A simple proposal to improve the power of income convergence tests

•I propose to replace trend with level stationarity in income convergence tests.•This replacement improves the power of the tests.•It is supported by a clear and well known definition of convergence.•It is illustrated with simulation and empirical results.

I make a simple proposal to replace trend stationarity with level stationarity as the alternative hypothesis in unit root tests for income convergence. This replacement improves the power of the tests and is supported by a clear and well known definition of convergence. A small Monte Carlo study and an empirical example illustrate this improvement.