This paper investigates cross-country productivity convergence at a sectoral level using multivariate unit-root tests. Our empirical analysis counts with three distinctive features. First, it allows all the coefficients in the panel specification to vary across countries. Second, it accounts for the presence of significant cross-country correlations found in the data. Third, when the null hypothesis of non convergence is rejected, a second test determines the number of converging countries. Based on a sample of thirteen OECD countries our results show evidence of convergence in three out of six sectors, namely, agriculture, construction, and transportation and communication services.