Effects of Endogenous Longevity on Transitional Dynamics of Intergenerational Mobility

ABSTRACT

This paper explains the mechanism that causes the two motions of intergenerational mobility, monotonic motion and cyclical motion. Increasing longevity encourages incentives for education investment while decreasing transfers, which is the funding source for education. If longevity increases slowly, mobility increases monotonically. However, if longevity increases rapidly with economic development, mobility is cyclical owing to a largely decreasing transfer. This result is consistent with the empirical evidence in the literature on intergenerational mobility. In fact, China, where longevity increased rapidly, experienced a cyclical motion of mobility, whereas Norway, where longevity increased slowly, has experienced a monotonic motion of mobility.

KEYWORDS:

• Endogenous longevity
• transitional dynamics
• intergenerational mobility
• economic development

JEL CLASSIFICATIONS:

• I12
• J62
• O11

Acknowledgements

The author is deeply grateful to Tamotsu Nakamura for valuable comments. In addition, I wish to thank Hideaki Uchida, Kenichi Hashimoto, Tetsugen Haruyama and participants at the 2019 Spring meeting of Japanese Association of Applied Economics. I appreciate the anonymous referee for their constructive suggestion concerning this research. The usual disclaimer applies.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 Liu et al. (2020) also show an increase and then a decrease in mobility in China between 1989 and 2011.

2 In fact, demographic variables, such as fertility and longevity, have a significant effect on mobility and income inequality. Aso and Nakamura (2020) show that the fertility difference between the educated and uneducated plays an important role in mobility.

3 Maoz and Moav (1999) analyse the transitional dynamics of intergenerational mobility, income inequality and economic development in a simple framework. Thus, we can clearly show the effects of endogenous longevity on the transitional dynamics of the economy by incorporating these effects into the Maoz and Moav model.

4 In fact, life expectancy at birth is an S-shaped curve in China as indicated by Figure 1.

5 The modelling of transfer follows Zhang, Zhang, and Lee (2001).

6 If $\mathrm{\partial }f(E_{t+1})/\mathrm{\partial }{E}_{t+1}>0$, the incentive increases despite the decreasing income inequality with the increasing educated share. This increase in the incentives causes the educated share to increase incrementally, and hence the economy may explode. Thus, this assumption technically guarantees a steady state. Using numerical analysis under plausible parameters, we show in Appendix A that $\mathrm{\partial }f(E_{t+1})/\mathrm{\partial }{E}_{t+1}<0$ holds for $E_{t+1}\in (0,\hat{E})$.

7 If the survival rate is an exogenous value, the transitional dynamics of mobility depend only on the education cost share as in Maoz and Moav (1999), and hence only the monotonic motion of mobility emerges in the economy.

8 If we take the parameter $0<\delta <1$, then we get the similar result, that is, monotonic motion of mobility.

9 $\chi$ is scale parameter and we choose the values of $\chi$ for which the longevity function is concave and convex, respectively. In addition, there is no upper limit to the value of $\chi$ since even if its value is sufficiently large, it only lowers $\underset{\_}{\pi }=\overline{\pi }/(1+\chi )$.

Additional information

Funding

The author gratefully acknowledges the financial support of Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (22K13407).