Reduced forms and weak instrumentation

This paper develops exact finite sample and asymptotic distributions for a class of reduced form estimators and predictors, allowing for the presence of unidentified or weakly identified structural equations. Weak instrument asymptotic theory is developed directly from finite sample results, unifying earlier findings and showing the usefulness of structural information in making predictions from reduced form systems in applications. Asymptotic results are reported for predictions from models with many weak instruments. Of particular interest is the finding that, in unidentified and weakly identified structural models, partially restricted reduced form predictors have considerably smaller forecast mean square errors than unrestricted reduced forms. These results are related to the use of shrinkage methods in system-wide reduced form estimation.