The Role of Immigration in Sustaining the Social Security System: A Political Economy Approach

voters exceeds the number of next period old voters, which means that the de-
cisive voter is always young. Therefore, if the initial capital per (native-born)
worker is in the range [F(τι),F(τ 1)], there is a "demographic steady" equi-
librium path, where the optimal strategy of the young is always to vote for no
restrictions on immigration and a positive tax rate which depends on the capital
per (native-born) worker. If the initial capital is not in the range [F (τ 1), F (τ 1)],
zero tax rate and a positive immigration quotas are chosen by the young. Cap-
ital evolves in a way that it is possible to have a period where the amount of
capital per (native-born) worker enters the range [F(τ 1), F(τ 1)]; if it does, from
then on the current young again vote for no restrictions on immigration and a
tax rate which depends on the capital per (native-born) worker.

2. If the sum of the population growth rates is negative, n < 0, then the
number of old voters always exceeds the number of young voters. This means
that the decisive voter is always old. In that case the old sets the tax rate at
the "Laffer point", and no restrictions on immigration.

3. If the sum of the population growth rates is positive, but the native-
born population growth rate is negative, n < 0 and m + n > 0, there are two
possible equilibrium path types. If the initial capital per (native-born) worker is
in a certain range (defined in the proposition), there is a "demographic steady"
equilibrium path where the optimal strategy of the young is to set a tax rate
that depends on the capital per (native-born) worker, and to set no restrictions
on immigration. If the initial capital per (native-born) worker is outside this
range, there is a "demographic switching" equilibrium path where some level of
immigration always prevails and there is an alternate taxation policy. Capital
evolves over time in a way that there could be a period where the capital per
(native-born) worker enters the relevant range; Once in this range, the optimal
strategy of the young is to set a tax rate that depends on the capital per (native-
born) worker, and to set no restrictions on immigration.

5 The Effect of Aging

We are now in position to conduct a comparative dynamics across demographic
regimes. We analyze the effect of aging of the native born population on the
size of the social security system and on immigration restrictions. Aging of
the population is specified by a reduction in the population growth rate of the
population (life expectancy is assumed to be exogenously fixed).

Proposition 6 1. Aging of the native born population can move the system to

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