  A factor model with a break in its factor loadings is observationally
equivalent to a model without changes in the loadings but a change in the
variance of its factors. This effectively transforms a structural change
problem of high dimension into a problem of low dimension. This paper considers
the likelihood ratio (LR) test for a variance change in the estimated factors.
The LR test implicitly explores a special feature of the estimated factors: the
pre-break and post-break variances can be a singular matrix under the
alternative hypothesis, making the LR test diverging faster and thus more
powerful than Wald-type tests. The better power property of the LR test is also
confirmed by simulations. We also consider mean changes and multiple breaks. We
apply the procedure to the factor modelling and structural change of the US
employment using monthly industry-level-data.
