On the Informativeness of Descriptive Statistics for Structural Estimates

We propose a way to formalize the relationship between descriptive analysis and structural estimation. A researcher reports an estimate ĉ of a structural quantity of interest c that is valid under some models. The researcher also reports descriptive statistics γ̂ that estimate features γ of the distribution of the data, and highlights the economic relationship between γ and c under the model. We compare the bound on the absolute bias of ĉ across all models in a local neighborhood of the assumed model with the bound across a subset of these models under which the assumed relationship between γ and c is correct. Our main result shows that the ratio of these tight bounds depends only on a quantity we call the informativeness of γ̂ for ĉ. Informativeness can be easily estimated even for complex models. We recommend that researchers report estimated informativeness alongside their descriptive analyses, and we illustrate with applications to three recent papers