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This paper develops the inferential theory for latent factor models estimatedfrom large dimensional panel data with missing observations. We propose aneasy-to-use all-purpose estimator for a latent factor model by applyingprincipal component analysis to an adjusted covariance matrix estimated frompartially observed panel data. We derive the asymptotic distribution for theestimated factors, loadings and the imputed values under an approximate factormodel and general missing patterns. The key application is to estimatecounterfactual outcomes in causal inference from panel data. The unobservedcontrol group is modeled as missing values, which are inferred from the latentfactor model. The inferential theory for the imputed values allows us to testfor individual treatment effects at any time under general adoption patternswhere the units can be affected by unobserved factors.

Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference