Optimal progressive income taxation in a Bewley-Grossman framework

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 amplifies 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 coefficient 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.