This paper extends the cross‐sectionally augmented panel unit‐root test (CIPS) developed by Pesaran et al. (2013, Journal of Econometrics, Vol. 175, pp. 94–115) to allow for smoothing structural changes in deterministic terms modelled by a Fourier function. The proposed statistic is called the break augmented CIPS (BCIPS) statistic. We show that the non‐standard limiting distribution of the (truncated) BCIPS statistic exists and tabulate its critical values. Monte‐Carlo experiments point out that the sizes and powers of the BCIPS statistic are generally satisfactory as long as the number of time periods, T, is not less than fifty. The BCIPS test is then applied to examine the validity of long‐run purchasing power parity.