We use a switching probit model and the income-limit-based structure of Medicaid eligibility for children to estimate treatment effects of Medicaid expansions not found in existing work on public insurance.  In particular, we estimate rates of Medicaid take-up, private insurance coverage, and crowd-out for the currently eligible overall and for different demographic groups, and we estimate corresponding rates for children made eligible by a counterfactual nonmarginal increase in the Medicaid income limits.  We find strikingly different rates across demographic groups, with individuals in traditionally less disadvantaged groups having a considerably lower response to the coverage for which they are eligible.