On average, children who attend schools for gifted students have lower self-esteem than children of equal intelligence who attend regular schools with students of widely varying abilities. If we consider research about factors affecting youngsters' sense of self, we can explain this finding in which one of the following ways

Self-esteem is built based on children's interactions with the environment. People often compare themselves to others, whether subjectively, by judging themselves versus someone else, or objectively, like comparing test results. In a regular school, where intelligence follows a close to parametric distribution, those is the highest percentiles have very positive comparisons with their peers, thus boosting their self-esteem. In gifted school where the distribution of intelligence is more flat, students often lack the reinforcement of over performing and getting that positive comparison.