To date, the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the conventional covariance matrix are invalid. Although misspecification is a generic phenomenon and correct specification is rare in reality, there has to date been no theory proposed for inference when a conditional quantile model may be misspecified. In this paper, we allow for possible misspecification of a linear conditional quantile regression model. We obtain consistency of the quantile estimator for certain "pseudo-true" parameter values and asymptotic normality of the quantile estimator when the model is misspecified. In this case, the asymptotic covariance matrix has a novel form, not seen in earlier work, and we provide a consistent estimator of the asymptotic covariance matrix. We also propose a quick and simple test for conditional quantile misspecification based on the quantile residuals.
|Title of host publication||Maximum Likelihood Estimation of Misspecified Models|
|Subtitle of host publication||Twenty Years Later|
|Number of pages||26|
|ISBN (Print)||0762310758, 9780762310753|
|Publication status||Published - 2003|
|Name||Advances in Econometrics|
Bibliographical noteFunding Information:
The authors would like to thank Douglas Stone for providing the data used in the paper and Clive Granger, Patrick Fitzsimmons, Alex Kane, Paul Newbold, Christophe Muller, Christian Gourieroux, Adrian Pagan, and Jin Seo Cho for their helpful comments. White’s research was supported by NSF grants SBR-9811562 and SES-0111238 and Kim’s research was supported by a grant from the University of Nottingham.
All Science Journal Classification (ASJC) codes
- Economics and Econometrics