In recent decades, there has been an increase in life expectancy and a rapid increase of the very senior dependency ratio in developed countries. In this context, we examine the optimal levels of public pensions and public long-term care (LTC) insurance. According to the most reasonable estimates of correlations among individual incomes, risks of mortality and dependency, we show that it is always desirable for a utilitarian social planner to have a balanced budget increase in LTC benefits at the expense of public pension benefits, until the cost of LTC is fully covered. This is true with or without liquidity constraints. For a Rawlsian planner, the balance between the two schemes depends on a comparison of the ratio of the survival probability to the dependence risk of the poor with its population average.
Nishimura, Y., & Pestieau, P. (2022). Old age or dependence. Which social insurance? Journal of Public Economic Theory, 24, 639-652. https://hdl.handle.net/2078.5/273523 (Original work published 2022)