This study empirically investigates the extent to which firms in the European Union, once acquired through a cross‐border acquisition, show different productivity levels as compared to those firms that have not been acquired. Our identification strategy relies on the combination of Propensity Scores and the Staggered Difference‐in‐Difference estimator, using firms' balance sheet data for the years 2008–2018. We find that cross‐border acquisitions decrease the productivity of the acquired firms, especially in the manufacturing sector, both high‐ and low‐tech. We also find evidence of origin and sector heterogeneity. Firms targeted by acquirers with ultimate owners originating in emerging market economies and Offshore Financial Centres also decrease productivity of target firms operating in high‐tech manufacturing sectors.