How to Decide: An Information-Theoretic Approach to Partially Identified Complex Problems
Amos Golan, American University, SFIPractically all modeling and inference problems entail a vexing problem: the available information is usually too complex and insufficient to ensure a unique solution. An information-theoretic (IT) model provides an alternative approach to finding solutions to partially identified (underdetermined) problems. In such models, we can identify only a solution set rather than point-identifying the parameters of interest, given our limited information. This solution set is usually an interval. Based on this incomplete information, how should one make a prediction, choose a treatment, or make other decisions to maximize welfare? The choice depends on whether the criterion is Bayesian, maximizing the minimum welfare (maximin), minimizing the maximum risk (Wald, 1944), information-theoretical, or other. A paper by Manski (2021) discusses the first three of these approaches, focusing on a statistical decision theory approach that minimizes the maximum risk or regret (minimax regret, or MMR). In this talk I will discuss an information-theoretical approach as an alternative. I compare it to other commonly used approaches. Using Manski s simulations for a missing data and a treatment problem in the social sciences, including an empirical example, I will show that the IT performs the same or better than MMR. In additional simulations, IT dominates various other statistical decision functions. IT has an axiomatic underpinning and is computationally efficient. (This talk is based on joint work with Jeffrey Perloff,)
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