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Treatment Effect Deviation as an Alternative to Blinder–Oaxaca Decomposition for Studying Social Inequality

The Blinder–Oaxaca decomposition (BOD) is a popular method for studying the contributions of explanatory factors to social inequality. The results have often been given causal interpretations. While recent work and this article both show that some types of BOD are equivalent to a counterfactual-based treatment effect/selection bias decomposition, this equivalence does not hold in general. Given this lack of general equivalence, in this article based on the counterfactual framework, we propose a method of treatment effect deviation (TED) to study social inequality. Essentially, the TED assesses to what extent the omission of particular covariates (i.e., selection bias in the omitted variables) can alter the estimated treatment effect. The TED has a better causal interpretation and can be estimated nonparametrically (and hence is more robust to model misspecification errors). Therefore, the TED may serve as an alternative to or may be used in tandem with the BOD. We illustrate the new method through two case studies. In the first case study, we show that the TED provides a more credible estimate of the treatment effect on the treated than does the BOD. However, both the TED and the BOD highlight the importance of accounting for prior earning in estimating the training effect. In the second case study, the results of the two methods differ notably, but both agree that normative factors play a significant role in generating the rural–urban disparity in social policy preference in China.