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 ρ for 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