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

When there is an additional state variable- the stock of capital per (native-born)
worker, there is another channel of influence on next period political-economy
policy variables. There can be another possible strategy of the young, a "de-
mographic steady" strategy, where she chooses to admit the maximum amount
of immigrant, and in so doing she renders a majority of young every period. In
this case, both "demographic switching" and "demographic steady" strategies
are incorporated creating a "combined strategy" equilibrium.

An interesting extension could be to introduce heterogeneity within the
native-born and the immigrant’s population in terms of labor productivity. This
would bring into the current model intragenerational distribution aspects. In
addition it would also create other possible types of representative voters i.e. old
native-born/ immigrants and young native-born/ immigrants voters, which can
create an interaction between fiscal leakages across income groups and young
voter strategies.

7 Appendix

7.1 Proposition I:

Proof. We must show that the vector of policy decision rules, Ψ = (T, G), as
defined in the proposition, satisfies the equilibrium conditions:

1. Ψ(Yt-1) = argmax∏t Vi(Yt-1, ∏t, ∏t+1), subject to ∏t+ι = Ψ(γt).

2. Ψ(Yt-1) = Ψ(Yt-ι).

If ut ≥ 1, then the decisive voter is old. Substituting for lt from equation
(8) into (12), the utility of the old can be rewritten as:

^τt^{(1 - τ}t) ^{ψ [(1 + n})⁺ Yt-1(^{1 + m)](1 +} Yt)
(1 + γ_t-1)

It is straightforward to show that V ^o(γ_t-1) is maximized by setting πt =
( Ψ+1,1).

If ut < 1, then the decisive voter is young. From equation (9), the utility of
the young voter subject to πt+1 = Ψ(γ_t), is given by:

Log[ Ψ+ι^{(1 - τ} t)''^{ψ ]} ɪ                       if

Log[ψΨ+i(1 - τt)'   ] + βLog[^2ψ+1 (^1-ψ+¹()ι+γⁱ_t+n^+γt(^1+m)] ] otherwise

(38)

In that case V^y(γ_t-1) is maximized by setting π_t = (0, — mm). It should be noted
that in the case where the population growth rates are both positive, m, n > 0,

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