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Population Pyramids Yield Accurate Estimates of Total Fertility Rates

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Demography

Abstract

The primary fertility index for a population, the total fertility rate (TFR), cannot be calculated for many areas and periods because it requires disaggregation of births by mother’s age. Here we discuss a flexible framework for estimating TFR using inputs as minimal as a population pyramid. We develop five variants, each with increasing complexity and data requirements. We test accuracy across a diverse set of data sources that comprise more than 2,400 fertility schedules with known TFR values, including the Human Fertility Database, Demographic and Health Surveys, U.S. counties, and nonhuman species. We show that even the simplest and least accurate variant has a median error of only 0.09 births per woman over 2,400 fertility schedules, suggesting accurate TFR estimation over a wide range of demographic conditions. We anticipate that this framework will extend fertility analysis to new subpopulations, periods, geographies, and even species. To demonstrate the framework’s utility in new applications, we produce subnational estimates of African fertility levels, reconstruct historical European TFRs for periods up to 150 years before the collection of detailed birth records, and estimate TFR for the United States conditional on race and household income.

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Notes

  1. We assume that fertility is 0 outside this range, so F10 = 0 in Eq. (2) when a = 15.

  2. The coefficient values 10.65 and –12.55 are appropriate when W includes women aged [15, 50). Researchers could use a similar regression procedure with HMD data to produce different coefficients for other definitions of the reproductive age span.

  3. The highest values in m correspond to age groups [20, 25) and [25, 30), so that those age groups represent the highest shares of lifetime fertility. Because the first column of X has monotonically increasing values, the first element of β affects the mean age of childbearing: higher values raise the log odds of late relative to early fertility. Similarly, the second element of β affects the variance of age-specific fertility, with higher β2 causing higher concentration of fertility in the 20s and lower variance.

  4. A Poisson model assumes equality between the mean and variance of the number of surviving children. This strong assumption generally does not hold in practice (e.g., Barakat 2017: figure 1). Individual heterogeneity in age-specific rates would tend to produce overdispersion (variance > mean), whereas strong social norms about childbearing might tend to produce underdispersion (variance < mean). In a comprehensive empirical study of cohort parity, Barakat (2014) found evidence for effects in both directions. Underdispersion is more common at low parities and vice versa. The good performance of the bTFR estimator in our empirical tests suggests that the Poisson model is adequate for estimating TFR from age-sex distributions.

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Acknowledgments

We thank A. Bronikowski, R. Lawler, and S. Alberts for their assistance with their primate data, and B. Jarosz and K. Devivo for feedback on earlier versions.

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Authors and Affiliations

  1. Department of Sociology and Center for Demography and Population Health, Florida State University, Tallahassee, FL, 32306, USA

    Mathew E. Hauer

  2. Department of Economics and Center for Demography and Population Health, Florida State University, Tallahassee, FL, 32306, USA

    Carl P. Schmertmann

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Correspondence to Mathew E. Hauer.

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Hauer, M.E., Schmertmann, C.P. Population Pyramids Yield Accurate Estimates of Total Fertility Rates. Demography 57, 221–241 (2020). https://doi.org/10.1007/s13524-019-00842-x

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