In previous section, we find that, because of low birth rate, a private ed-ucation system is more sensitive to the variation in life expectancy and pension replacement ratio than a public education system and then leads lower balanced growth rate when an economy with sufficiently high life expectancy and pension replacement rate. For this reason, it seems in-teresting to see whether growth can be promoted by implementing some policies, such as voucher program (subsidy of private education), which eliminates the educational expenditure per child and then encourage par-ents give more birth for sharing pension burden in an economy with
”great” PAYG social security program.
The intertemporal budget contraint for the households in a private schooling regime with voucher program can be revised as follows:
crtm+ 1 − vrtertnrt+ cort
rt+1 = 1 − τrt− qrt1 − ϕnrtwrthrt+ Vrt+1
rt+1 (37)
where vrt is subsidy rate of private education expenditure and qrt is a propotional tax for financing voucher program. Government also runs balanced budget to subsidize private education and the budget constraint of voucher program is:
vrtertnrt= qrt1 − ϕnrtwrthrt (38) where assume that the scale of voucher program is determined exoge-nously by government not by voting process.
Table 4 and 5 indicates that compared to private schooling regime (no subsidy, v=0), subsidizing educational fee per child can raise about 0.05–
0.07 (50% of subsidy, v=0.5) and 0.09–0.12 (90% of subsidy, v=0.9) total fertility rate and then reduce the tax burden of PAYG social security. The results also reveals that the relationship between the level of subsidy for private education and economic growth depends on the life expectancy of an economy and the policy of pension benefit.
In the case of low longevity or small pension replacement ratio, where
”resource-dilution” effect dominates ”tax-sharing” effect, more subsidy of educational investment results in lower economic growth. On the con-trary, when an economy has high life expectancy or implements the pol-icy of providing large pension benefit for old, ”tax-sharing” effect is stronger than ”resource-dilution” effect, government should provide more subsidy of educational investment to raise growth rate.
Table 4: Longevity and subsidy of education
Variables low longevity (p=0.1) high longevity (p=0.9) v=0 v=0.5 v=0.9 v=0 v=0.5 v=0.9
FertilityTFR 1.16 1.23 1.28 1.01 1.06 1.10
Social Securityτ 7.38 6.98 6.67 76.04 72.80 70.22
SavingS 5.21 5.27 5.32 4.43 5.14 5.73
Education InvestmentE 18.89 17.94 17.18 4.82 5.22 5.49 Balanced Growthg 3.28 3.23 3.19 2.42 2.49 2.54 1 Except longevity, all parameters are the same as the setting in baseline model.
Table 5: Replacement ratio and subsidy of education
Variables low replacement (B=0.2) high replacement (B=0.9)
v=0 v=0.5 v=0.9 v=0 v=0.5 v=0.9
FertilityTFR 1.01 1.06 1.10 1.11 1.16 1.21
Social Securityτ 19.82 18.94 18.24 81.35 77.42 74.29
SavingS 15.46 15.81 16.10 2.01 2.50 2.91
Education InvestmentE 16.15 15.55 15.08 3.78 4.34 4.73
Balanced Growthg 3.52 3.49 3.46 2.02 2.15 2.24
1 Except replacement ratio, all parameters are the same as the setting in baseline model.
4 Empirical Implications
The prediction of our model implies that comparing to a private school-ing system, a public schoolschool-ing system can encourage parents to have more births and then leads to a lower tax rate of PAYG social security in the fu-ture. Due to the lack of data, there are few empirical studies examining the impact of educational systems and policies on macroeconomic variables or demographic structure across countries. In this section, we use the in-ternationally comparable data provided by OECD and WDI (World De-velopment Indicators) to investigate preliminary relationships between educational systems, birth rate and social security burden.
Table 6 lists the whole 17 countires in our sample. We especially choose these high income OECD countries for two reasons. First, the life ex-pectancy at birth in these countries are sufficiently high and similar to each other, which matches the demographic feature of our model and also controls the effect of longevity on fertility rate and social security tax rate. Second, some countries, for example Italy and Germany, also satify our standard but their data is not reliable6.
6we also use secondary private school enrollment rate in 1985 from UNSCO to check the reliability of our classification for education systems
Table 6: Education systems, fertility rate and social security
Country Percentage Share of Total Fertility Rate Chnage in Social security
Private Funding,% tax rate 1990-2003, %
Australia 15.93 1.87 1.62
New Zeland 1.01 2.05 -2.25
Switzerland 6.56 1.51 3.39
To classify education systems in our sample, we follow de la Croix and Doepke (2007) and choose 90% of the public share in all level educaton as a criterion. If an economy has ”more” than 90% of public funding for education in 1993, we assort this country to a group of public educaton system. If an economy has ”less” than 90% of public funding for education in 1993, we assort this country to a group of private educaton system.
Table 7: Fertility rate and private educational funding
Size of N.obs Average Share of Total
Private Edu. Private Funding,% Fertiltiy Rate
Large( 10%) 8 30.19 1.66
Samll( 10%) 9 4.07 1.84
Mean difference test -0.18 (t-stat=-1.67)
Fig. 4 and table 6 reveal that the countries with larger share of private funding for education ”seem” to have lower birth rates than those with larger share of public funding for education. Computing the correlation between the propotion of private educational spending in 1993 and total fertility rate in 1993, we find that the correlation coeffcient is −0.4070, which is moderately negative. Table 7 provides the mean difference test and shows the difference of total fertility rate between the countries with larger private sector and those with larger public sector is−0.1845, whose
t-statistic is−1.67 and p-value is close to 10% significance.
Figure 4: Fertility rate and private funding on education
1.21.41.61.822.2
Total Fertility Rate per Woman in 1993
0 20 40 60 80
Friction of Private Educational Spending in 1993, %
Figure 5: The increase in social security program and private funding on education
−4−20246
Change in Social Security Tax rate 1990−−2003, %
0 20 40 60 80
Friction of Private Educational Spending in 1993, %
The predicted difference of fertility rate is roughly resemble the above empirical evidences. The another implication of our theory needed to
be examined is that countries with public education regime tend to have lower social security tax burden in the future years. Fig. 5 and table 6 show that the countries with larger percentage of private funding on education in 1993 have larger growth in a tax rate of social security during 1990 to 2003 than those with larger percentage of public funding on education in 1993. Some countries with smaller private education sectors, such as Luxembourg, Finland and New Zeland, even have the negative growth in the size of social security program.
Table 8: Growth of social security program and private educational funding Size of N.obs Average Share of Increase in Size of Private Edu. Private Funding,% Social Security
Large( 10%) 8 30.19 2.06
Samll( 10%) 9 4.07 0.16
Mean difference test 1.90 (t-stat=-1.92)
Table 8 indicates the difference of growth in social security system be-tween two group is significant (t-stat=−1.92). The tax rate expends 2.06%
in the countries with a larger scale of private education but increase only 0.15% in the countries with a smaller scale of private education. Accord-ing to Ehrlich and Kim (2005), their estimation shows that 1% increase in social secruity tax rate will reduce 0.028% in growth rate per capita. The gap between two groups is almost 2%, that is, the long-run growth rate decreases by 0.056% for the countries with larger size of private educa-tion.
5 Conclusion
The design of educational policies and social security program are im-portant issues to modern policy makers, especially to those in developed countries. However, not many previous studies considered these two poli-cies jointly. This paper proposes a three periods overlapping generation model with endogenous fertility to study the interaction between educa-tional systems and PAYG social security program.
We first conclude that If government does not implement PAYG social security program, a private education system can yield higher long-run economic growth than a public education system. This is because free public schooling distorts fertility choice of parents and leads high fer-tiltiy rate. More children bring a negative ”resource-dilution effect” to an economy and results in less educational investment and slower economic growth.
However, on the other hand, if govenment implements PAYG social security program, a public education system may stimulate higher growth rate than a private education system when an economy has sufficiently old life expectancy or suffciently high pension replacement rate. The reason for this result is that the practice of PAYG social security system makes children have ”tax-sharing effect”, which reduces tax burden of PAYG so-cial security and benefits long-run growth, and furthermore the ”tax-sharing effect” dominates the ”resource-dilution effect” in an economy with high longevity or the policy of high pension benefit.
Thirdly, we also find that government can militgate the financial pres-sure of PAYG social security program by providing public schooling or voucher program and get some supports from our empirical work.
Our analysis highlights the importance of interaction between edu-cational systems and social security programs in an aging economy. We suggest that to improve economic growth it is necessary for policy makers to think these two policies together.
6 Technical Appendix
Proof of Proposition 1
Proof. Differentiating ni in Eq.(19) and Eq.(28) with respect to p, it is very straightforward to find the following relation:
∂ni
∂p < 0 i = r, u (39)
An increase in life expectancy leads agent have fewer children and results in higher PAYG social security tax rate.
Proof of Proposition 2
Proof. In order to compare the balanced-growth rate between private education regime and public education regime, it is usful to know how three growth determinants affect growth rate first.
Differentiating 1+ gi in Eq.(36) with respect to ni, Si and Ei respec-tively. We can find:
∂gi
∂ni < 0,∂gi
∂Si 0, ∂gi
∂Ei 0 i = r, u (40)
Lower fertilty rate, higher saving rate and higher education expendi-ture can lead higher growth rate.Given any p and τ = 0 in ni, Si and Ei
respectively we know the following relation:
nrt= γ − βδpσ
ϕ1 + pσ + γ < γ pσ
ϕ1 + pσ + γ = nut
Srt = pσ
1 + pσ + βδ = 1 + pσpσθ
1 + pσ + βδ = Sut
Ert = βδϕ1 + pσ + γ
γ − βδ1 + pσ + βδ βδϕ1 + pσ + γ
γ1 + pσ + βδ = Eut
An economy under private education regime has lower fertility rate, the same saving rate and higher education expenditure than one under
public education regime, which results that balanced-growth rate in pri-vate education regime is higher than in public education regime.
Proof of Proposition 3
Proof. From Eq.(9) we know lower fertility rate or higher life expectancy will lead higher pay-as-you-go social securtiy tax rate.
∂τi
∂ni
< 0, ∂τi
∂p 0 i = r, u (41)
Also form Proposition 2 we find an economy under private education regime has lower fertility rate than one under public education(nr < nu).In our model life expectancy p is exogenous so given any p we know τr τu.
To examine the effect of τi on physical/human capital accumulation and balanced growth rate, First, we can differentiate ni, Si and Ei with respect to τi respectively and find:
∂ni
∂τi 0,∂Si
∂τi < 0, ∂Ei
∂τi < 0 i = r, u (42) Higher PAYG social security tax rate increase fertility rate (because the substitute effect of tax rate is larger than its income effect), reduce physical and human capital investment and thereby leads lower balanced growth rate.
7 Reference
Becker, G.S., Lewis, H.G., (1973) ”On the Interaction between the Quan-tity and Quality of Children.” The Journal of Political Economy, 81, 279-288.
Bordin, M. (2005), ”Public education and capital accumulation” Research in Economics, 59:2, 85-109.
Breyer, F. and Craig, B. (1997), ”Voting on social security: Evidence from OECD countries” European Journal of Political Economy, 13:4, 705-724.
Card D, Krueger A (1992) ”Does school quality matter? Returns to edu-cation and the characteristics of public schools in the United States”
The Journal of Political Economy, 100:1, 1-40
Chen, H. J. (2005). ”Educational systems,growth and income distribu-tion:a quantitative study.” Journal of Development Economics, 76:2, 325-353.
Cigno, A. (1992). ”Children and pensions.” Journal of Population Eco-nomics, 5:3, 175-183.
de la Croix, D. and M. Doepke (2003). ”Inequality and Growth: Why Dif-ferential Fertility Matters.” The American Economic Review, 93, 1091-1113.
de la Croix, D. and M. Doepke (2004). ”Public versus private education when differential fertility matters.” Journal of Development Economics, 73, 607-629.
de la Croix, D. and M. Doepke (2007). ”To Segregate or to Integrate:
Education Politics and Democracy.” manuscript.
Docquier F. and Paddison, O. (2003). ”Social Security Benefit Rules, Growth and Inequality.” Journal of Macroeconomics, 25, 47-71.
Ehrlich, I. and Kim, J. (2005). ”Social Security, Demographic Trends, and Economic Growth: Theory and Evidence from the International Ex-perience.” manuscript.
Glomm, G. and B. Ravikumar (1992). ”Public versus Private Investment in Human Capital:Endogenous Growth and Income Inequality.” The Journal of Political Economy, 100:4, 818-834.
Gradstein, M. and Kaganovich, M. (2004), ”Aging population and educa-tion finance” Journal of Public Economics, 88, 2469-2485.
Grob, U. and Wolter, S. C. (2005), ”Demographic change and public ed-ucation spending: a conflict between young and old?” manuscript.
Groezen, B. V., Meijdam L. and T. Leers. (2003). ”Social security and endogenous fertility: pensions and child allowances as siamese twins.”
Journal of Public Economics, 87, 233-251.
Groezen, B. V., Meijdam L. (2008). ”Growing old and staying young: pop-ulation policy in an ageing closed economy.” Journal of Poppop-ulation Eco-nomics, 21, 573-588.
Harris, A. R., Evans, W. N. and Schwab, R. M. (2001), ”Education spend-ing in an agspend-ing America” Journal of Public Economics, 81, 449-472.
Haveman, R. and Wolfe, B. (1995), ”The Determinants of Children’s At-tainments: a Review of Methods and Findings” Journal of Economic Literature, 33:4, 1829-1878.
Johnson GE, Stafford FP (1973) ”Social returns to quantity and quality of schooling” Journal of Human Resource, 8:2, 139-155.
Kaganovich, M. and I. Zilcha (1999). ”Education, Social Security, and Growth.” Journal of Public Economics, 71, 289-309.
Kemnitz, A. (2000), ”Social security, public education, and growth in a representative democracy.” Journal of Population Economics, 13, 443-462.
Knowles, J. (1999a), ”Can Parental Decisions Explain U.S. Income In-equality?.” , Working Paper, University of Pennylvania.
Oshio, T. (2005). ”Social Security, Child allowances, and endogenous fer-tility.” manuscript.
Pecchenino, R. A. and P. S. Pollard (2002). ”Dependent children and aged parents:funding education and social security in an aging economy.”
Journal of Macroeconomics,24, 145-169.
Poterba, J. M.(1997). ”Demographic structure and the political economy of public education.” Journal of Policy Analysis and Management,16, 48-66.
Rojas, J. A. (2004). ”On the interaction between education and social security.” Review of Economic Dynamics, 7, 932-957.
Soares, J. (2006). ”A dynamic general equilibrium analysis of the politi-cal economy of public education.” Journal of Population Economics,19, 367-389.
Zhang, J. (1996). ”Optimal Public Investment in Education and Endoge-nous Growth.” Scandinavian Journal of Economics, 98:3, 387-404.
Zhang, J., Zhang, J. and Lee, R. (2001). ”Mortality decline and long-run economic growhth” Journal of Public Economics, 80, 485-507.
Zhang, J., Zhang, J. and Lee, R. (2003). ”Rising Longevity, education, savings, and growth.” Journal of Development Economics , 70, 83-101.
Zhang, J.and Zhang, J (2003). ”Long-run Effects of Unfunded Social Security with Earnings-dependent Benefits”, Journal of Economic Dy-namics and Control,28:3, 617-641.