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Frank T. Denton and Byron G. Spencer

natural replacement rate is approximately 2.07; we experiment with different rates in later
simulations.) The proportion of old people (Seniors plus Aged) increases from 16.8 per-
cent at t = 0 to 26.6 percent at t = 1, and then almost doubles the initial level, rising to 31.5
and 31.9 percent. Concomitantly, the proportion of Children decreases. The ratio of labour
force to population falls from 48.1 percent at t = 0 to 44.5 percent at t = 1, and then to 42.2
and 41.7 percent, producing sharp declines in the national income index: from a base of
100.0 at t = 0, income falls to 96.8 at t = 1, 86.1 at t = 2, and 75.6 at t = 3. Income per ca-
pita falls accordingly, but less precipitously after one generation, since the population is
also declining: the unweighted measure falls to 92.6, 87.9, and 86.8; the weighted measure
falls even more — to 90.7, 85.2, and 84.2. Such is the population/economy trajectory in
the absence of immigration. We have run the simulations out for several more generations
beyond the three for which results are shown in the table but the longer-run pattern is clear
after three: a continuing high proportion of old people relative to the base generation, a
continuing lower proportion of children, a much reduced labour force-to-population ratio,
a declining national income, and a much lower level of income per capita, weighted or
unweighted.
Immigration is introduced in Table 1 (and in subsequent tables) at three quota levels: 10,
20, and 30 percent per generation. (The corresponding annual rates are approximately 0.48,
0.92, and 1.32 percent; a sustained level of .48 would be considered rather high by modern
international standards for an industrialized country, and 1.32 as very high.) As noted
above, the age distribution chosen for this first set of simulations with immigration is the
distribution of the population as it was at t = 0; it is chosen simply as a reference case. One
effect is to stop the decline of the population (with the exception of a very slight dip when
q = 10 percent, at t = 3). The proportion of old people is a little lower than in the
no-immigration case and the labour force/population ratio a little higher, although it takes
a very high quota rate to have much effect in that regard. The immediate decline of nation-
al income is arrested: with q = 10 percent income roughly levels off; it increases signifi-
cantly with q = 20 percent and rapidly with q = 30 percent. But income per capita (either
measure) never recovers; it is higher than the corresponding no-immigration level in all
cases but still well below what is was at t = 0. In short, bringing in immigrants with the
base level age distribution can moderate the income decline induced by population aging,
but only in limited degree if one takes account of the effect of immigration on the size of
the population as well as the level of economic activity, and then only with a high quota
level.
3.2 Immigration with Working-age Concentration

Choosing an age distribution with a high concentration of immigrants in the working ages
— Young Adults and Middle Aged — makes a big difference. Table 2 assumes two such
distributions: (a) 50 percent Young Adults, 25 percent Middle Aged, plus 25 percent
Children; (b) 75 percent Young Adults, no Middle Aged, plus 25 percent Children. Both
distributions raise the labour force/population ratio and increase the level of national in-
come per capita (either measure) above what it would have been had there been no immi-
gration, and also above the level resulting from the immigrant age distribution assumed in
Table 1. The effects are greater, the higher the quota. The immediate effect (t = 1) is the
same for both distributions but by the second generation (t = 2) the Middle Aged immi-
grants admitted previously under distribution (a) have become Seniors, and thus started to
add to the dependent population. Under distribution (b) this effect is delayed until the third
generation (t = 3).
A fraction of the decline in income per capita from the base period is offset under either
distribution. The quota matters greatly in this regard but whatever the quota, the distribution

International Journal of Population Studies | 2015, Volume 1, Issue 1 81