  Through a routine normalization of the factor variance, standard methods for
estimating factor models in macroeconomics do not distinguish between breaks of
the factor variance and factor loadings. We argue that it is important to
distinguish between structural breaks in the factor variance and loadings
within factor models commonly employed in macroeconomics as both can lead to
markedly different interpretations when viewed via the lens of the underlying
dynamic factor model. We then develop a projection-based decomposition that
leads to two standard and easy-to-implement Wald tests to disentangle
structural breaks in the factor variance and factor loadings. Applying our
procedure to U.S. macroeconomic data, we find evidence of both types of breaks
associated with the Great Moderation and the Great Recession. Through our
projection-based decomposition, we estimate that the Great Moderation is
associated with an over 60% reduction in the total factor variance,
highlighting the relevance of disentangling breaks in the factor structure.
