The inter-institutional dynamics in the European Union (EU) have significantly evolved over time. The growing importance of the European Council, changes in the composition of the European Commission and the expanding role of the European Parliament have led to increasingly contested policy-making at the EU level. While the European Commission has traditionally been regarded as the dominant actor, EU policy-making has become increasingly inter-institutional, raising the question: Who drives policy priorities in the EU? To address this, we analyze the communication of policy priorities among the European Council, European Commission and European Parliament in the field of migration. We apply a novel text-as-data classification of policy priority using trained and fine-tuned transformer-based models (BERT) on a full sample of Commission speeches, Council conclusions and speeches from the European Parliament. Based on the text classifications, we statistically model the interactions and streams of influence between the different institutions using Vector Autoregression Models. The results uncover the growing harmonization and inter-institutional dynamics in the European Union. Whereas the Commission started to communicate priorities in the domain of migration only after the Lisbon Treaty entered into force, the Council shifted from a global view on migration crises to an inward looking actor, whose priorities mainly aligned with the view of Commissioners and Commission presidents.