Maybe a lot. The ratio of the minimum wage to the average wage enters a Phillips-curve equation with a coefficient that is highly significant, stable, and robust. One interpretation of these results is that the relative level of the minimum wage affects the Non-Accelerating Inflation Rate of Unemployment or NAIRU. My estimates are consistent with the reduction in the relative level of the minimum wage since 1980 lowering the U.S. NAIRU about 1 1 2 percentage points, while raising the NAIRU in continental Europe. However, other interpretations are also possible.