Excerpt from: “Structural Relations, Cointegration and Identification: Some Simple Results and Their Application” (Working Pa

An important question is the role of these results under mis-specification. It has been assumed thus far that the variables in the investigation are linked by a closed dynamic system of form (2.5), in which β has a structural interpretation. We should also know how to interpret regressions when some variables that appear in the long-run solution of (2.5) are missing from the data set. Of course, those identified structural relations whose included variables are present still appear in the IC set. The complicating factor is that the IC vectors may include solved relations derived from structural relations that do not themselves appear in the set. Take example (2.7) again, under the assumptions 41 32 0 β = β = , but suppose that t q is unobserved. Among the remaining three variables we find a single IC relation that, as we know, is a reduced form, but is derived from a structural relation that does not exist for the included data. This means that Theorems 4 and 5 do not always apply to incomplete models, although note that Theorems 1, 2 and 3 are true in all circumstances.