A comparison of bias approximations for the 2SLS estimator

We consider the bias of the 2SLS estimator in the linear instrumental variables regression with one endogenous regressor only. By using asymptotic expansion techniques we approximate 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments. The resulting approximation encompasses existing bias approximations, which are valid in particular cases only. Simulations show that the developed approximation gives an accurate description of the 2SLS bias in case of either weak or many instruments or both.