We estimate a New Keynesian wage Phillips curve for a panel of 24 OECD countries and allow the degree of wage indexation to past inflation to vary according to structural characteristics. We find that the degree of wage indexation is significantly lower for countries with an inflation target. However, this effect vanishes when we control for the degree of goods market competition. By contrast, more goods market competition is consistently associated with lower wage indexation. This robust finding puts into question whether embedding a constant degree of wage indexation in standard DSGE models is truly structural.