Linear instrumental variables model averaging estimation

Model averaging (MA) estimators in the linear instrumental variables regression framework are considered. The obtaining of weights for averaging across individual estimates by direct smoothing of selection criteria arising from the estimation stage is proposed. This is particularly relevant in applications in which there is a large number of candidate instruments and, therefore, a considerable number of instrument sets arising from different combinations of the available instruments. The asymptotic properties of the estimator are derived under homoskedastic and heteroskedastic errors. A simple Monte Carlo study contrasts the performance of MA procedures with existing instrument selection procedures, showing that MA estimators compare very favourably in many relevant setups. Finally, this method is illustrated with an empirical application to returns to education.