The Optimal Size and Progressivity of Old-Age Social Security

Almost every public pension system shares two attributes: earning deductions to finance benefits, and benefits that depend on earnings. This paper analyzes theoretically and empirically the trade-off between social insurance and incentive provision faced by reforms to these two attributes. First, I combine the social insurance and the optimal linear-income literature to build a model with a flexible pension contribution rate and benefits' progressivity that incorporates inter-temporal and inter-worker types of redistribution and incentive distortion. The model is general, allowing workers to be heterogeneous on productivity and retirement preparedness, and they exhibit present-focused bias. I then estimate the model by leveraging three quasi-experimental variations on the design of the Chilean pension system and administrative data merged with a panel survey. I find that taxable earnings respond to changes in the benefit-earnings link, future pension payments, and net-of-tax rate, which increases the costs of reforms. I also find that lifetime payroll earnings have a strong positive relationship with productivity and retirement preparedness, and that pension transfers are effective in increasing retirement consumption. Therefore, there is a large inter-worker redistribution value through the pension system. Overall, there are significant social gains from marginal reforms: a 1% increase in the contribution rate and in the benefit progressivity generates social gains of 0.08% and 0.29% of the GDP, respectively. The optimal design has a pension contribution rate of 17% and focuses 42% of pension public spending on workers below the median of lifetime earnings.