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Frank T. Denton and Byron G. Spencer

bearing their own children; three generations later they will be of retirement and depen-
dency age, and so it goes.
There is also the question of how high to set the quota — how many immigrants to ad-
mit in any period. It may be theoretically possible to effect a major shift in population age
distribution by setting the quota very high but practical constraints are prohibitive. There
are limits to how many newcomers can be absorbed into the society without disruptive
effects in any one generation. The question then is how much beneficial effect on the
economy can be expected from a realistic quota, given the choice of immigration age dis-
tribution. We experiment with alternative combinations of age distribution and quota size.

2.4 Calibration and Notation

A characteristic of the Alphan population is that it is the same at generation t = 0 as the
2001 Canadian census population, and thus exhibits the same distorted age distribution
and evidence of population aging (Statistics Canada, 2013b). Moreover: the age-sex-spe-
cific survival rates incorporated into the Q matrix are identical to Canadian rates, and can
be calculated directly from the 2001 Canadian life tables; the initial (total) fertility rate of
1.6 children per woman is the Canadian rate in 2011; and the ratio of male to female births,
set at 1.05, is approximately the longstanding Canadian ratio. (We emphasize that the use
of Canadian demographic data for calibration is simply a matter of convenience. We take
advantage of the fact that Canada provides a good example of a developed country with a
“population aging problem”, but we are certainly not attempting to model the Canadian
economy, population dynamics, or immigration patterns and policy. See the Appendix for
details and references.)
The age-sex labour force participation rates — the proportions of (employed) labour
force in the population, the elements of the vector r — are roughly consistent (in broad
pattern) with Canadian rates in the decade centered on 2001, with the qualifications that
the rates for Children are zero and the rates for Young Adults and Middle Aged are equal.
The rates for females, the top half of , are (0, 0.75, 0.75, 0.10, 0); the rates for males, the
bottom half of r, are (0, 0.85, 0.85, 0.20, 0).
Since output Z is proportional to labour input, and results are shown only as indexes,
there is no need to set values for ϕ or the underlying β, γ, µ and θ parameters (Equation
(4)). The rate of growth of productivity, g is set to zero in the initial simulations, but al-
lowed to vary in some later ones.
The simulations involve runs with different immigrant age distributions and some sim-
ple notation is helpful in presenting results. First, note that all simulations assume that
immigrants in each age group are equally divided between males and females; we do not
experiment with differences in sex composition. This cuts to five the number of values that
would have to be reported in defining a distribution. Moreover, we assume in most cases
(Table 1 is an exception) that immigration policy choices are restricted to Children, Young
Adults, and the Middle Aged; no Seniors or Aged immigrants are permitted since immi-
grants in those age groups would simply add to the numbers of dependents (aside from a
small proportion of Seniors who enter the labour force). Our focus is on immigration as a
policy device for influencing the economy, and offsetting the effects of domestic popula-
tion aging. Permitting older immigrants to enter might be considered desirable for other
reasons but its effect on immigration as an economic policy tool would be to weaken it. A
practical result of this exclusion for presentation purposes is that the number needed to be
reported in defining an immigration age distribution is now reduced to three. We choose
the symbol AGEIM to stand for “age distribution of immigrants” and report the propor-
tions in percentage form. AGEIM (25, 50, 25), for example, means that immigrants are

International Journal of Population Studies | 2015, Volume 1, Issue 1 79