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Estimating the COVID-19 Infection Rate: Anatomy of an Inference Problem


  • Charles F. Manski

    (Institute for Fiscal Studies and Northwestern University)

  • Francesca Molinari

    (Institute for Fiscal Studies and Cornell University)


As a consequence of missing data on tests for infection and imperfect accuracy of tests, reported rates of cumulative population infection by the SARS CoV-2 virus are lower than actual rates of infection. Hence, reported rates of severe illness conditional on infection are higher than actual rates. Understanding the time path of the COVID-19 pandemic has been hampered by the absence of bounds on infection rates that are credible and informative. This paper explains the logical problem of bounding these rates and reports illustrative findings, using data from Illinois, New York, and Italy. We combine the data with assumptions on the infection rate in the untested population and on the accuracy of the tests that appear credible in the current context. We find that the infection rate might be substantially higher than reported. We also find that the infection fatality rate in Illinois, New York, and Italy is substantially lower than reported.

Suggested Citation

  • Charles F. Manski & Francesca Molinari, 2020. "Estimating the COVID-19 Infection Rate: Anatomy of an Inference Problem," CeMMAP working papers CWP20/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:20/20

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    References listed on IDEAS

    1. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    2. Charles F. Manski & John V. Pepper, 2018. "How Do Right-to-Carry Laws Affect Crime Rates? Coping with Ambiguity Using Bounded-Variation Assumptions," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 232-244, May.
    3. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751,
    4. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    5. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    6. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access
    • I19 - Health, Education, and Welfare - - Health - - - Other

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