A first-stage representation for instrumental variables quantile regression

Summary This paper develops a first-stage linear regression representation for an instrumental variables (IV) quantile regression (QR) model. The quantile first stage is analogous to the least-squares case, i.e., a linear projection of the endogenous variables on the instruments and other exogenous...

Full description

Saved in:
Bibliographic Details
Published in:The econometrics journal 2023-09, Vol.26 (3), p.350-377
Main Authors: Alejo, Javier, Galvao, Antonio F, Montes-Rojas, Gabriel
Format: Article
Language:English
Subjects:
Density
Endogenous
Innovations
Statistical significance
Variables
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Summary This paper develops a first-stage linear regression representation for an instrumental variables (IV) quantile regression (QR) model. The quantile first stage is analogous to the least-squares case, i.e., a linear projection of the endogenous variables on the instruments and other exogenous covariates, with the difference that the QR case is a weighted projection. The weights are given by the conditional density function of the innovation term in the QR structural model, at a given quantile. We also show that the required Jacobian identification conditions for IVQR models are embedded in the quantile first stage. We then suggest procedures to evaluate the validity of instruments by evaluating their statistical significance using the first-stage representation. Monte Carlo experiments provide numerical evidence that the proposed tests work as expected in terms of empirical size and power. An empirical application illustrates the methods.
ISSN:1368-4221
1368-423X
DOI:10.1093/ectj/utad010