There is robust evidence that higher minimum wages increase family incomes at the bottom of the distribution. The long run (3 or more years) minimum wage elasticity of the non-elderly poverty rate with respect to the minimum wage ranges between -0.220 and -0.459 across alternative specifications. The long run minimum wage elasticities for the 10th and 15th unconditional quantiles of family income range between 0.152 and 0.430 depending on specification. A reduction in public assistance partly offsets these income gains, which are on average 66% as large when using an expanded income definition including tax credits and non-cash transfers.