Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure

Joshua Angrist, Victor Chernozhukov and Ivan Fernandez-Val ()

No 10428, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: Quantile regression(QR) fits a linear model for conditional quantiles, just as ordinary least squares (OLS) fits a linear model for conditional means. An attractive feature of OLS is that it gives the minimum mean square error linear approximation to the conditional expectation function even when the linear model is misspecified. Empirical research using quantile regression with discrete covariates suggests that QR may have a similar property, but the exact nature of the linear approximation has remained elusive. In this paper, we show that QR can be interpreted as minimizing a weighted mean-squared error loss function for specification error. The weighting function is an average density of the dependent variable near the true conditional quantile. The weighted least squares interpretation of QR is used to derive an omitted variables bias formula and a partial quantile correlation concept, similar to the relationship between partial correlation and OLS. We also derive general asymptotic results for QR processes allowing for misspecification of the conditional quantile function, extending earlier results from a single quantile to the entire process. The approximation properties of QR are illustrated through an analysis of the wage structure and residual inequality in US Census data for 1980, 1990, and 2000. The results suggest continued residual inequality growth in the 1990s, primarily in the upper half of the wage distribution and for college graduates.

JEL-codes: C13 J31 (search for similar items in EconPapers)
Date: 2004-04
New Economics Papers: this item is included in nep-ecm
Note: LS
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Published as Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, 03.

Downloads: (external link)
http://www.nber.org/papers/w10428.pdf (application/pdf)

Related works:
Journal Article: Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure (2006)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberwo:10428

Ordering information: This working paper can be ordered from
http://www.nber.org/papers/w10428

Access Statistics for this paper

More papers in NBER Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().