Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Nov, 2020, Volume 88, Issue 6

On the Informativeness of Descriptive Statistics for Structural Estimates

https://doi.org/10.3982/ECTA16768
p. 2231-2258

Isaiah Andrews, Matthew Gentzkow, Jesse M. Shapiro

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 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 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.


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