Collaborative Research: Asymptotic Approximations for Sequential Decision Problems in Econometrics

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Economic and social data are often collected over time. The data collection method may sometimes be adjusted to respond to lessons learnt during the data collection in earlier periods. In these situations, researchers may need to estimate policy effects, test hypotheses, or adjust experimental designs dynamically as new data become available. The estimation method will need to adjust as the data changes. There are currently no efficient methods for drawing inference from data collected in such sequential manner. This project will develop new and innovative methods for analyzing such sequential statistical problems. The project will devise methods that are easy to solve mathematically and allow researchers to properly evaluate dynamically collected data and maximize the efficiency with which the data is used to draw policy conclusions. These methods will be useful in several areas of economics, biostatistics, medicine, and other social sciences. The results of this research will improve methods of policy evaluation, hence improve the functioning of the US economy and governance.This project will develop new methods for analyzing statistical decision problem in dynamic settings. We will extend the limits of experiments framework to incorporate the informational structure in various forms of sequential data collection. The first part of the research will focus on sequential settings where the information available to the analyst is fixed or set exogenously to the collected data. The second part of the project will include settings where sequential collection of data evolves dynamically to reflect information gained from earlier portions of the data. For each of these settings, two key research outputs will be: (i) new information-adapted asymptotic representation theorems; and (ii) a new asymptotic optimality framework and findings. The results of this research will improve methods of policy evaluation, hence improve the functioning of the US economy and governance.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.