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Least squares regression estimates of causal effects are conditional-variance-weighted estimates of individual-level causal effects. In this paper, we extract from the literature on counterfactual causality a simple nine-step routine to determine whether or not the implicit weighting of regression has generated a misleading estimate of the average causal effect. The diagnostic routine is presented along with a detailed and original demonstration, using data from the 2002 and 2004 waves of the Education Longitudinal Study, for a contested but important causal effect in educational research: the effect of Catholic schooling, in comparison to public schooling, on the achievement of high school students in the United States.
Morgan et al. (Tue,) studied this question.