Regression discontinuity design with multivalued treatments

We study identification and estimation in the regression discontinuity design with a multivalued treatment. We show that heterogeneity in the first stage discontinuities can be used for the identification of the marginal treatment effects under an alternative assumption, namely, the homogeneity of the LATEs along some covariates. This assumption can often be tested and relaxed. Our estimator can be programmed as a simple two-stage least squares regression, and packaged standard errors and tests can also be used. We apply our method to estimate the effect of Medicare insurance coverage on health care utilization.