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2.1. UNRESTRICTED VECTOR AUTOREGRESSIONS 31is labeled a in (2.12). The forecast error variance in q 1t attributable toinnovations in q 2t is given by the Þrst diagonal element in the secondsummation (labeled b). Similarly, the second diagonal element of a isthe forecast error variance in q 2t attributable to innovations in q 1t andthe second diagonal element in b is the forecast error variance in q 2tattributable to innovations in itself.A problem you may encountered in practice is that the forecast errordecomposition and impulse responses may be sensitive to the orderingof the variables in the orthogonalizing process, so it may be a goodidea to experiment with which variable is q 1t and which one is q 2t . Asecond problem is that the procedures outlined above are purely of astatistical nature and have little or no economic content. In chapter(8.4) we will cover a popular method for using economic theory toidentify the shocks.Potential Pitfalls of Unrestricted VARsCooley and LeRoy [32] criticize unrestricted VAR accounting becausethe statistical concepts of Granger causality and econometric exogeneityare very different from standard notions of economic exogeneity.Their point is that the unrestricted VAR is the reduced form of somestructural model from which it is not possible to discover the true relationsof cause and effect. Impulse response analyses from unrestrictedVARs do not necessarily tell us anything about the effect of policy interventionson the economy. In order to deduce cause and effect, youneed to make explicit assumptions about the underlying economic environment.We present the Cooley—LeRoy critique in terms of the two-equationmodel consisting of the money supply and the nominal exchange ratem = ² 1 , (2.13)s = γm + ² 2 , (2.14)iidwhere the error terms are related by ² 2 = λ² 1 + ² 3 with ² 1 ∼ N(0, σ1),2iid² 3 ∼ N(0, σ3)andE(² 2 1 ² 3 ) = 0. Then you can rewrite (2.13) and (2.14)asm = ² 1 , (2.15)