Non-convergent incomes with a new DF-Fourier test: most likely you go your way (and I'll go mine)

Motivated by the purpose to assess the income convergence hypothesis, a simple new Fourier-type unit root test of the Dickey-Fuller family is introduced and analysed. In spite of a few shortcomings that it shares with rival tests, the proposed test generally improves upon them in terms of power performance in small samples. The empirical results that it produces for a recent and updated sample of data for 25 countries clearly contrast with previous evidence produced by the Fourier approach and, more generally, they also contradict a recent wave of optimism concerning income convergence, as they are mostly unfavourable to it. This evidence appears to be particularly robust to the possibility of undetected convergence.\\