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The Methuselah Effect: The Pernicious Impact of Unreported Deaths on Old-Age Mortality Estimates

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Demography

Abstract

We examine inferences about old-age mortality that arise when researchers use survey data matched to death records. We show that even small rates of failure to match respondents can lead to substantial bias in the measurement of mortality rates at older ages. This type of measurement error is consequential for three strands in the demographic literature: (1) the deceleration in mortality rates at old ages; (2) the black-white mortality crossover; and (3) the relatively low rate of old-age mortality among Hispanics, often called the “Hispanic paradox.” Using the National Longitudinal Survey of Older Men matched to death records in both the U.S. Vital Statistics system and the Social Security Death Index, we demonstrate that even small rates of missing mortality matching plausibly lead to an appearance of mortality deceleration when none exists and can generate a spurious black-white mortality crossover. We confirm these findings using data from the National Health Interview Survey matched to the U.S. Vital Statistics system, a data set known as the “gold standard” (Cowper et al. 2002) for estimating age-specific mortality. Moreover, with these data, we show that the Hispanic paradox is also plausibly explained by a similar undercount.

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Notes

  1. This law was first quantified in 1939, when Greenwood and Irwin (1939) found that the one-year probability of death at advanced age asymptotically approaches a limit of 0.44 for women and 0.54 for men. Such a law suggests that there may be no fixed upper limit to human longevity and thus no fixed maximal human lifespan (Gavrilov and Gavrilova 2006; Thatcher et al. 1998).

  2. One could imagine an error process operating predominantly in the other direction, if deaths are recorded that do not occur. This could be called the “Twain effect” (per Mark Twain’s suggestion that “the report of my death was an exaggeration”). The Twain effect would cause underestimation of the denominator in subsequent years. Here again, consequent error would progressively worsen as the cohort ages. Later, we argue that this effect is not important in our application.

  3. Preston et al. (1998) showed that when age is recorded in single years earlier in life (instead of five-year intervals), this virtually eliminates biases in ASMRs from age misreporting.

  4. Yet another advantage of this approach is that longitudinal surveys often collect data on family and other contextual variables, which then allows researchers to assess relationships between early-life factors and subsequent mortality.

  5. Readers may wonder why the vital statistics match used data through 2008 whereas the SSA Death Index is through 2012. Although we informally refer to the Census Bureau as “matching on the respondent’s Social Security number (SSN),” this is true only in an indirect sense. The Census Bureau matches on a personal identification key (PIK), which is a number that has a one-to-one match with the respondent’s SSN, to protect the confidentiality of respondents. All files used for matching must, therefore, contain this unique PIK for matching, a process known as “being PIKed.” At the time of our match, the most recent PIKed file from vital statistics was through 2008, whereas the files from SSA were through 2012.

  6. For instance, in collecting data for the current NLS cohorts (the NLSY 1979 and NLSY 1997 cohorts), NORC requires interviewers’ proxies to provide either an obituary or a death certificate before recording a death.

  7. We also estimated the measurement model with the VS08 match, and it performed equally well with those data.

  8. Programs are available from the authors. Our procedure for limiting the measurement error to be between 0 and 1 entails the use of a logistic error model, specifying error to be α = e γ / (1 + e γ) and then allowing γ to differ for whites and blacks.

  9. Specifically, the extinct generation approach stipulates that all missing deaths are Methuselah error, while the ME model estimates the rate of Methuselah error.

  10. The number of person-years in our NHIS-NDI analysis is 119,007.

  11. Biological models that allow for mortality deceleration in drosophila and other nonprimates may be quite different than the human biology of aging. Older theories, such as those that posit limits to cell replication, should perhaps be reconsidered.

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Acknowledgments

We gratefully acknowledge support from the Eunice Kennedy Shriver National Institute of Child Health and Human Development (RO1 HD062747). We thank the editors, three anonymous reviewers, David Card, Amitabh Chandra, James Saxon, Douglas Staiger, Lydia Veliko, and seminar participants at UC Berkeley, Indiana University/Purdue University of Indianapolis, New York University, and Washington University for helpful comments. All errors are our own.

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Authors and Affiliations

  1. Harris School, University of Chicago, Chicago, IL, USA

    Dan A. Black & Yu-Chieh Hsu

  2. IZA, Bonn, Germany

    Dan A. Black & Lowell J. Taylor

  3. NORC, Chicago, IL, USA

    Dan A. Black, Yu-Chieh Hsu, Seth G. Sanders & Lowell J. Taylor

  4. Department of Economics and Sanford School, Duke University, Durham, NC, USA

    Seth G. Sanders

  5. Department of Mathmatics and Statistics, Swarthmore College, Swarthmore, PA, USA

    Lynne Steuerle Schofield

  6. Heinz School, Carnegie Mellon University, Pittsburgh, PA, USA

    Lowell J. Taylor

  7. National Bureau of Economic Research, Cambridge, MA, USA

    Lowell J. Taylor

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Correspondence to Dan A. Black.

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Black, D.A., Hsu, YC., Sanders, S.G. et al. The Methuselah Effect: The Pernicious Impact of Unreported Deaths on Old-Age Mortality Estimates. Demography 54, 2001–2024 (2017). https://doi.org/10.1007/s13524-017-0623-x

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