A Generalized Factor Model with Local Factors
47 Pages Posted: 26 Apr 2019 Last revised: 29 Apr 2020
Date Written: 2019-04-19
I extend the theory on factor models by incorporating local factors into the model. Local factors only affect an unknown subset of the observed variables. This implies a continuum of eigenvalues of the covariance matrix, as is commonly observed in applications. I derive which factors are pervasive enough to be economically important and which factors are pervasive enough to be estimable using the common principal component estimator. I then introduce a new class of estimators to determine the number of those relevant factors. Unlike existing estimators, my estimators use not only the eigenvalues of the covariance matrix, but also its eigenvectors. I find strong evidence of local factors in a large panel of US macroeconomic indicators.
Keywords: high-dimensional data, factor models, weak factors, local factors, sparsity
JEL Classification: C38, C52, C55
Suggested Citation: Suggested Citation