Two-stage-least-squares (2SLS) estimates are biased towards the probability limit of OLS estimates. This bias grows with the degree of over-identification and can generate highly misleading results. In this paper we propose two simple alternatives to 2SLS and limited-information-maximum-likelihood (LIML) estimators for models with more instruments than endogenous regressors. These estimators can be interpreted as instrumental variables procedures using an instrument that is independent of disturbances even in finite samples. Independence is achieved by using a leave-one-out jackknife-type fitted value in place of the usual first stage equation. The new estimators are first-order equivalent to 2SLS but with finite-sample properties superior, in terms of bias and coverage rate of confidence intervals, compared to those of 2SLS and similar to those of LIML, when there are many instruments.
