Tests for parameter instability in dynamic factor models

In this paper, we develop tests for structural breaks of factor loadings in dynamicfactor models. We focus on the joint null hypothesis that all factor loadings areconstant over time. Because the number of factor loading parameters goes to infinityas the sample size grows, conventional tests cannot be used. Based on the fact thatthe presence of a structural change in factor loadings yields a structural changein second moments of factors obtained from the full sample principal componentestimation, we reduce the infinite-dimensional problem into a finite-dimensionalone and our statistic compares the pre- and postbreak subsample second momentsof estimated factors. Our test is consistent under the alternative hypothesis in whicha fraction of or all factor loadings have structural changes. The Monte Carlo resultsshow that our test has good finite-sample size and power.