Immigration and Social Security: A Political-Economy Approach

1. Immigration and Social Security: APolitical-Economy Approach Edith Sand and Assaf Razin Tel-Aviv University, Cornell University April 1 2008 Photo: Mexican Border,March 7, 2006

2. 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

3. 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.

4. STEEP INCREASE IN MIGRATION

5. 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.

6. Age Distribution, 2000Foreign-Born Population Who Entered the U.S. 1990-2000 and Native-Born Population Source: U.S. Census Bureau, Census 2000 Special Tabulations (STP-159)

7. Fertility of Immigrants in the U.S., 2002 Source: Center for Immigration Studies, 2002.

8. 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)

9. 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)

10. 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.

11. 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.

12. Outline • Baseline Model: no private savings and fixed wages– unique equilibrium • Extended Model: endogenous wages, private saving and capital accumulation—multiple equilibria • Results • Conclusion

13. 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.

14. 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.

15. 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)

16. 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)

17. 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)

18. 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, .

19. 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.

20. 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.

21. 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.

22. Sub-game perfect Markov equilibrium

23. -tax rate -migration quota 1 1 0 Ratio of old to young voters 0 Sub-game Markov Perfect Equilibrium The equilibrium is characterized by both taxation and immigration policy decision rules: Ratio of old to young voters

24. Equilibrium Paths • If n, m>0, the level of Social Security benefits is zero. • If n + m<0, migration quotas are at the maximum and the Social Security benefits are maximized. • 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.

25. 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.

26. 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.

27. 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.

28. 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.

29. 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.

30. 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.

31. 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.

32. 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.

33. 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

34. 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.

35. 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

36. 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.

37. 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)

38. 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)

41. 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.

42. An Extended-Model- Specific Equilibrium (continued) Extended-Model- Specificequilibrium 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.

47. “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)

48. “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.

49. Demographic Switching Equilibrium

50. Demographic Switching Equilibrium (continued)