an equilibrium path with a certain level of taxation/social security benefits (the
"Laffer point" tax rate) and no restrictions on immigration.
2. The aging of the native-born population enlarges immigration quotas set
by the young in the "demographic switching" equilibrium path, while decreasing
the tax rate in the "demographic steady" equilibrium path.
3. In the "combined strategy" equilibrium, aging can move the system from
a "demographic switching" equilibrium path to "demographic steady" equilibrium
path; or vise versa.
The intuition of the result is as follows. Sharp aging trend of the native-born
population, can move the system to an equilibrium path where the sum of the
population growth rates are negative, n + m < 0. In this case, the old are in
the majority every period. The old liberalize immigration policy as much as
possible and sustain the social security system by setting the tax rate at the
"Laffer point".
Aging of the native-born population increases the political-economy deter-
mined immigration quota when the young is in the majority. This quota,
γt = Min[γ*, — mm], is what is chosen by the current young in the "demographic
switching" equilibrium path . The effect of aging of the native-born population
on immigration policy works itself out through the ratio of old to young voters
in the next period, ut+1 = (i+n)++Y(1+m). This dependency ratio effects the
political-economy quota as follows: in the case where γt = — mm, the depen-
dency ratio effects the quota through the identity of next period decisive voter;
whereas in the case where γt = γ*, the dependency ratio effect goes through
next period capital per (native born) worker (this results from the fact the ef-
fect of the quotas on the ratio, ut+i: larger quota increases the amount of total
savings but since there are also more young in the next period, it has the overall
effect of decreasing the capital per (native born) worker)). Since a larger quota
decreases the ratio of next period old to young voters (it increases the number
of next period immigrant descendants more than the number of next period
old immigrant), it will decrease the ratio of next period old to young voters
less the lower is the native born population growth rate. Thus, aging has the
overall effect of raising the optimal immigration quota of the young voter in the
"demographic switching" equilibrium path.
Aging of the native-born population also decreases the tax rate set by the
young in the "demographic steady" equilibrium path, τ (kt). This is due to the
fact that aging increases total savings which raises the amount of capital per
(native-born) worker. Since the tax rate is a decreasing function of the capital
per (native-born) worker state variable, the aging of the native-born population
23