New Keynesian models of the Phillips curve in the spirit of Galí and Gertler (1999) generally assume a short-run trade-off between inflation and a measure of excess demand due to nominal rigidities, while in the long run inflation is constant at the Non-Accelerating Inflation Rate of Unemployment (NAIRU). By contrast, Gordon (1997) in his "triangle model" of inflation models a time-varying NAIRU. We combine both approaches and estimate state-space models of the hybrid New Keynesian Phillips curve (NKPC), where excess demand is measured by the unemployment gap and the NAIRU is allowed to vary over time as in Gordon (1997). Moreover, inflation expectations are measured directly from surveys on household?s inflation expectations and not instrumented for. Our model is estimated for the US, the UK, Italy and Spain and we find considerable variation in the NAIRU over time with NAIRU estimates significantly different from HP-filter derived measures such as usually employed in dynamic stochastic general equilibrium (DSGE) models. In contrast to GMM results for the hybrid NKPC, we find that backward looking behaviour generally seems to be quantitatively more important for inflation than forward looking behaviour.