Tests for Parameter Instability in Dynamic Factor Models

We develop tests for structural breaks of factor loadings in dynamic factor models. We focus on the joint null hypothesis that all factor loadings are constant over time. Because the number of factor loading parameters goes to infinity as the sample size grows, the conventional test cannot be used. Based on the fact that the estimated factors will demonstrate a higher dimension under the alternative hypothesis than under the null, we reduce the infinite-dimensional problem into a finite-dimensional one and our statistic compares the preand post-break subsample second moments of estimated factors. Our test is consistent under the alternative hypothesis in which a fraction of or all factor loadings have structural changes. The Monte Carlo results show that our test has good finite-sample size and power. In an empirical illustration, we find some evidence of structural break in the factor loadings in early 1980s in the United States.