On the Informativeness of Descriptive Statistics for Structural Estimates
Researchers often present treatment-control differences or other descriptive statistics alongside structural estimates that answer policy or counterfactual questions of interest. We ask to what extent confidence in the researcher's interpretation of the former should increase a reader's confidence in the latter. We consider a structural estimate ĉ that may depend on a vector of descriptive statistics ̂γ. We define a class of misspecified models in a neighborhood of the assumed model. We then compare the bounds on the bias of ĉ due to misspecification across all models in this class with the bounds across the subset of these models in which misspecification does not affect ̂γ. Our main result shows that the ratio of the lengths of these tight bounds depends only on a quantity we call the informativeness of ̂γ for ĉ, which can be easily estimated even for complex models. We recommend that researchers report the estimated informativeness of descriptive statistics. We illustrate with applications to three recent papers.
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Document Object Identifier (DOI): 10.3386/w25217