An Instrumental Variable Consistent Estimation Procedure to Overcome the Problem of Endogenous Variables in Multilevel Models

It is far from unusual for a multilevel model to contain a regressor that can be regarded as an endogenous variable. The term endogeneity as opposed to exogeneity is a familiar term in econometrics. Often it manifests itself by explanatory variable being subject to the same influences as the response variable. It is thus not exogenous in the model being fitted. More particularly it may mean that variables which are regarded as endogenous are not independent of the random effects in the model. In such circumstances a basic assumption of modelling is not met and obtaining consistent estimators of the parameters is not straightforward. Many standard multilevel procedures (e.g. Iterative Generalised Least Squares) rely on the independence of regressors and model disturbances for their consistency properties. Obviously in the case of the presence of endogenous explanatory variables this does not generally hold. We present here a modelling strategy based on instrumental variables and introduce a MlwiN macro that provides desired consistent estimators.