PAYG pensions with endogenous fertility Volker Meier Ifo Institute for Economic Research.
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Transcript of PAYG pensions with endogenous fertility Volker Meier Ifo Institute for Economic Research.
![Page 1: PAYG pensions with endogenous fertility Volker Meier Ifo Institute for Economic Research.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649d595503460f94a3928a/html5/thumbnails/1.jpg)
PAYG pensions with endogenous fertility
Volker Meier
Ifo Institute for Economic Research
![Page 2: PAYG pensions with endogenous fertility Volker Meier Ifo Institute for Economic Research.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649d595503460f94a3928a/html5/thumbnails/2.jpg)
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
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Fundamental Problem
• Contracts with minors to finance education cannot be enforced => underinvestment
• Solution: Public schooling + Transfers from young to old (PAYG pension scheme)
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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
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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
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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)
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Basic Model
• Kolmar (1997)
• Standard overlapping generations structure
• Identical individuals, small open economy
• Labor supply exogenous
• Childhood, working period, retirement
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Budget equations
• consumption per child
• consumption in working age
• consumption in retirement
:)1( ttttyt sxnwc
:11 ttot Rsc
:tx
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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
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Utility function
• Utility:
• Decisions on savings and number of children
• First-order conditions:
),,( 1 tot
yt nccU
0
0
31
21
21
Un
UxU
RUU
t
pt
t
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Comparative Statics
• Number of children increases with higher child factor in PAYG scheme => return on PAYG contributions rises with higher child factor
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Welfare analysis
• With endogenous fertility: Pareto criterion not applicable (Golosov et al., 2007)
• Here: additional individuals share burden
• Welfare function must be specified
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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
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Interpretation
• Fiscal externalities vanish when government imitates family transfer scheme
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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
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Policy analysis
• Number of children increases in child benefit
• Maximization of indirect utility in steady state wrt level of child benefit
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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*
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Extension 1: Endogenous Labor Supply
• Fenge and Meier (2005)
• Opportunity cost of having children:
with
swnfc ty 11
0'',0',0)0( fff
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Pension formula and fertility
• Pension:
• Fertility decision:
tt
tttttt n
nf
nfnnfw
)(1
)(111 1111
0)(')1( 31
21
U
nUnwfU
t
tt
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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
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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
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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
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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
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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
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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
![Page 26: PAYG pensions with endogenous fertility Volker Meier Ifo Institute for Economic Research.](https://reader035.fdocuments.in/reader035/viewer/2022081519/56649d595503460f94a3928a/html5/thumbnails/26.jpg)
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
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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
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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
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Consumption and utility
Consumption in working age
• Without children:
• With children:
Utility
• Without children:
• With children:
iiii mswc 00 1
iiiiniin ewxnmswc )(1
000 iii zvcU
kkinin
kin wzvcU
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Pension formula
• Childless individuals:
• Parents:
ii w0
kikin nwnw
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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
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„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
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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
,,,
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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
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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
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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
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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
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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