A Generalized Factor Model with Local Factors∗

I extend the theory on factor models by incorporating “local” factors into the model. Local factors affect a decreasing fraction of the observed variables. This implies a continuum of eigenvalues of the covariance matrix, as is commonly observed in applications. I derive conditions under which local factors will be estimated consistently using the common principal component estimator. I further propose a novel class of estimators for the number of factors. Unlike estimators that have been proposed in the past, my estimators use information in the eigenvectors as well as in the eigenvalues. Monte Carlo evidence suggests significant finite sample gains over existing estimators. In an empirical application, I find evidence of local factors in a large panel of US macroeconomic indicators. JEL-Classification: C38, C52, C55