Markov equilibrium of social security: An analytic solution under CRRA utility and the future of social security

The politico-economic sustainability of pay-as-you-go social security has been studied with the help of two-period overlapping generation models under Markovian equilibrium concepts. The literature has mostly used logarithmic utility for tractability, whereas versions under the more general isoelastic CRRA utility have only been analyzed computationally. This paper demonstrates that a prototypical social security model under CRRA utility has a closed-form solution; it revisits previously obtained computational conclusions and presents new findings and extensions. Quantitatively, the model can explain the observed path of payroll tax rates in the USA and predicts increased tax rates as the equilibrium response to lower future population growth rates. The model predicts a gradual increase in tax rates, from the current 12.4% to about 15% or so in 2060, and then staying at that level. Benefits are expected to decrease slowly, by about 2% (or less) per decade, starting in 2030.