Covariate balancing for causal inference on categorical and continuous treatments

Novel estimators of causal effects for categorical and continuous treatments are proposed 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 the 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, 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. A data analysis suggests a nonlinear effect of BMI on self-reported health decline among the elderly.