Fiscal Externalities to Childbearing in Aging Populations Joshua R. - - PowerPoint PPT Presentation

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Fiscal Externalities to Childbearing in Aging Populations Joshua R. - - PowerPoint PPT Presentation

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Max Planck Institute for Demographic Research Fiscal Externalities to Childbearing in Aging Populations Joshua R. Goldstein Miguel Snchez-Romero Third EuroNTA workshop, Friday 29th October Outline Outline Motivation Literature Model

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Max Planck Institute for Demographic Research

Fiscal Externalities to Childbearing in Aging Populations

Joshua R. Goldstein Miguel Sánchez-Romero

Third EuroNTA workshop, Friday 29th October

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Outline

Outline Motivation Literature Model Preliminary results Future research Appendix

(MPIDR) NPV October 29th 2010 Stockholm 2 / 19

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Motivation

Motivation

Holding current public transfers constant, taxes are expected to rise dramatically with population aging.

  • Positive:

Higher fertility provides more tax payers, which may lower taxes

  • Negative:

Demand social benefits and public expenditures: Health, Education, Pensions, etc. Research question Does bearing a child produce positive or negative fiscal externalities? Novelties

◮ We study a low fertility country ◮ Introduction of more endogeneity (towards general equilibrium)

(MPIDR) NPV October 29th 2010 Stockholm 3 / 19

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Motivation

Net Present Value

Definition NPV without descendants Present value, weighted by survival probability, of taxes paid minus all public costs along the lifetime. NPVt(0) ≡ NPVt =

Ω

0 e−¯ rxlt(x){θt+x(n)tax(x)−benefitst(x)}dx.

(1)

Ω

0 Nt(x){θt(n)tax(x)−benefitst(x)}dx = 0

¯ r discount factor lt(x) cohort survival probability θt(n) demographic adjustment of PAYG taxes

(MPIDR) NPV October 29th 2010 Stockholm 4 / 19

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Literature

References

Fiscal net present value (NPV) of childbearing:

NPV/Yl r Lee, R. and Miller, T. (1990) $ 105.000 in 1985 dollars 4 3% Lee, R. (1997) $ 92.-245.000 in 1996 dollars 3-8 3% Svensson, A. et al. (2008) 254.000 SEK in 2005 krones <1 2.5% Connolly, M. et al. (2009) £122.000 in 2005 pounds 4 3.5% Wolf, D. et al. (2010) $ 217.000 in 2009 dollars 4 3%

all studies are on high fertility populations

(MPIDR) NPV October 29th 2010 Stockholm 5 / 19

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Literature

Caveats

  • Results are very sensitive to assumptions:

e.g. discount rates, mean age of retirement, productivity growth, increases on public expenditures such as health care. Objective

  • Understand the implications of population aging on the fiscal value of

children

  • Replicate these works with NTA-based profiles, so that the NPV of

childbearing can be extended to all NTA countries

  • Extend the partial equilibrium results to the general equilibrium context

(MPIDR) NPV October 29th 2010 Stockholm 6 / 19

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Model

How do we have to calculate the NPV?

Linage vs. Single Child * Single child: * Linage: NPVt(n) =

n

∑

k=0

NPVt+k·µ(0)·NRRk ·e−kµr (2) where µ is the mean-age of childbearing Public Goods and Services Services: health and education Goods: we assume that ‘Others’ are all pure public goods

(MPIDR) NPV October 29th 2010 Stockholm 7 / 19

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Model

How do we have to calculate the NPV?

Impact of population aging on NPV The sign

  • −dNPVt

dn

  • is given by

Partial General A+ > A− A+ > A− A+ > A− A+ > A− +

  • ++ if r′(n) < 0
  • - if r′(n) < 0

+/- if r′(n) > 0

  • /+ if r′(n) > 0

National debt

  • In a closed economy national debt (Dt) affects the economy through

higher interest rates. Partial vs. General equilibrium models.

  • In a closed economy Individuals purchase government’s debt → Interest
  • n debt is a benefit

(MPIDR) NPV October 29th 2010 Stockholm 8 / 19

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Model

Economy

Households

  • Rational
  • No bequest motive
  • Homogenous preferences (CRRA) but face different mortality risk
  • Altruistic only when their offspring are children, LMM (2000, 2001, 2003)
  • Enter into the labor market at age 21 and retire at age 63

Neoclassical Firm

  • Maximize Profits
  • Cobb-Douglas production function a la Barro (1990) F(K,AL,G)

Government

  • Provides public benefits (retirement benefits) and public goods and

services (education, health, others)

  • Levies taxes on capital, personal income, and consumption.
  • The government might run the economy with debt

(MPIDR) NPV October 29th 2010 Stockholm 9 / 19

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Preliminary results

Results

Table: Fiscal Net Present Value of a Child, Cohort 2010 Discount U.N. Pop. NPV(0)/Yl NPV(2)/Yl factor Projection Sweden US Spain Sweden US Spain 3% MV 1.7 2.1 3.1 4.5 5.5 6.2 5% MV 0.3 1.0 1.6 0.6 1.7 2.3 7% MV

  • 0.6

0.3 0.7

  • 0.7

0.4 0.8 Endogenous 2.9% MV

  • 3.8
  • 7.3

3.5% MV 1.3

  • 3.1
  • 3.6%

MV

  • 1.8
  • 4.1
  • (MPIDR)

NPV October 29th 2010 Stockholm 10 / 19

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Preliminary results

Results

Table: Fiscal Net Present Value of a Child by Expenditure, Cohort 2010 (MV) Discount Country NPV(0)/Yl factor pensions education health

  • thers

Total 3% Sweden 1.4

  • 2.2

1.1 1.5 1.7 US 1.1

  • 1.1

0.6 1.5 2.1 Spain 1.9

  • 1.2

0.8 1.7 3.1 Endogenous 3.5% Sweden 1.4

  • 2.2

0.9 1.3 1.3 3.6% US 1.0

  • 1.1

0.6 1.3 1.8 2.9% Spain 2.0

  • 1.1

1.0 2.0 3.8 Note: The endogenous interest rate is calculated as the average real interest rate over the lifespan of the individual obtained from the general equilibrium model.

(MPIDR) NPV October 29th 2010 Stockholm 11 / 19

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Future research

Conclusions

◮ NTA can be used to help policy makers to evaluate the fiscal NPV of

childbearing

◮ Implement general equilibrium models to assess the realism of our

assumption

◮ Introduce direct and opportunity costs of childbearing by parents

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Future research

THANK YOU!

(MPIDR) NPV October 29th 2010 Stockholm 13 / 19

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Appendix

How do we have to calculate the NPV?

Pure Public Goods Nondepletable commodity * Following Barro (1990, JPE) we use the Cobb-Douglas production function: Y ≡ F(K,AL,G) = (Kt)α−η (AtLt)1−α (Gt)η where ∂F ∂G = 1 ⇔ G = ηY. Hence ∆Y ⇒ ∆G but ∆N ⇒ ∇T per capita. National debt

  • In a closed economy national debt (Dt) affects the economy through

higher interest rates. Partial vs. General equilibrium models.

  • In a closed economy Individuals purchase government’s debt → Interest
  • n debt is a benefit

(MPIDR) NPV October 29th 2010 Stockholm 14 / 19

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Appendix

Economy

Households

  • Rational
  • No bequest motive
  • Homogenous preferences (CRRA) but face different mortality risk
  • Altruistic only when their offspring are children, LMM (2000, 2001, 2003)
  • Enter into the labor market at age 21 and retire at age 63

Vt,x (at,x ) = max

ct,x

  λt,x c1−σ

t,x

−1 1−σ +βpt,x Vt+1,x+1(at+1,x+1)    s.t.

  • (1+τp

t )λt,x ct,x +at+1,x+1 = (1+rt )(at,x +ht,x )+(1−τi )[(1−τss t )yl t,x +bt,x ].

as,Tw = 0 and at,x ≥ 0 (3)

(MPIDR) NPV October 29th 2010 Stockholm 15 / 19

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Appendix

Economy

Neoclassical Firm

  • Maximize Profits
  • Following Barro (1990, JPE) we use a Cobb-Douglas production function

as follows F(K,AL,G) Following Hasset & Hubbard (2002) the cash flow of the firm is given by:

Jt = max

{Ks,Ls,Is}∞ s=t ∞

∑

s=t

Xs

s

∏

z=t

1 1+rz Xt = (1−τc

t )(F(Kt ,At Lt ,Gt )−Gt −ωt At Lt )−It ,

(4)

and

Kt =

Ω

∑

x=Tw

at,x Nt,x −Dt , Lt =

Tr −1

∑

x=Tw

εx Nt+1,x+1. (5)

(MPIDR) NPV October 29th 2010 Stockholm 16 / 19

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Appendix

Economy

Government

  • Collect taxes to provide public benefits and public goods and services
  • The government might run the economy with debt

Public benefits (retirement pensions)

Ω−1

∑

x=Tr

bt,x Nt+1,x+1 = τss

t Tr −1

∑

x=Tw

yl t,x Nt+1,x+1, (6)

Public expenditures (health & education & others (Gt))

Ω−1

∑

x=0 ∑ j∈J

gj

t,x Nt+1,x+1 +rt Dt −(Dt+1 −Dt ) = τp t Ω−1

∑

x=0

λt,x ct,x Nt+1,x+1 +τc

t

rt +δ 1−τc

t

Kt +

Ω−1

∑

x=Tw

τi

t

  • (1−τss

t )yl t,x +bt,x

  • Nt+1,x+1,

(7)

(MPIDR) NPV October 29th 2010 Stockholm 17 / 19

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Appendix

First order conditions

Household

cσ

t+1,x+1

cσ

t,x

≥ 1+τp

t

1+τp

t+1

βpt+1,x+1(1+rt+1), (8) with equality iff at,x > 0. Firm ωt At = FL(Kt ,At Lt ,Gt ) (9) rt +δ = FK (Kt ,At Lt ,Gt )·(1−τc

t )

(10) It = Kt+1 −Kt (1−δ) (11) 1 = FG(Kt ,At Lt ,Gt ) (12) where δ is the capital depreciation rate.

(MPIDR) NPV October 29th 2010 Stockholm 18 / 19

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Appendix

Economy

Equilibrium

Definition: Let x ∈ X and t ∈ T . In this economy a Competitive Equilibrium with Transfers is a list of sequences of quantities ct,x, at,x, Nt,x, At, Lt, Kt, Gt, prices ωt, rt, taxes τc

t , τss t , τp t , τi t , public benefits bt,x, public consumptions {gj t,x}j∈J, and private

transfers ht,x, (λt,x −1)ct,x such that, at each point in time t:

  • 1. the firm maximizes its value Jt by choosing K, L, and I according to (9)-(11).
  • 2. individuals maximize their expected lifetime utility subject to their flow budget

constraint

  • 3. both government budget constraints are satisfied
  • 4. both capital and labor market clearing conditions hold
  • 5. total private transfers given equal total private transfers received
  • 6. and the good market clears

(MPIDR) NPV October 29th 2010 Stockholm 19 / 19