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Causal Effect Estimation for Multivariate Continuous Treatments

Causal inference is widely used in various fields, such as biology, psychology and economics, etc. In observational studies, we need to balance the covariates before estimating causal effect. This study extends the one-dimensional entropy balancing method to multiple dimensions to balance the covariates. Both parametric and nonparametric methods are proposed to estimate the causal effect of multivariate continuous treatments and theoretical properties of the two estimations are provided. Furthermore, the simulation results show that the proposed method is better than other methods in various cases. Finally, we apply the method to analyze the impact of the duration and frequency of smoking on medical expenditure. The results show that the frequency of smoking increases medical expenditure significantly while the duration of smoking does not.