*Economists have long suspected that ideas travel with people, yet formal growth models typically assume that R&D labour reallocates without frictions, while search-and-matching models of the labour market rarely incorporate innovation. I build a tractable framework that brings these two blocks together. In the model, scientists search for jobs across sectors connected by a mobility network. Innovation in each sector then builds on knowledge from other sectors, channeled through these mobility flows. This setup raises key questions: Is it always true that easing labour mobility fosters knowledge spillovers and growth? Should policies aimed at boosting sectoral innovation work through direct R&D subsidies, or by improving the circulation of ideas via labour mobility?

**This study examines income-smoothing dynamics within the European Union and the euro area at the regional (NUTS2) level over the period 2000–2020, focusing on the various channels of adjustment to wage shocks and quantifying the degree of smoothing achieved. Demographic variations are explicitly analyzed as a smoothing channel, with distinctions drawn between natural population balance and migration. Our findings shed light on the relative importance of different revenue-smoothing mechanisms, highlighting significant differences across the core, semi-periphery, and periphery of the EU, as well as temporal changes in these dynamics. In particular, we find that property income plays a significant and growing role in absorbing wage shocks, especially in certain regions of the euro area. The large disparities in income smoothing across EU regions thus indicate a multi-speed process in income smoothing. While the euro area remains heterogeneous, it nonetheless exhibits less disparities than the broader EU.