On the Informativeness of Descriptive Statistics for Structural Estimates - Andrews, Isaiah; Gentzkow, Matthew; Shapiro, Jesse M. (Econometrica, 2020)
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 exactly or asymptotically unbiased under some base model. The researcher also reports descriptive statistics<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mover accent="true"><a:mi>γ</a:mi><a:mo>ˆ</a:mo></a:mover></a:math>that estimate features γ of the distribution of the data that are related to c under the base model. A reader entertains a less restrictive model that is local to the base model, under which the estimate ĉ may be biased. We study the reduction in worst‐case bias from a restriction that requires the reader's model to respect the relationship between c and γ specified by the base model. Our main result shows that the proportional reduction in worst‐case bias depends only on a quantity we call the informativeness of<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mover accent="true"><d:mi>γ</d:mi><d:mo>ˆ</d:mo></d:mover></d:math>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.