Medicaid is a government programme that also provides health insurance to the elderly who have few assets and either low income or catastrophic health care expenses. We ask how the Medicaid rules map into the reality of Medicaid recipiency, and we ask what other observable characteristics are important to determine who ends up on Medicaid. The data show that both singles and couples with high retirement income can end up on Medicaid at very advanced ages. We find that, conditioning on a large number of observable characteristics, including those that directly relate to Medicaid eligibility criteria, single women are more likely to end up on Medicaid – so are non‐white people, but, surprisingly, their higher recipiency is concentrated in the higher income percentiles. We also find that people with low incomes who have a high‐school diploma or higher degree are much less likely to end up receiving Medicaid than their less‐educated counterparts. All of these effects are large and depend on retirement income in a very non‐linear way.