  This paper develops the inferential theory for latent factor models estimated
from large dimensional panel data with missing observations. We propose an
easy-to-use all-purpose estimator for a latent factor model by applying
principal component analysis to an adjusted covariance matrix estimated from
partially observed panel data. We derive the asymptotic distribution for the
estimated factors, loadings and the imputed values under an approximate factor
model and general missing patterns. The key application is to estimate
counterfactual outcomes in causal inference from panel data. The unobserved
control group is modeled as missing values, which are inferred from the latent
factor model. The inferential theory for the imputed values allows us to test
for individual treatment effects at any time under general adoption patterns
where the units can be affected by unobserved factors.
