Causal Inference in Possibly Nonlinear Factor Models

This paper develops a general causal inference method for treatment effects models under selection on unobservables. A large set of covariates that admits an unknown, possibly nonlinear factor structure is exploited to control for the latent confounders. The key building block is a local principal subspace approximation procedure that combines $K$-nearest neighbors matching and principal component analysis. Estimators of many causal parameters, including average treatment effects and counterfactual distributions, are constructed based on doubly-robust score functions. Large-sample properties of these estimators are established, which only require relatively mild conditions on the principal subspace approximation. The results are illustrated with an empirical application studying the effect of political connections on stock returns of financial firms, and a Monte Carlo experiment. The main technical and methodological results regarding the general local principal subspace approximation method may be of independent interest.