Optimal Health Insurance and the Distortionary Effects of the Tax Subsidy

This paper develops a model of optimal health insurance in the presence of a tax-deductible premium.  The presence of a health insurance subsidy in the United States tax code, which enables individuals to pay premiums in pre-tax dollars, encourages the purchase of more generous health insurance plans.  While there is a long literature discussing the possible consequences of subsidizing health insurance through the tax code, we have almost no theoretical or empirical evidence about how this tax subsidy distorts the optimal cost-sharing schedule for a household.  The model characterizes the non-linear cost-sharing schedule desired by the household given the household's preferences for protection from financial risk balanced with its preferences for a low premium.  The household contracts with a risk-neutral insurer that only observes the household's annual medical expenditures.  Consequently, the household must demand a health insurance plan which meets a series of incentive compatibility constraints to commit to consuming specific amounts of care in each health state. The tax subsidy makes cost-sharing less attractive at all possible medical expenditures, but this effect is not uniform.  I model this relationship explicitly.  The framework is also extended to include the Affordable Care Act's ``Cadillac Tax" on plans with expensive premiums.  The Cadillac Tax has the opposite effect of the tax subsidy and increases coinsurance rates though, again, not uniformly.  The model is tested empirically using claims data in the Medical Expenditure Panel Survey and a regression discontinuity strategy that uses discrete changes in the marginal tax rate at the Social Security taxable maximum for identification.