PAYG pensions with endogenous fertility

PAYG pensions with endogenous fertility

Volker Meier

Ifo Institute for Economic Research

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

Fundamental Problem

• Contracts with minors to finance education cannot be enforced => underinvestment

• Solution: Public schooling + Transfers from young to old (PAYG pension scheme)

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

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

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)

Basic Model

• Kolmar (1997)

• Standard overlapping generations structure

• Identical individuals, small open economy

• Labor supply exogenous

• Childhood, working period, retirement

Budget equations

• consumption per child

• consumption in working age

• consumption in retirement

:)1( ttttyt sxnwc

:11 ttot Rsc

:tx

Pension formulas

• Funded pension:

• Standard PAYG pension:

• Child-related PAYG pension:

• Generalized PAYG pension:

• : child factor

tft wR 1

11 ttgt wn

11 ttct wn

gt

ct

pt 111 1

Utility function

• Utility:

• Decisions on savings and number of children

• First-order conditions:

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yt nccU

0

0

31

21

21

Un

UxU

RUU

t

pt

t

Comparative Statics

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

Welfare analysis

• With endogenous fertility: Pareto criterion not applicable (Golosov et al., 2007)

• Here: additional individuals share burden

• Welfare function must be specified

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

Interpretation

• Fiscal externalities vanish when government imitates family transfer scheme

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:

11 ttgt wn

,b

ttttttyt sxbnwc 1

Policy analysis

• Number of children increases in child benefit

• Maximization of indirect utility in steady state wrt level of child benefit

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

Rwb tt /1*

Extension 1: Endogenous Labor Supply

• Fenge and Meier (2005)

• Opportunity cost of having children:

with

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0'',0',0)0( fff

Pension formula and fertility

• Pension:

• Fertility decision:

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nf

nfnnfw

)(1

)(111 1111

0)(')1( 31

21

U

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t

tt

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

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

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

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

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

Extension 2: Stochastic Fertility

• Cremer, Gahvari and Pestieau (2006)

• Investment in children:

• Probabilities of having children,

• Average number of children:

m

12 nn in0,0;1 ''

2'212 pppp);(mpi

2211 npnpn

Problem of Social Planner

• Maximization of steady-state lifetime utility

• Budget constraints

Storage:

PAYG:

2

1)()()(

i

oyi cvcump

2

1

1

1)(

ii

oity

ii xnmr

ccymp

2

1

1

)()(

ii

oity

ii xnmmn

ccymp

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

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

lh ww

)( imp

)( ieqie

Consumption and utility

Consumption in working age

• Without children:

• With children:

Utility

• Without children:

• With children:

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000 iii zvcU

kkinin

kin wzvcU

Pension formula

• Childless individuals:

• Parents:

ii w0

kikin nwnw

Saving, fertility, education

• Saving decision

• Without children:

• With children:

• Education and fertility: expected cost = expected marginal benefit to individual

0)('1 0 izRv

0)](')(1)(')([1 lini

hini zveqzveqR

„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

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

ll

hh EUNEUNW

,,,

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:

0

0

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

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

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

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