Panel CointegrationTesting in the Presenceof a Time Trend

The purpose of this paper is to propose a new likelihood-based panel cointegration testin the presence of a linear time trend in the data generating process. This new test is an extensionof the likelihood ratio (LR) test of Saikkonen & L¨utkepohl (2000) for trend-adjusteddata to the panel data framework, and is called the panel SL test. The idea is first to take theaverage of the individual LR (trace) statistics over the cross-sections and then to standardizethe test statistic with the appropriate asymptotic moments. Under the null hypothesis, thisstandardized statistic has a limiting normal distribution as the number of time periods (T)and the number of cross-sections (N) tend to infinity sequentially. In addition to the approximationbased on asymptotic moments, a second approximation approach involving themoments from a vector autoregressive process of order one is also introduced. By means ofa Monte Carlo study the finite sample size and size-adjusted power properties of the test areinvestigated. The test presents reasonable size with the increase in T and N, and has highpower in small samples.