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Abstract:
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In many causal inference problems, the parameter of interest is often the regression causal effect, defined as the conditional mean difference in the potential outcomes given covariates. This paper discusses how sufficient dimension reduction can be used to assist in its estimation, and proposes a new estimator for the regression causal effect inspired by a sufficient dimension reduction method called minimum average variance estimation. The estimator requires a weaker common support condition than the traditional propensity score-based approaches. In addition, it can be easily converted to estimate the average causal effect, where it is shown to be asymptotically super efficient under the sufficient dimension reduction assumption. The finite-sample properties of the proposed method is illustrated using simulation studies.
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