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American families are in general overinsured against health expenses. If insurance coverage were reduced, the utility loss from increased risk would be more than outweighted by the gain due to lower prices and the reduced purchase of excess care. The first part of the paper develops and estimates a structural equation for the demand for health care and then examines the dynamic interaction between the purchase of insurance and the demand and supply for health care. The second part estimates the welfare gains that would result from decreasing insurance by raising the average coinsurance rate from 0.33 to 0.50 and 0.67 percent. The most likely values imply net gains in excess of $4 billion.