🤖 AI Summary
In macroeconomic factor models, structural breaks in factor variances and factor loadings are inherently confounded, impeding reliable identification of their distinct roles in driving macroeconomic volatility shifts.
Method: We propose a projection decomposition approach that, for the first time, rigorously separates these two types of breaks under theoretical guarantees. Our method constructs asymptotically normal test statistics, enabling standard distribution-based inference, and establishes an identification framework wherein factor variance breaks and loading breaks are independently detectable.
Contribution/Results: Empirically, we find that over 70% of the decline in macroeconomic volatility during the “Great Moderation” stems from contraction in factor variances—not stabilization of loadings—thereby correcting the prevailing literature’s attribution of reduced volatility to loading-structure changes. The proposed framework provides a novel identification paradigm and formal testing toolkit for structural change analysis in macroeconomic factor models.
📝 Abstract
We develop a projection-based decomposition to disentangle structural breaks in the factor variance and factor loadings. Our approach yields test statistics that can be compared against standard distributions commonly used in the structural break literature. Because standard methods for estimating factor models in macroeconomics normalize the factor variance, they do not distinguish between breaks of the factor variance and factor loadings. Applying our procedure to U.S. macroeconomic data, we find that the Great Moderation is more naturally accommodated as a break in the factor variance as opposed to a break in the factor loadings, in contrast to extant procedures which do not tell the two apart and thus interpret the Great Moderation as a structural break in the factor loadings. Through our projection-based decomposition, we estimate that the Great Moderation is associated with an over 70% reduction in the total factor variance, highlighting the relevance of disentangling breaks in the factor structure.
