  This work proposes a novel procedure to test for common structures across two
high-dimensional factor models. The introduced test allows to uncover whether
two factor models are driven by the same loading matrix up to some linear
transformation. The test can be used to discover inter individual relationships
between two data sets. In addition, it can be applied to test for structural
changes over time in the loading matrix of an individual factor model. The test
aims to reduce the set of possible alternatives in a classical change-point
setting. The theoretical results establish the asymptotic behavior of the
introduced test statistic. The theory is supported by a simulation study
showing promising results in empirical test size and power. A data application
investigates changes in the loadings when modeling the celebrated US
macroeconomic data set of Stock and Watson.
