For males, we can observe that the official 2nd order trend is very close over all ages to the long-term trend. However, the observed middle- and long-term trends are very close to each other. What is remarkable is that the yearly improvement over the last 10 years (short term) has deaccelerated compared to the middle and long term for ages up to 75. In contrast, the average yearly improvements for ages 76 to 88 have been even larger than the middle- and long-term trend. Thus, the official 2nd order trend overestimates the mortality improvements for younger ages up to 75 and underestimates the improvements for ages 76 to 88. For ages beyond 89, the official trend is on average13 5% higher than the middle-term trend.
For females, we can observe that the official 2nd order trend follows very closely the mortality improvements over the last 25 years. However, it also becomes clear that the mortality improvements over the last 10 years are significantly lower between ages 60 to 78 than the improvements observed over the last 25 and 40 years. We can clearly see a continuous deacceleration in the improvements for this age range. For ages 79 to 90, all trends are close to each other. Only for ages beyond 90 can we observe a higher improvement between the short- and middle-term trends.
On the one hand, we can state very generally that the recently published 2nd order trend function is very similar to the average mortality improvements observed in Spain for the 25 years prior to 2015.
On the other hand, from a methodological perspective, we can see differences compared to the German actuarial Table DAV 2004R, where they use two trends: short- and middle-term trends. During the projection of cashflows, the short-term trend is used until year T1. Between T1 and T2 there is a linear dampening of this trend to finally reach a certain percentage of the middle-term trend in year T2.
We have two additional comments on these findings in Spain. It is important in future work to better understand if the observed mortality improvements for males between 77 and 88 (which are above the official 2nd order trend) will remain above the official trend or whether it is meaningful to assume some dampening over time. Considering females, the question to ask is if the official 2nd order trend is the right best-estimate for ages 60 to 78 since it is much higher than the observed short-term trend.
Comparison to Other Countries
A follow‑up question is how the mortality improvement in Spain over time compares to other countries. For this purpose, we selected three countries of the European Union to compare with Spain: Germany, France, and Italy. We focused our attention on the middle-term (25 years) trend.
Middle-Term Trend Comparison
For males ages 60 to 72, the middle-term average mortality improvements between Spain, Germany, and France are very similar. The improvements observed in Italy are significantly higher than in the other three countries. For ages beyond 72, the improvement observed in Italy is closer to those observed in the other countries. It is important to note that Spain presents the lowest mortality improvements compared to the rest of the countries (similar to Italy from age 85 and older). This can be seen in Figure 6.
Figure 6 — Comparison of mortality improvement in Spain, Germany, France, and Italy (male)