Social security and institutions for intergenerational, intragenerational, and international risk-sharing

Social security system old-age insurance systems are devices for the sharing of income risks of elderly people with others. Risks can be shared intergenerationally (with the young of the same country), intragenerationally (with other elderly of the same country), or internationally (with foreigners). Barriers to individuals themselves sharing their risks intergenerationally, intragenerationally, or internationally are described. Optimal design of government-sponsored social security systems is considered in light of these barriers. Alternative benefits and contributions formulas for pay-as-you-go social security systems are defined and compared with existing and proposed formulas in terms of their ability to fulfill the government's role in promoting risk-sharing. Benefits for each retired person may be tied to that person's lifetime income without causing (as with the U.S. benefits formula today) aggregate benefits for all elderly today to be tied to their past aggregate income.