There is a large literature documenting that workers in exporting firms receive higher wages on average than workers in non-exporting firms. This is also the case for Denmark, where the unconditional exporter wage gap is 3 percent. However, little is known about the sources behind the gap: Is it because more productive (and/or higher paying) firms export, because more productive workers select into the export sector, or is it because matches in the export sector are more productive? In this paper we decompose the gap in wages into these different sources and assess their relative importance. We are the first to show that the presence of exporter-specific worker traits, that are unobservable to the econometrician, is the primary driver of the gap. To reach this finding, we employ a novel econometric strategy and exploit two state-of-art estimators. We start out with an AKM-style wage equation with worker, firm, and match fixed effects. We then use the model in a series of classical decompositions of the exporter wage gap. We show that allowing workers to have time-invariant traits specific to the exporting sector is very important for correctly assessing which factors drive the exporter wage gap. Our results suggest that workers in exporting firms have e.g. skills that are particularly valuable in the exporting sector, therefore generating higher wages in that sector. We also show that workers make job transitions based on these differential returns and thereby the exporter wage gap becomes a result of workers selecting into the export or non-export sector based on their comparative advantage. Finally, we show that our findings are not changed substantially if we instead perform the analysis in a non-linear framework instead of the linear AKM-style framework.