I propose a method to correct for test scores manipulation and apply it to a natural experiment in the Italian education system consisting in the random assignment of external monitors to classrooms. The empirical strategy is based on a likelihood approach, using nonlinear panel data methods to obtain clean estimates of cheating controlling for unobserved heterogeneity. The likelihood of each classroom's scores is later used to correct them for cheating. Cheating is not associated with an increase in the correlation of the answers after we control for mean test scores. The method produces estimates of manipulation more frequent in the South and Islands and among female students and immigrants in Italian tests. A simulation shows how the manipulation reduces the accuracy of an exam in reflecting students' knowledge, and the correction proposed in this paper makes up for about a half of this loss.