A generalized factor model with local factors

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