On the equivalence of repartitioned MIMO IV parameter estimators

This paper concerns a particular property of the basic instrumental variable (IV) estimator that is useful for multiple-input multiple-output (MIMO) modeling problems where it is not obvious how to partition the available signals between the sets of inputs and outputs. In general, a repartitioning of the input and output signals will result in a different model compared to the original input–output choice. It is important to distinguish cases where a repartitioning results in an algebraically equivalent model and cases where the resulting model transformation is more complex and depends also on particular system and signal properties. The latter situation typically occurs when models are estimated from data. We here show that the basic IV estimator is an exception since it provides algebraically equivalent estimates regardless of true system structure, noise properties, or amount of data. This equivalence result is illustrated in two simulation examples.