摘要：Two different tools to evaluate quantile regression forecasts are proposed: MAD, to summarize forecast errors, and a fluctuation test to evaluate in-sample predictions. The scores of the PISA test to evaluate students’ proficiency are considered. Growth analysis relates school attainment to economic growth. The analysis is complemented by investigating the estimated regression and predictions not only at the centre but also in the tails. For out-of-sample forecasts, the estimates in one wave are employed to forecast the following waves. The reliability of in-sample forecasts is controlled by excluding the part of the sample selected by a specific rule: boys to predict girls, public schools to forecast private ones, vocational schools to predict non-vocational, etc. The gradient computed in the subset is compared to its analogue computed in the full sample in order to verify the validity of the estimated equation and thus of the in-sample predictions.
