A high minimum wage (relative to average wages) raises nominal wage growth and hence inflation. This effect can be offset by extra unemployment; so the minimum wage increases the Non-Accelerating Inflation Rate of Unemployment or NAIRU. This effect is clearly discernible and robust to variations in model specification and sample period. It is consistent with international comparisons and the behavior of prices. I estimate that the reduction in the relative level of the minimum wage over the last two decades accounts for a reduction in the NAIRU of about 1 ½ percentage points. It can also account for the substantial reduction in the NAIRU in the United States relative to continental Europe.