Like many topics which repeat on the forums, this article from the National Bureau of Economic Research and dated November 2015, seems closely related to an article dated September 2014 and discussed in a thread at that time: Does Gifted Education Work? For Which Students?

Originally Posted by aeh
who were cognitively qualified
It may be worth keeping in mind that the report states these students qualified using lower criteria: IQ 116 rather than IQ 130.

Originally Posted by aeh
a significant fraction of them were able to make up the difference
It does not suggest that they made up the difference, just that they made more rapid gains during the time period measured.

Originally Posted by aeh
despite lack of access to quality instruction previously
A variety of factors may have been in play limiting their prior achievements; This is not necessarily due to lack of access to quality instruction previously.

Originally Posted by aeh
Alternatively, it may be that the conventionally-identified students were not receiving sufficiently challenging instruction, even within the GT program.
BINGO! Unfortunately, capping the growth of the top students is one means of closing the achievement gap, excellence gap, or opportunity gap.