We propose unit root tests for panel data with a small number of time periods, T , and increments that follow an AR(1) process under the null. The model is a fixed-effect panel version of the augmented Dickey–Fuller regression of order 1. Individual-specific linear trends may also be included. The test statistics are t-type statistics based on leastsquares estimates from which the Nickell bias is removed. Their limiting distributions (for an increasing number of independent cross-section units, N, and fixed T ) are standard normal. Our test generalizes the panel unit root test of Harris and Tzavalis, which is based on an unaugmented Dickey–Fuller regression. As an illustration, we examine whether the Law of One Price holds in the European car market since the start of stage three of the EMU in 1999. We find strong evidence of price convergence in the EMU countries.