中决策可以根据中间结果依次做出。更广泛的影响：具有部分识别的模型在整个社会科学和生命科学中出现。该研究将为其他社会科学、调查分析、生物统计学等领域的研究人员提供估计和推理工具。处理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做出最佳的治疗和政策建议。

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.