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This paper proposes a maximum likelihood estimator for a common co-integration space in large panels of co-integrated Vector Autoregressive models. The method pioneered by Pesaran (2006) and further refined in Dees, Mauro, Pesaran, and Smith (2007) is used to reduce the dimension of the parameter space of the model and control for cross section dependence. The common co-integration space is estimated using standard optimization methods.. Test statistics for the existence of a common co-integration space against the hypothesis of heterogeneous co-integration spaces are derived. A bootstrap algorithm to generat pseudo data under the hypothesis of a common co-integration space is proposed, and bootstrap test statistics are derived. Identification of the co-integration vectors of the panel is also discussed.