Before revision:  To deal with weak or irrelevant instruments, we generalize the approximate MSE under the presence of a possibly growing set of irrelevant instruments, which provides useful guidance under weak IV environments. The Monte Carlo simulation results show that the proposed estimator outperforms alternative methods when instruments are correlated with each other and there exists high endogeneity.
After revision:  To deal with weak or irrelevant instruments, we generalize the approximate MSE under the presence of a possibly growing set of irrelevant instruments, which suggests to choose a smaller k than otherwise. An extensive simulation experiment shows potentially huge improvement in the bias and the MSE by using the CSA-2SLS when instruments are correlated with each other and there exists high endogeneity.