Collaborative Research: Applications of Asymptotic Statistical Decision Theory in Econometrics

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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.