With much attention focused on universal medical insurance, the abstract of a new NBER Working Paper reminds us that government insurance often crowds out private insurance:

The continued interest in public insurance expansions as a means of covering the uninsured highlights the importance of estimates of "crowd-out", or the extent to which such expansions reduce private insurance coverage. Ten years ago, Cutler and Gruber (1996) suggested that such crowd-out might be quite large, but much subsequent research has questioned this conclusion. We revisit this issue by using improved data and incorporating the research approaches that have led to varying estimates. We focus in particular on the public insurance expansions of the 1996-2002 period. Our results clearly show that crowd-out is significant; the central tendency in our results is a crowd-out rate of about 60%. This finding emerges most strongly when we consider family-level measures of public insurance eligibility. We also find that recent anti-crowd-out provisions in public expansions may have had the opposite effect, lowering take-up by the uninsured faster than they lower crowd-out of private insurance.

A 60% crowd out rate is quite large--for every 5 people taking up government medical insurance, 3 drop private insurance. This is an awfully expensive price for covering 2 additional people.