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The Long Shadow of Pandemic: Understanding the lingering effects of cause-specific mortality shocks

Yanxin Liu, Kenneth Q. Zhou

Abstract

In the aftermath of the COVID-19 pandemic, empirical data have revealed that large-scale health crises not only cause immediate disruptions in mortality dynamics but also have persistent effects that may last for several years. Existing mortality models largely assume that mortality shocks are transitory and overlook how their effects can be long-lasting and heterogeneous across age groups and causes of death. In response to this limitation, we propose a novel stochastic mortality model that captures age- and cause-specific long-lasting effects of mortality jumps through a gamma-density-like decay function, estimated via a customized conditional maximum likelihood algorithm. Applying the model to recent U.S. mortality data, we reveal divergent persistence patterns across demographic groups and provide key insights into the tail risk profiles of life insurance and annuity products. Our scenario-based analyses further show that neglecting persistent shock effects can lead to suboptimal hedging, while the proposed model enables what-if testing to analyze such effects under potential future health crises.

The Long Shadow of Pandemic: Understanding the lingering effects of cause-specific mortality shocks

Abstract

In the aftermath of the COVID-19 pandemic, empirical data have revealed that large-scale health crises not only cause immediate disruptions in mortality dynamics but also have persistent effects that may last for several years. Existing mortality models largely assume that mortality shocks are transitory and overlook how their effects can be long-lasting and heterogeneous across age groups and causes of death. In response to this limitation, we propose a novel stochastic mortality model that captures age- and cause-specific long-lasting effects of mortality jumps through a gamma-density-like decay function, estimated via a customized conditional maximum likelihood algorithm. Applying the model to recent U.S. mortality data, we reveal divergent persistence patterns across demographic groups and provide key insights into the tail risk profiles of life insurance and annuity products. Our scenario-based analyses further show that neglecting persistent shock effects can lead to suboptimal hedging, while the proposed model enables what-if testing to analyze such effects under potential future health crises.
Paper Structure (31 sections, 63 equations, 12 figures, 7 tables, 1 algorithm)

This paper contains 31 sections, 63 equations, 12 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Data and Motivation
  3. Data Description
  4. Mortality Trends
  5. Heterogeneity by Age and Cause
  6. Evidence of Long-Lasting Effects
  7. The Proposed Model
  8. Model Structure
  9. Model Assumptions
  10. Model Estimation
  11. Defining Mortality Improvement Rates
  12. Designing a Matrix Representation
  13. Deriving the Log-Likelihood Function
  14. Model Analysis
  15. Estimation Results
  16. ...and 16 more sections

Figures (12)

  • Figure 1: Period life expectancy at age 35 (dotted line) and year-over-year changes (vertical bars) for U.S. males and females, 1995--2023, with highlighted markers indicating the COVID-19 pandemic period.
  • Figure 2: Percentage change in mortality rates from 2019 to 2020 by age group and cause of death for U.S. males (left) and females (right).
  • Figure 3: Excess log mortality rates in years 2020--2023 by cause of death for U.S. males; box plots show age distributions, dots show age-standardized means, and splines show temporal trajectories.
  • Figure 4: Estimated values of $B_x$ and $b_x$ with 95% confidence intervals from the 3WPF-CLJ model fitted to U.S. male mortality data from 1968 to 2023.
  • Figure 5: Estimated values of $\mu_{x,c}$ with 95% confidence intervals from the 3WPF-CLJ model fitted to U.S. male mortality data from 1968 to 2023.
  • ...and 7 more figures