Fertility Policies and Social Security Reforms in China

Transcription

1 Fertility Policies and Social Security Reforms in China Nicolas Coeurdacier (SciencesPo & CEPR) Stéphane Guibaud (SciencesPo) Keyu Jin (LSE) IMF-BOK Conference Seoul, September / 33

2 Motivation China s unique fertility policies and imminent social security reforms How do they affect national saving, domestic and global interest rates? What are the necessary pension system adjustments to ensure viability? China s One-Child Policy Hastened demographic aging Large increase in household saving (Choukhmane, Coeurdacier, and Jin (2013)) 2 / 33

3 Main Objective Key Innovation: endogenizing Fertility Feedback loop 1: fertility affects social security which, in turn, affects fertility Feedback loop 2: interest rates affect fertility which affect saving and interest rates Creates an additional (indirect) channel through which policy, institutional reforms and economic development can impinge on national saving and the social security system. Develop appropriate framework that accounts for GE and feedback effects of fertility, social security and interest rates with various levels of financial openness. 3 / 33

4 Model Ingredients 3-period overlapping generations model Intergenerational transfers Production economy capital accumulation Social security system Closed and open-economy cases 4 / 33

5 Production Production Y t = (K t 1 ) α [A t (e t L y,t + L m,t )] 1 α, Capital accumulation K t = (1 δ)k t 1 + I t. Wages wy,t i = e t (1 α)a t (k t 1 ) α, wm,t i = (1 α)a t (k t 1 ) α, Rate of Return R t = 1 δ + α (k t 1 ) α 1 where e < 1 and k t 1 K t 1 /[A t (e t L y,t + L m,t )] 5 / 33

6 The Social Security System The social security system evolves according to τ t+1 w y,t+1 L y,t+1 +τ t+1 w m,t+1 L m,t+1 +R t+1 B t = σ t+1 w m,t L o,t+1 +B t+1 Let b t Bt Y t ; τ taxes ; σ replacement ratio B = 0 PAYGO system σ defined benefits system τ t = σ t+1 for all t defined contribution system 6 / 33

7 Households Preferences U t = log(c y,t ) + v log(n t ) + β log(c m,t+1 ) + β 2 log(c o,t+2 ) where v > 0 (preference for children), and 0 < β < 1. Sequence of budget constraints: c y,t + a yt = (1 τ t )w y,t c m,t+1 + a m,t+1 = (1 τ t+1 )w m,t+1 + R t+1 a y,t + T m,t+1 c o,t+2 = R t+2 a m,t+1 + σ t+2 w m,t+1 + T o,t+2. Transfers: T m,t+1 = ( φn t + ψ nϖ 1 t 1 ϖ ) w m,t+1. T o,t+2 = ψ nϖ t ϖ w m,t+2. 7 / 33

8 Assumption (1) Credit constraints: a y,t+1 = θ w m,t+1 R t+1, Optimal Fertility v n t = β c m,t+1 (φw m,t+1 ψnϖ 1 t R t+2 w m,t+2 ) First relationship describing {k t ; n t 1 } given {b t ; τ t ; σ t } t 0 8 / 33

9 Optimal Saving: [( ) ] β a m,t+1 = 1 + β 1 τ t+1 θ φn t ψnϖ 1 t 1 w m,t+1 ϖ ψnt ϖ w m,t+2 σ t+2 w m,t+1 (1 + β)ϖ R t β R t+2 Capital markets equilibrium L m,t+1 a m,t+1 + L y,t+1 a y,t+1 + B t+1 = K t+1, Second relationship describing {k t ; n t 1 } given {b t ; τ t ; σ t } t 0 9 / 33

10 Long-Run Analysis σ t = σ, τ t = τ, b t = b Assumption (2) Transfers are not subject to decreasing returns in children: ϖ = 1 Assumption (3) e = 0 Assumption (4) τ < 1 θ ψ ( So that a positive number of kids will be desired ) 10 / 33

11 Three Key Relationships 1. Based on saving: ng A Φ + σ R KK (n) =. (KK) + b β (1 τ θ φn ψ) + (1 + β) 1 α ( ) where Φ (1 + β) α 1 α + θ + ψ 1+β. Four channels where n affects saving: (1) MPK; (2) expenditure effect ; (3) transfer effect ; (4) share of young borrowers Partial eqb. comparative statics: R KK θ > 0; R KK b > 0; R KK α > 0; R KK g A > 0 11 / 33

12 Three Key Relationships 2. Based on fertility: R NN (n ) = ( where we denote λ 0 ng A ψ + λ 0 σ nφ λ 0 (1 τ θ ψ), v v+β(1+β) ). (NN) Partial eqb. comparative statics: n n n < 0; > 0; φ v θ < 0; n > 0 g A 12 / 33

13 Three Key Relationships 3. Based on social security dynamics: ( ) R 1 b = σ τ, ng A ng A (SS) R > ng A need to run primary surplus to stabilize debt R < ng A can still run primary deficit even with debt Target a given level of b, let τ, σ adjust. KK, NN, SS curves combine to determine n, R. 13 / 33

14 PAYGO b = 0 Long run: τ t = τ and σ t = σ Scheme 1: τ Scheme 2: σ Three key equations: R KK (n) = ng A Φ + σ β (1 τ θ φn ψ) R NN (n) = ng A ψ + λ 0 σ nφ λ 0 (1 τ θ ψ) τ = σ ng A (KK) (NN) (SS) 14 / 33

15 Consider Scheme 1: τ, σ adjusts n τ = R τ = ( ) (1 τ θ ψ) ψβ + λ0 Φ + λ 0 (1 + β) τ φ ψβ + Φ + (1 + βλ 0 ) τ ( ) ( ) ga ψβ + λ0 Φ + λ 0 (1 + β) τ βφ 1 λ 0 Comparing LF (τ = σ = 0) and paygo (τ > 0; σ > 0): R SS > R LF due to lower saving n SS < n LF : children and social security are somewhat substitutable Impact of a one-child policy is larger under LF 15 / 33

16 PAYGO: Endogenous Fertility paygo: σ = τng Proposition: Under endogenous fertility, a fall in productivity growth g A lowers fertility under a paygo scheme where taxes endogenously adjust ( σ scheme) but leave fertility unchanged if replacement rate endogenously adjust ( τ scheme). Interest rates fall in both cases but more so under a σ scheme. That is, n g A σ R g A σ > n. = 0 g A > R. > 0 g A τ τ 16 / 33

17 PAYGO: Constrained Fertility Proposition: Implementing a binding fertility constraint n = n max raises saving by more under a paygo scheme where replacement ratios endogenously adjust than under a paygo scheme where taxes endogenously adjust. That is, R > R. n max σ n max τ 17 / 33

18 Illustrations: Parameter Values Table : Benchmark Calibration End. variable Steady-state value Comment/Description n σ 1.43 Fertility of 2.86 R σ % Annual basis τ σ 7.6% / Parameter Calibrated value Target/Description (Data source) β 0.99 Annual basis g A 1 4.5% Annual basis. Total Factor Productivity growth rate ( ) v 0.12 Targeted to match the fertility in of (Census) θ 1% Saving rate of the α 30% Capital Share ω 0.7 Elasticity of transfers to elderly w.r.t the nb. of siblings (CHARLS) φ 8% Average education expenditures over income (UHS) ψ 10% Choukhmane et al. (2013), Curtis et al. (2011) σ 30% Aggregate replacement ratios adjusted for coverage (UHS) b 0 Paygo simulation 18 / 33

19 Figure : Laissez-Faire Real interest rate (annual basis) 12% (KK) 10% R LF 8% (NN) 6% R nmax 4% 1 1,5 2 2,5 3 3,5 4 4,5 n n max LF Fertility Notes: τ = σ = 0; benchmark parameters. 19 / 33

20 Figure : From Laissez-Faire to PAYGO Real interest rate (annual basis) 12% 10% R σ (KK) 8% (NN) 6% 4% 1 1,5 2 2,5 3 3,5 4 4,5 n σ Fertility Notes: Move to σ = 0.3; benchmark parameters. 20 / 33

21 Policy and Growth Experiments Next, perform policy experiments Transitory Dynamics General case: b 0 σ scheme Compare endogenous and exogenous fertility in a closed-economy, later compare with open-economy cases 21 / 33

22 Figure : One Child Policy (Autarky) 10 Net interest rate (annualized, in percentage points) endogenous fertility exogenous fertility 5 3 Fertility (number of children per family) endogenous fertility exogenous fertility endogenous fertility exogenous fertility Contribution rate (in percentage points) 10 5 Notes: This figure illustrates the effect of implementing a one child policy constraint at t = 3, and relaxing it in t = / 33

23 Figure : A Permanent Increase in the Replacement Ratio (Autarky) 10 Net interest rate (annualized, in percentage points) endogenous fertility exogenous fertility 9 3 Fertility (number of children per family) endogenous fertility exogenous fertility endogenous fertility exogenous fertility Contribution rate (in percentage points) Notes: σ = 0.3 increases permanently to σ = / 33

24 Figure : One-child Policy + Permanent Growth Slowdown (Autarky) 10 Net interest rate (annualized, in percentage points) endogenous fertility exogenous fertility 2 3 Fertility (number of children per family) endogenous fertility exogenous fertility endogenous fertility exogenous fertility Contribution rate (in percentage points) Notes: one-child policy implemented in period 3 and relaxed in 4, a permanent growth slowdown from annual rate of 4.5% to 1.5% in period / 33

25 Small Open Economy In the general case where b 0: R = ng A ψ + λ 0 σ nφ λ 0 (1 τ θ ψ), ( ) R 1 b = ng A σ ng A τ, (NN) (SS) Under σ (1 τ σ θ ψ) + σ/r n σ = λ 0 φ ψ (g A /R ) σ τ σ =. n σ g A 25 / 33

26 Figure : Financial Integration (SMOE) Autarky Small open economy Net interest rate (annualized, in percentage points) Fertility (number of children per family) Autarky Small open economy Autarky Small open economy Contribution rate (in percentage points) Notes: Integration takes place in t=2, R = 9.5%. 26 / 33

27 Figure : One-Child Policy (SMOE) 10 Net interest rate (annualized, in percentage points) Autarky Small open economy 5 3 Fertility (number of children per family) Autarky Small open economy Autarky Small open economy Contribution rate (in percentage points) Notes: Benchmark parameters; one-child policy implemented in period 3 and relaxed in / 33

28 Figure : The one child policy: running down the trust fund (SMOE vs autarky). Net interest rate (annualized, in percentage points) Autarky Small open economy Fertility (number of children per family) Autarky Small open economy Autarky Small open economy Contribution rate (in percentage points) Notes: b = 0.02 > 0. At t=2, China integrates with the rest of the world characterized by R = 9.5%. The one-child policy is implemented at t=3 and relaxed at t=4. China reduce b to at t=4 and 0 at t=5. 28 / 33

29 Figure : A Permanent Increase in the Replacement Ratio (SMOE) 9.5 Net interest rate (annualized, in percentage points) Autarky Small open economy Fertility (number of children per family) Autarky Small open economy Autarky Small open economy Contribution rate (in percentage points) Notes: σ = 0.3 rises permanently to σ = 0.5 in period / 33

30 Figure : SMOE: One-child Policy + Permanent Growth Slowdown 10 Net interest rate (annualized, in percentage points) Autarky Small open economy 2 3 Fertility (number of children per family) Autarky Small open economy Autarky Small open economy Contribution rate (in percentage points) Notes: one-child policy implemented in period 3 and relaxed in 4, a permanent growth slowdown from annual rate of 4.5% to 1.5% occurs in period / 33

31 Conclusion Fertility and Social Security Interact Implications of fertility policies and reforms on required social security adjustment depends on endogenous responses of fertility and interest rates Social security schemes become also important given that their impact on fertility is different The framework can be used to study the impact of other economic, financial, and policy developments 31 / 33

32 Figure : PAYGO: A Fall in Intergenerational Transfers Real interest rate (annual) 12% 10% KK 8% 6% 4% Fer/lity Notes: This figure illustrates the effect of a fall in ψ from 10% to 5%., keeping σ = 0.3 constant and allowing τ to vary. NN 32 / 33

33 Figure : A Loosening of Credit Constraints (PAYGO) Real interest rate (annual) 12% KK 10% 8% 6% NN 4% Fer/lity Notes: This figure illustrates the effect of increasing θ = 0.02 to θ = 0.2, keeping σ = 0.3 and allowing τ to vary. 33 / 33