Estimating the Value of Public Insurance Using Complementary Private Insurance

The welfare associated with public insurance is often difficult to quantify. Relative to private insurance, a fundamental difficulty is that public insurance is typically compulsory, so the demand for coverage is unobserved and thus cannot be used to analyze welfare. However, in many public insurance settings, individuals can purchase private insurance to supplement their public coverage. In this paper, we outline an approach to use data and variation from private complementary insurance to quantify welfare associated with several counterfactuals related to compulsory public insurance. Using administrative data from one large firm on employee long-term disability insurance, we then apply this approach empirically to quantify the value of disability insurance among this population. We use premium variation among the employer-provided disability policies to quantify the surplus that would be generated by increasing the replacement rate of disability insurance for our sample population ― a counterfactual that is within the set of insurance contracts observed in this setting. In addition, we estimate a lower bound on the surplus generated by public disability insurance in this context. Our findings suggest that public disability insurance generates substantial surplus for this population, and there may be gains to increasing the generosity of coverage in this context