A Cautionary Tale about Linear Probability Models : Yet Another Reply to Holm, Hjorth Trolle, and Jæger

In this open working paper, I respond to Holm, Hjorth-Trolle, and Jæger (2024), who have recently addressed my comment (Yastrebov, 2023) on their original work (Holm et al., 2019). In my comment, I raised the concern that the authors’ most original hypothesis—regarding unequal responses of advantaged and disadvantaged students to negative information shocks—does not have a sound theoretical basis and that its empirical test may not be entirely convincing. In their rejoinder, the authors disagree with my critique and defend their interpretation. However, despite some clarifications offered, they make some further confusing statements and ignore one of my major criticisms—a temptation to interpret differences in marginal effects from a linear probability model (LPM) substantively. I revisit these concerns, and show, with a simulation, that in interpreting their main empirical finding—i.e., that the effects of ability on the probabilities of enrolling and completing high school converge with increasing family socioeconomic status—the authors might be erroneously attributing the properties of probability distributions to a substantive process (such as compensatory advantage or status demotion avoidance). The argument I am making is not at all new (to the authors included) but is apparently worth revisiting as a reminder to use LPMs with caution.