Partial Identification, Distributional Preferences, and the Welfare Ranking of Policies

Abstract We discuss the tension between “what we can get” (identification) and “what we want” (parameters of interest) in models of policy choice (treatment assignment). Our nonstandard empirical object of interest is the ranking of counterfactual policies. Partial identification of treatment effects maps into a partial welfare ranking of treatment assignment policies. We characterize the identified ranking and show how the identifiability of the ranking depends on identifying assumptions, the feasible policy set, and distributional preferences. An application to the project STAR experiment illustrates this dependence. This paper connects the literatures on partial identification, robust statistics, and choice under Knightian uncertainty.

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