This paper studies the long-run impact of public debt expansion on economic growth and investigates whether the debt-growth relation varies with the level of indebtedness. Our contribution is both theoretical and empirical. On the theoretical side, we develop tests for threshold effects in the context of dynamic heterogeneous panel data models with cross-sectionally dependent errors and illustrate, by means of Monte Carlo experiments, that they perform well in small samples. On the empirical side, using data on a sample of 40 countries (grouped into advanced and developing) over the 1965-2010 period, we and no evidence for a universally applicable threshold effect in the relationship between public debt and economic growth, once we account for the impact of global factors and their spillover effects. Regardless of the threshold, however, we find significant negative long-run effects of public debt build-up on output growth. Provided that public debt is on a downward trajectory, a country with a high level of debt can grow just as fast as its peers.