variables are influenced only by the current migration policy. The extended
model with private savings and capital accumulation includes another equilib-
rium type (in addition to the one similar equilibrium as in the base line model).
The new type features both a "demographic switching" strategy and a "demo-
graphic steady" strategy.
We characterize subgame-perfect Markov equilibrium paths for different pat-
terns of population growth rates among the native-born and immigrants pop-
ulations. We are thus able to demonstrate that the older are the native-born
population the more likely is that the immigration policy is liberalized; which
in turn has a positive effect on the sustainability of the social security system.
The paper is organized as follows. We survey related literature in Section
2. Section 3 provides analysis of the base line model, where there is no private
savings, the economy does not accumulate capital, and factor prices are exoge-
nous. Section 4 extends the base line model to include private saving, capital
accumulation, and an endogenous determination of the wage and the interest
rate. Section 5 considers the effect of aging in the extended model. Section 6
concludes.
2 Literature Background
An empirical investigation of the effect of the proportion of elderly people in
the population on the size of social security benefit per retiree turn out not to
be significant (Mulligan and Sala-i-Martin (1999) and Breyer and Craig (1997))
and also negative (Razin, Sadka and Swagel 2002a). Bergstrom and Hartman
(2005) estimate the expected present value of benefits and costs to US voters for
a small permanent increase in social security benefits. In addition, they explore
the sensitivity of political support for social security and reach the conclusion
that a once and for all decrease in benefits would be defeated by a majority
of selfish voters. Cooley and Soares (1999), Bohn (2005), and Boldrin and
Rustichini (2000) analyze the consequences of aging in a general equilibrium
model of social security with production, which results in a rise in the size of
social security systems. Models of altruism between generations reach the same
conclusion (Tabellini (2000) and Hansson and Stuart (1989)). Analyzing the
effect of interest groups on social security suggest ambiguous results. While
some models emphasize the raise in the political power of the elderly (Verbon
and Verhoeven (1992)), other models argue that aging will reduce social security,
since larger groups experience higher deadweight costs and larger free rider
effects, and will thus be less efficient in exerting political pressure (Becker and