We estimate the slope of the Phillips curve in the euro area, allowing for nonlinearities - or kinks - in the relationship between labor market slack and inflation. We exploit cross-country variation in labor market conditions in the period 2001-2024, absorbing aggregate shocks and endogenous monetary policy reactions with time fixed effects. We find that while the Phillips curve is usually quite flat, it becomes at least three times as steep if the labor market is sufficiently tight. This kink is more pronounced in the euro area than in the United States, potentially because of more rigid labor markets. Our estimates imply, however, that despite this nonlinearity, the majority of the post-Covid inflation surge was due to factors other than tight labor markets.