This paper presents a simulation analysis of KPSS stationarity tests when applied to a series with a shift in its mean. More specifically, we show that the size of KPSS test is affected by both the amount of the break and its position in the sample, remaining unaffected by the sign of the change. We therefore propose a modified stationarity test, with the null hypothesis being the presence of stationarity fluctuations around a level containing an exogenous structural break. Critical values are obtained through Monte Carlo simulation and summarised in a response surface. We also study the empirical siza and power of the proposed test in different situations, mainly those with a wrong especification or break location. Finally, an empirical aplication is presented showing the behaviour of the proposed test when applied to a classical series affected by a level shift.

Key words: KPSS test, breaks, Monte Carlo simulation, critical values.
JEL classification: C15, C32.