This paper examines the interaction between public and private insurance in the context of the US Medicare program, which serves those aged 65 and older as well as the disabled who meet specific eligibility requirements. Specifically, the paper examines the extent to which increasing enrollment in Medicare managed care (which provides more comprehensive coverage than basic Medicare) influences premiums in the privately purchased Medicare supplemental insurance market (called ‘Medigap’). We employ a fixed effects instrumental variables approach to analyze the association between premiums charged by two large Medigap insurers and Medicare HMO penetration rates, examining over 60 geographic areas during the period 1994–2000. It is hypothesized that greater Medicare HMO penetration will lead to adverse selection into the Medigap market, resulting in higher premiums. The findings suggest a moderate upward effect on premiums, with elasticities ranging from 0.09 to 0.25. Controlling for other factors, moving from a 12% to a 22% Medicare HMO penetration rate would raise average Medigap premiums from $1,314 to $1,615. We discuss the implications of these results with respect to the design of national health care systems that include both public and private insurers.