This study examines the economic determinants of labor mobility within the European Union using data from 23 EU member states over the period 2000–2019. To address both model uncertainty and reverse causality, we employ Bayesian model averaging within a dynamic panel framework with weakly exogenous regressors. We find strong persistence in EU migration flows, largely driven by network effects operating through migrants already present in destination countries. While both earnings and unemployment differentials influence migration, the effect of earnings is 18 to 24 times stronger, suggesting that the search for higher income dominates the motive of escaping unemployment. This finding challenges the notion that labor mobility currently serves as an effective adjustment mechanism in the EU. However, as unemployment differentials tend to widen during recessions and their aftermath, migration may still contribute to economic adjustment when it is most needed. We find no evidence that differences in social benefits, taxation, or human capital significantly affect migration flows, contradicting prior empirical findings and media narratives suggesting the existence of welfare migration. Our results highlight the importance of addressing model uncertainty and endogeneity to accurately assess the drivers of labor mobility in the European context.