This paper analyzes the conditions under which consistent estimation can be achieved in instrumental Variables (IV) regression when the available instruments are weak, in the local-to-zero sense of Staiger and Stock (1997) and using the many-instrument framework of Morimune (1983) and Bekker...

We provide analytical formulae for the asymptotic bias (ABIAS) and mean squared error (AMSE) of the IV estimator, and obtain approximations thereof based on an asymptotic scheme which essentially requires the expectation of the first stage F-statistic to converge to a finite (possibly small)...

This paper develops Wald type tests for general possibly nonlinear restrictions, in the context of heteroskedastic IV regression with many weak instruments. In particular, it is first shown that consistency and asymptotically normality can be obtained when estimating structural parameters using...