Despite the abundance of different econometric techniques introduced in the empirical literature on convergence, it is usually assumed that shocks are uncorrelated across countries. This is surely unlikely for most of the datasets considered and we investigate a possibility so far ignored, namely the annual panel estimator where shocks are allowed to be correlated across countries. Our analysis is restricted to the case of more time periods than countries (T>N) which allows us to estimate by Maximum Likelihood with an unrestricted variance-covariance matrix of cross-country shocks. The paper examines by Monte Carlo robustness against certain possible mis-specifications, namely measurement error and heterogeneity of the convergence coefficients. Our analysis indicates that ML estimators are robust to plausible measurement error and variation of convergence rates across countries and are more efficient than conventional estimators for plausible values of cross-country error correlation. We consider in detail the relationship between the distribution of the ML estimator and the initial conditions. Applying our findings to a panel of OECD countries for the post-war period, we show that ML is effectively unbiased and more efficient than or conventional panel estimators OLS on a cross-section of countries. We argue the reason this estimators is so well behaved is that many OECD countries were far from their equilibrium values at the beginning of the period.