The paper investigates the role of domestic and global determinants of euro area core inflation. We analyse the entire conditional distribution of inflation by estimating a Phillips curve type relationship using an expectile regression approach, extended to capture time-varying effects. The main findings are as follows. First, both the domestic and foreign output gap are significant drivers of euro area core inflation, once external demand pressures are properly orthogonalized in a modified measure of domestic gap. However, the inflationary impact of the domestic component is relatively stronger. Second, the domestic output gap has a bigger influence in the right tail of the conditional distribution of inflation. Third, adding international price pressures in the regression weakens the link between inflation and the foreign output gap. Fourth, in a time-varying perspective, there is an increase in the response of inflation to the domestic gap in the last decade but only at the lower quantiles. Overall, the evidence on the so-called "globalization hypothesis" is mixed: while the pass-through to inflation of foreign prices and the exchange rate increased over time at all quantiles, the impact of global slack remained broadly stable, particularly in the central part of the distribution.