The US government increasingly provides public health insurance coverage through private firms. We examine associated welfare implications for beneficiaries, using a ‘revealed preference’ framework based on beneficiaries’ program attrition rates. Focusing on the Medicaid program in New York State, we exploit quasi-random variation in the initial assignment at birth to public versus private Medicaid based on birth weight. We find that infants assigned to private Medicaid at birth are less likely to subsequently leave Medicaid. We provide suggestive evidence that reduced attrition reflects beneficiary responses to improved program quality, rather than alternative mechanisms such as private Medicaid plans reducing re-enrollment barriers.