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We study optimal income tax progressivity in an environment where individuals are exposed to idiosyncratic income and health risks over the lifecycle. Our results, based on a calibration for the US economy, indicate that the presence of health risk combined with incomplete insurance markets amplies the social insurance role of progressive income taxes. The government is required to set higher optimal levels of tax progressivity in order to provide more social insurance for unhealthy low income individuals who have limited access to health insurance. The optimal progressive income tax system includes a tax break for income below $36,400 and high marginal tax rates of over 50 percent for income above $200,000: The tax progressivity (Suits) index-a Gini coeffcient for income tax contributions by income-of the optimal tax system is around 0.53, compared to 0.17 in the benchmark tax system. Yet, the optimal tax system in our model is more progressive than the optimal tax systems in models abstracting from health risk (e.g., Conesa and Krueger (2006) and Heathcote, Storesletten and Violante (2017)). Importantly, the optimal level of tax progressivity is strongly affected by the design of the health insurance system. When health expenditure risk is reduced or removed from the model, the optimal tax system becomes less progressive and thus more similar to the optimal progressivity levels reported in the previous literature.

Optimal Progressive Income Taxation in a Bewley-Grossman Framework