Helmuth Cremer, and Philippe De Donder, “Life expectancy heterogeneity and the political support for collective annuities”, TSE Working Paper, n. 14-496, May 2014.
Individuals, differing in productivity and life expectancy, vote over the size and type of a collective annuity. Its type is represented by the fraction of the contributive (Bismarckian) component (based on the worker's past earnings) as opposed to the non-contributive (Beveridgean) part (based on average contribution). The equilibrium collective annuity is either a large mostly Bismarckian program, a smaller pure Beveridgean one (in accordance with empirical evidence), or nil. A larger correlation between longevity and productivity, or a larger average life expectancy, both make the equilibrium collective annuity program more Beveridgean, although at the expense of its size.
Helmuth Cremer, and Philippe De Donder, “Life expectancy heterogeneity and the political support for collective annuities”, The Scandinavian Journal of Economics, vol. 118, July 2016, pp. 594–615.