Sage Journals: Discover world-class research

Abstract

The article considers a test of specification for quantile regressions. The test relies on the increase of the objective function and the worsening of the fit when unnecessary constraints are imposed. It compares the objective functions of restricted and unrestricted models and, in its different formulations, it verifies (a) forecast ability, (b) structural breaks, and (c) exclusion restrictions. The quantile-based tests are more informative than their ordinary least squares (OLS) analogues because they allow to analyze the model not only at the center but also in the tails of the conditional distribution. In this example, contrarily to the OLS findings, the quantile-based test uncovers in (a) the forecast weakness of the selected model at the upper quantile; (b) a break occurring in the tails and not in the center of the conditional distribution; and (c) that the excluded variable has a relevant impact at the upper quantile. Monte Carlo experiments analyze the behavior of the different definitions of the test with non-normal errors, comparing least squares and quantile regression results.

Keywords

quantile regression test structural change forecasts exclusion restriction

Get full access to this article

View all access options for this article.

References

Andrews

(1993). Tests for parameter instability and structural change with unknown changing point. Econometrica, 61, 821–856.

Angrist

Chernozhukov

Fernandez-Val

(2006). Quantile regression under misspecification, with an application to the U.S. wage structure. Econometrica, 74, 539–563.

Bai

(1995). Least absolute deviation estimation of a shift. Econometric Theory, 11, 403–436.

Chernozhukov

Fernàndez-Val

(2005). Subsampling inference on quantile regression processes. Sankhya, 67, 253–276.

Chow

(1960). Tests of equality between sets of coefficients in two linear regressions. Econometrica, 28, 591–605.

Clark

McCracken

(2005). The power of the tests of predictive ability in the presence of structural breaks. Journal of Econometrics, 124, 1–31.

Furno

(2007). Parameter instability in quantile regression. Statistical Modelling, 7, 345–362.

Furno

(2009). Tests for structural break in quantile regressions.

Furno

(2010). Quantile regression analysis of the Italian school system. Statistical Modelling, 10, 333–351.

10.

Gagliardini

Trojani

Urga

(2005). Robust GMM tests for structural breaks. Journal of Econometrics, 129, 139–182.

11.

Godfrey

Orme

(2000). Controlling the significance levels of prediction error tests for linear regression models. Econometrics Journal, 3, 66–83.

12.

Zhu

(2003). A lack-of-fit test for quantile regression. Journal of the American Statistical Association, 98, 1013–1022.

13.

Huskova

Picek

(2005). Bootstrap in detection of changes in linear regression. Sankhya, 67, 200–226.

14.

Kim

White

(2002). Estimation, inference and specification testing for possibly misspecified quantile regressions. Advances in Econometrics, 17, 107–132.

15.

Koenker

Machado

(1999). Goodness of fit and related inference processes for quantile regression. Journal of the American Statistical Association, 94, 1296–1310.

16.

Koenker

Xiao

(2002). Inference on the quantile regression process. Econometrica, 70, 1583–1612.

17.

(2008). Testing for structural change in regression quantiles. Journal of Econometrics, 146, 170–184.

Goodness of Fit and Misspecification in Quantile Regressions

Abstract

Keywords

Get full access to this article

References