Public pension systems rely on formal earnings to provide old-age social insurance. However, in the presence of low levels of formal earnings, pervasive in the undeveloped world, these systems provide insufficient retirement protection, and that protection is concentrated in high-income households. This paper studies theoretically and empirically how the presence of low formal earnings affects the optimal design of public pensions on its two core characteristics: the pension contribution rate and the link between lifetime formal earnings and benefits. I introduce a framework to capture the welfare effect of these reforms by combining the social insurance with the optimal linear-income literature, identifying the sufficient statistics that govern the trade-off between more retirement insurance and more incentive distortion of private savings and formal earnings. I then estimate these statistics in Chile, a country with low levels of formal employment and a pension system with a strong earnings-benefits link, using administrative data merged with a panel survey. I find that low earners are the most vulnerable at retirement and are less protected by the public system. Consequently, low earners drop their consumption three times more than high earners at retirement. I then estimate the distortions of reforming the contribution rate and the earnings-benefits link by leveraging two quasi-experimental variations on the design of the Chilean pension system. I find that formal earnings respond to the design of the pension system, but this response is driven mainly by the earnings-benefits link, not the future pension payments. Furthermore, there is a large marginal propensity to consume out benefits at retirement, implying a minor distortion on retirement private savings. Overall, the trade-off is weighted in favor of more progressivity but not of more contribution: there are large social gains from flattening the earnings-benefits link, while the social gains of increasing the pension contribution rate are modest.