Risky Insurance: Life Cycle Insurance Portfolio Choice with Incomplete Markets

Résumé

We provide survey evidence that individuals believe there is substantial nonpayment risk in annuity, life insurance, and long-term care insurance (LTCI) products. Using simple statistical analysis we show that nonpayment beliefs predict insurance ownership and that the insurance ownership rate would be much larger if people believed there was zero nonpayment risk. To better quantify how nonpayment risk affects insurance ownership and how different features of insurance products affect consumer welfare, we develop an incomplete-markets life-cycle model of the demand for life in- surance, annuities, LTCI, and a risk free bond. We incorporate features of real-world insurance products such as perceived nonpayment risk, high loads above actuarial fair prices, and quantity restrictions (e.g., age restrictions on purchases, short-selling constraints). Both high prices and nonpayment risk substantially decrease insurance ownership. Compared to our rational expectations baseline, the welfare loss from sub-optimally owning zero insurance is 0.4 percent in consumption equivalent units. If the products had no risk and were sold at actuarially fair prices, the welfare cost of zero insurance ownership is much larger at 7.9 percent. If subjective beliefs are wrong and payments are always made, correcting beliefs increases welfare by 4 percent.