The intergenerational education spillovers of pension reform in China

Abstract

Economic theory establishes that pension privatization weakens the link between old and young and so reduces the incentive to invest in public education in an economy with lower return rate of capital than growth rate of wage. However, empirical studies of the link change are few. In this paper, we investigate the effects of pension privatization and the central government’s subsidy to individual accounts on public education spending in a three-period overlapping generation model. And then, we take contemporary pension reforms in a number of Chinese provinces as offering natural experiment conditions. Using a difference-in-difference framework and 282 municipal districts panel data over years 1998–2009, we test the pension-education theoretical link change. Both our theoretical and empirical results confirm that pension privatization is adversely associated with local public spending on education in China. Private pension subsidies, moreover, magnify this effect. Our study supports the theoretical assertion and selective empirical findings of a negative intergenerational effect of pension privatization.

Appendix

The government’s exclusive objective is to maximize the social welfare of the working-age generation. The local government’s optimization problem thus is:

$$ \operatorname{Max}\kern0.5em G=\ln {c}_{2,t}+\rho \ln {c}_{3,t+1} $$

(16)

$$ s.t.{c}_{2,t}=\frac{1}{1+\rho}\left[\left(1-{\lambda}_t^p-{\lambda}_t^m-{\tau}_t\right){w}_t{h}_t+\frac{1}{1+{r}_{t+1}}\left({p}_{t+1}+{m}_{t+1}\right)\right] $$

(17)

$$ {c}_{3,t}=\left(1+{r}_{t+1}\right)\rho {c}_{2,t} $$

(18)

$$ {m}_{t+1}+{p}_{t+1}={\lambda}_{t+1}^p{w}_{t+1}{\left({e}_t{w}_t\right)}^{\beta }{h}_t+{\theta \lambda}_t^m{w}_t{h}_t\left(1+{r}_{t+1}\right) $$

(19)

$$ {e}_t{w}_t{h}_t={\tau}_t{w}_t{h}_t $$

(20)

where e _t w _t h _t  = τ _t w _t h _t means that the local government exhausts education taxes collected on public education spending.

Substituting Eqs. (17)–(20) into Eq. (16) gives:

$$ G=\left(1+\rho \right)\ln \left[\frac{w_t{h}_t}{1+\rho}\left(1-{\lambda}_t^p-{\lambda}_t^m-{e}_t+\frac{\lambda_{t+1}^p{w}_{t+1}{e}_t^{\beta }{w}_t^{\beta -1}}{1+{r}_{t+1}}+{\theta \lambda}_t^m\right)\right]+\rho \ln \left[\left(1+{r}_{t+1}\right)\rho \right] $$

Since a local government sees the wage rate and interest rate in the next period as given, the government just chooses the optimal public education spending. So the FOC satisfies:

$$ \frac{dG}{de_t}=\frac{\left(-{w}_t{h}_t+\frac{\lambda_{t+1}^p{w}_{t+1}\beta {e}_t^{\beta \hbox{-} 1}{w}_t^{\beta }{h}_t}{1+{r}_{t+1}}\right)}{\left[\frac{w_t{h}_t}{1+\rho}\right(1-{\lambda}_t^p-{\lambda}_t^m-{e}_t+\frac{\lambda_{t+1}^p{w}_{t+1}{e}_t^{\beta }{w}_t^{\beta -1}}{1+{r}_{t+1}}+{\theta \lambda}_t^m\Big]}=0 $$

(21)

From Eq. (21), we can get:

$$ {e_t}^{1-\beta }=\frac{w_{t+1}}{1+{r}_{t+1}}{\beta \lambda}_{t+1}^p{w_t}^{\beta -1} $$

(22)

Since we assume that the capital fully depreciates after one period’s production, the available capital next period is sourced entirely from savings in the current period, namely ${K}_{t+1}=\left({s}_t+{\lambda}_t^m\right){w}_t{H}_t$. Thus, we obtain:

$$ {k}_{t+1}=\frac{K_{t+1}}{H_{t+1}}=\left({s}_t+{\lambda}_t^m\right){w_t}^{1-\beta }{e}_t^{-\beta }. $$

(23)

Substituting $\frac{w_{t+1}}{1+{r}_{t=1}}=\frac{w_{t+1}}{1+{r}_{t=1}}{k}_{t+1}$ and Eq. (23) into Eq. (22) gives:

$$ {e}_t=\frac{1-\alpha }{\alpha }{\beta \lambda}_{t+1}^p\left({s}_t+{\lambda}_t^m\right). $$

(24)

Substituting Eqs. (19) and (22) into Eq. (3) gives:

$$ {s}_t+{\lambda}_t^m=\frac{\rho }{1+\rho}\left(1-{\lambda}_t^p-{e}_t\right)-\frac{1}{1+\rho}\frac{e_t}{\beta }+\frac{1-\theta }{1+\rho }{\lambda}_t^m. $$

(25)

Substituting Eq. (25) into Eq. (24) gives:

$$ {\displaystyle \begin{array}{c}{e}_t=\frac{1-\alpha }{\alpha }{\beta \lambda}_{t+1}^p\left[\frac{\rho }{1+\rho}\left(1-{\lambda}_t^p-{e}_t\right)-\frac{1}{1+\rho}\frac{e_t}{\beta }+\frac{1-\theta }{1+\rho }{\lambda}_t^m\right]\\ {}\mathrm{or}\kern0.5em {e}_t=\frac{\left(1-\alpha \right){\beta \lambda}_{t+1}^p\left[\rho \left(1-{\lambda}_t^p\right)+\left(1-\theta \right){\lambda}_t^m\right]}{\alpha \left(1+\rho \right)+\left(1-\alpha \right)\left(1+\rho \beta \right){\lambda}_{t+1}^p}.\end{array}} $$

(26)

Substituting Eq. (26) into eq. (25) gives:

$$ {s}_t+{\lambda}_t^m=\frac{\alpha \left[\rho \left(1-{\lambda}_t^p\right)+\left(1-\theta \right){\lambda}_t^m\right]}{\alpha \left(1+\rho \right)+\left(1-\alpha \right)\left(1+\rho \beta \right){\lambda}_{t+1}^p}. $$

(27)