Policy-oriented parties and the choice between social and private insurance

We study the political economy of social insurance in a world where individuals differ in both income and risk. Social insurance is financed through distortionary taxation and redistributes across income and risk. Individuals vote on social insurance which they can complement with insurance bought on the private market. Private insurance is actuarially fair but suffers from adverse selection which results in a screening equilibrium with partial coverage. The equilibrium social insurance is the result of bi-partisan electoral competition game where parties maximize the utility of their members. We calculate the equilibrium social insurance offered by the two parties as well as their equilibrium membership, and study how the equilibrium outcome is affected by electoral uncertainty, distortions from taxation, risk aversion and the distribution of risk and income. We then calibrate the model to US data from the PSID survey. Lastly, we study how the political demand for social insurance is affected by the possibility to redistribute through income taxation.