We derive bounds for the average of math and language scores of elementary school students in Italy correcting for pervasive score manipulation. Information on the fraction of manipulated data is retrieved from a natural experiment that randomly assigns external monitors to schools. We show how bounds can be tightened imposing restrictions on the measurement properties of the manipulation indicator developed by the government agency charged with test administration and data collection. We additionally assume that manipulation is more likely in those classes at the lower end of the distribution of true scores. Our results show that regional rankings by academic performance are reversed once manipulation is properly taken into account.