Fiscal Externalities to Childbearing in Aging Populations

Transcription

1 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

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

3 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

4 Net Present Value Motivation Definition NPV without descendants Present value, weighted by survival probability, of taxes paid minus all public costs along the lifetime. Ω NPV t (0) NPV t = e rx l t (x){θ t+x (n)tax(x) benefits t (x)}dx. (1) 0 Ω N t (x){θ t (n)tax(x) benefits t (x)}dx = 0 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

5 References Literature Fiscal net present value (NPV) of childbearing: NPV/Y l r Lee, R. and Miller, T. (1990) $ in 1985 dollars 4 3% Lee, R. (1997) $ in 1996 dollars 3-8 3% Svensson, A. et al. (2008) SEK in 2005 krones <1 2.5% Connolly, M. et al. (2009) in 2005 pounds 4 3.5% Wolf, D. et al. (2010) $ in 2009 dollars 4 3% all studies are on high fertility populations (MPIDR) NPV October 29th 2010 Stockholm 5 / 19

6 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

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

8 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) < 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

9 Economy Model 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

10 Results Preliminary 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 % MV % MV Endogenous 2.9% MV % MV % MV (MPIDR) NPV October 29th 2010 Stockholm 10 / 19

11 Results Preliminary 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 US Spain Endogenous 3.5% Sweden % US % Spain 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

12 Conclusions Future research 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

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

14 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 Hence National debt F G = 1 G = ηy. Y G but N T per capita. - 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

15 Economy Appendix 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 V t,x (a t,x ) = max c t,x λ c 1 σ t,x t,x 1 1 σ + βp t,x V t+1,x+1 (a t+1,x+1 ) s.t. (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 ]. a s,tw = 0 and a t,x 0 (3) (MPIDR) NPV October 29th 2010 Stockholm 15 / 19

16 Economy Appendix 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 J t = max {Ks,Ls,Is } X s s=t s=t z=t 1 + r z 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, (4) and Ω Tr 1 K t = a t,x N t,x D t, L t = ε x N t+1,x+1. (5) x=tw x=tw (MPIDR) NPV October 29th 2010 Stockholm 16 / 19

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

18 First order conditions Appendix Household c t+1,x+1 σ ct,x σ 1 + τp t 1 + τ p βp t+1,x+1 (1 + r t+1 ), (8) 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 τt c ) (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

19 Economy Appendix 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, taxes τt c, τss t, τ p t, τi t, public benefits b t,x, public consumptions {g j 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