Endogenous Population Growth, Social Security, and Dynamic Inefficiency

Population growth rate matters for determining the optimal amount of capital in the context of dynamic inefficiency. From the aspect of social security, if there are pension schemes, individuals have no motive for having a child as income source for retirement periods. Thus, it is important to take into account an interaction between social security and population growth rate when the optimal level of social security is considered. This paper finds the optimal social security level in an 80-period overlapping generations model with endogenous population growth. It is shown that the optimal payroll tax rate is 0% in the benchmark case, and the optimal payroll tax rate is lower than that in the exogenous case in the economic with dynamic inefficiency at the case there is no social security. This is due to the effect of borrowing constraints and some properties with children, such as requiring parents to make a certain amount of payment for many periods and giving no chance to be free from rearing children, that dominates the effect of efficiency gains. These effects lower the fertility rate, which will lower the population growth rate, and hence lower the optimal social security level.