Welfare and generational equity in sustainable unfunded pension systems

Using stochastic simulations we analyze how public pension structures spread the risks arising from demographic and economic shocks across generations. We consider several actual and hypothetical sustainable PAYGO pension structures, including: (1) versions of the US Social Security system with annual adjustments of taxes or benefits to maintain fiscal balance; (2) Sweden's Notional Defined Contribution system and several variants developed to improve fiscal stability; and (3) the German system, which also includes annual adjustments to maintain fiscal balance. For each system, we present descriptive measures of uncertainty in representative outcomes for a typical generation and across generations. We then estimate expected utility for generations based on simplifying assumptions and incorporate these expected utility calculations in an overall social welfare measure. Using a horizontal equity index, we also compare the different systems' performance in terms of how neighboring generations are treated. While the actual Swedish system smoothes stochastic fluctuations more than any other and produces the highest degree of horizontal equity, it does so by accumulating a buffer stock of assets that alleviates the need for frequent adjustments. In terms of social welfare, this accumulation of assets leads to a lower average rate of return that more than offsets the benefits of risk reduction, leaving systems with more frequent adjustments that spread risks broadly among generations as those most preferred.