Causal Inference in Possibly Nonlinear Factor Models
This addresses the challenge of causal inference in economics and social sciences where confounders are measured with noise, offering a method that is robust to nonlinearities, but it is incremental as it builds on existing factor model and matching techniques.
The paper tackles the problem of causal inference with noisily measured confounders in possibly nonlinear factor models, developing a method that combines K-nearest neighbors matching and principal component analysis to estimate treatment effects, such as average treatment effects and counterfactual distributions, with large-sample properties established under mild conditions.
This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are 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 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.