Chapter 20 Social Security

1. Chapter 20 Social Security

2. Reading • Essential reading • Hindriks, J and G.D. Myles Intermediate Public Economics. (Cambridge: MIT Press, 2005) Chapter 20. • Further reading • Banks, J. and Emmerson, C. (2000) “Public and private pension spending: principles, practice and the need for reform”, Fiscal Studies, 21, 1 - 63. • Diamond, P.A. (1997) “Macroeconomic aspects of social security reform”, Brookings Papers on Economic Activity, 1 – 87. • Mulligan, C.B., Gil, R. and Sala-i-Martin, X. (2004) “Do democracies have different public policies than nondemocracies?” Journal of Economic Perspectives, 18, 51 - 74. • Samuelson, P.A. (1975) “Optimum social security in a life-cycle growth model”, International Economic Review, 16, 539 - 544.

3. Reading • Challenging reading • Bernheim, B.D. and Bagwell, K. (1988) “Is everything neutral?”, Journal of Political Economy, 96, 308 - 338. • Diamond, P.A. (2001) “Issues in Social Security Reform” in S. Friedman and D. Jacobs (eds.), The Future of the Safety Net: Social Insurance and Employee Benefits (Ithaca: Cornell University Press). • Galasso, V. and Profeta, P. (2004) “Lessons for an aging society: the political sustainability of social security systems”, Economic Policy, 38, 63 - 115. • Miles, D. (1998) “The implications of switching from unfunded to funded pension systems”, National Institute Economic Review, 71 - 86. • Mulligan, C.B., Gil, R. and Sala-i-Martin,X. (2002) “Social Security and Democracy”, NBER Working Paper no. 8958.

4. Introduction • One part of social security is the provision of pensions to the retired • Pensions raise questions about: • The transfer of resources between generations • The effect on incentives to save • The policy relevance of pensions is emphasized by the “pension crisis” • The crisis may force major revision in pensions provision

5. Types of System • Pensions may be paid from: • An accumulated fund • From current tax contributions • Pay-as-you-go: Taxes on workers pay the pensions of the retired • The systems in the US, UK, and many other countries are (approximately) pay-as-you-go • A pay-as-you-go systems satisfies Benefits received by retired = Contributions of workers

6. Types of System • Let b be the pension, R the number of retired, t the average social security contribution, and E the number of workers, then bR=tE • With constant population growth at rate n b=[1 + n]t • The system effectively pays interest at rate n on taxes • The return is determined by population growth

7. Types of System • Fully funded: Taxes are invested by the social security system and returned, with interest, as a pension • The budget identity is Pensions = Social security tax plus interest = Investment plus return • Denoting the interest rate by r b=[1 + r]t • A fully funded system forces each worker to save an amount t

8. Types of System • A pay-as-you-go system leads to an intergenerational transfer • A fully funded system causes an intertemporal reallocation • The returns (r and n) will differ except at a Golden Rule allocation • Systems between these extremes are non-fully funded • Hold some investment but may also rely on tax financing or disinvestment

9. The Pensions Crisis • There are three factors causing the pensions crisis • The fall in the birth rate • The increase in longevity • The fall in the retirement age • These factors cause the proportion of retired in the population to grow • The output of each worker must support an ever larger number of people

10. The Pensions Crisis • The dependency ratio measures the proportion of retired relative to workers • Tab.20.1 reports this ratio for several countries • The ratio is forecast to increase substantially • For Japan the rise is especially dramatic Table 20.1:Dependency ratio (population over 65 as a proportion of population 15 - 64) Source: OECD (www.oecd.org/dataoecd/40/27/2492139.xls)

11. The Pensions Crisis • Define the dependency ratio D by D = R/E • For a pay-as-you-go system t = bD • As D increases either • The tax rate rises for given b • The pension falls for given t • Without changes in b and/or t the system goes into deficit as D increases • None of the options is politically attractive

12. The Pensions Crisis • Fig. 20.1 shows the forecast deficit for the US Old Age and Survivors Insurance fund • The income rate is the ratio of income to the taxable payroll • The cost rate is the ratio of cost to taxable payroll • Holding b and t constant the system goes into permanent deficit from 2018 onwards Figure 20.1:Annual Income and Cost Forecast for OASI (www.ssa.gov/OACT/TR/TR04)

13. The Pensions Crisis • The UK government has followed a policy of reducing the real value of the pension • Tab. 20.2 reveals the extent of this decrease • The pension has fallen from 40% of average earnings to 26% in 25 years • It is forecast to continue to fall Table 20.2:Forecasts for UK Basic State Pension Source: UK Department of Work and Pensions (www.dwp.gov.uk/asd/asd1/abstract/Abstrat2003.pdf)

14. The Simplest Program • Assume an overlapping generations economy: • With no production • With constant population • A good that cannot be saved • Consumers have an endowment of 1 unit of consumption when young • They have no endowment when old • Consumers would prefer to smooth consumption over the lifecycle

15. The Simplest Program • The only competitive equilibrium has no trade • Young and old wish to trade • The old have nothing to trade • All consumption takes place when young • This autarkic equilibrium is not Pareto-efficient • A social security program can engineer a Pareto-improvement by making intergenerational transfers

16. The Simplest Program • Fig. 20.2 shows the effect of a pay-as-you-go system • A tax of ½ a unit of consumption is paid by young • A pension of ½ a unit is received by old • This is a Pareto-improvement over the no-trade equilibrium Figure 20.2: Pareto-Improvement and Social Security

17. The Simplest Program • A correctly designed system can achieve the Pareto-efficient allocation ( {x1*, x2*} in Fig. 20.2) • This result shows the benefits of introducing intergenerational transfers • The system has to be pay-as-you-go since a fully funded program requires a commodity that can be saved • These conclusions generalize to economies with production

18. Social Security and Production • Social security can affect saving and capital accumulation • The consequence depends on the position of the economy relative to the Golden Rule • Consider a program that taxes each worker t and pays a pension b • The program owns units of capital at time t, or units of capital per unit of labor • A program is optimal if t, b, and are feasible and the economy achieves the Golden Rule

19. Social Security and Production • A feasible program satisfies the budget constraint • In the steady state this becomes • Assuming the economy is at the Golden Rule with r = n the budget constraint becomes • A pay-as-you-go program with b = [1 + n]t attains the Golden Rule

20. Social Security and Production • A fully-funded system does not affect equilibrium • The budget constraint of a fully funded program is • At the steady state this becomes • The individual budget steady-state budget is • The program variables cancel • Individuals adjust saving to offset social security • Social security crowds out private saving

21. Population Growth • The fall in the rate of population growth is one of the causes of the pensions crisis • With a pay-as-you-go program a given level of pension requires a higher rate of tax • Assume initially that there is no pension program • Holding k fixed the consumption possibility frontier shows that • First period consumption is decreased but second period consumption is increased

22. Population Growth • The effect of population growth on consumption possibilities is shown in Fig. 20.3 • An increase in n shifts the frontier upwards • Evaluated at the Golden Rule • The Golden Rule allocation moves along a line with gradient – [1 + n] Figure 20.3:Population Growth and Consumption Possibilities

23. Population Growth • The effect of an increase in n on welfare depends on the capital stock • If k < k* welfare is reduced as the capital stock moves further from k* • This is shown be the move from e0 to e1 in Fig. 20.4 • If k>k* welfare is increased Figure 20.4:Population Growth and Consumption Possibilities

24. Population Growth • Assume the social security program is adjusted to maintain the Golden Rule • As n increases the frontier shifts and the tangent line becomes steeper • As shown in Fig. 20.5 the Golden Rule allocation moves to a point below the original tangent line • Per capital consumption is reduced Figure 20.5:Population Growth and Social Security

25. Sustaining a Program • In the economy without production the introduction of social security is a Pareto improvement • But it is not privately rational • The young in any generation can gain by not giving a pension to the old provided they still expect to receive a pension • Giving a transfer is not a Nash equilibrium strategy • This raises the question of how the program can be sustained

26. Sustaining a Program • One explanation is that the young are altruistic • They care about the consumption level or utility of the old • Altruism alters the nature of preferences but is not inconsistent with the aim of maximizing utility • Altruistic preferences can be written as or • Both forms of utility provide a private incentive for the young to transfer resources to the old

27. Sustaining a Program • A second reason why a program can be sustained is the threat of removal of pension • Not making a transfer to the old is a Nash equilibrium strategy • This argument relies on believing a transfer will still be received • The social security program is repeated over many periods so more complex strategies are possible • Punishment strategies can be adopted

28. Sustaining a Program • Don’t contribute is the Nash equilibrium strategy of the game in Fig. 20.6 • If the game is repeated an equilibrium strategy is “Contribute until the other player chooses Don’t contribute, then always play don’t contribute” • This is a punishment strategy Figure 20.6:Social Security Game

29. Sustaining a Program • Assume the discount factor is d • The payoff from always playing Contribute is 5 + 5d + 5d2 + … = 5[1/1 – d] • If Don’t contribute is played the payoff is 10 + 2d +2d2 + … = 10 + 2[d/1 – d] • The payoff from Contribute is higher is d > 5/8 • The punishment strategy supports the efficient equilibrium • The same mechanism can work for social security

30. Ricardian Equivalence • Ricardian equivalence applies when changes in government policy do not affect economic equilibrium • This occurs when changes in individual behavior completely offset the policy change • Changes in private saving ensure a fully-funded social security system does not affect the capital-labor ratio • This was an example of Ricardian equivalence

31. Ricardian Equivalence • Ricardian equivalence can also apply to programs that are not fully funded • A program that is not fully funded will affect a number of generations • The costs and benefits of the program are distributed across time • If generations are linked through intergenerational concern then a dynasty of consumers can offset a program • This generates Ricardian equivalence for a broader range of policies

32. Ricardian Equivalence • Assume utility is given by • Substituting for gives • Repeating shows that the consumer at t cares about all future consumption levels • If population growth is 0 the budget constraints of the two generations alive at t are

33. Ricardian Equivalence • With a pension the budget constraints are • Nothing changes if the bequest changes to • The same logic can be applied to any series of transfers • Reallocation of resources by the household offsets the effect of the transfer

34. Ricardian Equivalence • The dynasty adjusts bequests to eliminate the effect of the policy • This argument is limited by the need for there to be active intergenerational altruism • The initial bequest must also be larger than the pension (unless transfers from children to parents are allowed) • Ricardian equivalence can also be applied to government debt

35. Social Security Reform • Increasing longevity and the decline in the birth rate are increasing the dependency ratio • Many pension programs are unsustainable with significant tax increases • This has lead to numerous reform proposals • The reform most often discussed is to move to a fully funded system • A fully funded system can be government-run or utilize private pensions

36. Social Security Reform • The transition from pay-as-you-go to fully funded social security will take time • Those currently in work will bear two costs • Financing the pensions of the retired • Purchase capital to finance their own pensions • The welfare of those currently working will be reduced • The benefits will accrue to future generations • This leads to political resistance to reforms

37. Social Security Reform • Tab. 20.3 reports a simulation of transition for the UK • The pension is 20% of average earnings for the UK and 40% for Europe • Pension reform is announced in 1997, implemented in 2020, and completed in 2040 • The numbers are the change in wage in base case equivalent to the reform Table 20.3:Gains and Losses in transition Source: Miles (1998)

38. Social Security Reform • Reform reduces welfare for the young and middle-aged • These are the voters who must support the reform if it is to be implemented • Tab. 20.4 illustrates the political problem • The age of the median voter is forecast to rise • This is the group that suffer from pension reform Table 20.4:Age of the Median Voter Source: Galasso and Profeta (2004)

39. Social Security Reform • A fully-funded government system is equivalent to private pensions • Provided both invest in the same assets • In the US the state system invests only in long-term Treasury debt • This implies low risk and low return • Few private investors would select this portfolio • Reform in the US could also allow investment in risky asset • But this raises questions about the acceptable degree of risk

40. Social Security Reform • A further issue is the choice between defined benefit and defined contribution systems • A defined contribution system involves investments in a fund which are annuitized on retirement • The risk falls on the worker since the value of the fund is uncertain • A defined benefit system involves contributions which are a constant proportion of income and a known fraction of income is paid as a pension • The risk falls on the pension fund to meet commitments