Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/171848
Authors: 
Lee, Ying-Ying
Year of Publication: 
2016
Citation: 
[Journal:] Econometrics [ISSN:] 2225-1146 [Volume:] 4 [Year:] 2016 [Issue:] 1 [Pages:] 1-14
Abstract: 
Allowing for misspecification in the linear conditional quantile function, this paper provides a new interpretation and the semiparametric efficiency bound for the quantile regression parameter b(t) in Koenker and Bassett (1978). The first result on interpretation shows that under a mean-squared loss function, the probability limit of the Koenker-Bassett estimator minimizes a weighted distribution approximation error, defined as FY(X'b(t)/X)-t, i.e., the deviation of the conditional distribution function, evaluated at the linear quantile approximation, from the quantile level. The second result implies that the Koenker-Bassett estimator semiparametrically efficiently estimates the quantile regression parameter that produces parsimonious descriptive statistics for the conditional distribution. Therefore, quantile regression shares the attractive features of ordinary least squares: interpretability and semiparametric efficiency under misspecification.
Subjects: 
semiparametric efficiency bounds
misspecification
conditional quantile function
conditional distribution function
best linear approximation
JEL: 
C14
C21
Persistent Identifier of the first edition: 
Creative Commons License: 
http://creativecommons.org/licenses/by/4.0/
Document Type: 
Article
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