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 tenth and fifteenth 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 percent as large when using an expanded income definition including tax credits and noncash transfers. (JEL D31, I32, I38, J31, J38)