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On the Informativeness of Descriptive Statistics for Structural Estimates

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  • Isaiah Andrews
  • Matthew Gentzkow
  • Jesse M. Shapiro

Abstract

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 γ̂ 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 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.

Suggested Citation

  • Isaiah Andrews & Matthew Gentzkow & Jesse M. Shapiro, 2018. "On the Informativeness of Descriptive Statistics for Structural Estimates," NBER Working Papers 25217, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:25217
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    Cited by:

    1. Timothy B. Armstrong & Michal Kolesár, 2021. "Sensitivity analysis using approximate moment condition models," Quantitative Economics, Econometric Society, vol. 12(1), pages 77-108, January.
    2. Philipp Eisenhauer & Lena Janys & Christopher Walsh & Janós Gabler, 2023. "Structural Models for Policy-Making," CRC TR 224 Discussion Paper Series crctr224_2023_484, University of Bonn and University of Mannheim, Germany.
    3. Stéphane Bonhomme & Martin Weidner, 2018. "Minimizing sensitivity to model misspecification," CeMMAP working papers CWP59/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Maximilian Blesch & Philipp Eisenhauer, 2021. "Robust decision-making under risk and ambiguity," Papers 2104.12573, arXiv.org, revised Oct 2021.
    5. Stéphane Bonhomme & Martin Weidner, 2020. "Minimizing Sensitivity to Model Misspecification," CeMMAP working papers CWP37/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. St'ephane Bonhomme & Martin Weidner, 2019. "Posterior Average Effects," Papers 1906.06360, arXiv.org, revised Sep 2021.
    7. Nathan Canen & Kyungchul Song, 2021. "Counterfactual analysis under partial identification using locally robust refinement," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(4), pages 416-436, June.
    8. Stéphane Bonhomme & Martin Weidner, 2022. "Minimizing sensitivity to model misspecification," Quantitative Economics, Econometric Society, vol. 13(3), pages 907-954, July.
    9. Raffaella Giacomini & Toru Kitagawa & Matthew Read, 2021. "Robust Bayesian Analysis for Econometrics," Working Paper Series WP-2021-11, Federal Reserve Bank of Chicago.
    10. Maximilian Blesch & Philipp Eisenhauer, 2023. "Robust Decision-Making under Risk and Ambiguity," Rationality and Competition Discussion Paper Series 463, CRC TRR 190 Rationality and Competition.
    11. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    12. Chen, Xiaohong & Hansen, Lars Peter & Hansen, Peter G., 2024. "Robust inference for moment condition models without rational expectations," Journal of Econometrics, Elsevier, vol. 243(1).
    13. Philipp Eisenhauer & Janos Gabler & Lena Janys, 2021. "Structural Models for Policy-Making: Coping with Parametric Uncertainty," ECONtribute Discussion Papers Series 082, University of Bonn and University of Cologne, Germany.
    14. Eisenhauer, Philipp & Gabler, Janos & Janys, Lena, 2021. "Structural Models for Policy-Making: Coping with Parametric Uncertainty," IZA Discussion Papers 14317, Institute of Labor Economics (IZA).
    15. Jens Klooster & Mikhail Zhelonkin, 2024. "Outlier robust inference in the instrumental variable model with applications to causal effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 86-106, January.
    16. Philipp Eisenhauer & Jano's Gabler & Lena Janys & Christopher Walsh, 2021. "Structural models for policy-making: Coping with parametric uncertainty," Papers 2103.01115, arXiv.org, revised Jun 2022.
    17. Walter Beckert & Daniel Kaliski, 2019. "Honest inference for discrete outcomes," CeMMAP working papers CWP67/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Maximilian Blesch & Philipp Eisenhauer, 2021. "Robust Decision-Making Under Risk and Ambiguity," ECONtribute Discussion Papers Series 104, University of Bonn and University of Cologne, Germany.
    19. Timothy Christensen & Benjamin Connault, 2023. "Counterfactual Sensitivity and Robustness," Econometrica, Econometric Society, vol. 91(1), pages 263-298, January.
    20. Andres Santos, 2020. "A Comment on: “On the Informativeness of Descriptive Statistics for Structural Estimates” by Isaiah Andrews, Matthew Gentzkow, and Jesse M. Shapiro," Econometrica, Econometric Society, vol. 88(6), pages 2271-2276, November.

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    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private
    • I25 - Health, Education, and Welfare - - Education - - - Education and Economic Development

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