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