On the Informativeness of Descriptive Statistics for Structural Estimates

57 Pages Posted: 5 Nov 2018

See all articles by Isaiah Andrews

Isaiah Andrews

Harvard Society of Fellows

Matthew Gentzkow

Stanford University

Jesse M. Shapiro

Brown University; National Bureau of Economic Research (NBER)

Date Written: November 2018

Abstract

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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Suggested Citation

Andrews, Isaiah and Gentzkow, Matthew and Shapiro, Jesse M., On the Informativeness of Descriptive Statistics for Structural Estimates (November 2018). NBER Working Paper No. w25217. Available at SSRN: https://ssrn.com/abstract=3278517

Isaiah Andrews (Contact Author)

Harvard Society of Fellows ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Matthew Gentzkow

Stanford University ( email )

Jesse M. Shapiro

Brown University ( email )

64 Waterman Street
Providence, RI 02912
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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