Immigration and Social Security: A

Political-Economy Approach

Edith Sand and Assaf Razin

Tel-Aviv University, Cornell University

April 1 2008

Photo: Mexican Border, March 7, 2006

How Immigrants Saved Social Security

•Immigration is good for the financial wealth of social security because more workers means more tax revenue. In the fine print of 2008 Annual Report on Social Security, released last week the program trustees noted growing numbers of “other than legal” workers are expected to bolster the program over the coming decades.

•prilA 2, 2008EDITORIALNYTIMES

Contribution of paper

• New analysis: intergenerational conflicts about social security and immigration: Immigrants affect the conflict between young and old over the size of the PAYG Social Security system.

• New feature: a strategic voting feature, in addition to the traditional labor supply effect.

Net migration rates, OECD countries, 1956-2003

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

All countries

Net migration as a percent of the total resident population

Source : Labour Force Statistics, OECD, 2006.

Demographic characteristics of immigrants:

• Their age-distribution density is more

concentrated in the young (labor-force

age) distribution than the native-born.

• They have higher birth rates than native-

born.

Age Distribution, 2000 Foreign-Born Population Who Entered the U.S. 1990-2000 and Native-Born Population

Source: U.S. Census Bureau, Census 2000 Special Tabulations (STP-159)

0

5

10

15

20

25

30

35

0- 4 5- 9 10- 14 15- 19 20- 24 25- 34 35- 44 45- 54 55- 59 60- 64 65- 74 75- 84 85 +

Age

Precentage

Foreign-Born Population

Native Population

Fertility of Immigrants in the U.S., 2002

CountryTFR in The U.S.Mexico3.51

Philippines2.30

China2.26

India2.23

Vietnam1.70

Korea1.57

Cuba1.79

El Salvador2.97

Canada1.86

United Kingdom2.84

Average2.86

Source: Center for Immigration Studies, 2002.

Background Literature on Immigration

• Simon (1995): New immigrants contribute more to the public coffers in taxes than they drew out in welfare services.

• Empirical papers: general equilibrium impacts of more immigrants.

Lee and Miller (2000)

Storesletten (2000)

Razin Sadka and Swagell (JpubE 2002)

Background Literature on Social Security• The dynamic sustainability of a PAYG in Political

Economy models. Galasso (1999)

Boldrin and Rusthicini (2000)

The political-economy effect of low skilled immigrants on the size of the intra-generational redistributive policy.

Dolmas and Huffman (2004)

Ortega (2005)

Razin, Sadka and Swagell (2002)

Description of the Model

---A dynamic overlapping-generation

---Immigration policy and a the size of the PAYG Social Security system are jointly determined by majority voting.

Issues and Features

• Can immigrants resolve the fiscal problem of the PAYG Social Security system especially in the presence of the aging of the population?

• Can young vote for liberal immigration policy even though wages are depressed by immigration?

• Political Economy Feature: Not only current economic considerations (e.g. wages) about migration are considered- but also the immigrants’ future political power. Immigrants not only depress wages. Through their children they increase the future tax base and thus the benefits to the current young when becoming old. But in the future they can also change the political power balance that tilts the voters against enlarged banefits.

Outline

• Baseline Model: no private savings and fixed wages– unique equilibrium

• Extended Model: endogenous wages, private saving and capital accumulation—multiple equilibria

• Results

• Conclusion

Baseline Model

• OLG model with two periods.

• PAYG Social Security but no private savings.

• Immigration:– Immigrants enter the economy when young.

– They obtains the right to vote only in the next period, when old.

– They have a higher population growth rate than that of the native born.

• The tax and immigration policies are determined each period through majority voting.

Preferences

• 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.

tto bbU )(

11

1 ln1

)1(ln),,(

tt

tttttty b

lwlbwU

]1,0[

0

iU

Technology

• The production function is a linear production function:

(3)

where is the output, and is the aggregate labor

supply in period t.

Labor supply is given by:

(4) )1( ttt wl

tt NY

tY tN

Labor Supply

• The aggregate labor supply is:

(5)

where denotes immigration quotas, and is the number of the native born workers.

• Immigrants have a higher population growth rate than the native born, :

(6)

• The number of native born individuals is:

(7)

)1( tttt lLN

]1,1[m

]1,0[

mn ]1,1[n

)1()1( 111 mLnLL tttt

tL

Social Security System- PAYG

The government levies a flat tax on the young's wage

income, which fully finances the social security benefits

paid to the old.

(8)

Re-arranging the expression yields:

(9)

)1()1( 11 tttttttt LwlLb

)1(

)1)](1()1[(

1

1

t

tttttt

mnwlb

Voter Preferences

The indirect utility functions of old individual is:

(10)

Preferences of the old:

– Largest possible migration quotas, .

– The tax rate which maximizes the Social Security

benefits, .

)1(

)1)](1()1[(),,,(

1

11

t

ttttttttt

o mnlwLV

1

*t

1t

Voter Preferences

The indirect utility function of young individual is:

(11)

Preferences of the young:

– Minimal tax rate, .

– Regarding migration quotas the young has

ambiguous preferences.

)1(

)1)](1()1[(ln)1(

1ln),,,( 1111

11t

tttttttttttt

y mnlwlwV

0t

Voting Attitudes

A higher migration quotas increase more the number of

young than old in the next period.

• It increases the next period Social Security benefits.

• It can affect the decisive voter’s identity( young or old) in the next period.

=> Therefore, the young voter favors the largest possible

quotas, which yet changes the decisive voter's identity in

the next period from young to old.

Sub-game Markov Perfect Equilibrium Path

Sub-game Markov Perfect Equilibrium:

The vector of expected next-period policy decision rules as a function of the current state variables, upon which the current decisive voter acts, is the same vector of policy decision rules chosen by the current decisive voter as a function of previous period state variable.

Sub-game perfect Markov equilibrium

Sub-game Markov Perfect Equilibrium

The equilibrium is characterized by both taxation and immigration policy decision rules:

otherwise

uifm

nG

t

ttt

1

1)(*

1

t

0 1

1*

-tax rate

Ratio of old to young voters

0 1

t

*

1-migration quota

Ratio of old to young voters

otherwise

uifT

t

tt

t

1

10)( *1

Equilibrium Paths

1. If n, m>0, the level of Social Security benefits is zero.

2. If n + m<0, migration quotas are at the maximum and

the Social Security benefits are maximized.

3. If n<0 and n + m>0, there is a cycling equilibrium path: • If In a given present period, the old sets no restriction on

immigration and the Social Security benefits are maximized;

• Then, In the next period the young set the Social Security

benefits to zero and there are some restrictions on

immigration.

Interpretation: Type I Equilibrium

•The first equilibrium path is the one where the population growth rate of the native-born and the immigrant population growth rate are both positive; that is, n, m>0. In this case, the level of social security benefits is zero. This is due to the fact that for every level of immigration, the number of next period young voters exceeds the number of next period old voters. Therefore, the decisive voter in the current and all the following periods is the young voter, and her preferences are for zero labor tax. The young voter is indifferent concerning the level of immigration because it has no influence on her current income, nor on the next period decisive voter's identity. The resulting equilibrium path is one in which there is a majority of young voters, and the Social Security System is dismantled, for ever.

Interpretation: Second-II Equilibrium

•If the sum of the native-born and immigrant population growth rates is negative, m + n<0, the number of next period old voters always 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 maximum flow of immigrants.

Interpretation: Type-III Equilibrium

•The third equilibrium path obtains if the native-born and immigrant populations growth rates are: n<0, and

•m + n > 0 . This equilibrium path is characterized by a cycling taxation/social-security policy over two consecutive periods. Some positive level of immigration always prevails. This is due to a "demographic switching" strategy of the current and next period young voters. The reason is that when there is a majority of old, their preferable immigration quota is at the maximum and the tax rate is at the "Laffer point". Because m+n>0 and the old decisive voter allows as much as possible immigrants, the number of next period young voters exceed the number of next period old voters.

Type-III Equilibrium (continued)

•Thus, in the next period the decisive voter must be the young. This voter opts for a zero tax rate, and does vote strategically on immigration levels. This means setting immigration at the threshold level ,-n / m. The identity of the next period decisive voter will change from young to old (a possibility of such demographic changes exists because the native-born population growth rate is negative). This creates a cycling taxation/social security policy, with a certain level of immigration, depending on the identity of the decisive voter.

Evaluation

•In the baseline model, a perishable consumption good is produced using only labor as an input; transfers from young to old (paid by flat rate tax on labor income) are the only means of guaranteeing old-age consumption. Each generational cohort lives two periods, supplying labor in-elastically when young, and deriving utility from consumption in both periods of life.

•If there were not to be immigration, it is a standard outcome in this framework that if the population growth rate is positive, young always outnumber the old. Therefore, a pay-as-you-go social security system cannot be sustained under majority voting. If, however, population growth is negative, so that the old outnumber the young, then the pay-as-you-go system can be sustained with a constant tax rate that maximize the social security benefits ( the preferred point of old cohort at each period). Now introduce immigration into the standard framework. Immigrants arrive young but cannot

vote until they are old .

• Their children, who are identical to young native born, can vote when young. Moreover, immigrants (though not their offspring) have a birth rate that is larger from the native born rate. Immigration policy can be described by a endogenously determined quota variable. We restrict the feasible choices of the quota with doubling the population being

an upper bound on immigration .

•The central tension faced by today's young in thinking about policy is that both the ratio of young to old in the next period, and the ratio of taxpayers to old dependents in the next period increase in the present period immigration quota. A higher value of the latter this period will raise the number of young tax payers per old dependent next period, but also increase the voting power of the young next period, perhaps putting them in the majority. If the native born and the immigrants' birth rate are positive (while by assumption the latter rate exceeds the former), then young voters always outnumber old voters, and the pay-as-you-go social security system will not be sustainable as a Markov equilibrium.

• So immigration is of no help in this case. On the other hand, if the native-born birth rate is negative, then the social security system is sustainable absent immigration. In this case the question is not whether immigration helps sustain social security, but whether it threatens its sustainability. Assuming that birth rate of natives is negative, the sort of equilibrium that arises depends on the sum of native-born and immigrants birth rates. If the sum of native-born and immigrants' birth rates is negative, admitting no immigrants today guarantees an old majority tomorrow. Even if current young choose the maximum allowable immigration so as to maximize next period benefits, there will still be a majority of the old tomorrow. Both current old and current young agree on letting in the maximal amount of immigrants, and except perhaps for the initial period, the majority of voters will always be old. Therefore the tax rate is set at the "Laffer " rate. Immigration does not yet add much to the survival of the social security system in this case

•But when the sum of native-born and immigrants' birth rates is positive and the native-born birth rate is negative, immigration adds an interesting twist. It in essence poses a threat to social security that in the absence of migration will be assured. In this case the numbers of old and young next period are equal and by assumption ties are decided in favor of the old. Then current young's desire for higher immigration, to maximize their old-age benefits, is constrained by their desire to maintain old majority next period. If the young are currently in the majority the set the current tax rate equal zero (implying no benefits for the current old) and set immigration quota at an intermediate level that barely makes the old majority in the next period. Next period, the old median voter sets the tax at the "laffer" rate and the immigration quota at the maximum level. The latter guarantees that the young will be in majority in subsequent period; and the cycle repeats itself.

The Extended Model

• Young individual is allowed to save.

• Aggregate savings of the young generates next

period aggregate capital.

• Aggregate capital is being used as a factor of

production, in a constant return to scale production

function.

• Wage and interest rate are endogenously

determined

Utility Function

The utility of the young and old agents:

(12)

(13)

where is the interest rate, and is the savings

of the young in period t.

11 )1(),,( tttttto srbrsbU

tttt

tttttttty srb

lswlrbwU )1(ln

1)1(ln),,,( 11

1

11

tstr

Technology

• The Cobb-Douglas production function is assumed to

use both labor and capital as its factors of production:

(14)

where is the aggregate amount of capital.

• The wage rate and interest rate are determined by the

first order conditions:

(15)

(16)

tttt klw )1)(1(

ttt KNY 1

tK

1)1( 111 tttt klr

The Individual Economic Decisions

• The labor-leisure and saving-consumption decisions are:

(17)

(18)

• The market clearing condition requires that the net

domestic saving generates net domestic investment:

(19)

)1( ttt wl

1

1

1)1(

11

1

t

ttttt r

blws

t

ttt

mnks

1

)1(11

An Markov-sub-game-Equilibrium Path Specific to the Extended Model

Adding capital creates in addition to an equilibrium

similar to the baseline model, another equilibrium.

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.

An Extended-Model- Specific Equilibrium (continued)

Extended-Model- Specific equilibrium is a combination

of two strategies:

• The "demographic switching" strategy.

• The "demographic steady“ strategy. This strategy is characterized by:

An equilibrium tax rate which is a decreasing function of the capital per (native-born) worker.

A liberalized immigration policy leading to a majority for the young, every period.

“Demographic Steady“ Strategy

• The tax rate is a non-increasing function of the amount

of capital per (native-born) worker. Assuming differently:

(15)

• The openness rate is always maximal.

(16)

1111 ttttt ksbk

1111

1

)(

tttt

t

ttt bkk

k

sw

“Demographic Steady“ Strategy

For a low capital per worker the “demographic steady”

strategy dominates.

• For low capital per worker, the current tax rate is higher

under the “demographic steady” strategy, leading to

lower next period capital per worker.

• Due to diminishing marginal returns to capital, lower next

capital per worker increases the return to capital more

than proportionally, thereby increasing the income of the

young.

Demographic Switching Equilibrium

Demographic Switching Equilibrium (continued)

"demographic switching " equilibrium

• Markov sub game Perfect equilibrium (referred to by "demographic switching " equilibrium) policy rules do not depend on the capital per (native-born) worker state variable.

In a given period, the economy is fully opened to immigration, and Social Security benefits are maximized.

• In the next period there are no Social Security benefits and there are some restrictions on immigration.

Multiple Equilibria

Both the Demographic Steady Equilibrium Path and the Demographic Switching Equilibrium Path could exist for the same initial values of the capital stock. The decision rule of the Demographic Steady Equilibrium Path depends on both u and k; the decision rule of the Demographic Switching Equilibrium Path depends on u only.

•While the Demographic Switching equilibrium path exist for all possible initial values of k, the demographic steady equilibrium path exists only for a closed range of the capital stock.

•Namely, the demographic switching equilibrium path exists for all possible values of capital stock , inside and outside the closed range for which the demographic steady path exists, and outside this range.

Effects of Immigration

A cycling equilibrium path exists only due to immigration:

• On the one hand, it increases the Social Security benefits.

• On the other hand immigration poses a threat to the Social Security system, that in the absence of

migration would have been assured.

The effect of ageing

In the cycling path, ageing of the native born population: – Increases migration quotas in periods where there is a majority

of young.– Decreases social security benefits in periods where there is a

majority of old.

If n decreases below a certain threshold (n + m < 0), it leads to an equilibrium path where:

– The old are in the majority every period. – The immigration policy is liberalized.– The Social Security system is sustained at its maximal level.

Under the demographic steady equilibrium path:

– Immigration increases the volume of the Social Security benefits.

– Ageing decreases the Social Security benefits.

Evaluation of the effect of Migration

•The first equilibrium type- the "demographic swithching" equilibrium- of the no-migration economy yields two possible equilibrium paths: If the population growth rate is positive, young always outnumber the old. Therefore, a pay-as-you-go social security system cannot be sustained under majority voting. If, however, population growth is negative, so that the old outnumber the young, then the pay-as-you-go system can be sustained with a constant tax rate

that maximize the social security benefits..

•Now introducing immigration to this framework. If the native born and the immigrants' birth rate are positive (while by assumption the latter rate exceeds the former), then young voters always outnumber old voters, and the pay-as-you-go social security system will not be sustainable as a Markov equilibrium. So

immigration is of no help in this case .

•On the other hand, if the native-born birth rate is negative, then the social security system is sustainable absent immigration. In this case, though immigration increases the total amount of tax collected, it also threatens the sustainability of social security. Assuming that birth rate of natives is negative, the sort of equilibrium that arises depends on the sum of native-born and immigrants birth rates. If the sum of native-born and immigrants' birth rates is negative, admitting no immigrants today guarantees an old majority tomorrow. Even if current young choose the maximum allowable immigration so as to maximize next period benefits, there will still be a majority of the old tomorrow.

Immigration does not yet add much to the survival of the social security

system in this case•Both current old and current young agree

on letting in the maximal amount of immigrants, and except perhaps for the initial period, the majority of voters will always be old. Therefore the tax rate is set at the "Laffer " rate. Immigration does not yet add much to the survival of the social security system in this case.

Immigration adds an interesting twist in the Switching Equilibrium

•But when the sum of native-born and immigrants' birth rates is positive and the native-born birth rate is negative, immigration adds an interesting twist. It in essence poses a threat to social security that in the absence of migration will be assured. In this case the numbers of old and young next period are equal and by assumption ties are decided in favor of the old. Then current young's desire for higher immigration, to maximize their old-age benefits, is constrained by their desire to maintain old majority next period. If the young are currently in the majority the set the current tax rate equal zero (implying no benefits for the current old) and set immigration quota at an intermediate level that barely makes the old majority in the next period. Next period, the old median voter sets the tax at the "laffer" rate and the immigration quota at the maximum level. The latter guarantees that the young will be in majority in subsequent period; and the cycle repeats itself. Therefore, in this case immigrants, by having a higher population growth rate than native born, changes the demographic balance in favor of a future younger population that menace the sustainability of social security ..

Migration increases the total amount of tax collected, but not

critical to survival of social security•The second equilibrium type- the "demographic steady"

equilibrium- with-no-migration yields stable steady states characterized by lower sustainable social security benefits. This results not only from the fact that migration increases the total amount of tax collected and thereby the social security benefits received, but also from the indirect effect throughout savings. By lowering the savings of the young, migration leads to higher equilibrium tax rate in the "demographic steady" strategy which has an additional positive effect on social security benefits.

Conclusion

•The steady-demographic equilibrium features a new strategy of the young depending on the capital per (native born) state variable (a second state variable in addition to the state variable in the base-line model which is the ratio of old to young). For a range of (native-born) worker values, the optimal strategy of the young is always to vote for a positive tax rate (a decreasing function of the capital stock) and maximum migration quota, thus creating a stable steady state where both migration and the social security system are both sustainable. The size of the social security system depends on the capital per native-born worker and on the exogenously given ceiling on migration quotas. Thus the political-economy sustainable migration boosts up the size of the social security's tax revenue.

social security provides an effective incentive for the liberalizing of

immigration policy

•Although social security provides effectively an incentive to a sustainable liberal immigration policy, it is not the only such incentive. When factor prices are endogenous, in the extended model, the young will also have an incentive to allow immigrants in order to increase the future return to capital, even without a social security system.