Abstract
In this study, reforms on childcare allowances and public pensions are examined in an extended lifecycle simulation model with endogenous fertility. A slight increase in family policies such as childcare allowances leads to increases in the total population but the magnitude of change is not large. As childcare allowances increase, however, the total population is cumulatively and progressively augmented, resulting in substantial growth in the total population and national income in the long run. Furthermore, from a long-term perspective, increases in childcare subsidies or decreases in public pension benefits are potentially Pareto-improving.
Acknowledgements
I am grateful for the insightful comments and suggestions of Professors Alan J. Auerbach, Ronald D. Lee and Emmanuel Saez (The University of California, Berkeley). In addition, I want to thank Associate Professor Yoshinari Nomura (Okayama University), who helped me in writing the computer program used for the simulations. Professors Toshihiro Ihori (GRIPS), Yasushi Iwamoto (The University of Tokyo), Akira Yakita (Nagoya City University), Chuanchuan Zhang (The Central University of Finance and Economics), and Hyun-Hoon Lee (Kangwon National University) kindly offered many useful comments. I also wish to express my appreciation to the Editor of this journal, Professor Johann Brunner (Johannes Kepler University Linz), and to the two anonymous referees, for providing numerous insightful and thoughtful comments. Finally, I wish to acknowledge the financial support of the Ministry of Education, Culture, Sports, Science and Technology in Japan (Grant-in-Aid for Scientific Research (C) No. 15K03514).
Appendix
A Utility Maximization Problem
The utility maximization problem over time for each household in Section 2 is regarded as the maximization of
where
The first-order conditions on the number of children
where
The combination of eqs. (33) and (36) produces eqs. (9) and (10). If the initial value,
The combination of eqs. (34) and (36) produces eqs. (11) and (12). If the initial value,
For
If the value of
For
The value of
From eq. (2) and the terminal condition
where
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