CAREER: Identification as Optimization

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Using data to answer questions in economics requires maintaining assumptions with stronger assumptions leading to stronger conclusions. However, stronger assumptions are also more likely to lead to wrong conclusions. Researchers therefore need methods that bridge these tensions; methods not currently available. This research project will develop new methods that can be used to provide better control on the tradeoff between the strength of assumptions and correct conclusions. The results of the research project will provide researchers with tools to improve empirical economic research and therefore provide policy makers with more accurate policy inputs. The research project therefore advances national economic prosperity by providing better and more reliable tools for evidence-based economic policy analysis in many areas such as antitrust enforcement. The research project also provides pedagogical advances that better integrate economics into a broader STEM education on data science, computer science, and applied mathematics. The results of this project will also establish the U.S. as the global leader in developing better tools for economic analyses.Identification is a critical concept in empirical economics and many other fields. It exhibits an inherent tradeoff: Stronger conclusions require stronger assumptions, but stronger assumptions may lead to wrong conclusions. Empirical researchers differ in their preferences for resolving this tradeoff. The goal of the proposed research is to widen the choice of available methodology in a way that gives researchers more flexibility in exploring the assumptions-conclusions frontier. The proposed research will achieve this goal by casting the identification problem as an optimization problem. This transforms the abstract question of identification into the concrete mathematical operation of maximizing a function subject to constraints. This enables the application of computational and theoretical tools from applied mathematics and operations research. The proposed research will apply this identification-as-optimizations link to three different empirical problems: (1) nonparametric discrete choice modeling; (2) sensitivity analysis in dynamic programming models; and (3) extrapolation in instrumental variable and regression discontinuity designs. The results of this research project will provide enhanced method for empirical research, hence better inputs into economic policy making.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.