Forecasting Human Longevity under Changing Mortality Patterns

Accurate forecasting of human longevity requires models that capture both long-term mortality improvement and structural changes in the age pattern of death. This paper introduces a time-dependent extension of the Gompertz mortality model designed for forecasting applications and econometric analysis of life expectancy. The framework allows the level and slope of adult mortality to evolve over calendar time, consistent with the empirically observed Strehler–Mildvan correlation, in which declining baseline mortality is accompanied by increasing age-related mortality slopes.

A central contribution of the paper is a method for constructing complete cohort life tables directly from observed period life tables. By embedding calendar-time trends into the Gompertz hazard function, cohort-specific survival functions and life expectancy can be forecast without requiring decades of realized cohort mortality data. Analytical expressions are derived for key period quantities, including life expectancy, modal age at death, and dispersion, while cohort quantities are obtained using numerical integration and accurate modal-age-based approximations.

The model implies a finite upper bound on life expectancy when mortality compression is present, offering a structural explanation for the observed deceleration in longevity gains. Using U.S. life table data from 2000 to 2020, we estimate time trends in Gompertz parameters and generate forecasts for the 2020 birth cohort. The results show that cohort life expectancy exceeds period life expectancy, but remains well below the levels implied by linear extrapolation models, particularly at advanced ages.

Overall, the proposed framework provides a transparent, parsimonious, and econometrically interpretable approach to longevity forecasting. It bridges demographic mortality modeling and forecasting methodology, offering a practical tool for long-term projections under changing mortality dynamics.