By Yingzhou He, Zhiguo Wang, and Jay Vadiveloo
How to enjoy old age to the fullest satisfaction
Motivation
They say there are two certainties in life—death and taxes. This article is not about taxes, but rather focuses on how to live life to the fullest as we age.
As actuaries, we often use life expectancy as a barometer on how many future years we have left. So, a 65-year-old with a 20-year life expectancy can expect 20 more years of living—and that would impact their lifestyle and spending habits over the next 20 years. But life expectancy does not tell you in how many of these 20 years the individual will be happy.
Suppose Individual A is expected to have 15 healthy future years and 5 unhealthy future years, while Individual B has 5 expected healthy years and 15 unhealthy years before death. It is clear that the old age planning and expense management for Individual A will be very different compared to Individual B. This is why the Goldenson Center came up with the Healthy Life Expectancy (HLE) metric,[1] which measures the future years that an individual is expected to stay healthy.
Since it was published, the HLE metric has been hugely popular both from an informational point of view as well as for its applications in retirement financial planning.
While the HLE metric is very useful, it has its limitations. It only recognizes two decrements for an individual’s healthy life to terminate—death and disability. It does not capture the many stages of disability an individual may experience, nor the possibility of health improvement after getting disabled.
The Golden Years Life Expectancy (GYLE) metric was developed for older individuals where there could be several stages of disability levels and the need to measure the ability to move between these levels. In several of these levels of disablement, while the individual cannot be deemed healthy, they can still lead a full and productive life. So, one can think of GYLE as a more granular version of HLE, and we believe it could be extremely useful for older individuals as they plan for old age.
Modeling Framework
Based on literature research,[2] we recognize five stages of disability for an individual 65 and older.
0. No limitation
1. Mild limitation
2. Moderate limitation
3. Severe limitation
4. Profound limitation
5. Death
In order to develop the model, we need the following baseline assumptions.
- Baseline annual transition morbidity probabilities of moving from one stage of disability to another, recognizing that an individual could stay in the same stage, worsen, or improve to one lower stage.
- Baseline annual mortality rates using standard Society of Actuaries mortality rates.
- Adjustments to the baseline mortality and morbidity at each stage of disability based on individual characteristics of the individual and disability level.
Figure 1 demonstrates the transition scenarios of our GYLE model.
Various references from the literature were utilized to develop the baseline assumptions and adjustments to the baseline assumptions. We then constructed a Markov-Chain-Monte-Carlo (MC-MC) simulation model, and thousands of simulations were run to estimate the Golden Years Life Expectancy (GYLE) and Life Expectancy (LE) realizations from different initial stages of disability.
Risk factors, such as chronic diseases and mental health, play a significant role in an older individuals’ health. People without or with less severe chronic diseases and mental health issues are expected to have longer golden years. We capture these risk factors and apply the related adjustment factors to modify the mortality and morbidity transition probabilities. Some of the risk factors, such as physical activities and diet, also motivate older individuals to lead healthier lifestyles in their retirement to enjoy longer golden years.
The medical cost is a critical concern for older individuals throughout their retirement. Generally, if an elderly person is in a better state of health and experiences milder levels of disability, the medical expenses will be reduced. The medical cost will increase while the older individual transfers to a worse stage of disablement. The estimated annual medical costs based on the older individual’s current health status and future possible transitions will provide good guidance in planning for future medical costs for older individuals.
Results for GYLE and LE Computation
Figure 2 and corresponding Table 1 show the GYLE and LE results in years for a Stage 4 disabled female at various ages.
It is interesting to note how significantly smaller the GYLE is relative to the LE, and the percentage reduction in years increases as the individual gets older. This has significant implications for anyone interested in managing the old age phase in life. The GYLE is an indication of the remaining “quality years” left for an individual—and this has tremendous implications on making decisions on the old-age lifestyle to adopt and how to financially plan for it.
The Goldenson Center has developed a useful online calculator that can provide LE and GYLE calculation when the users input their age, gender, and current stage of disability: https://gyle.infinityfreeapp.com/.
Average Medical Cost for GYLE Model
We are also interested in understanding how age and level of disability affect a retiree’s medical expenses. We use the annual (average) medical cost to measure this effect.
Table 2 shows the average medical cost for five females at different ages at retirement and at different stages of disability.
We observe two conclusions from the table:
- The average medical cost will increase when the initial disability stage worsens.
- The average medical cost generally will escalate as the retiree ages.
Conclusion
While old age is unavoidable, we can control the quality of life as we age. Our GYLE model estimates the future healthy years we have left at different stages of disability and the estimated annual medical costs, which can help us control and manage the quality of life as we age.
YINGZHOU HE, Ph.D., is an assistant professor of actuarial science at the University of Central Missouri. ZHIGUO WANG, Ph.D., is a visiting assistant professor in the University of Connecticut (UConn) Department of Mathematics. JAY VADIVELOO, MAAA, FSA, Ph.D., is the director of the Goldenson Center for Actuarial Research at UConn.
Endnotes
[1] “Model Behavior—Applications of Artificial Intelligence in Actuarial Science”; Contingencies; November/December 2023. [2] “Projecting the Needs and Costs of Long Term Care in Australia”; Leung, Edward; 2004. [3] “Estimating transition probabilities in mobility and total costs for Medicare beneficiaries”; Archives of Physical Medicine and Rehabilitation; December 2010.
