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 estimable using the common principal component estimator. I then introduce a new class of estimators to determine the number of those relevant factors. Unlike estimators that have been proposed in the past, my estimators are the first to use information in the eigenvectors as well as in the eigenvalues. I find strong evidence for the presence of local factors in a large panel of US macroeconomic indicators.
We consider a linear panel event-study design in which unobserved confounds may be related both to the outcome and to the policy variable of interest. We provide sufficient conditions to identify the causal effect of the policy by exploiting covariates related to the policy only through the confounds. Our model implies a set of moment equations that are linear in parameters. The effect of the policy can be estimated by 2SLS, and causal inference is valid even when endogeneity leads to pre-event trends (“pre-trends”) in the outcome. Alternative approaches, such as estimation following a test for pre-trends, perform poorly.