Finite Sample Inference for Quantile Regression Models

39 Pages Posted: 3 Feb 2006  

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics; New Economic School

Christian Hansen

University of Chicago - Booth School of Business - Econometrics and Statistics

Michael Jansson

University of California, Berkeley - Department of Economics

Date Written: January 31, 2006

Abstract

Under minimal assumptions finite sample confidence bands for quantile regression models can be constructed. These confidence bands are based on the "conditional pivotal property" of estimating equations that quantile regression methods aim to solve and will provide valid finite sample inference for both linear and nonlinear quantile models regardless of whether the covariates are endogenous or exogenous. The confidence regions can be computed using MCMC, and confidence bounds for single parameters of interest can be computed through a simple combination of optimization and search algorithms. We illustrate the finite sample procedure through a brief simulation study and two empirical examples: estimating a heterogeneous demand elasticity and estimating heterogeneous returns to schooling. In all cases, we find pronounced differences between confidence regions formed using the usual asymptotics and confidence regions formed using the finite sample procedure in cases where the usual asymptotics are suspect, such as inference about tail quantiles or inference when identification is partial or weak. The evidence strongly suggests that the finite sample methods may usefully complement existing inference methods for quantile regression when the standard assumptions fail or are suspect.

Keywords: Quantile Regression, Extremal Quantile Regression, Instrumental Quantile Regression

JEL Classification: C1, C3

Suggested Citation

Chernozhukov, Victor and Hansen, Christian and Jansson, Michael, Finite Sample Inference for Quantile Regression Models (January 31, 2006). MIT Department of Economics Working Paper No. 06-03. Available at SSRN: https://ssrn.com/abstract=880467 or http://dx.doi.org/10.2139/ssrn.880467

Victor Chernozhukov (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-262f
Cambridge, MA 02142
United States
617-253-4767 (Phone)
617-253-1330 (Fax)

HOME PAGE: http://www.mit.edu/~vchern/

New Economic School

47 Nakhimovsky Prospekt
Moscow, 117418
Russia

Christian Hansen

University of Chicago - Booth School of Business - Econometrics and Statistics ( email )

Chicago, IL 60637
United States
773-834-1702 (Phone)

Michael Jansson

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

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