FINTECH THRUST SEMINAR | Factor Analysis for Large Non-Stationary Panels with Endogenous Missingness and Applications to Causal Inference

Factor Analysis for Large Non-Stationary Panels with Endogenous Missingness and Applications to Causal Inference

Abstract:

This paper studies the imputation and inference for large-dimensional non-stationary panel data with general missing observations. Our novel method, Within-Transform-PCA (wi-PCA), transforms the data under endogenous missingness to remove non-stationarities and heterogeneous mean effects before estimating an approximate latent factor structure with PCA. This within-transformation is equivalent to estimating two-way non-stationary fixed effects separately from the latent factor structure. Our approach allows for one of the most general and broadly applicable models for data generation and missing patterns in the factor modeling literature. We provide entry-wise inferential theory for the values imputed with wi-PCA. The key application of wi-PCA is the estimation of counterfactuals on causal panels, where we allow for two-way endogenous treatment effects, time trends and general latent confounders. In an empirical study of the liberalization of marijuana, we show that wi-PCA yields more accurate estimates of treatment effects and more credible economic conclusions compared to its two special cases of conventional difference-in-differences and PCA.