Causal Inference in Possibly Nonlinear Factor Models

This paper develops a causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large number of noisy proxies are available and linked with the underlying latent confounders through an unknown, possibly nonlinear factor structure. The main building block is a local principal subspace approximation procedure that combines K-nearest-neighbor 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, and their large-sample properties are established. These results require the collection of proxies to be jointly informative about the latent confounders relevant to the outcome and treatment, while allowing some proxies to be uninformative, their identities to be unknown, and measurement errors to be correlated with the outcome or treatment. We also obtain uniformly consistent estimators of the conditional average treatment effect at each unit's confounder values. 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.