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This paper addresses two prominent theses in social stratification research,the great equalizer thesis and Mare's (1980) school transition thesis. Boththeses are premised on a descriptive regularity: the association betweensocioeconomic background and an outcome variable changes when conditioning onan intermediate treatment. The interpretation of this descriptive regularity iscomplicated by social actors' differential selection into treatment based ontheir potential outcomes under treatment. In particular, if the descriptiveregularity is driven by selection, then the theses do not have a substantiveinterpretation. We propose a set of novel counterfactual slope estimands, whichcapture the two theses under the hypothetical scenario where differentialselection into treatment is eliminated. Thus, we use the counterfactual slopesto construct selection-free tests for the two theses. Compared with theexisting literature, we are the first to provide explicit, nonparametric, andcausal estimands, which enable us to conduct principled selection-free tests.We develop efficient and robust estimators by deriving the efficient influencefunctions of the estimands. We apply our framework to a nationallyrepresentative dataset in the United States and re-evaluate the two theses.Findings from our selection-free tests show that the descriptive regularity ofthe two theses is misleading for substantive interpretations.

Counterfactual Slope and Its Applications to Social Stratification