Predictions in Quantile Regressions

DOI: 10.4236/ojs.2014.47048   PDF   HTML     3,612 Downloads   4,210 Views   Citations


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.

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Furno, M. (2014) Predictions in Quantile Regressions. Open Journal of Statistics, 4, 504-517. doi: 10.4236/ojs.2014.47048.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Mayr, A., Horthorn, T. and Fenske, N. (2012) Prediction Intervals for Future BMI Values of Individual Children—A Non-Parametric Approach by Quantile Boosting. BMC Medical Research Methodology, 12, 1-13.
[2] Friederichs, P. and Hense, A. (2007) Statistical Downscaling of Extreme Precipitation Events Using Censored Quantile Regression. Monthly Weather Review, 135, 2365-2378.
[3] Barro, R. (1997) Determinants of Economic Growth: A Cross-Country Empirical Study. MIT Press, Cambridge.
[4] Mankiw, N., Romer, D. and Weil, D. (1992) A Contribution to the Empirics of Economic Growth. Quarterly Journal of Economics, 107, 407-437.
[5] Hanushek, E. (2006) School Resources. In: Hanushek, E.A. and Welch, F., Eds., Handbook of Economics of Education, Vol. II, North Holland, Amsterdam.
[6] Hanushek, E. and Woessmann, L. (2011) The Economics of International Differences in Educational Achievement. In: Hanushek, E.A., Machin, S.J. and Woessmann, L., Eds., Handbook of Economics of Education, Vol. III, North Holland, Amsterdam.
[7] Koenker, R. and Bassett, G. (1978) Regression Quantiles. Econometrica, 46, 33-50.
[8] Koenker, R. (2005) Quantile Regression. Cambridge University Press, Cambridge.
[9] Koenker, R. and Machado, J. (1999) Goodness of Fit and Related Inference for Quantile Regression. Journal of the American Statistical Association, 94, 1296-1310.
[10] Davino, C., Furno, M. and Vistocco, D. (2014) Quantile Regression: Theory and Applications. Wiley, Hoboken.
[11] Hao, L. and Naiman, D. (2007) Quantile Regression. Sage, London.
[12] Qu, Z. (2008) Testing for Structural Change in Regression Quantiles. Journal of Econometrics, 146, 170-184.
[13] Oka, T. and Qu, Z. (2011) Estimating Structural Changes in Regression Quantiles. Journal of Econometrics, 162, 248-267.
[14] Xiao, Z. (2009) Quantile Cointegrating Regression. Journal of Econometrics, 150, 248-260.

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