An Information-Theoretic Approach to Partially Identified Problems

An information-theoretic maximum entropy (ME) model provides an alternative approach to finding solutions to partially identified models. In these models, we can identify only a solution set rather than point-identifying the parameters of interest, given our limited information. Manski (2021) and others propose using statistical decision functions in general, and the minimax-regret (MMR) criterion in particular, to select a unique solution. Using Manski’s simulations for a missing data and a treatment problem, including an empirical example, we show that ME performs as well as or better than MMR. In additional simulations, ME dominates various other statistical decision functions. ME has an axiomatic underpinning and is computationally efficient.