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A simulation analysis of the longer-term effects of immigration on per capita income in an aging population

by itself, with no immigration, would wipe out immediately (t = 1) the decline of national
income per capita brought about by population aging, and raise the income per capita level
further in subsequent generations. Coupling even a 5 percent growth rate with positive
immigration quotas would set an upward trajectory for income per capita. It would seem
then that even a modest rate of productivity growth would eliminate all concerns about the
economic effects of population aging. However, that interpretation is superficial.
Suppose, to make a point, that while the productivity growth rate in Alpha is 5 percent,
the growth rate in the rest of the world is 10 percent. Relative to other countries Alpha’s
national income per capita would then fall by about 4.5 percent in the first generation (on
top of whatever was the decline resulting from population aging), by 8.9 percent in the
second, and so on. The point is that to be interpreted realistically, the productivity growth
rate should be defined as the difference from the growth rate in the rest of the world.
Moreover, if the economy were open rather than closed it would find its terms of trade
deteriorating and its relative standard of living falling as a result of its slower productivity
growth. If is defined as a differential rate of productivity growth, a positive rate would
indeed offset some or all of the effects of population aging on the economy. Zero produc-
tivity growth, as we have assumed in the earlier simulations, would then imply that prod-
uctivity was growing in Alpha at the same rate as elsewhere and that income was meas-
ured correspondingly, in relative terms.

3.6 What if the Fertility Rate were to Increase?
The “natural replacement” fertility rate is a little under 2.1 children per woman. That is the
rate required for the population to achieve a stationary state in the long run — constant
population size and an unchanging age distribution. A higher rate would result in conti-
nuous population increase, a lower rate in continuous population decline. What if the rate
were to increase from the 1.6 level assumed up to now?
Letting F stand for fertility rate, we experiment with two higher levels, starting at t = 1:
the levels are F = 2.0745 (the natural replacement rate to four decimal places) and F = 2.5,
a value well above replacement. Would such higher rates add to or diminish the effects of
population aging on the economy?
The results of the experiments are presented in Table 6. To isolate fertility effects we
assume no immigration. The top panel of the table repeats the no-immigration results from
Table 1, with the fertility rate held at 1.6. The middle and bottom panels show results for
the two higher rates.
With F equal to the replacement rate, the population increases more rapidly at t = 1, and
remains at the higher level thereafter, thus arresting the long-run population decline ob-
served previously. But a higher value of F means more children in the first generation,
more dependents in the population, a lower labour force/population ratio, and a lower level
of national income per capita. The unweighted per capita income index has dropped sig-
nificantly, from 92.6 (when the fertility rate was 1.6) to 87.0 with the new higher rate; the
weighted index has dropped somewhat less, from 90.7 to 87.5. In the second generation
(t = 2) the children of the first have come of working age but a new cohort of child depen-
dents has taken their place, and there are only small changes in the labour force/population
ratio and per capita income indexes. There are some further differences in generation 3 but
overall the picture is generally similar to that of generation 2.
Much the same can be said, qualitatively, for the results of the further increase in fertility
rate to 2.5. What were smaller effects with replacement fertility though have now become
bigger ones. Most notably, the reduction of per capita income (weighted or unweighted) in
the first generation is much greater.
In sum, the effect on the economy of an increase in the fertility rate in the first generation

International Journal of Population Studies | 2015, Volume 1, Issue 1 86