Inference for large dimensional factor models under general missing data patterns

This paper establishes the inferential theory for the least squares estimation of large factor models with missing data. We propose a unified framework for asymptotic analysis of factor models that covers a wide range of missing patterns, including heterogenous random missing, selection on covariates/factors/loadings, block/staggered missing, mixed frequency and ragged edge. We establish the average convergence rates of the estimated factor space and loading space, the limit distributions of the estimated factors and loadings, as well as the limit distributions of the estimated average treatment effects and the parameter estimates in the factor-augmented regressions. These results allow us to impute the unbalanced panel appropriately or make inference for the heterogenous treatment effects. For computation, we can use the nuclear norm regularized estimator as the initial value for the EM algorithm and iterate until convergence. Empirically, we apply our method to test the average treatment effects of partisan alignment on grant allocation in UK.