Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure
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.
|Date of creation:||Apr 2004|
|Publication status:||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.|
|Contact details of provider:|| Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.|
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- Giacomini, Raffaella & Komunjer, Ivana, 2005.
"Evaluation and Combination of Conditional Quantile Forecasts,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 23, pages 416-431, October.
- Giacomini, Raffaella & Komunjer, Ivana, 2002. "Evaluation and Combination of Conditional Quantile Forecasts," University of California at San Diego, Economics Working Paper Series qt4n99t4wz, Department of Economics, UC San Diego.
- Raffaella Giacomini & Ivana Komunjer, 2003. "Evaluation and Combination of Conditional Quantile Forecasts," Boston College Working Papers in Economics 571, Boston College Department of Economics.
- Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-1460, November.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366 Elsevier.
- Joshua Angrist & Alan Krueger, 1998. "Empirical Strategies in Labor Economics," Working Papers 780, Princeton University, Department of Economics, Industrial Relations Section..
- Joshua Angrist & Alan Krueger, 1998. "Empirical Strategies in Labor Economics," Working papers 98-7, Massachusetts Institute of Technology (MIT), Department of Economics.
- Hahn, Jinyong, 1997. "Bayesian Bootstrap of the Quantile Regression Estimator: A Large Sample Study," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 795-808, November.
- Katz, Lawrence F. & Autor, David H., 1999. "Changes in the wage structure and earnings inequality," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 26, pages 1463-1555 Elsevier.
- White, Halbert & Kim, Tae-Hwan, 2002. "Estimation, Inference, and Specification Testing for Possibly Misspecified Quantile Regression," University of California at San Diego, Economics Working Paper Series qt1s38s0dn, Department of Economics, UC San Diego.
- Amanda Gosling & Stephen Machin & Costas Meghir, 2000. "The Changing Distribution of Male Wages in the U.K," Review of Economic Studies, Oxford University Press, vol. 67(4), pages 635-666.
- Amanda Gosling & Stephen Machin & Costas Meghir, 1994. "The changing distribution of male wages in the UK," IFS Working Papers W94/13, Institute for Fiscal Studies.
- A Gosling & Stephen Machin, 1995. "The Changing Distribution of Male Wages in the UK," CEP Discussion Papers dp0271, Centre for Economic Performance, LSE.
- Juhn, Chinhui & Murphy, Kevin M & Pierce, Brooks, 1993. "Wage Inequality and the Rise in Returns to Skill," Journal of Political Economy, University of Chicago Press, vol. 101(3), pages 410-442, June.
- Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
- Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
- Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, January.
- Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
- Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
- José Mata & José A. F. Machado, 2005. "Counterfactual decomposition of changes in wage distributions using quantile regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 445-465.
- Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier.
- Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
- White, Halbert, 1980. "Using Least Squares to Approximate Unknown Regression Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 149-170, February. Full references (including those not matched with items on IDEAS)
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