statistic distributed as a χ2 with one degree of freedom. This restriction is not
rejected when the loglikelihoods of this restricted model is compared with the exact-
identified model in equation (B.3), the differences are not significant.
Lastly, as suggested by the demand theory, we impose and test in the cointegra-
tion vectors the properties of both symmetry and homogeneity. In addition to the
symmetry restriction, β32 = β41 , the restriction of homogeneity for each equation is
added, that is, (β31 + β32 = -β51) and (β32 + β42 = -β52). Thus, the cointegration
vector is given as:
-~⅛-
βSH =
-1
0 β31
* β61 β71
(B.5)
^ 0 - 1 β32 β42 * β62 β72 j
As shown in the text, the LR statistic, distributed as a χ2 with three degrees of
freedom, is then used to test these joint theoretical restrictions.
32
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