On the optimal linkage of social security benefits to payroll taxes

• This paper identifies a welfare-enhancing social security reform.
• This is achieved by adjusting the US Social Security Administration׳s benefit formula.
• It provides a justification for wage indexing and puts forth an argument for “population indexing”.
• A higher weight on the young’ s earnings increases their labor supply while reducing the middle-aged’s.
• Optimal net tax rates are non-uniform over the life cycle but zero on the steady-state golden-rule path.

This paper employs a three period overlapping generations’ model to investigate (i) the labor supply effects of the linkage between the benefits of a pay-as-you-go social security program and the payroll taxes that finance them and (ii) the nature of the optimal linkage. The main result of the paper is that, for a given statuary tax rate, the weights that must be placed on earnings of different periods (in benefit calculation) depend on population and productivity growth rates only. This result implies that the optimal net tax rates are not uniform over the life cycle unless the economy is on its steady state golden rule path. Moreover, if the economy is on the golden rule path, the optimal net tax rates are not only uniform but also zero. The paper also demonstrates that, if preferences are additively separable, as more weight is placed on earnings when young labor supply by the young increases while labor supply by the middle-aged decreases.