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Control Group: Nearly elderly (aged 55-64) who did not receive Medicare.
Treatment Group: Elderly (aged 65-74) who received health insurance.
It is reasonable is assume that both these groups are similar in characteristics so that any difference in health changes can be attributed to Medicare.
Perhaps surprisingly, Finkelstein and McKnight come to the conclusion that Medicare did not have any effect on elderly mortality in the period studied.
The only discernable benefit of government insurance comes through a reduction in the risk of large out-of-pocket health expenses. It is unclear why private health insurance would not be able to do this. But government insurance also induces people to shift from private to public insurance. While the aim of public health insurance should be to provide insurance to persons who would otherwise remain uninsured, Gruber and Simon (2008) find that the crowding out effect of Medicaid is 60%. This means that out of every 10 people who take Medicaid, 6 leave their private insurance plans.
http://www.nber.org/papers/w11609
http://www.nber.org/papers/w12858