Before revision:  Thus, we are able to use the first-stage result and suggest testing procedures to evaluate the adequacy of instruments in IVQR models by evaluating their statistical significance . In the QR case, the instruments may be relevant at some quantiles but not at others or at the mean . Monte Carlo experiments provide numerical evidence that the proposed tests work as expected in terms of empirical size and power in finite samples.
After revision:  Thus, we are able to use the first-stage result and suggest testing procedures to evaluate the adequacy of instruments in IVQR models 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 or at the mean . Monte Carlo experiments provide numerical evidence that the proposed tests work as expected in terms of empirical size and power in finite samples.