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

because it raises the return on savings of the current young. If the immigration
quota preferred by the young, for its direct effect on wages, is high enough, the
young decisive voter will not manipulate next period young to old ratio, and set
his preferable immigration quota at a level equal to the next period quota set
by next period young decisive voter. Note that since there is no social security
system, there is no additional equilibrium as in the previous model. This is due
to the fact that the "demographic steady" strategy of this equilibrium results
from the dependency of the tax rate cum benefit rate on the capital per (native
born) worker, which does not exist in the present model.

The absence of social security system simplifies the assumptions of the model,
as follows:

The utility of the representative young and old individuals are derived only
from their own earned income and saving,

_lΨ+1

U^y(wt, τt,st, rt+1) = Log(wtlt - st - ψ +   + βLog((1 + rt+ι)st)    (75)

U ^o(st-1, rt, ) = (1 + rt)st-1                          (76)

This generates the standard saving-consumption and labor-leisure decisions:

st = 1+β (^β ψ+ι^wt^lt)                  ⁽⁷⁷⁾

Ψ

l_t^Ψ = wt

Factor prices are determined as in the extended model.

The indirect utility of the young and old respectively can be written as
follows:

Vy(kt,Yt,Yt+ι) = A +(1+ β)Log ζ((1 - α)k_t^α(1 + Yt)^-α)

(1 — a

α ((1 - α)( 1+β⅛,+⅞m)((1 — α)kα(1 + Y.)^-α)^ψ+t)^-ψ(1 + 7.+1)*) ’+’

(79a)

V^o(Yt-i,kt) = α ((1 - α)kt^-ψ(1 + Yt)ψ^ψ+^a kt (!+^(++-!(!+m)) (80)

The definition of the Markov sub-game perfect political equilibrium is similar
to the previous definition, but has only one policy decision rule, the immigration
policy rule, γ_t = G(γ_t-1).

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