Equilibrium social insurance with policy-motivated parties

We study the political economy of social insurance with voters' heterogeneity on two dimensions: income and risk levels. Individuals vote over the extent of social insurance, which they can complement on the private market. We model political competition à la Wittman, with two parties maximizing the utility of their members. We obtain equilibrium policy differentiation with the Left party proposing more social insurance than the Right party. The Right party attracts the less risky and richer individuals, and the Left party attracts the more risky and poorer individuals. In equilibrium, each party is tying for winning. Unlike the median voter outcome, our equilibrium outcome depends on the whole income and risk distribution. Conditional on the risk distribution, more income inequality does not necessarily lead to higher demand for social insurance. In fact we find that more income polarization leads both parties to propose less social insurance. We also contrast our political equilibrium with the Rawlsian and utilitarian outcomes. Finally, we provide in the Appendix a first try at calibrating the model with real data, using U.S. data from the PSID survey.