This paper studies the role of social insurance as a redistributive mechanism in presence of an optimal (linear or general) income tax. It considers a second-best setting with two unobservable individual characteristics: ability, measured by the wage rate and risk, measured by the probability of incurring a loss. It shows that both tax progressivity and the optimal level of social insurance crucially depend on the correlation between ability and risk.
Cremer, H., & Pestieau, P. (1996). Redistributive taxation and social insurance. International Tax and Public Finance, 3(3), 281-295. https://doi.org/10.1007/BF00418945 (Original work published 1996)