Covariate balancing for causal inference on categorical and continuous treatments

TL;DR

This paper introduces new covariate balancing estimators for causal inference with categorical and continuous treatments, demonstrating their theoretical properties and finite sample performance through simulations and real data analysis.

Contribution

It develops novel covariate balancing estimators that are consistent, asymptotically normal, and attain efficiency bounds under correct model specification.

Findings

Estimators are consistent and asymptotically normal.

Achieve semiparametric efficiency in categorical treatment case.

Show bias and variance at nonparametric rates for continuous treatments.

Abstract

We propose novel estimators for categorical and continuous treatments by using an optimal covariate balancing strategy for inverse probability weighting. The resulting estimators are shown to be consistent and asymptotically normal for causal contrasts of interest, either when the model explaining treatment assignment is correctly specified, or when the correct set of bases for the outcome models has been chosen and the assignment model is sufficiently rich. For the categorical treatment case, we show that the estimator attains the semiparametric efficiency bound when all models are correctly specified. For the continuous case, the causal parameter of interest is a function of the treatment dose. The latter is not parametrized and the estimators proposed are shown to have bias and variance of the classical nonparametric rate. Asymptotic results are complemented with simulations illustrating the finite sample properties. Our analysis of a data set suggests a nonlinear effect of BMI on the decline in self reported health.