GARCH-based identification and estimation of triangular systems

The diagonal GARCH(1,1) model is shown to support identification of the triangular system and is argued as a second moment analog to traditional exclusion restrictions. Estimators for this result include QML and GMM. The GMM estimator contains many (potential weak) moment conditions that can be the source of bias. As a result, a jackknife GMM estimator is proposed that remains consistent in the presence of many such moments. A small Monte Carlo study of the GMM and jackknife GMM estimators is also included.