A novel test of economic convergence in time series

This paper proposes a novel test for the hypothesis of economic convergence. We extend the standard definition of convergence based on the parity condition and say that two economies converge if the time series of economic output are positively cointegrated and cotrended. With this definition in place, our main contribution is to propose a test of positive cointegration that does not require estimation of the cointegrating relationship, but is able to differentiate between positive and negative cointegration. Once the possibility of positive cointegration is established in a first stage, we test for cotrending in a second stage. Our sequential proposal enjoys an excellent performance in small samples due to the fast convergence of our novel test statistic under positive cointegration. This is illustrated in a simulation exercise where we report clear evidence showing the outperformance of our proposed method compared to existing methods in the related literature that test for economic convergence using cointegration methods. The results are particularly strong for sample sizes between 25 and 50 observations. The empirical application testing for economic convergence between the G7 group of countries over the period 1990–2022 confirms these findings.