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

International Migration

A smaller labour force means less

economic growth and faltering social

security system. In this context,

migration is regarded by many as one

of the necessary factors for the

sustainability of the this system.

Abstract

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.

Literature

Cooley and Soares (1999) 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)).

Storesletten (2000) and Lee and Miller (2000) calibrate a general equilibrium overlapping generations model to investigates whether a reform of immigration policies could resolve the fiscal problems associated with the aging. Storesletten finds that selective immigration policies, involving increased inflow of working-age high and medium-skilled immigrants, can remove the need for a future fiscal reform. Lee and Miller on the other hand reach the conclusion that since immigrants have lower education and higher fertility rates than that of the native-

born, a higher amount of immigrant admitted into the economy will east temporarily the projected fiscal burden of retiring baby boomers in few decades although its overall fiscal consequences would be quite small.

Razin and Sadka (2000, 2004) address the issue of the fiscal burden associated with immigrants in a pay-as-you-go fiscal system. They show that the additional obligation of the fiscal system to pay pension benefits to the incoming migrants, when they retire, could be shifted forward indefinitely. If, hypothetically, the world would come to a stop at a certain point of time in the future, the young generation at that point would bear the deferred cost of the present migration. But in an ever-lasting economy, the migrants, by supplying work and helping the financing the pension

benefit of period zero to native-born retirees, are a boon to the host country population: old, young, and future generations.

A pioneering paper which studied immigration policy in a political economy setup was the paper by Benhabib (1997). He examines the determination of immigration policies that impose capital and skill (human capital) requirements on heterogeneous immigrants through majority voting process.

Dolmas and Huffman (2004) and Ortega (2005) add another angle to the political debate and model the joint decisions over immigration quotas and redistributive tax policy. Both address the voting process in a dynamic set-up, where the native-born voters' preferences over immigration are influenced by the prospect that immigrants will be voting over future tax policy.

Prescott and Rios-Rull (2000)argue that a necessary feature for equilibrium isthat beliefs about the behavior of future agentsare rational. Prescott and Rios-Rull conclude that the existing equilibrium concepts in the earlier literature do not satisfy this condition. They then propose an alternative equilibrium concept, organizational equilibrium, that satisfiesthis condition. They show that equilibrium exists, it is unique, and it improves over autarkywithout achieving optimality.

Outline

• Base line Model

• The Extended Model: Private Saving, Capital Accumulation and Endogenous Factor Prices

• The Effect of Aging

Pay-as-You-Go Social Security and Age Dependent Self Interests

The net present value of costs and benefits from a pay-as-you-go social security are negative for the young people and positive for the elderly. If people all vote their economic interest, there will be a pivotal age such those who are younger, favor smaller social security benefits and those who are older will favor larger benefits.

Once-and-for-all Election vs. Repeated Elections

• Browning pointed out that if a single once-and-for-all election were held to determine the level of social security, then a coalition of persons of median age and higher would select an inefficient pension plan that benefits the current elderly at the expense of all future generations.

• If the issue of social security levels is however frequently visited by voters, the matter is much less clear.

Social Security Sustainability

Cooley and Soares (1999) and Boldrin and Rusticini study the interaction between capital accumulation and social security in general equilibrium models, where levels of social security payments are determined periodically bymajority voting.

Base-Line Model

The economy is populated by overlapping generations of identical individuals. Individuals live for two periods. When young, the representative individual works and makes labor-leisure. Underdeveloped capital markets do not allow any private savings. Social security is therefore the only means of intertemporal transfers. When old, the individual retires, and receives social security benefits. The tax-transfer system is "pay as you go" where in every period the government levies a flat tax on the young's wage income, which fully finances the social security benefits paid to the old. 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. Immigrants are fully integrated into the social security system upon arrival into the country. Offspring of immigrants are like native-born in all respects (in particular, they have the same rate of population growth).

A Model of Social Security and Migration (Sand and Razin (2007))

• The economy is populated by OLG of identical individuals, who live two periods. When young, the representative individual works and makes labor-leisure and saving-consumption decisions. When old, she retires and receives social security benefits and the rental rate income from capital accumulation.

• The tax-transfer system is "pay as you go" where in every period. The government levies a flat tax on the young's wage income, which fully finances the social security benefits paid to the old.

• 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.

• Immigrants are fully integrated into the social security system upon arrival into the country.

• 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 .

Labor supply is given by:

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tt NY

tY tN t

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

(5)

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, :

(6)

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

(7)

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• The tax/transfer is a “pay as you go”.

The balanced government budget constraint implies:

(8)

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• The tax/transfer is a “pay as you go”.

The balanced government budget constraint implies:

(8)

Re-arranging the expression yields:

(9)

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• The indirect utility functions of old individual is:

(10)

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

"Laffer point" tax rate, .

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• The indirect utility functions of old individual is:

(11)

• The young favors a minimal tax rate. Yet, his preferences

regarding the openness rate, is more ambiguous: on the one

hand a higher openness rate increases next period transfer

payments, but on the other hand it also increases the

number of next period young voters. Thus, she will favor

the larger possible quotas, which yet changes next period

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

period in order to lead to a majority of old.

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Markov Sub-game Perfect Political Economy Equilibrium

The subgame-perfect Markov equilibrium notion states that the expected policy function, which depends on the minimal present state variables, must be self-fulfilling.

The policy variables which are the tax rate, ,and the openness rate, , have to maximize the decisive voter's indirect utility function, while taking into account that next period decision rules depend on the state variable i.e. the current immigration quotas.

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The Model’s Markov Perfect Equilibrium

Proposition 1: The Markov equilibrium is:

(14)

(15)

where is the ratio of old to young voters, and

otherwise

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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 take into

account the effect of admitting immigrants now, will have on

the composition of voters and their voting preferences in the

next period.

Moreover, 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 “cycling” 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 .

1

0, mn

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

If , then for every level of immigration quotas 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 for ever.

0, mn

0, mn

The Second Equilibrium path

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

If the sum of the native born and immigrant population growth rates is negative, , 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.

1 t

0mn

0mn 1t

The Third Equilibrium path• If , and , there a “cycling” path which is

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

The reason is that when there is a majority of old their preferable openness rate is maximal and their tax rate is at the "Laffer point". But since the old decisive voter set a maximal rate of openness 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 openness rate which changes the identity of the next period decisive voter to an old voter (there exist such an openness rate since ).

0mn

0n

0n 0mn

Extending the Sand-Razin Model: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 “switching” equilibrium type as in the base line model, two

other equilibria types.

The added state variable, stock of capital per native-born workers, , plays a crucial role of qualitatively affecting the policy variables.

This is due to the fact that rational voters take into account that the current policy variables can affect next period policy variables not only through the composition of old to young voters in the next period (the current immigration quotas), but also through . Thus, there is another possible strategy of the young, a "non-switching" strategy, where she chooses to admit the maximum amount of immigrant, and in so doing she renders a majority of young every period.

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

(16)

(17)

where is the interest rate, and is the savings of the

young at period t.

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The extended model with capital accumulation

• The production function is a Cobb-Douglas production function

which is assumed to use both labor and capital as its factors of

production:

(18)

• where is the aggregate amount of capital and is defined as

in the previous section.

• The wage rate and interest rate are determined by the marginal

productivity conditions (capital is assumed to depreciate completely

at the end of the period):

(19)

(20)

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The “Switching” Equilibrium Type

The first equilibrium type, similarly to the base-line model, is characterized by a "switching" strategy where the young decisive voter chooses to admit a limited number of immigrants in order to change the decisive voter's identity from young to old in the next period. The added effect caused by the existence of savings has no qualitative influence on the equilibrium strategy.

Equilibrium Types of the Extended Model

In the two other equilibria types, current policy variables can affect next period policy variables also through the added state variable- . Thus, there is another possible strategy of the young, a "non-switching" strategy, where she chooses to admit the maximum amount of immigrant, leading to a majority of young every period and where the tax rate is a function of . These equilibria which combine both strategies, are characterized by a range of values of for which the “switching” strategy is optimal as in the baseline model, while for other values of the "non-switching" strategy dominates.

The “Combined strategies” Equilibrium Types

tk

tk

tk

tk

The two “combined strategies” equilibria differ from each other by the fact that in the "non-switching" strategy, in one equilibrium the optimal strategy is characterized by a tax rate which is decreasing in , while in the other equilibrium it is increasing in .The difference in the equilibrium taxes, result from conflicting forces of the effect of the next period tax rate on next period capital per native-born work force.

tk

tk

On one hand, a higher tax rate in the next period raises future social security benefits. Larger benefits, tend to reduce current savings. This would cause a reduction in ("Effect One").

On the other hand, a higher next period tax rate tend to decrease the amount of hours worked next period and lower the next period interest rate. The consequent fall in the current young future income induces more savings. This tends to increase ("Effect Two").

In the “Combined strategies ” Equilibrium , where the tax rate is decreasing in , "Effect One" is stronger than "Effect Two“.

1tk

1tk

tk

The “Combined Strategies” Equilibrium paths

1. If and , the tax rate depends on and there are no restrictions on immigration. If is not in that range there are at least few periods in which there is no taxation and some restriction on immigration.

2. If , the tax rate is at the "Laffer point“; and there are no restrictions on immigration.

3. If and , there is a range of , for which the tax rate depends on and there is full openness to immigration. If is not in this range, there are at least few periods in which there is a "cycling" 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 there is no taxation and some restrictions on immigration.

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tk

0 nm

tk

0n 0 nm tktk tk

The Effect of Aging

Result 1: Aging can move the system to an equilibrium where the sum of the population growth rates are negative, . In this case, the old are in the majority every period which set the tax rate at the "Laffer point", and no restriction on immigration.

Result 2: The aging of the native born (immigrants) population enlarge (reduce) immigration quotas set by the young in the "cycling" equilibrium paths.

Result 3: In the "combined strategy" equilibrium types, aging can move the system from a "cycling" equilibrium path to an equilibrium path where the tax rate depends on and there are no restrictions on immigration or vise versa.

tk

0 nm

The aging of 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 set the tax rate at the "Laffer point", and liberalize immigration policy as much as possible.

Aging of the native-born population enlarge the immigration quotas in the "cycling" equilibrium path when there is a majority of the young. The effect of aging of the native-born population on immigration policy results from the fact that aging decreases the number of next period young native born individuals which changes the ratio of old to young voters in the next period.

Larger quotas increases the number of next period immigrant descendants more than the number of next period old immigrant (since we assumed m>n). Thus, it will decrease the ratio of next period old to young voters less the lower is the native born population growth rate.

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.

All over the world, declining population growth rates and rising life expectancy have strong impact on the social security system, as we know it. Due to decreased fertility rates and longer life expectancy, the EU population, in particular, is undergoing a long term trend of ageing, leading to a likely fall in the working population in the 25 states from 303 million to 297 million by 2020.

Ageing and Social Security

Intra-generational Redistribution Aspects

Razin, Sadka, and Swagel (2001) examine the

problems that arise in the social security

systems in countries with increasing life

expectancy and falling birth rates, where there

are skilled and unskilled labor force.

Razin and Sadka (2001) looks at the effect of

migration of various skill levels on the equilibrium.

The Razin-Sadka-Swagel Model

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Fiscal LeakageEffect

Median Voter Shift Effect

Income tax: levied on labor and capital

An income tax is generally levied on both labor and capital. The working young bear mostly the tax on labor income, whereas the retired old, who already accumulated savings, bear the brunt of the capital tax. Therefore, there arise two types of conflicts in the determination of the income tax: the standard intra-generational conflict between the poor and rich, and an intergenerational conflict between the young and the old.

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Fiscal Leakages We study two politico-economic forces that

determine the size of the welfare state, when its population ages: changes in the voting pivots and fiscal leakages from tax payers to transfer recipients. Tax revenues are generally biased in favor of the old (old-age social security, medicare, etc.). Therefore, one would expect the pro-tax coalition to gain more political clout as population ages; consequently, aging should tilt the political power balance in favor of expanding the welfare state.

However, a careful scrutiny of the politico-economic equilibrium reveals more factors at play. First, the equilibrium is governed by the preferences of two voting pivots, one young and one old. Aging may change the young pivot to a richer, more anti-tax individual. Second, the fiscal leakage of revenues from the larger number of old taxpayers of the capital tax component of the income tax to the young may encourage the latter to vote for more taxes.

But, on the other hand, the fiscal leakage from the young taxpayers of the labor tax component of the income tax to a larger number of old beneficiaries may tame the appetite of the young for more taxes. As a result, the welfare state does not necessarily expands, when its population ages.

Privatization The aging of the population shakes the public

finance of pay-as-you-go social security systems. Razin and Sadka (2004) develop a political-economy framework in which this demographic change leads to the downsizing of the social security system, and, as a consequence, to the emergence of supplemental individual retirement

programs.

Allowing for a one-shot budget deficit, earmarked to accommodate the cost of the social security reforms, is shown to facilitate the transition from a national to a private pension system.

The old, naturally, oppose the (partial) transition from a PAYG, old age social security system to individual retirement accounts, because they lose some of their pension benefits. They also have a strong moral claim that they contributed their fair share to the social security system, when they were young, but they receive at retirement less than what they paid when they were young.

Their opposition, strengthened perhaps by being morally justified, can be accommodated, in part or in full, if the government is allowed to make a one-shot, debt-financed transfer to the social security system, so as to allow the system to pay pension benefits in excess of the social security tax revenues.

This deficit is carried forward to the future, and its debt-service is smoothed over the next few generations, so that its future tax implications for the current young generation is not significant. Such a reform-earmarked budget deficit may indeed be considered in the expected revision of the Stability and Growth Pact in the EU.

For simplicity, suppose that the government makes a

transfer at the exact amount that is required to keep

the pension benefits of the current old intact,

despite the reduction in the social security tax rate.

Specifically, when falls, then the term b,

that is financed by this , falls as well.

All unskilled people have the same lifetime income, regardless of their cost-of-education parameter, e. Therefore, the attitude towards the (tax-benefit) pair is the same for all of them. Hence, the change in the median voter has no consequence on the outcome of the majority voting, when this median voter is an unskilled individual. For skilled individuals, lifetime income increases when the education-cost parameter, e, declines.

Because the social security system is progressive with respect to the cost-of-education parameter, the net benefit from it (that is, the present value of the expected pension benefit minus the social security tax) declines, as lifetime income increases (that is, as e falls). Therefore, a decline in the cost-of-education parameter of the median voter lowers the political-economy equilibrium social security tax and pension benefit.

But we assume that the government compensates the old generation, so as to maintain the total pension benefits intact. Therefore, despite the fall in b, the old are indifferent to the reduction in (and, consequently, the reduction in b). Thus, the outcome of the majority voting is now effectively determined by the young only.

The median voter is now a median among the young population only. This median voter has a lower cost-of-education index than before; that is, e(M) will fall.