Likelihood ratio test for structural changes in factor models

TL;DR

This paper develops a likelihood ratio test for detecting structural changes in factor models, focusing on variance shifts in factors, and demonstrates its superior power over Wald tests through simulations and real US employment data analysis.

Contribution

It introduces a likelihood ratio test that effectively detects variance changes in factors, especially when the alternative involves singular matrices, improving power over existing methods.

Findings

LR test outperforms Wald tests in power

Simulation confirms the LR test's effectiveness

Application to US employment data reveals structural changes

Abstract

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.