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

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

Outline Outline Motivation Literature Model Preliminary results Future research Appendix (MPIDR) NPV October 29th 2010 Stockholm 2 / 19

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

Motivation Net Present Value Definition NPV without descendants Present value, weighted by survival probability, of taxes paid minus all public costs along the lifetime. � Ω 0 e − ¯ rx l t ( x ) { θ t + x ( n ) tax ( x ) − benefits t ( x ) } dx . NPV t ( 0 ) ≡ NPV t = (1) � Ω 0 N t ( x ) { θ t ( n ) tax ( x ) − benefits t ( x ) } dx = 0 ¯ r discount factor l t ( x ) cohort survival probability θ t ( n ) demographic adjustment of PAYG taxes (MPIDR) NPV October 29th 2010 Stockholm 4 / 19

Literature References Fiscal net present value (NPV) of childbearing: NPV/Y l 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

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

Model How do we have to calculate the NPV? Linage vs. Single Child * Single child: * Linage: n NPV t + k · µ ( 0 ) · NRR k · e − k µ r ∑ NPV t ( n ) = (2) k = 0 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

Model How do we have to calculate the NPV? Impact of population aging on NPV � � − dNPV t The sign is given by dn 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 ( D t ) affects the economy through higher interest rates. Partial vs. General equilibrium models. - In a closed economy Individuals purchase government’s debt → Interest on debt is a benefit (MPIDR) NPV October 29th 2010 Stockholm 8 / 19

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

Preliminary results Results Table: Fiscal Net Present Value of a Child, Cohort 2010 Discount U.N. Pop. NPV(0)/Y l NPV(2)/Y l 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

Preliminary results Results Table: Fiscal Net Present Value of a Child by Expenditure, Cohort 2010 (MV) Discount Country NPV(0)/Y l factor pensions education health others 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

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 (MPIDR) NPV October 29th 2010 Stockholm 12 / 19

Future research THANK YOU! (MPIDR) NPV October 29th 2010 Stockholm 13 / 19

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 ) = ( K t ) α − η ( A t L t ) 1 − α ( G t ) η where ∂ F ∂ G = 1 ⇔ G = η Y . Hence ∆ Y ⇒ ∆ G but ∆ N ⇒ ∇ T per capita . National debt - In a closed economy national debt ( D t ) affects the economy through higher interest rates. Partial vs. General equilibrium models. - In a closed economy Individuals purchase government’s debt → Interest on debt is a benefit (MPIDR) NPV October 29th 2010 Stockholm 14 / 19

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  c 1 − σ  − 1  t , x  V t , x ( a t , x ) = max  λ t , x + β p t , x V t + 1 , x + 1 ( a t + 1 , x + 1 ) ct , x 1 − σ  (3) ( 1 + τ p t ) λ t , x c t , x + a t + 1 , x + 1 = ( 1 + r t )( a t , x + h t , x )+( 1 − τ i )[( 1 − τ ss � t ) y l t , x + b t , x ] . � � s . t . � � a s , Tw = 0 and a t , x ≥ 0 � (MPIDR) NPV October 29th 2010 Stockholm 15 / 19

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: ∞ s 1 max ∑ ∏ J t = X s { Ks , Ls , Is } ∞ 1 + r z (4) s = t z = t s = t X t = ( 1 − τ c t )( F ( K t , A t L t , G t ) − G t − ω t A t L t ) − I t , and Tr − 1 Ω ∑ ∑ (5) K t = a t , x N t , x − D t , L t = ε x N t + 1 , x + 1 . x = Tw x = Tw (MPIDR) NPV October 29th 2010 Stockholm 16 / 19

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 Tr − 1 b t , x N t + 1 , x + 1 = τ ss ∑ ∑ y l t , x N t + 1 , x + 1 , (6) t x = Tr x = Tw Public expenditures (health & education & others ( G t )) Ω − 1 Ω − 1 r t + δ g j t , x N t + 1 , x + 1 + r t D t − ( D t + 1 − D t ) = τ p x = 0 ∑ ∑ ∑ λ t , x c t , x N t + 1 , x + 1 + τ c K t t t 1 − τ c t j ∈ J x = 0 Ω − 1 τ i � ( 1 − τ ss � ∑ + t ) y l t , x + b t , x N t + 1 , x + 1 , (7) t x = Tw (MPIDR) NPV October 29th 2010 Stockholm 17 / 19

Appendix First order conditions Household c σ 1 + τ p t + 1 , x + 1 t ≥ β p t + 1 , x + 1 ( 1 + r t + 1 ) , (8) c σ 1 + τ p t , x t + 1 with equality iff a t , x > 0. Firm ω t A t = F L ( K t , A t L t , G t ) (9) r t + δ = F K ( K t , A t L t , G t ) · ( 1 − τ c t ) (10) I t = K t + 1 − K t ( 1 − δ ) (11) 1 = F G ( K t , A t L t , G t ) (12) where δ is the capital depreciation rate. (MPIDR) NPV October 29th 2010 Stockholm 18 / 19

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 c t , x , a t , x , N t , x , A t , L t , K t , G t , prices ω t , r t , t , τ p t , public benefits b t , x , public consumptions { g j taxes τ c t , τ ss t , τ i t , x } j ∈ J , and private transfers h t , x , ( λ t , x − 1 ) c t , x such that, at each point in time t : 1. the firm maximizes its value J t 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