A first-stage representation for instrumental variables quantile regression

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

Buenos Aires

Conferencia; V Jornadas Argentinas de Econometría; 2019

This paper develops a first-stage linear regression representation for the instrumental variables (IV) quantile regression (QR) model. The quantile first-stage is analogous to the least squares case, i.e., a conditional mean regression of the endogenous variables on the instruments, with the difference that the QR case is a weighted regression. The weights are given by the conditional density function of the innovation term in the QR structural model, conditional on the endogeneous and exogenous covariates, and the instruments as well, at a given quantile. In addition, we show that the required Jacobian identification conditions for IVQR models are embedded in the quantile first-stage. Hence, we suggest testing procedures to evaluate the adequacy of instruments by evaluating their statistical significance using the first-stage result. This procedure may be specially useful in QR since the instruments may be relevant at some quantiles but not at others, which indicates the use of weak identification robust inference. Monte Carlo experiments provide numerical evidence that the proposed tests work as expected in terms of empirical size and power in finite samples. An empirical application illustrates that checking for the statistical significance of the instruments at different quantiles is important.