  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.
