Old Age Sticks Analysis

What Old Age Sticks Analysis Actually Is

It is a method used primarily in actuarial science and pension fund valuation to estimate mortality improvements at older ages. The basic premise is that traditional life tables tend to flatten out or become unreliable past age 85 or 90, so practitioners use a sticking point approach where you anchor observed mortality rates at a specific age and then project forward using assumed improvement rates rather than raw tabular data. The result is a set of projected survival probabilities that better reflect real-world longevity trends. You need a base mortality table first. Something like the SSAB or the RP-2014 series works if you are working in the US context. Pick your stick age, which is the age where you stop applying tabular data and start applying your own improvement assumptions. Most actuaries stick at 85, 90, or sometimes 100 depending on the plan population. The choice matters because it changes the entire tail of your projection. Once you pick the stick age, you pull the base mortality rates from your table up to that age, then apply an annual improvement rate beyond it. The improvement rate is usually somewhere between 1 and 2 percent per year for most working populations, but it can vary significantly if you are dealing with a cohort that has different health characteristics. I have seen firms use as low as 0.5 percent and as high as 3 percent depending on the demographic profile.

The Mechanics Behind the Method

The math itself is straightforward. You take the q_x value at your stick age from the base table, then apply a growth factor for each future year. The formula looks something like q_{x+t} = q_x * (1 - improvement_rate)^t where t is the number of years past the stick age. You then convert those q values into p values and build out a full mortality table for projection purposes. What most people miss is that the choice of improvement rate has a disproportionate effect on reserve calculations. A difference of just 0.5 percent in the assumed improvement rate can swing liabilities by several percentage points over a 20-year projection horizon. I learned this the hard way during a pension valuation where my initial model used a flat 1.5 percent improvement assumption across all post-stick ages, and the actuary reviewing it pointed out that our plan had a significantly healthier-than-average population. We ended up revising the improvement rate downward to 0.75 percent beyond age 90, which reduced the projected liability by about 8 percent.

Common Pitfalls

The biggest mistake I see is treating the stick age as a fixed decision without considering the specific population. If your covered lives are significantly younger or older than the standard population your base table was built on, sticking at 85 when you should stick at 90 or vice versa will introduce systematic bias. Another frequent error is applying the same improvement rate uniformly across all ages beyond the stick point. Mortality improvement tends to decelerate at very advanced ages, and using a flat rate overestimates improvement where it is least warranted. A more subtle issue involves the interaction between your stick age and your interest rate assumption. In a low-rate environment, the present value of future benefits is more sensitive to mortality assumptions, which means the choice of stick age and improvement rate becomes materially more important. I worked on a project where the discount rate was under 3 percent, and changing the stick age from 90 to 95 increased the present value of liabilities by roughly 4 percent purely through the mortality tail effect.

When It Does Not Work Well

Old Age Sticks Analysis breaks down in populations with unusual mortality patterns, such as highly select groups, disabled populations, or cohorts exposed to significant non-mortality risks. It also struggles when you need to model catastrophic mortality events or sudden improvements in elderly care that are not captured by gradual improvement assumptions. For those situations, you are better off using a stochastic mortality model or consulting specialized longevity research. If you are looking for software to implement this, most actuarial platforms like Prophet, AXIS, or ProMod have built-in functionality for setting stick ages and improvement rates. There is no standalone public download for the method itself since it is a technique rather than a product, but if you want reference materials, the Society of Actuaries publishes guidance on mortality projection methods that covers this approach in detail.

Practical Implementation Notes

When you set up the analysis, document every assumption clearly. The stick age, the improvement rate, the base table, and any deviations from standard practice should all be recorded with rationale. I once had a file where someone had changed the improvement rate without noting it, and it took me three hours to trace where the numbers diverged from the prior valuation. Proper documentation prevents that kind of situation. The analysis usually takes between 30 minutes and an hour to set up properly for a standard population, longer if you are working with multiple cohorts or unusual demographic profiles. Testing the sensitivity of your results to different stick ages and improvement rates is worth the extra time, especially if these numbers will be used for financial reporting or regulatory purposes where assumptions are subject to review.