Change Point in Panel Data with Small Fixed Panel Size: Ratio and Non-Ratio Test Statistics

The main goal is to develop and, consequently, compare stochastic methods for detection whether a structural change in panel data occurred at some unknown time or not. Panel data of our interest consist of a moderate or relatively large number of panels, while the panels contain a small number of observations. Testing procedures to detect a possible common change in means of the panels are established. Ratio and non-ratio type test statistics are considered. Their asymptotic distributions under the no change null hypothesis are derived. Moreover, we prove the consistency of the tests under the alternative. The main advantage of the ratio type statistics compared to the non-ratio ones is that the variance of the observations neither has to be known nor estimated. A simulation study reveals that the proposed ratio statistic outperforms the non-ratio one by keeping the significance level under the null, mainly when stronger dependence within the panel is taken into account. However, the non-ratio statistic rejects the null in the simulations more often than it should, which yields higher power compared to the ratio statistic.