Graduated income tax rates and transfer programs create piecewise-linear budget constraints that consist of budget segments and kink points. With any change in these tax rules, each individual may switch between a kink point and a budget segment, between two budget segments, or between two kink points. With errors in the estimated labor supply equation, the new choice is uncertain, and so the welfare effects of a tax change are uncertain. We propose a simulation-based method to compute expected welfare effects that is easy to implement and that fully accounts for uncertainties about choices around kink points. Our method also provides information about expected changes in working hours.