http://papers.nber.org/papers/w18791

Full paper at http://belkcollegeofbusiness.uncc.edu/EconomicsSeminar/papers_2012-2013/Cook-Kang%201-26-2013%20(3).pdf

Birthdays, Schooling, and Crime: New Evidence on the
Dropout-Crime Nexus
by Philip J. Cook, Songman Kang - #18791 (ED)

Abstract:

Based on administrative data for five cohorts of public school
children in North Carolina, we demonstrate that those born just after
the cut date for starting school are likely to outperform those born
just before in reading and math in middle school, and are less likely
to be involved in juvenile delinquency. On the other hand, those
born after the cut date are more likely to drop out of high school
before graduation and commit a felony offense by age 19. We also
present suggestive evidence that the higher dropout rate is due to
the fact that youths born after the cut date have longer exposure to
the legal possibility of dropping out. The "crime" and "dropout"
differences are strong but somewhat muted by the fact that youths
born just before the cut date are substantially more likely to be
held back in school. We document considerable heterogeneity in
educational and criminal outcomes by sex, race and other indicators
of socioeconomic disadvantage.

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This paper is about the general population, not gifted children. Consistent with the dropout effect found in this paper, I have read that acceleration increases the chance that gifted children will earn graduate degrees.