Planning for the Optimal Mix of Paygo Tax and Funded Savings
The paper uses an overlapping generations model to analyse the problem of a benevolent planner determining the pay-as-you-go tax rate and the level of funded savings, in an economy where both are policy variables. We characterize the conditions under which it is desirable to have both a positive tax rate and a positive level of savings. The optimal size of the tax rate and of savings depend both on the stochastic characteristics of earnings growth and the return to savings, and on the shape of the utility function of the representative agent. Among the comparative statics results presented, the central one is that increasing the variability of earnings raises the desirability of a pay-as-you-go system, under general conditions. This is consistent with earlier analyses of pay-as-you-go as a provider of intergenerational insurance. A numerical example using the CARA utility and normal distributions illustrates the calculation of optimal tax and savings levels, using annual data for post-War France.
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