This paper defines parametric conditions under which a subset of variables
is weakly exogenous with respect to the (multi)-cointegration parameters in
I(2) VAR systems. The weak exogeneity conditions can be interpreted in ter
ms of common trends, corresponding to the cumulation of the errors from the
marginal equations into the I(2) trends, or in terms of 'no levels and dif
ference feedback' into the marginal model equations. A modified version of
the two-stage procedure proposed in Johansen (1995) is adopted for conditio
nal statistical inference. Corresponding tests for the above restrictions a
re derived and discussed. Asymptotic properties of the tests and of the con
ditional estimators are analyzed. It is shown that if the conditions of wea
k exogeneity do not apply, the conditional estimators of the long-run param
eters can be inconsistent and/or present limit distributions with nuisance
parameters, according to which part of the conditions fails to hold. A test
for weak exogeneity restrictions as a routine check before any analysis of
conditional models is strongly recommended. (C) 1999 Elsevier Science S.A.
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