Social insurance and contribution density

1. by Salvador Valdés-Prieto [1] CeRP Annual Conference, September 18-19, 2008, Moncalieri, Torino[1] Professor of Economics at the Pontificia Universidad Católica de Chile, svaldes@faceapuc.cl Social insurance and contribution density

2. Why density of contribution matters • Coverage: % of employment that contributes • China 2005: 48% of urban employees • Poland 2006: 68% through ZUS • South Korea 2000: 58% of the labor force • Brazil 2002: 49% of employment • Mexico 2003: 38% of employment • Cont. Europe with generous UI: low % of labor force • Mandates do not guarantee high density of contribution. Low Density Inadequate Pensions, even when the benefit formula is generous for high-density participants. Complaints against contributory pensions: Failure?

3. This paper offers • A formal model of density choice and adequacy in contributory mandatory old age pensions. • A model of unrealistic optimism (Weinstein 1980), where the bias is located in the budget constraint. Preferences are standard. UO provides a benevolent role for social insurance. • Models to find the optimal contribution rate for Bismarckian social insurance. Analogous to the standard optimal income tax problem. • Add income inequality and a non-contributory pension. Models identify the joint optimal parameters for a two-pillar pension system.

4. This paper’s findings • A mandate creates a distortion in density. A subsidy to earnings on covered jobs can be eff. • Even if income inequality is absent, some social insurance is socially desirable if UO is present. • Non-contributory pensions crowd out contributory pensions. Effect depends on g • In the absence of unrealistic optimism, the saving distortions caused by non-contributory pens. do not justify social insurance (mandate). • Given inequality, the socially optimal subsidy withdrawal rate is positive, but less than 100%.

5. A model to determine density • The State is unable to enforce in many jobs a mandate to contribute based on all earnings. • The State may be unwilling to enforce a mandate to contribute on jobs taken primarily by the poor. • D  [0,1] = proportion of time in the active phase of life on which the individual contributes for old-age. “Contribution density” yc = gross earnings in covered jobs per period, in the active phase. i= c, ex. yex = earnings per period in jobs or activities that are exempt or uncovered, in the active phase. zex = xex/xc. This is the “earnings differential”.

6. A model to determine density ep = earnings from work in old age, as a proportion of yc. Yp =productiv ratio when old, expected when active. Yp < 1. ta = net taxes on earnings caused by other branches of social ins, applicable only to covered jobs in the active phase. The contributory system for the middle class: Bismarckian • = equivalent rate that would apply if all the actual contributions were paid by workers. c = internal rate of return (real) paid by the contributory system to each generation of participants, net of taxes. The replacement rate is .(1+ c) pre tax.

7. A model to determine density • Income identities for an individual, before any voluntary saving: (1a) (1b)‏ => • The effective rate of return on contributions can be higher than (1+ c), if salaries paid by the uncovered jobs are sufficiently low.

8. A model to determine density F = stock of independent saving. r(+) = r.(1-tS) = rate of return on saving (F > 0)‏ r(-) = r(+) + s = rate on consumer loans (F < 0). Because s >>0, individuals cannot use cheap consumer credit to undo mandatory contributions. The period budget constraints are: (2a) (2b) Preferences: Labor supplies in both phases are assumed to be inelastic due to institutional constraints

9. A model of unrealistic optimism • If individuals visualize old age correctly and act as planned, they save adequately in the absence of SI. Is there a benevolent role for SI? • Time-inconsistency (Laibson 1997) creates a voluntary demand for commitment devices to save for general purposes. Since the private supply of commitment devices is plentiful, if each individual assesses the value of commitment devices rationaly, the market eq is eff. • Consumer inertia and changes in the default option have a major impact on equilibria (Madrian and Shea, 2001). If individuals are rational, they value being relieved from their own inertia. There exists a voluntary demand for jobs bundled with anti-inertia devices. The State’s role is limited to popularizing the supply of anti-inertia devices. • Neither of these situations justifies mandates (SI).

10. A model of unrealistic optimism • Evidence: the young detest the mandate to save. First-pass explanations: • 1. They are right. Mandatory saving has a net lower return than independent financial saving. Not in Chile: fully funded, low fees (about 0.60% per yera of assets), choice of risk level among 5 balanced portfolios. • 2. They are right. Mandatory saving is too illiquid. Independent financial saving is more valuable. • In both hypothesis, the old agree with the young in detesting the mandate.

11. A model of unrealistic optimism • Evidence: the young detest the mandate to save. Torche and Wagner (1997) using Chilean individual data for 1990: workers consider that about half of their mandatory contribution for old age is a pure tax. • Evidence: Old are grateful for mandates and SI, on a lifetime basis. Reversal of opinion. • Psychology has documented a high prevalence of “unrealistic optimism” (UO) (Weinstein 1980, Weinstein & Klein 1996, Puri & Robinson 2007).

12. A model of unrealistic optimism • The optimistic bias can take several forms regarding old age saving (simultaneously): • Labor productivity in old age may be smaller than hoped for when young. • Duration of old age may be underestimated, • Out-of-pocket expenses caused by the decline in health may be underestimated. UO and the “Retirement consumption puzzle” • Surprises may occur gradually over time, say starting at age 40, so consumption drops should be small in any given year. No need for large consumption surprise at the date of retirement.

13. A model of unrealistic optimism • 0 ≤ yp < ybiasedp < 1. Behavior is given by: • Because of the two-period lives assumption, in this model learning occurs only at old age. This model forces a retirement consumption puzzle, which the UO hypothesis does not require.

14. Cp Fbiased Abiased ep biased F ep unbiased A Ca A model of unrealistic optimism

15. A model of unrealistic optimism The best personalized social insurance: q* solves P3

16. A model of unrealistic optimism Results about the best personalized SI: • In situations 1 and 2a, D*= 0. Since changes in q do not affect welfare, the planner is unable to attenuate the impact of UO. • In situations 3 and 2c, D*= 1. If F* is interior, • Differences in after-tax returns between the mandatory saving and independent saving have the expected effect on q*. • The optimistic bias favors q* > 0.

17. A model of unrealistic optimism More results about the best personalized SI: • In situation 2b, D* is interior and the sign of q* is ambiguous: • first effect is negative. An interior density allows to raise consumption at a smaller cost than the interest of consumer credit, even if rc is good (if rc = r.(1-tS)). If q rises, the ind still loses the difference between MRT a d. • Second effect is UO, and favors positive q*. And the best personalized q* is heterogeneous. See P3.

18. Optimal uniform social insurance • To focus on SI alone, eliminate income inequality: productivity is assumed to be the same for all individuals: x = 1 for all. • Due to heterogeneity in b and zex, and to asymmetric information about this heterogeneity, the State can only use a uniform contribution rate. This uniformity makes SI more inefficient. • Fiscal balance considers three taxes: ta, tS and a new tax La , levied only in the active phase, whose role is to balance the fiscal budget.

19. Optimal uniform social insurance • La is assumed to be a lump-sum, of which l% is dissipated in efficiency losses and tax administration. (Regulatory economics) • La does not apply in old age, so changes in La do not affect the welfare of the generation that is old at of the change. • Since tS is levied on the old, its revenue is divided by (1+gCR). • Social welfare is the simple sum of the lifetime utilities, as assessed by those same individuals when old.

20. Optimal uniform social insurance

21. Optimal uniform social insurance Policy lesson: An increase in the contribution rate induces some individuals to switch to exempt jobs and reduce density, and reduces pension adequacy. • Should the planner complement the mandate with a subsidy to earnings, on covered jobs alone? • Simulations can give an answer. This insight comes from the focus on density.

22. Redistributive concerns and non-contributory pensions • The model must be extended to incorporate income inequality.This creates demand for progressive redistribution.This creates non-contributory pensions. • Family that encompasses flat universal pensions, minimum pensions, in-between. • CP(D) is the contributory pension (self financed), • BP is a basic pension or subsidy. • g is the subsidy’s “withdrawal rate”, with g e (0,1).

23. Redistributive concerns and non-contributory pensions • g = 0 is a flat universal pension, as in Denmark and New Zealand. • g = 1 is a minimum pension subsidy (supplies the amount needed to meet a legislated goal) • g in between: Since 1957 Finland introduced the first NCP of this type, with a withdrawal rate of 50% (g = 0,50) (Antolin et al 2001). About 80% of all Finnish pensioners obtain some supplement from this first pillar. • Sweden (since 2003) and Norway (since 2010) have a simular scheme with 2 levels for g (first g = 1 and then g = 0,48 and 0,60, respectively). • Chile introduces from 2008 g = 0,32.

24. F2 Cp C E B’ MCPWS D A’ Subsiy at B’ Contributory pension at B’ BP B A Ca Redistributive concerns and non-contributory pensions Impacts of NCS on D* and F* • Cases 1 and 2a (D* = 0): DD* = 0 and DF* << 0. • Cases 3 and 2c, (D* =1): DD* = 0 and DF* < 0. • Case 2b: DD* < 0 and DF* = 0.

25. Redistributive concerns and non-contributory pensions Another benevolent justification for Soc Insur? • NCS distort voluntary saving F*. • To limit this loss, a planner should mandate everybody to save the efficient amount. This would be benevolent despite the absence of UO. • In this hypothesis, NCS crowd-in mandates to contribute for old age. The channel is the benevolent policymaker’s reaction function. • Is this hypothesis consistent? The mandate deepens the original distortion in density, caused by the non-contributory subsidy. • This mandate, in the absence of UO, reduces welfare for the middle class, because it distorts D

26. Redistributive concerns and non-contributory pensions The socially optimal withdrawal rate under UO and income inequality: • Policy question 1: is the optimal size of the old-age subsidy withdrawal rate g at one extreme? • Policy question 2: should contributory pensions incorporate progressive redistribution in its benefit formula? (abandoning Bismarck?). Alternatively, the tax-expenditure system would satisfy redistributive concerns alone, more eff. • Another way to pose question 2 is whether a special progressive tax on contributory pensions alone is superfluous.

27. Redistributive concerns and non-contributory pensions To answer both questions together, consider a simple tax-expenditure system and solve P7:

28. Concluding comments • Next steps: numerical simulation of problems P3 to P7, and sensitivity analysis. • This paper offers a new framework to guide the design of “multipillar” pension systems (World Bank, 1994). • Density → adequacy → failure • Density can be improved by streamlining the design of noncontributory subsidies, to minimize the crowding-out effect. This can improve adequacy and satisfaction.