The Tax Reform Act of 1986 introduced a new tax subsidy for health insurance purchases by self-employed persons. This paper analyzes the changing patterns of insurance demand before and after this reform to generate new estimates of how the after tax price of insurance affects the discrete choice of whether to buy insurance. We employ both traditional regression models for insurance demand, in which after-tax price of insurance is an explanatory variable. as well as nonparametric tests that compare changes in insurance purchases by self-employed individuals with the coincident changes for other groups. Our analysis suggests that I one percent increase in the cost of insurance coverage reduces the probability that a self-employed household will be insured by as much as 1.8 percentage points. (This abstract was borrowed from another version of this item.)