One aspect mentioned, but under-emphasized, may be found in the article's phrase "where parents were more involved in education."
Greater parental involvement appears correlated with greater achievement which appears correlated with greater likelihood of referral.
Parental inattention to education appears correlated with less achievement which appears correlated with less likelihood of referral.
Although correlation does not imply causation, the article seems to indicate that correlation of SES with student referral to the gifted program implies causation... by not exploring other possible and plausible explanations such as degree of parental involvement or inattention... as well as by using statements such as "gifted programs amplify inequality because they disproportionately recruit children from high-income families".
Rather than the authors being concerned with "gifted status" (a phrase mentioned in the nber report), possibly a better focus might be on an examination of the content and experience of the particular gifted program, including aptness and "fit" of the curriculum placement, pacing, and instruction in the zone of proximal development, delivered in the company of intellectual peers who exhibit a similar level of readiness and ability.
