Modern theories of inflation incorporate a vertical long-run Phillips curve and are usually estimated using techniques that ignore the non-stationary behaviour of inflation. Consequently, the estimates obtained are imprecise and unable to test the veracity of a vertical long-run Phillips curve. We estimate a Phillips curve model taking into account the non-stationary properties in inflation and identify a small but significant positive relationship between inflation and unemployment. The results also provide some evidence that the trade-off between inflation and the rate of unemployment in the short-run worsens as the mean rate of inflation increases. © 2007 Elsevier Inc. All rights reserved.