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A Practical Method to Reduce Privacy Loss when Disclosing Statistics Based on Small Samples

Author

Listed:
  • Raj Chetty
  • John N. Friedman
Abstract
We develop a simple method to reduce privacy loss when disclosing statistics such as OLS regression estimates based on samples with small numbers of observations. We focus on the case where the dataset can be broken into many groups (“cells”) and one is interested in releasing statistics for one or more of these cells. Building on ideas from the differential privacy literature, we add noise to the statistic of interest in proportion to the statistic's maximum observed sensitivity, defined as the maximum change in the statistic from adding or removing a single observation across all the cells in the data. Intuitively, our approach permits the release of statistics in arbitrarily small samples by adding sufficient noise to the estimates to protect privacy. Although our method does not offer a formal privacy guarantee, it generally outperforms widely used methods of disclosure limitation such as count-based cell suppression both in terms of privacy loss and statistical bias. We illustrate how the method can be implemented by discussing how it was used to release estimates of social mobility by Census tract in the Opportunity Atlas. We also provide a step-by-step guide and illustrative Stata code to implement our approach.

Suggested Citation

  • Raj Chetty & John N. Friedman, 2019. "A Practical Method to Reduce Privacy Loss when Disclosing Statistics Based on Small Samples," NBER Working Papers 25626, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:25626
    Note: CH LS PE
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    References listed on IDEAS

    as
    1. Joshua D. Angrist & Parag A. Pathak & Christopher R. Walters, 2013. "Explaining Charter School Effectiveness," American Economic Journal: Applied Economics, American Economic Association, vol. 5(4), pages 1-27, October.
    2. John M. Abowd & Ian M. Schmutte, 2019. "An Economic Analysis of Privacy Protection and Statistical Accuracy as Social Choices," American Economic Review, American Economic Association, vol. 109(1), pages 171-202, January.
    3. John M. Abowd & Ian M. Schmutte, 2015. "Economic Analysis and Statistical Disclosure Limitation," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 50(1 (Spring), pages 221-293.
    4. John M. Abowd & Ian M. Schmutte, 2015. "Economic Analysis and Statistical Disclosure Limitation," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 46(1 (Spring), pages 221-293.
    5. J. Trent Alexander & Michael Davern & Betsey Stevenson, 2010. "Inaccurate age and sex data in the Census PUMS files: Evidence and Implications," NBER Working Papers 15703, National Bureau of Economic Research, Inc.
    6. Wasserman, Larry & Zhou, Shuheng, 2010. "A Statistical Framework for Differential Privacy," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 375-389.
    7. Raj Chetty & John N. Friedman & Nathaniel Hendren & Maggie R. Jones & Sonya R. Porter, 2018. "The Opportunity Atlas: Mapping the Childhood Roots of Social Mobility," Working Papers 18-42, Center for Economic Studies, U.S. Census Bureau.
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    Citations

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    Cited by:

    1. Vilhuber, Lars, 2023. "Reproducibility and transparency versus privacy and confidentiality: Reflections from a data editor," Journal of Econometrics, Elsevier, vol. 235(2), pages 2285-2294.
    2. Ron S. Jarmin & John M. Abowd & Robert Ashmead & Ryan Cumings-Menon & Nathan Goldschlag & Michael B. Hawes & Sallie Ann Keller & Daniel Kifer & Philip Leclerc & Jerome P. Reiter & Rolando A. Rodrígue, 2023. "An in-depth examination of requirements for disclosure risk assessment," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 120(43), pages 2220558120-, October.
    3. Michler, Jeffrey D. & Josephson, Anna & Kilic, Talip & Murray, Siobhan, 2022. "Privacy protection, measurement error, and the integration of remote sensing and socioeconomic survey data," Journal of Development Economics, Elsevier, vol. 158(C).
    4. Dionissi Aliprantis & Hal Martin, 2020. "Neighborhood Sorting Obscures Neighborhood Effects in the Opportunity Atlas," Working Papers 20-37, Federal Reserve Bank of Cleveland.
    5. Atheendar S Venkataramani & Rourke O’Brien & Gregory L Whitehorn & Alexander C Tsai, 2020. "Economic influences on population health in the United States: Toward policymaking driven by data and evidence," PLOS Medicine, Public Library of Science, vol. 17(9), pages 1-17, September.
    6. Ian M. Schmutte & Nathan Yoder, 2022. "Information Design for Differential Privacy," Papers 2202.05452, arXiv.org, revised Jul 2024.
    7. Craig Wesley Carpenter & Anders Van Sandt & Scott Loveridge, 2022. "Measurement error in US regional economic data," Journal of Regional Science, Wiley Blackwell, vol. 62(1), pages 57-80, January.
    8. Braathen, Christian & Thorsen, Inge & Ubøe, Jan, 2022. "Adjusting for Cell Suppression in Commuting Trip Data," Discussion Papers 2022/13, Norwegian School of Economics, Department of Business and Management Science.

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    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • H0 - Public Economics - - General

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