TY - JOUR
AU - Angrist,Joshua
AU - Chernozhukov,Victor
AU - Fernandez-Val,Ivan
TI - Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure
JF - National Bureau of Economic Research Working Paper Series
VL - No. 10428
PY - 2004
Y2 - April 2004
DO - 10.3386/w10428
UR - http://www.nber.org/papers/w10428
L1 - http://www.nber.org/papers/w10428.pdf
N1 - Author contact info:
Joshua Angrist
Department of Economics, E17-226
MIT
77 Massachusetts Avenue
Cambridge, MA 02139
Tel: 617/253-8909
Fax: 617/253-1330
E-Mail: angrist@mit.edu
Victor Chernozhukov
Department of Economics
MIT
Cambridge, MA 02142
E-Mail: vchern@mit.edu
Iván Fernández-Val
Department of Economics
Boston University
270 Bay State Rd
Boston, MA 02215
E-Mail: ivanf@bu.edu
AB - 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.
ER -