Income convergence: the Dickey-Fuller test under the simultaneous presence of stochastic and deterministic trends

We investigate the efficiency of the Dickey-Fuller (DF) test as a tool to examine the convergence hypothesis. In doing so, we first describe two possible outcomes, overlooked in previous studies, namely Loose Catching-up and Loose Lagging-behind. Results suggest that this test is useful when the intention is to discriminate between a unit root process and a trend stationary process, though unreliable when used to differentiate between a unit root process and a process with both deterministic and stochastic trends. This issue may explain the lack of support for the convergence hypothesis in the aforementioned literature.