Disability insurance means that if you are unlucky enough to suffer an accident or illness that prevents you from working, you will still receive income. It is also possible to purchase annuities (which are sort of a reverse life insurance): these are assets that pay out a certain amount each year while you are alive and allow you to insure yourself against the uncertain time of your death. Early discussions of Social Security highlighted the insurance role of the program. During the Great Depression, it became clear that insurance provided through markets was woefully incomplete. Thus the government created a variety of safety nets, financed by public funds. Social Security was one of these programs. An early pamphlet on Social Security summarizes this view:
In general, the Social Security Act helps to assure some income to people who cannot earn and to steady the income of millions of wage earners during their working years and their old age. In one way and another taxation is spread over large groups of people to carry the cost of giving some security to those who are unfortunate or incapacitated at any one time. The act is a foundation on which we have begun to build security as States and as a people, against the risks which families cannot meet one by one. 
Financial sophistication has increased markedly since the 1930s, but insurance markets are still far from perfect, so most people agree that the government should continue to provide the insurance that private markets fail to deliver. As President George W. Bush’s Council of Economic Advisors wrote, “To protect against this risk [of living an unusually long time], a portion of the retirement wealth that a worker has accumulated must be converted into an annuity, a contract that makes scheduled payments to the individual and his or her dependents for the remainder of their lifetimes.”  Once we acknowledge two things—(1) there is major uncertainty in life, and (2) insurance markets are lacking—we see a clear role for Social Security. The Complexity of Optimization There is another reason to think that our analysis of Carlo was much too simple. For Carlo, it was quite straightforward to determine his optimal level of consumption: all he had to do was to calculate his lifetime income, divide by the number of years of life that he had left, and he knew his optimal level of consumption. We said earlier that the basic idea of this life-cycle model continues to hold even in a more complicated world, where incomes are not constant, real interest rates are not zero, and consumption needs may vary over one’s lifetime. If you have a PhD in economics, you even learn to solve these problems in a world of uncertainty. Yet when one considers all the uncertainties of life, the problem certainly becomes very complex. Most individuals do not have PhDs in economics, and most people—even including those with economics PhDs—are not able to forecast their income and consumption needs very accurately. As a result, it seems likely that many people are not capable of making good decisions when they are thinking about consumption and saving over their entire lifetimes
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