Life expectancy heterogeneity and the political support for collective annuities

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 workers 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.