The resulting historical time series for the two disturbances st could then be identified with the residuals of the model’s structural equations further.

If the model fit the properties of the U.S. time series perfectly, the vector st constructed in this way would be orthogonal to the identified monetary policy disturbance In practice, the right hand side of (1.26) does depend upon the first element of the vector of VAR residuals etl which we identify as the monetary policy disturbance. Perhaps more troubling is the observation that if the real disturbances st are generated by a law of motion of the kind implied by conjoining (1.26) with equation (1.25) for the evolution of Zu then we should not expect all three of the independent structural disturbances et that matter for the evolution of st to be revealed by data on the three variables in Zt alone. (This is because one of the VAR innovations corresponds to the monetary policy shock, so that only the other two orthogonal innovations can reveal information about the real disturbances.)

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