Pre-event trends in the panel event-study design (Joint with Christian Hansen and Jesse M. Shapiro) [Online Appendix]

American Economic Review, Forthcoming

abstract 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 perform poorly in our simulations.

Working Papers

A Generalized Factor Model with Local Factors [Online Appendix]

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 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.

Identification through Sparsity in Factor Models [New Draft Coming Soon]

abstract The presence of local factors, only affecting a subset of the outcomes, is natural in many economic applications and implies (approximate) sparsity in the loading matrix. This paper proposes to use this insight to solve the rotational indeterminacy of standard factor models. The intuition is that all rotations of a sparse vector are dense, and that there is no sparse rotation of a dense vector. A criterion based on the l1-norm of the loading matrix can identify the true rotation for local factors, enabling us to consistently estimate individual factors and to interpret them as structural objects.