Optimal health insurance

I formulate expected-utility-maximizing models for health insurance with a single optimal coinsurance (C*) and (separately) a single optimal deductible (D*). While so-doing, I formalize Nyman's challenge to standard welfare-loss models, clarifying when and by how much this alters unadjusted models. Using MEPS-calibrated lognormal distributions and incorporating skewness and kurtosis measures of financial risk, I show how C* shifts as various economic parameters change. For reasonable parameter values, C* < 0.1, much lower than variance-only estimates would conclude. Omitting higher-order risk parameters importantly understates risk and hence understates optimal insurance coverage. I separately develop methods to determine D*, showing that it is approximately a fixed percentage of income that falls as the distribution of financial risks rise. This finding contrasts with existing US public policy regarding high-deductible health plans, which employ fixed deductibles, independent of income.