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This paper provides an analytical characterization of Markov perfect equilibria in a model with repeated voting, where agents vote over distortionary income redistribution. A key result is that the future constituency for redistributive policies depends positively on current redistribution, since this affects both private investments and the future distribution of voters. The model features multiple equilibria. In some equilibria, positive redistribution persists forever. In other equilibria, even a majority of beneficiaries of redistribution vote strategically so as to induce the end of the welfare state next period. Skill-biased technical change makes the survival of the welfare state less likely.
Hassler et al. (Sat,) studied this question.