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

ApproachBy

Edith Sand and Assaf Razin

The Eitan Berglas School of Economics, Tel- Aviv University,

and Cornell University

Scope

In the political debate people express the idea that immigrants are good because they can help pay for the old. The paper explores this idea in a dynamic political-economy setup. We characterize sub-game perfect Markov equilibria where immigration policy and pay-as-you-go (PAYG) social security system are jointly determined through a majority voting process. The main feature of the model is that immigrants are desirable

for the sustainability of the social security system, because the political system is able to manipulate the ratio of old to young and thereby the coalition which supports future high social security benefits. We demonstrate that the older is 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.

Outline

• Baseline Model: OLG model, repeated voting, sub-game perfect equilibrium, migrant-native differential population growth rates.

• The Extended Model: private saving, capital accumulation and endogenous factor prices.

• The Effect of Aging.

Features of the Base-Line Model

• OLG two periods.• PAYG Social Security with no private savings.• Immigrants enter the economy when young, and

gain the right to vote only in the next period, when old. They have the same preferences as those of the native-born, except from having a higher population growth rate.

• Offspring of immigrants are like native-born in all respects (in particular, they have the same rate of population growth).

• The utility of the young and old agents are logarithmic:

(1)

(2)

where is the utility function, is the discount factor

and is the labor supply elasticity with respect to the wage

rate.

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Baseline model

• The production function is a linear production function:

(3)

where is the output, and is the labor supply in period t .

• The tax/transfer is a “pay as you go”, where both immigrants and native born contribute to and benefit from the welfare state in the same way. The balanced government budget constraint implies:

(4)

• The labor-leisure decision of young individuals is given by:

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• A worker can be either native born or immigrant. The labor supply in period t is:

(6)

where denotes the economy’s immigration quotas, and is the number of the native born workers in period t.

• The immigrant population, , has a higher population growth rate than that of the native-born population,

(7)

but their descendants’ population growth rate is the same.

• The number of native born individuals in period t is:

(8)

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• The indirect utility functions of old individual is:

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• The old favors the larger possible quotas, , and the

"Laffer point" tax rate, .

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Young voter’s preferences

• The young favors a minimal tax rate. Preferences

regarding the migration quota: 1. A higher migration quota

increases next period transfer payments. 2. Migration

quota also increases the number of next period young

voters.

• The young voter favor the larger possible quotas, which on

the one hand increases social security benefits in the next

period, on the other hand changes next period decisive

voter's identity from young to old in the next period in

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Markov Sub-game Perfect Political Economy Equilibrium

The Markov subgame-perfect equilibrium means that the vector of expected policy decision rules (the tax rate, τ and the immigration quotas, γ), which depends on the current state variable (i.e. the migration quota at time t) is also the same vector policy decision rules chosen by the current decisive voter as a function of previous period state variable (i.e. the migration quota at time t-1).

The EquilibriumProposition 1: The Markov equilibrium is:

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where is the ratio of old to young voters, and

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Because immigrants enter the country while young and gain

the right to vote only in the next period when they are old, the

equilibrium strategy adapted by current voters takes into

account the effect of the current level of immigration on

the composition of voters and their voting preferences in the

next period.

The equilibrium has a “switching” strategy: the

young decisive voter admits a limited number of immigrants,

in order to change the decisive voter's identity next period.

Strategic Voting

Equilibrium paths

There are three possible equilibrium paths:

1. if , level of social security benefits is zero.

2. if , migration quota is at the maximum, , and the tax rate is at the "Laffer point”, .

3. if and , there a “demographic switching” equilibrium path : in a given period, the economy is fully opened to immigration, , and the tax rate is at the "Laffer point”, . In the next period the tax rate/social security benefits is set to zero and there is some restrictions on immigration .

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The First Equilibrium path • If , the level of social security benefits is zero.

The number of young voters exceeds the number of old voters. Because the decisive voter is always young, and her preferences are for zero labor tax, no social security benefits will be paid to the old. The young is indifferent to immigration because it does not influences her current income, or the next period decisive voter's identity.

As a result, the equilibrium path is one where in every period there is a majority of young voters, who therefore destroys the social security system forever.

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The Second Equilibrium path

• If , migration quota is at the maximum, , and the tax rate is at the "Laffer point”, .

The number of next period old voters exceeds the number of next period young voters. Thus, along the equilibrium path a majority of old will always prevail, which validates a permanent existence for the social security system and a the maximum flow of immigrants.

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The Third Equilibrium path• If , and , there is a “demographic switching”

equilibrium path which is characterized by an alternate taxation/social security policy where some level of immigration always prevails.

When there is a majority of old their preferable migration quota is maximal and the tax rate is at the "Laffer point". But since migration quota is maximal and , the number of young voters exceed the number of old voters in the next period. Thus, the decisive voter in the next period is young who votes for a minimal tax rate and votes strategically for a certain level of migration quota which changes the identity of the next period decisive voter to an old voter (there exist such an migration quota since ).

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Capital Accumulation and Endogenous Factor Prices

The new features in the extended model are that young individual is able to save. The aggregate savings of the young which generates next period aggregate capital are being used as a factor of production, in a constant return to scale production function.

These new features create in addition to a very similar “demographic switching” equilibrium as in the base line model, another equilibrium: a "combined strategy" equilibrium.

The "combined strategy" equilibrium

The new equilibrium of the extended model, combines strategies concerning both the old-young composition in the population, and the level of capital: there is a range of values of the capital per (native-born) worker, for which the "demographic steady" strategy dominates; while for values outside this range, the "demographic switching" strategy dominates.

• The reason for the additional strategy results from the fact that there is another channel of influence of the current period policy variables on next period policy variables through savings. Thus, the young decisive voter may adopt a "demographic steady" strategy, where she admits the maximum amount of immigrant. In so doing the young decisive voter renders a majority for the young, every period.

• The "demographic steady“ strategy is characterized by an equilibrium tax rate which is a decreasing function of the capital per (native-born) worker, and no restrictions on immigration.

The "demographic steady" strategy

Aging: a decrease in n

I. Before: (1) the decisive voter switches between young and old (m+n>0 and n<0), or (2) the young is the decisive voter every period (n>0);

After (m+n<0): the old is in majority every period; the tax rate is set at the "Laffer point", and there is no restriction on immigration.

The aging of the native born liberalizes immigration policy, and set the tax rate at the "Laffer point“.

II. (1) Before (m+n>0; n<0): the decisive voter switches between young and old.

After: (m+n>0; n<0): the decisive voter switches between young and old .

The aging of the native born population enlarge immigration quotas set by the young in the "demographic switching" equilibrium path.

(2) Before: the decisive voter is young.

After: the decisive voter is young .

The aging of the native born population decreases the tax rate in the "demographic steady" equilibrium path.

III. (1) Before: combined strategy equilibrium. "demographic switching" equilibrium path.

After: combined strategy equilibrium. "demographic steady" equilibrium path.

(2) Before: combined strategy equilibrium. "demographic steady" equilibrium path.

After: combined strategy equilibrium. "demographic switching" equilibrium path.

Aging affects the capital per (native-born) worker, and thus can move the system from the "demographic switching" equilibrium path to the "demographic steady" equilibrium path or vice versa.

Result I: 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".

Result II:

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.

Aging has the overall effect of raising the optimal immigration quota of the young voter, .

The effect of a decrease in n works itself out through next period dependency ratio, . This dependency ratio effects the quota as follows: in the case where , the dependency ratio effects the quota through the identity of next period decisive voter; whereas in the case where , the dependency ratio effect goes through next period capital per (native born) worker, (due to the fact that a larger quota has the overall effect of decreasing ). Since a larger quota decreases the dependency ratio, it will decrease the ratio less the lower is n.

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Aging and the Tax Rate in the "demographic steady" equilibrium path

Aging decreases the tax rate set by the young in the "demographic steady" equilibrium path, .

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 decreases the optimal tax rate in the "demographic steady" equilibrium path.

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Result III:

Aging affect the capital per (native-born) worker, and thus can move the system from the "demographic switching" equilibrium path to the "demographic steady" equilibrium path or vise versa, since the equilibrium paths are defined over a closed range of the capital per (native-born) worker state variable.

Thus, the older is the native born population,

the more likely is that the migration policy is

liberalized and that the social security system

survives.

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