Equilibrium social insurance with policy-motivated parties
We study the political economy of social insurance with double heterogeneity of voters (e.e., different income and risk levels). Social insurance is ﬁnanced through distortionary taxation and redistributes across income and risks. Individuals vote over the extent of social insurance, which they can complement on the private market. Private insurance suffers from adverse selection which results into insurance rationing. We model political competition a la Wittman, with two parties maximizing the utility of their members. Party membership is endogenously determined. We show that although individuals differ in two dimensions, their preference for social insurance can be aggregated into a single dimensional type function. We then resort to numerical simulations to solve the political equilibrium outcome as a function of the distribution of income and risk. We obtain equilibrium policy differentiation with the Left party proposing more social insurance than the Right party. The Left party's equilibrium membership is made of low risk and high income individuals, with high risk and low income individuals forming the Right party's constituency. In equilibrium, each party is tying for winning. Unlike the median voter outcome, our equilibrium outcome depends on the whole income and risks distribution, and increasing income polarization leads both parties to propose less social insurance. We also compare the political equilibrium outcome with the Rawlsian and utilitarian outcomes.
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