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Tempo effects in period TFR: Inspecting the role of shape and scale variations in a cohort model

Author

Listed:
  • Stefano Mazzuco

    (Università degli Studi di Padova (UNIPD))

  • Lucia Zanotto

    (Università di Bologna (UNIBO))

Abstract

Background: The total fertility rate (TFR) is a fundamental demographic measure widely used for assessing fertility trends in populations. However, the TFR is susceptible to distortion due to timing effects, which can confound the understanding of true fertility patterns. Objective: This study investigates the impact of changes in the distribution of fertility rates on the period total fertility rate (PTFR) from a cohort perspective. Methods: We adopt a model representation that separates the quantum (the fertility that would occur without timing changes) from the tempo (timing changes) components. Using a skewed normal distribution to fit cohort fertility schedules, we explore the impact of variations in cohort mean age at childbearing, variance, and skewness on the PTFR. Simulation studies are also conducted to investigate the transient behavior of the TFR. Results: We demonstrate that the tempo distortion in PTFR depends on the speed and magnitude of shifts in scale and shape parameters. Adjusting PTFR for these variations yields different results compared to adjustments based solely on mean shifts, highlighting the importance of considering all tempo parameters. Conclusions: Analyzing tempo fluctuations from a cohort perspective reveals their significant impact on PTFR estimates. Additionally, it becomes evident that the changes observed at the cohort level are predominantly reflected in the period shift of the mean age at childbearing. Contribution: This research contributes to the ongoing discussion regarding the impact of cohort fertility schedule changes on PTFR. Our cohort-focused approach sheds light on the role of scale and shape variations and their implications for understanding fertility trends, emphasizing the need for a comprehensive assessment of tempo distortions in demographic analyses. The findings bear significance for policy evaluation in the context of demographic changes.

Suggested Citation

  • Stefano Mazzuco & Lucia Zanotto, 2025. "Tempo effects in period TFR: Inspecting the role of shape and scale variations in a cohort model," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 52(19), pages 559-588.
    • Handle: RePEc:dem:demres:v:52:y:2025:i:19
    DOI: 10.4054/DemRes.2025.52.19
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    References listed on IDEAS

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    1. Evert van Imhoff, 2001. "On the impossibility of inferring cohort fertility measures from period fertility measures," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 5(2), pages 23-64.
    2. Joshua Goldstein & Thomas Cassidy, 2014. "A Cohort Model of Fertility Postponement," Demography, Springer;Population Association of America (PAA), vol. 51(5), pages 1797-1819, October.
    3. Jan Hoem & Dan Madien & Jørgen Nielsen & Else-Marie Ohlsen & Hans Hansen & Bo Rennermalm, 1981. "Experiments in modelling recent Danish fertility curves," Demography, Springer;Population Association of America (PAA), vol. 18(2), pages 231-244, May.
    4. John Bongaarts & Tomáš Sobotka, 2012. "A Demographic Explanation for the Recent Rise in European Fertility," Population and Development Review, The Population Council, Inc., vol. 38(1), pages 83-120, March.
    5. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    6. Evert van Imhoff & Nico Keilman, 2000. "On the Quantum and Tempo of Fertility: Comment," Population and Development Review, The Population Council, Inc., vol. 26(3), pages 549-553, September.
    7. Young J. Kim & Robert Schoen, 2000. "On the Quantum and Tempo of Fertility: Limits to the Bongaarts‐Feeney Adjustment," Population and Development Review, The Population Council, Inc., vol. 26(3), pages 554-559, September.
    8. Stefano Mazzuco & Bruno Scarpa, 2015. "Fitting age-specific fertility rates by a flexible generalized skew normal probability density function," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(1), pages 187-203, January.
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    More about this item

    Keywords

    tempo distortion; total fertility rate (TFR); scale; shape; skew-normal distribution;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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