Improved accuracy of weak instument robust GMM statistics through bootstrap and Edgeworth approximations

We construct higher order expressions of (weak instrument robust) generalized method of moment (GMM) test statistics for iid data. We use them to obtain Edgeworth approximations and to reveal sensitivity to instrument quality. The Edgeworth approximations show that usage of bootstrapped
critical values reduces the order of the approximation error of the finite sample distribution of the weak instrument robust statistics compared to usage of asymptotic critical values. These results remain to hold when the instruments are weak and extend previous results on the bootstrap and the
Edgeworth approximation. We illustrate the resulting reduction of size distortions and conduct a power comparison using a panel autoregressive model of order one.