In a world of uneven climate policies, concerns about carbon leakage and competitiveness for heavy industries are the main arguments against the implementation of ambitious climate policies. In this paper we investigate a potential competitiveness-driven operational carbon leakage due to the European Union Emissions Trading scheme (EU ETS). We focus on two energy-intensive sectors, cement and steel, and phases I and II of the EU ETS. From a simple analytical model, we derive an equation linking net imports of cement and steel to local and foreign demand along with carbon price. We then econometrically estimate this relation both with ARIMA regression and Prais-Winsten estimation, finding that local and foreign demand are robust drivers of trade flows. We find no significant effect of the carbon price on net imports of steel and cement. We conclude that there is no evidence of carbon leakage in these sectors, at least in the short run.