Likelihood Ratio Test for Structural Changes in Factor Models

A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but with a change in the variance of its factors. This approach effectively transforms a high-dimensional structural change problem into a low-dimensional problem. 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 this procedure to the factor modeling of the US employment and study the structural change problem using monthly industry-level data.