The New Keynesian Phillips curve (NPC) differs from the conventional expectations-augmented Phillips curve in that it is forward-looking and links inflation to a measure of marginal cost instead of unemployment or the output gap. More fundamentally, the NPC is derived from New Keynesian models that combine nominal rigidities with individual optimising behaviour and model-consistent (rational) expectations. Because the NPC is grounded in micro-theory (unlike the conventional expectations-augmented Phillips curve), it is robust to some forms of the Lucas critique and may serve to analyse the impact structural changes such as increased price flexibility may have on inflation. New Keynesian Phillips curve estimates for Luxembourg using the Gali and Gertler (1999) hybrid form suggest that firms change prices often but tend to use backward-looking rules-of-thumb instead of resetting prices optimally using forward-looking expectations. In terms of policy implications, although the results suggest prices in Luxembourg are relatively flexible, the prevalence of backward-looking price setting implies greater inflation persistence and a higher sacrifice ratio attached to disinflationary monetary policy. From the perspective of individual firms, backward-looking price setting may be a rational response in a very small open economy because of its vulnerability to external shocks. Small size and openness plausibly imply higher costs of collecting information and lower benefits from optimal price setting.