Estimating the Value of Public Insurance Using Complementary Private Insurance

54 Pages Posted: 30 Aug 2016 Last revised: 17 Apr 2018

See all articles by Marika Cabral

Marika Cabral

University of Texas at Austin; National Bureau of Economic Research (NBER)

Mark R. Cullen

Stanford University

Multiple version iconThere are 2 versions of this paper

Date Written: March 21, 2018


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.

Keywords: Public Insurance, Private Insurance, Complementary Insurance, Disability Insurance

JEL Classification: H0, H53, I38, J68

Suggested Citation

Cabral, Marika and Cullen, Mark R., Estimating the Value of Public Insurance Using Complementary Private Insurance (March 21, 2018). Available at SSRN: or

Marika Cabral (Contact Author)

University of Texas at Austin ( email )

Department of Economics
2225 Speedway, BRB 1.116, C3100
Austin, TX 78712
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Mark R. Cullen

Stanford University ( email )

Stanford, CA 94305
United States

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