PAYG pensions with endogenous fertility

1. PAYG pensions with endogenous fertility Volker Meier Ifo Institute for Economic Research

2. Questions • Why do Pay-as-you-go (PAYG) pensions exist? • Nature and size of fiscal externalities? • Structure of second-best pension formulas? • Alternative instruments: child benefits, education subsidies

3. Fundamental Problem • Contracts with minors to finance education cannot be enforced => underinvestment • Solution: Public schooling + Transfers from young to old (PAYG pension scheme)

4. Fiscal externalities in PAYG • Usual pension formulas: flat (Beveridge) or contribution-related (Bismarck) • Consider PAYG with fixed contribution rate • Pensions rise with higher fertility and more education, not taken into account by parents

5. Impact of pensions on fertility • Evidence on negative impact (Cigno and Rosati, 1996; Cigno et al., 2003) • Reasons: reduction of transfer from children to parents

6. Size of fiscal externality • Here: fertility • Fiscal externality = present value of future contributions to PAYG scheme • Reason: pension of additional individual is financed by her children (Sinn, 2001)

7. Basic Model • Kolmar (1997) • Standard overlapping generations structure • Identical individuals, small open economy • Labor supply exogenous • Childhood, working period, retirement

8. Budget equations • consumption per child • consumption in working age • consumption in retirement

9. Pension formulas • Funded pension: • Standard PAYG pension: • Child-related PAYG pension: • Generalized PAYG pension: • : child factor

10. Utility function • Utility: • Decisions on savings and number of children • First-order conditions:

11. Comparative Statics • Number of children increases with higher child factor in PAYG scheme => return on PAYG contributions rises with higher child factor

12. Welfare analysis • With endogenous fertility: Pareto criterion not applicable (Golosov et al., 2007) • Here: additional individuals share burden • Welfare function must be specified

13. Policy analysis • Government maximizes indirect utility in steady state wrt PAYG tax, child factor • Outcome: no interior solution • Either: PAYG tax = 0 • Or: PAYG tax at maximum, child factor =1

14. Interpretation • Fiscal externalities vanish when government imitates family transfer scheme

15. Child benefits • Van Groezen et al. (2003) • PAYG and child benefits grow simultaneously, like Siamese twins • Only standard PAYG: • Benefit per child, child benefit tax rate: • Consumption in working age:

16. Policy analysis • Number of children increases in child benefit • Maximization of indirect utility in steady state wrt level of child benefit

17. Optimum child benefit • Optimum level: • Present value of child benefits = Present value of contributions of child toward pension scheme • Government again imitates family transfer scheme • Resulting allocation identical under both internalization schemes

18. Extension 1: Endogenous Labor Supply • Fenge and Meier (2005) • Opportunity cost of having children: with

19. Pension formula and fertility • Pension: • Fertility decision:

20. Optimum child factor with opportunity cost • Objective: maximize indirect utility in steady state • Optimum child factor always <1! • Reason: negative externality on pensions of currently old in fertility decision through labor supply reduction

21. Child benefit as alternative instrument • Optimum allocation can be achieved both by continuum of combinations of child factor and child benefit • Reason: fertility determines labor supply

22. Child factor vs family allowances • Fenge and Meier (2004): with endogenous labor supply + only direct cost of children • Contribution-related pensions: Optimum allocation can be achieved by continuum of combinations of child factor and family allowances and exclusive use of only one instrument

23. Credit constraints • Equivalence result in two-period OLG framework with identical households • Change in favor of family allowances with (i) finer multiperiod framework, (ii) heterogeneous households • Change in favor of fertility-related pension if government allows to borrow against this part of pension: constraint less tight

24. Benefit structure with flat pension • Optimum is never achieved with positive family allowance tax in combination with child factor below unity • Interior solution: Replacing family allowances by child factor reduces tax on labor supply • Boundary solution: additional family allowances if this increases labor supply

25. Extension 2: Stochastic Fertility • Cremer, Gahvari and Pestieau (2006) • Investment in children: • Probabilities of having children, • Average number of children:

26. Problem of Social Planner • Maximization of steady-state lifetime utility • Budget constraints Storage: PAYG:

27. Second-best allocations • Either storage or PAYG, never both • Endogenous fertility increases range in which PAYG is superior to storage • Pension increases in number of children • Contribution falls in number of children, larger families more than compensated for extra cost of children

28. Extension 3: Stochastic Fertility and Education • Meier and Wrede (2005) • Individuals with high and low wages: • Investment in fertility with stochastic outcome either 0 or n • Saving after number of children is known • Lower price of education ρfor high-skilled • Investment in education with stochastic outcome either low or high productivity

29. Consumption and utility Consumption in working age • Without children: • With children: Utility • Without children: • With children:

30. Pension formula • Childless individuals: • Parents:

31. Saving, fertility, education • Saving decision • Without children: • With children: • Education and fertility: expected cost = expected marginal benefit to individual

32. „First-best“ allocations • Maximize welfare of working age generation at exogenous tax rate • Marginal utilities across states in old age equalized • Education and migration: cost = marginal benefit to parent generation

33. Second-best pension schemes • Government maximizes aggregate expected utility wrt pension parameters s.t. focs on individual level for saving, education, fertility and pension budget constraint

34. Properties of second-best pension formulas • Any second-best pension formula characterized by • (a) partial assignment of children‘s contributions to parents: • (b) strictly positive fertility-related component:

35. Interpretation • Purely fertility-related component to insure parents against unfortunate outcome of education investment => PAYG superior to transfer arrangement within families • Alternative instruments: family allowances, scholarships

36. References (1) • Kolmar, M. (1997) Intergenerational redistribution in a small open economy with endogenous fertility. Journal of Population Economics 10, 335-356 • Van Groezen, B., Leers, T., Meijdam, L. (2003) Social security and endogenous fertility: pensions and child allowances as Siamese Twins. Journal of Public Economics 87, 233-251

37. References (2) • Fenge, R., Meier, V. (2005), Pensions and fertility incentives. Canadian Journal of Economics 38, 28-48 • Cremer, H., Gahvari, F., Pestieau, P. (2006), Pensions with endogenous and stochastic fertility. Journal of Public Economics 90, 2303-2321

38. References (3) • Fenge, R., Meier, V. (2004) Are family allowances and fertility-related pensions Siamese twins? CESifo Working Paper No. 1157, Munich. International Tax and Public Finance, forthcoming. • Meier, V., Wrede, M. (2005) Pension, fertility and education. CESifo Working Paper No. 1521, Munich