An Exact Recursive 2SLS Version of the Instrumental Variable Estimator. Stability Analysis

An exact symmetric recursive form is introduced for the Two-Stage-Least-Square estimator. Taking into account the relationship with the Instrumental Variable (IV) estimator, this algorithm can be viewed as symmetrized version of IV, able to work with overdimensionned IV vectors. An analysis of stability is proposed, in the deterministic case, but without boundedness hypothesis. It is shown that the a posteriori error tends towards zero, provided the Instrumental Variable satisfies a given sufficient condition.