Next Article in Journal
How Credible Are Shrinking Wage Elasticities of Married Women Labour Supply?
Next Article in Special Issue
Distribution of Budget Shares for Food: An Application of Quantile Regression to Food Security 1
Previous Article in Journal
Non-Parametric Estimation of Intraday Spot Volatility: Disentangling Instantaneous Trend and Seasonality
Previous Article in Special Issue
Counterfactual Distributions in Bivariate Models—A Conditional Quantile Approach
Article

Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification

Department of Economics, University of Oxford, Manor Road Building, Manor Road, Oxford OX1 3UQ, UK
Academic Editor: Gabriel Montes-Rojas
Econometrics 2016, 4(1), 2; https://doi.org/10.3390/econometrics4010002
Received: 4 October 2015 / Revised: 27 November 2015 / Accepted: 1 December 2015 / Published: 24 December 2015
(This article belongs to the Special Issue Quantile Methods)
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 β ( τ ) 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 \(F_{Y}(X'\beta(\tau)|X) - \tau\), 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. View Full-Text
Keywords: semiparametric efficiency bounds; misspecification; conditional quantile function; conditional distribution function; best linear approximation semiparametric efficiency bounds; misspecification; conditional quantile function; conditional distribution function; best linear approximation
Show Figures

Figure 1

MDPI and ACS Style

Lee, Y.-Y. Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification. Econometrics 2016, 4, 2. https://doi.org/10.3390/econometrics4010002

AMA Style

Lee Y-Y. Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification. Econometrics. 2016; 4(1):2. https://doi.org/10.3390/econometrics4010002

Chicago/Turabian Style

Lee, Ying-Ying. 2016. "Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification" Econometrics 4, no. 1: 2. https://doi.org/10.3390/econometrics4010002

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop