Page 99 - IJPS-10-4

International Journal of
Population Studies Mortality shapes population age structures

Figure 5. Observed (A) and standard, or stationary (A*) average age, by countries and regions, from 1951 to 2021 (United Nations, 2022).
Notes: There were 131 countries, only those with at least one million inhabitants, excluding Cambodia and North Korea, because of their high mortality
during the war years (1967 – 1975 and 1950 – 1953, respectively). There are six regions: Africa, Asia, Europe, Latin America and the Caribbean, Northern
America, and Oceania. In both panels, each case was observed 15 times: in 1951, 1956,…, 2021. If our predictions were 100% accurate, the age structure of
the observed populations would coincide with that of their standard (the stationary population), and all data points would lie on the bisector. The quadratic
interpolation (dotted red line) gives the general tendency of the scatter and suggests that points may indeed be moving in waves around the bisector, as
survival conditions improve.

The share of the population that is misallocated (by 5-year recent mortality (i.e., its capability of predicting the shape
age group) using our approach is presented in Figure 6. On of the age distribution) is remarkably high, and only a
average, this share is below 18% and never exceeded 36%. small fraction of individuals fall into an age group different
This means that using only information on recent mortality, from that predicted by our model.
age structures can be described with a modest margin of
error: they are 82% correct on average, and at least 64% 4. Discussion
correct in the worst case. Similar to previous observations, The main result of this paper is that the hypothesis that we set
using regions instead of individual countries reduces out at the beginning, and in Equation III, that current survival
random variations and improves the precision of the model conditions determine a large share of the observed age
estimates: ID declines to 15% on average, with a peak of only structures, seems to hold remarkably well. Not surprisingly,
25%. In both cases, the parabolic interpolation suggests that the model performs worse in the most turbulent phases of the
after reaching a peak when e is close to 55/60 years (i.e., demographic transition, but even these cases fit well with the
0
in the midst of the demographic transition), ID tends to general pattern that we sketched in our initial hypothesis.
decline and return to the extremely small values observed The observed age structures tend to resemble those of their
before the transition started. corresponding standard (the stationary population), with
occasional shocks, such as the demographic transition, that
3.3. Results for 10 countries in the HMD
drive the observed age structure away from its expected shape
The same results, but with closer adherence to model (the stationary case). However, after the shock is absorbed,
predictions, emerge with reference to a different period the standard shape tends to resurface.
(starting in 1860) and a different set of countries: the This holds in all the cases that we could investigate
developed countries included in the HMD, of which with our datasets: The HMD and the UN database, both
we took the 10 with the longest time series available including several countries in different epochs and
(Figure 7). As in the case of Figure 5, the initial phase of conditions. Incidentally, this result is consistent with the
the demographic transition breaks the (presumed) original dynamic analysis that we conducted elsewhere on the same
equilibrium (i.e., drives the points to the right, far from the topic, proving that the observed age structures “move”
bisector); however, once the process matures, the cloud over time following the evolution of the L series (De
x
of points tends to converge towards the bisector, where Santis & Salinari, 2023). It is worth noting that our analysis
A = A*, as predicted by the model. included only the observed or estimated data up to 2021.
The share of misclassified individuals is less than 9% If we had included population forecasts, as demonstrated
on average and never above 16% (Figure 8). Once again, by Fernandes et al. (2023), for instance, using UN (2022)
a quadratic interpolation provides insight into how demographic projections until the year 2100, the results,
things evolve over time, suggesting that the worst case although not reported here, would have been even better,
for our model is when A* is about 36 years (e is close with a closer correspondence between (forecasted) reality
0
to 55/60 years), i.e., in the middle of the demographic and (forecasted) stationary populations (the L series of
x
transition. Even then, however, the explicatory power of predicted life tables).

Volume 10 Issue 4 (2024) 93 https://doi.org/10.36922/ijps.377