Fertility, Inequality and Income Growth

Abstract

This paper sets an endogenous fertility model with a two-sector model: one for the final goods sector and the other for child care service sector. Results of theoretical analysis indicate that the subsidy for children raises the labor share of the child care service sector and that it can increase fertility. An aging population reduces fertility and the labor share of the child care service sector. In addition to these results, we consider monetary policy effects on fertility. Results show that monetary policy can raise fertility and the labor share of the child care service sector by virtue of an increase in the pension benefit if a pay-as-you-go pension exists.

This is a preview of subscription content, access via your institution.

Fig. 1

Notes

  1. 1.

    An aging population reduces fertility. Therefore, demand for the child care service sector decreases. However, some papers consider the grandparents’ child care in endogenous fertility, as demonstrated by Yasuoka et al. (2009).

  2. 2.

    Based on data from the Cabinet Office, Japan, the monetary stock increases considerably. In 2015, the monetary stock was 906.4 trillion JPY; it reached 974.0 trillion JPY. 7.4% rises. The inflation rate increased by 0.4% during 2015–2017. In some OECD countries, the policy of an increase in monetary stock is provided to avoid the bad economic status.

  3. 3.

    As shown by Ashraf et al. (2013), economic growth can reduce fertility because of an increase in the opportunity cost of having children, as shown by Galor and Weil (1996). Apps and Rees (2004) derive positive correlation between fertility and income. However, if the child care service cost depends on the income level, as shown by Yasuoka and Miyake (2010), then the fertility can not change fertility with income. Our paper depends positively on the income in the model with pension benefit because income growth raises the pension benefit. Then, an increase in lifetime income raises fertility.

  4. 4.

    This is a standard utility function in endogenous fertility model, as assumed by van Groezen et al. (2003) and others. The utility is pulled up directly by fertility.

  5. 5.

    This production function, which includes only labor input, is assumed by Yasuoka and Miyake (2010), Hashimoto and Tabata (2010), and others for studies in which child care or elderly care is examined. Child care and elderly care are regarded as labor-intensive services.

  6. 6.

    \(\left({\sigma }_{t}^{*}-\frac{{\sigma }_{t}^{*2}}{2}\right)+{\left(1-{\sigma }_{t}^{*}\right)}^{2}\) can be shown simply by \(\frac{{\sigma }_{t}^{*2}}{2}-{\sigma }_{t}^{*}+1\). However, our paper remains in the form of \(\left({\sigma }_{t}^{*}-\frac{{\sigma }_{t}^{*2}}{2}\right)+{\left(1-{\sigma }_{t}^{*}\right)}^{2}\). Also, \(\left({\sigma }_{t}^{*}-\frac{{\sigma }_{t}^{*2}}{2}\right){w}_{t}\) and \({\left(1-{\sigma }_{t}^{*}\right)}^{2}{w}_{t}\) respectively show the labor income share of the final goods sector and the child care service sector. We retain the form of \(\left({\sigma }_{t}^{*}-\frac{{\sigma }_{t}^{*2}}{2}\right)+{\left(1-{\sigma }_{t}^{*}\right)}^{2}\) because we can not understand the economic meanings of \(\frac{{\sigma }_{t}^{*2}}{2}-{\sigma }_{t}^{*}+1\).

  7. 7.

    The tax revenue of the final goods sector and child care service sector are shown respectively as \(\varepsilon \left({\sigma }_{t}^{*}-\frac{{\sigma }_{t}^{*2}}{2}\right){w}_{t+1}\) and \(\varepsilon {\left(1-{\sigma }_{t}^{*}\right)}^{2}{w}_{t+1}\). Because of the intergenerational population ratio \({n}_{t}\), the pension benefit per capita is given as (19).

  8. 8.

    For simplicity, \(\tau =0\mathrm{ \,and }\,\varepsilon =0\) are assumed in this section. There exist child allowance and pension benefits in this model if \(\tau \mathrm{and }\varepsilon \) are not zero. The child allowance raises demand for child care service because of a decrease in net child care cost. The pension benefit raises the demand for child care services because of an increase in lifetime income. Therefore, \({\sigma }^{*}\) in the case of \(\tau >0\, \mathrm {and} \,\varepsilon >0\) is less than \({\sigma }^{*}\) in the case of \(\tau =0\mathrm{ and }\varepsilon =0\). However, the strong effects of the aging population on the labor share of child care sector and fertility do not change.

  9. 9.

    The fertility is given by (20) if we consider the pension benefit. Then, the fertility depends on income growth. Income growth raises the pension benefit and then lifetime income increases. An increase in lifetime increase income fertility. Income growth pulls up the demand for child care service because of an increase in the fertility. Then the labor share of child care service sector rises.

  10. 10.

    (33) and (34) can be reduced to \(\frac{dn}{dq}>0\). This equation can be generally obtained in an endogenous fertility model. As reported by Fanti and Gori (2009, 2012), a child allowance can not always raise fertility because of a decrease in capital stock per capita. However, our paper can always raise fertility because child care service costs depend on the wage rate. Then, by virtue of increased fertility, the demand for child care service rises and the labor share of child care service can be pulled up.

  11. 11.

    Both the fertility and the labor share of child care service sector increase. This outcome is consistent with Fig. 1. However, the detail check must be examined to ascertain whether the model fits the data, as shown by Fig. 1.

  12. 12.

    The Appendix presents a detailed proof. The model with a pension benefit brings about the dynamics. The Appendix presents dynamics of the model with a pension.

  13. 13.

    As shown by (5), the wage rate of the child care service sector depends on the wage rate of the final goods sector. In addition to an increase in wage rate of final goods sector, an increase in the demand for the child care service sector raises the wage rate of child care service sector, which leaves a decrease in \({\sigma }^{*}\).

References

  1. Apps P, Rees, R (2004) Fertility, Taxation and Family Policy. Scandinavian J Econ 106(4):745–763

  2. Aronsson T, Sjögren T, Dalin T (2009) optimal taxation and redistribution in an OLG model with unemployment. In Tax Public Finance 16:198–218

    Article  Google Scholar 

  3. Ashraf Q, Weil D, Wilde J (2013) the effect of fertility reduction on economic growth. Popul Dev Rev 39:97–130

    Article  Google Scholar 

  4. Bhattacharya J, Haslag J, Martin A (2009) Optimal monetary policy and economic growth. Eur Econ Rev 53:210–221

    Article  Google Scholar 

  5. Blundell R, Duncan A, Meghir C (1998) estimating labor supply responses using tax reforms. Econometrica 66(4):827–862

    Article  Google Scholar 

  6. Blundell R, Duncan A, McCrae J, Meghir C (2000) The labour market impact of the working families tax credit. Fiscal Stud 21(1):75–103

    Article  Google Scholar 

  7. Blundell R, Costa DM, Meghir C, Shaw J (2016) Female labor supply, human capital, and welfare reform. Econometrica 84(5):1705–1753

    Article  Google Scholar 

  8. Caselli F (1999) Technological revolutions. Am Econ Rev 89(1):78–102

    Article  Google Scholar 

  9. Chang W, Chen Y, Chang J (2013) Growth and welfare effects of monetary policy with endogenous fertility. J Macroecon 35:117–130

    Article  Google Scholar 

  10. De Gregorio J (1993) Inflation, taxation, and long-run growth. J Monet Econ 31:271–298

    Article  Google Scholar 

  11. Eissa N, Hoynes H (2004) Taxes and the labor market participation of married couples: the earned income tax credit. J Public Econ 88(9–10):1931–1958

    Article  Google Scholar 

  12. Fanti L (2012) Fertility and money in an OLG model. In: Discussion Papers 2012/145, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.

  13. Fanti L, Gori L (2009) Population and neoclassical economic growth: a new child policy perspective. Econ Lett 104(1):27–30

    Article  Google Scholar 

  14. Fanti L, Gori L (2012) A note on endogenous fertility, child allowances and poverty traps. Econ Lett 117(3):722–726

    Article  Google Scholar 

  15. Francesconi M (2002) A joint dynamic model of fertility and work of married women. J Labor Econ 20(2):336–380

    Article  Google Scholar 

  16. Galor O, Weil D (1996) the gender gap, fertility, and growth. Am Econ Rev 86(3):374–387

    Google Scholar 

  17. Grossman G, Yanagawa N (1993) Asset bubbles and endogenous growth. J Monet Econ 31(1):3–19

    Article  Google Scholar 

  18. Hashimoto K, Tabata K (2010) Population aging, health care, and growth. J Popul Econ 23(2):571–593

    Article  Google Scholar 

  19. Kim KH (1989) Optimal linear income taxation, redistribution and labour supply. Econ Model 6(2):174–181

    Article  Google Scholar 

  20. Meckl J, Zink S (2004) Solow and heterogeneous labour: a neoclassical explanation of wage inequality. Econ J 114(498):825–843

    Article  Google Scholar 

  21. Mino K, Shibata A (1995) Monetary policy, overlapping generations, and patterns of growth. Economica 62:179–194

    Article  Google Scholar 

  22. Romer P (1986) Increasing returns and long-run growth. J Political Econ 94(5):1002–1037

    Article  Google Scholar 

  23. Shindo Y, Yanagihara M (2011) Education subsidies, tax policies and human capital accumulation in Japan: a general equilibrium analysis of the economy using heterogenous households. Stud Reg Sci 41(4):867–882 (In Japanese)

    Article  Google Scholar 

  24. Sidrauski M (1967) Rational choice and patterns of growth in a monetary economy. Am Econ Rev 57:534–544

    Google Scholar 

  25. van Groezen B, Meijdam L (2008) Growing old and staying young: population policy in an ageing closed economy. J Popul Econ 21(3):573–588

    Article  Google Scholar 

  26. van Groezen B, Leers T, Meijdam L (2003) Social security and endogenous fertility: pensions and child allowances as Siamese twins. J Public Econ 87(2):233–251

    Article  Google Scholar 

  27. Walsh C (2010) Monetary theory and policy, 3rd edn. MIT Press, Cambridge

    Google Scholar 

  28. Werning I (2007) Optimal fiscal policy with redistribution. Q J Econ 122(3):925–967

    Article  Google Scholar 

  29. Yakita A (2006) Life expectancy, money, and growth. J Popul Econ 19(3):579–592

    Article  Google Scholar 

  30. Yasuoka M (2018a) Money and pay-as-you-go pension. Econ MDPI Open Access J 6(2):1–15

    Google Scholar 

  31. Yasuoka M (2018b) Elderly care service in an aging society. J Econ Stud 46(1):18–34

    Article  Google Scholar 

  32. Yasuoka M, Goto N (2015) How is the child allowance to be financed? By income tax or consumption tax? Int Rev Econ 62(3):249–269

    Article  Google Scholar 

  33. Yasuoka M, Miyake A (2010) Change in the transition of the fertility rate. Econ Lett 106(2):78–80

    Article  Google Scholar 

  34. Yasuoka M, Azetsu K, Akiyama T (2009) Intergenerational child care support and the fluctuating fertility: a note. Econ Bull 29(4):2488–2501

    Google Scholar 

  35. Yasuoka M, Goto N (2011) Pension and child care policies with endogenous fertility. Econ Model 28(6):2478–2482

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank the anonymous reviewers for the beneficial comments. Research for this paper was supported financially by JSPS KAKENHI Grant Numbers 17K03746 and 17K03791. Nevertheless, any remaining errors are the authors’ responsibility.

Funding

JSPS KAKENHI Grant numbers 17K03746 and 17K03791.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Masaya Yasuoka.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest statement.

Availability of data and material (data transparency)

Our paper does not use data analysis.

Appendices

Appendix

The Sign of \(\frac{{\varvec{d}}{{\varvec{\sigma}}}^{\boldsymbol{*}}}{{\varvec{d}}{\varvec{g}}}\) (37)

Defining \(L= \alpha \left(\left(1-\varepsilon \right)\left(\left({\sigma }^{*}-\frac{{\sigma }^{*2}}{2}\right)+{\left(1-{\sigma }^{*}\right)}^{2}\right)+\frac{\varepsilon n\left(1+g\right)}{1+r}\right)\) and \(R={\left(1-{\sigma }^{*}\right)}^{2}\) as shown by (21), respectively, we can depict the following figure. (Fig. 

Fig. 2
figure2

Increase in \(g\)

2).

We can obtain the intersection of L and R and demonstrate that an increase in \(g\) reduces \({\sigma }^{*}\).

Dynamics in the Model with a Pay-as-you-Go Pension

With a pay-as-you-go pension, the dynamics occurs in the model. The dynamics in this model is shown as

$${n}_{t}=\frac{\alpha \rho \left(\left(1-\varepsilon \right)\left({\sigma }_{t}-\frac{{\sigma }_{t}^{2}}{2}+{\left(1-{\sigma }_{t}\right)}^{2}\right)+\frac{\varepsilon {n}_{t}\left(1+{g}_{t}\right)\left({\sigma }_{t+1}-\frac{{\sigma }_{t+1}^{2}}{2}+{\left(1-{\sigma }_{t+1}\right)}^{2}\right)}{1+r}\right)}{1-{\sigma }_{t}}.$$
(41)
$${n}_{t}=\rho \left(1-{\sigma }_{t}\right).$$
(42)
$$1+{g}_{t}=\frac{1}{{\sigma }_{t+1}{n}_{t}}\times \left(\left(1-\alpha -\frac{\beta }{1-\frac{1}{1+\pi }\frac{1}{1+r}}-\gamma \right)\left(1-\varepsilon \right)\left(1-\theta \right){a}^{1-\theta }\right.\left({\sigma }_{t}-\frac{{\sigma }_{t}^{2}}{2}+{\left(1-{\sigma }_{t}\right)}^{2}\right)$$
(43)
$$-\frac{\left(\alpha +\frac{\beta }{1-\frac{1}{1+\pi }\frac{1}{1+r}}+\gamma \right)\varepsilon {n}_{t}\left(1+{g}_{t}\right)\left({\sigma }_{t+1}-\frac{{\sigma }_{t+1}^{2}}{2}+{\left(1-{\sigma }_{t+1}\right)}^{2}\right)}{1+r}$$
$$1+{\pi }_{t}=\frac{1+\mu }{\left(1+{g}_{t}\right){n}_{t}}.$$
(44)

We replace (41), (43), and (44) with the following equations as

$${n}_{t}=n\left({\sigma }_{t},{\sigma }_{t+1},{g}_{t} \right),$$
(45)
$${g}_{t}=g\left({n}_{t},{\pi }_{t},{\sigma }_{t},{\sigma }_{t+1} \right),$$
(46)
$${\pi }_{t}=\pi \left({n}_{t}, {g}_{t}\right).$$
(47)

The values of \(\frac{d{\sigma }_{t+1}}{d{\sigma }_{t}}\) are shown as

$$\frac{d{\sigma }_{t+1}}{d{\sigma }_{t}}=\frac{-\rho +\frac{\partial n}{\partial {\sigma }_{t}}-\frac{\partial n}{\partial {g}_{t}}\frac{\frac{\partial g}{\partial {\sigma }_{t}}-\rho \left(\frac{\partial g}{\partial {n}_{t}}+\frac{\partial g}{\partial \pi }\frac{\partial \pi }{\partial {n}_{t}}\right)}{1-\frac{\partial g}{\partial \pi }\frac{\partial \pi }{\partial {g}_{t}}}}{\frac{\partial n}{\partial {\sigma }_{t+1}}+\frac{\frac{\partial n}{\partial {g}_{t}}\frac{\partial {g}_{t}}{\partial {\sigma }_{t+1}}}{1-\frac{\partial g}{\partial \pi }\frac{\partial \pi }{\partial {g}_{t}}}}.$$
(48)

The local stability condition is \(-1<\frac{d{\sigma }_{t+1}}{d{\sigma }_{t}}<1\) in the steady state.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shintani, M., Yasuoka, M. Fertility, Inequality and Income Growth. Ital Econ J (2021). https://doi.org/10.1007/s40797-021-00143-6

Download citation

Keywords

  • Aging population
  • Fertility
  • Income growth
  • Monetary policy
  • Subsidy

JEL Classification

  • J11
  • J14
  • E31
  • H22