This paper is motivated by our attempt to answer an empirical question: how is private health insurance take-up in Australia affected by the income threshold at which the Medicare Levy Surcharge (MLS) kicks in? We propose a new difference de-convolution kernel estimator for the location and size of regression discontinuities. We also propose a bootstrapping procedure for estimating confidence bands for the estimated discontinuity. Performance of the estimator is evaluated by Monte Carlo simulations before it is applied to estimating the effect of the income threshold of Medicare Levy Surcharge on the take-up of private health insurance in Australia using contaminated data.