Despite the increased importance of cyclically-adjusted measures of labour market slack for policymaking, estimates of the NAIRU have become increasingly fragile. Particularly for euro area countries, NAIRU estimates represent a crucial input to compute cyclically-adjusted budget balances adopted to formulate medium-term fiscal objectives under the EU fiscal surveillance framework. However, the apparent reduced sensitivity of inflation to labour market dynamics and unemployment gaps seriously undermines the use of Phillips curve equations in estimating the NAIRU. Estimates of the NAIRU are particularly problematic when changes in unemployment are both very large and rapid as in the aftermath of the global crisis. This paper proposes a refinement to the standard OECD approach of using a Kalman filter to estimate the NAIRU in the context of the Phillips curve. The proposed refinement strengthens the relationship between inflation and labour market developments by considering the risk of hysteresis effects associated with changes in long-term unemployment. Testing the revised methodology on a broad selection of OECD countries gives mixed results. For a group of countries in the euro area periphery (Greece, Ireland, Italy, Portugal and Spain) there is an increase in the magnitude and statistical significance of the unemployment gap, with the NAIRU revised upward by on average 1¾ percentage points. However, the revised methodology provides less improvement to the standard OECD methodology for a second set of countries considered, namely the G7 excluding Italy. The United States is an interesting intermediate case as the statistical evidence for the proposed methodology is marginal, but the policy implications of the revised point estimate of the NAIRU are major. JEL classification: C32, E24, E31, E32, J64. Keywords: Long-term unemployment, flattening Phillips curve, NAIRU, euro area periphery, Kalman filter.