  Testing for stability in linear panel data models has become an important
topic in both the statistics and econometrics research communities. The
available methodologies address testing for changes in the mean/linear trend,
or testing for breaks in the covariance structure by checking for the constancy
of common factor loadings. In such cases when an external shock induces a
change to the stochastic structure of panel data, it is unclear whether the
change would be reflected in the mean, the covariance structure, or both. In
this paper, we develop a test for structural stability of linear panel data
models that is based on monitoring for changes in the largest eigenvalue of the
sample covariance matrix. The asymptotic distribution of the proposed test
statistic is established under the null hypothesis that the mean and covariance
structure of the panel data's cross sectional units remain stable during the
observation period. We show that the test is consistent assuming common breaks
in the mean or factor loadings. These results are investigated by means of a
Monte Carlo simulation study, and their usefulness is demonstrated with an
application to U.S. treasury yield curve data, in which some interesting
features of the 2007-2008 subprime crisis are illuminated.
