You can't always get what you want? Estimator choice and the speed of convergence

We propose theory-based Monte Carlo simulations to quantify the extent to which the estimated speed of convergence depends on the underlying econometric techniques. Based on a theoretical growth model as the data generating process, we find that, given a true speed of convergence of around 5%, the estimated values range from 0.2% to 7.72%. This corresponds to a range of the half life of a given gap from around 9 years up to several hundred years. With the exception of the (very inefficient) system GMM estimator with the collapsed matrix of instruments, the true speed of convergence is outside of the 95% confidence intervals of all investigated state-of-the-art estimators. In terms of the squared percent error, the between estimator and the system GMM estimator with the non-collapsed matrix of instruments perform worst, while the system GMM estimator with the collapsed matrix of instruments and the corrected least squares dummy variable estimator perform best. Based on these results we argue that it is not a good strategy to rely on only one or two different estimators when assessing the speed of convergence, even if these estimators are seen as suitable for the given sources of biases and inefficiencies. Instead one should compare the outcomes of different estimators carefully in light of the results of Monte Carlo simulation studies.