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Estimating COVID-19 prevalence in the United States: A sample selection model approach

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  • David Benatia

    (CREST–ENSAE)

  • Raphael Godefroy

    (Université de Montréal)

  • Joshua Lewis

    (Université de Montréal)

Abstract

Background: Public health efforts to determine population infection rates from coronavirus disease 2019 (COVID-19) have been hampered by limitations in testing capabilities and the large shares of mild and asymptomatic cases. We developed a methodology that corrects observed positive test rates for non-random sampling to estimate population infection rates across U.S. states from March 31 to April 7. Methods: We adapted a sample selection model that corrects for non-random testing to estimate population infection rates. The methodology compares how the observed positive case rate vary with changes in the size of the tested population, and applies this gradient to infer total population infection rates. Model identification requires that variation in testing rates be uncorrelated with changes in underlying disease prevalence. To this end, we relied on data on day-to-day changes in completed tests across U.S. states for the period March 31 to April 7, which were primarily influenced by immediate supply-side constraints. We used this methodology to construct predicted infection rates across each state over the sample period. We also assessed the sensitivity of the results to controls for state-specific daily trends in infection rates. Results: The median population infection rate over the period March 31 to April 7 was 0.9% (IQR 0.64 1.77). The three states with the highest prevalence over the sample period were New York (8.5%), New Jersey (7.6%), and Louisiana (6.7%). Estimates from models that control for state-specific daily trends in infection rates were virtually identical to the baseline findings. The estimates imply a nationwide average of 12 population infections per diagnosed case. We found a negative bivariate relationship (corr. = -0.51) between total per capita state testing and the ratio of population infections per diagnosed case. Interpretation: The effectiveness of the public health response to the coronavirus pandemic will depend on timely information
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • David Benatia & Raphael Godefroy & Joshua Lewis, 2020. "Estimating COVID-19 prevalence in the United States: A sample selection model approach," Cahiers de recherche 2020-04, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:2020-04
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    File URL: http://hdl.handle.net/1866/23364
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    References listed on IDEAS

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    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    2. Clay, Karen & Lewis, Joshua & Severnini, Edson, 2018. "Pollution, Infectious Disease, and Mortality: Evidence from the 1918 Spanish Influenza Pandemic," The Journal of Economic History, Cambridge University Press, vol. 78(4), pages 1179-1209, December.
    3. Clay, Karen & Lewis, Joshua & Severnini, Edson, 2019. "What explains cross-city variation in mortality during the 1918 influenza pandemic? Evidence from 438 U.S. cities," Economics & Human Biology, Elsevier, vol. 35(C), pages 42-50.
    4. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    5. Heckman, James J. & Lalonde, Robert J. & Smith, Jeffrey A., 1999. "The economics and econometrics of active labor market programs," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 31, pages 1865-2097, Elsevier.
    6. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 33-58.
    7. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
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    1. > Economics of Welfare > Health Economics > Economics of Pandemics > Specific pandemics > Covid-19 > Modelling > Statistical Modelling

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    1. Huan Wang & Sarah‐Eve Dill & Huan Zhou & Yue Ma & Hao Xue & Sean Sylvia & Kumi Smith & Matthew Boswell & Alexis Medina & Prashant Loyalka & Cody Abby & Dimitris Friesen & Nathan Rose & Yian Guo & Scot, 2021. "Health, economic, and social implications of COVID‐19 for China's rural population," Agricultural Economics, International Association of Agricultural Economists, vol. 52(3), pages 495-504, May.

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