Working Paper

A Generalized Factor Model with Local Factors

Abstract: 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;

https://doi.org/10.21799/frbp.wp.2019.23

Bibliographic Information

Provider: Federal Reserve Bank of Philadelphia

Part of Series: Working Papers

Publication Date: 2019-04-19

Number: 19-23

Note: Superseded by Working Paper 21-15