We propose unit root tests for the AR(1) panel data model with AR(1) errors and a small number of observations, T, along the time dimension. Heterogenous initial conditions and drift in the data generating process are taken into account by including fixed effects and individual-specific linear trends in the regression. The test statistics are based on least-squares estimates from which the Nickell (1981) bias is removed. The limiting distributions of the test statistics (for an increasing number of independent cross-section units, N, and fixed T) are standard normal.
As an illustration of our panel unit root test, we examine whether the Law of One Price holds in the European car market since the start of the first phase of the EMU.