A Theory of Bullying Under-reporting

Abstract

Bullying is difficult to detect because victimization is not directly observed as a single objective state. This paper develops a simple theory of bullying under-reporting. Motivated by four descriptive regularities from Spanish classroom data, the model explains why peer-reported victimization can exceed self-reported victimization while most students nominate no victim and most peer-identified victims receive only one or two nominations. We start from a latent victimization state and model how it becomes, or fails to become, a report. Victims observe their own suffering but may not self-report because disclosure carries identity and psychological costs. Peers observe noisy social signals and report only if they classify the situation as bullying and are willing to bear the cost of speaking. The model also explains why self-and peer-reports often disagree and why silence by victims or bystanders should not be interpreted as absence of harm. A public-good extension shows that more potential observers need not eliminate under-reporting, because individual pivotality falls when bystanders can freeride on others’ reports. A simple static extension connects these reporting decisions to the aggressor’s incentives: when harm is unlikely to generate an effective institutional response, aggression carries a lower expected institutional cost. The theory yields practical implications for measurement, reporting systems, institutional response, and early detection.