Abstract This study analytically investigates the effects of pay-as-you-go social security and educational subsidies on the fertility rate, retirement age, and GDP per capita growth rate in an overlapping generations model, where parents invest resources toward their children’s human capital. We find that an old agent retires fully when his or her labor productivity is low and retires later when the labor productivity is high. Under the unique balanced-growth-path (BGP) equilibrium, when an old agent is still engaged in work, tax rates are neutral to the fertility rate, higher tax rates encourage him or her to retire earlier, a higher social security tax rate depresses the GDP per capita growth rate, and a higher tax rate for educational subsidies can accelerate growth. However, when an old agent fully retires, higher tax rates increase the fertility rate, a higher social security tax rate lowers the GDP per capita growth rate, and a higher tax rate for educational subsidies boosts growth. Additionally, if an old agent’s labor productivity increases, the fertility rate also increases. We also conduct numerical simulations and analyze how an old agent’s labor productivity affects the retirement age, fertility rate, and GDP per capita growth rate under the BGP equilibrium.

中文翻译：

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内生生育和内生退休的代际重叠模型中的现收现付社会保障和教育补贴

摘要 本研究在代际重叠模型中分析了现收现付社会保障和教育补贴对生育率、退休年龄和人均 GDP 增长率的影响，其中父母将资源投资于子女的人力资本。我们发现，一个老代理人在他或她的劳动生产率低时完全退休，而在劳动生产率高时退休。在独特的均衡增长路径（BGP）均衡下，当一个老代理人仍在从事工作时，税率对生育率是中性的，较高的税率鼓励他或她提前退休，较高的社会保障税率抑制人均 GDP 增长率，提高教育补贴税率可以加速增长。然而，当一位老特工完全退休时，较高的税率会提高生育率，较高的社会保障税率会降低人均GDP的增长率，较高的教育补贴税率会促进增长。此外，如果老代理人的劳动生产率提高，生育率也会提高。我们还进行了数值模拟，分析了 BGP 均衡下老年代理人的劳动生产率如何影响退休年龄、生育率和人均 GDP 增长率。