A comparison of bias approximations for the two-stage least squares (2SLS) estimator

We consider the bias of the two-stage least squares (2SLS) estimator in linear instrumental variable regression with only one endogenous regressor. By using asymptotic expansion techniques, we approximate the 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments.

► The 2SLS coefficient estimation bias is approximated. ► We consider various scenarios regarding the number and strength of instruments. ► The resulting approximation encompasses existing bias expressions. ► Simulations show that the developed approximation is accurate.