Before revision:  It is found that the limiting distribution of the estimated instrument effect has a discontinuity when the strength of the idiosyncratic beta is near zero , which makes usual inferences fail to be valid and produce misleading results. In addition, the usual "plug-in" method using the estimated asymptotic variance is only valid pointwise .
After revision:  It is found that the limiting distribution of the estimated instrument effect has a discontinuity when the strength of the idiosyncratic beta is near zero , which makes the usual "plug-in" method using the estimated asymptotic variance is only valid pointwise .