A first-stage representation for instrumental variables quantile regression

ALEJO, JAVIER; GALVAO, ANTONIO; MONTES-ROJAS, GABRIEL

ECONOMETRICS JOURNAL

WILEY-BLACKWELL PUBLISHING, INC

Lugar: Londres; Año: 2023

1368-4221

This paper develops a first-stage linear regression representation for aninstrumental variables (IV) quantile regression (QR) model. The quantile first-stage isanalogous to the least squares case, i.e., a linear projection of the endogenous variableson the instruments and other exogenous covariates, with the difference that the QR caseis a weighted projection. The weights are given by the conditional density function ofthe innovation term in the QR structural model, at a given quantile. We also show thatthe required Jacobian identification conditions for IVQR models are embedded in thequantile first-stage. We then suggest procedures to evaluate the validity of instrumentsby evaluating their statistical significance using the first-stage representation. MonteCarlo experiments provide numerical evidence that the proposed tests work as expectedin terms of empirical size and power. An empirical application illustrates the methods.