Optimal Taxation and Social Insurance with Endogenous Private Insurance

What is the optimal amount of redistributive taxation and social insurance? A recent literature in public economics has come closer to providing quantitative answers to this central policy question. This literature has derived “sufficient statistic” formulas that map elasticities estimated in the modern program evaluation literature into predictions about optimal policies (e.g., Peter A. Diamond 1998, Saez 2001, Robert Shimer and Ivan Werning 2007, Chetty 2009). One important limitation of existing sufficient statistic formulas is that they do not allow for private market insurance, implicitly assuming that the government is the sole provider of insurance. In practice, private markets have historically been an important source of insurance and continue to remain active today despite the substantial size of social insurance programs. Previous theoretical and empirical studies have recognized that the existence of private insurance can lower the optimal level of social insurance. However, there is no method of mapping reduced-form empirical estimates such as those of Cutler and