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252 CHAPTER 8. THE MUNDELL-FLEMING MODELtural VARs. 13 Clarida and Gali [28] employ Blanchard-Quah’ structuralVAR method using restrictions implied by the stochastic Mundell-Fleming model. To see how this works, consider the 3-dimensionalvector, x t =(∆(y t − yt ∗ ), ∆(p t − p ∗ t ), ∆q t ) 0 ,wherey is log industrialproduction, p is the log price level, and q is the log real exchange rateand starred variables are for the foreign country. Given the processesthat govern the exogenous variables (8.21) and (8.22), the stochasticMundell-Fleming model predicts that income and the real exchangerate are unit root processes, so the VAR should be speciÞed in termsof Þrst-differenced observations. The triangular structure also informsus that the variables are not cointegrated, since each of the variablesare driven by a different unit root process. 14As described in Chapter 2.1, Þrst Þt ap-th order VAR for x t andget the Wold moving average representationx t =∞Xj=0(C j L j )² t = C(L)² t , (8.45)where E(² t ² 0 t)=Σ, C 0 = I, andC(L) = P ∞j=0 C j L j is the one-sidedmatrix polynomial in the lag operator L. The theory predicts that inthe long run, x t is driven by the three dimensional vector of aggregatesupply, aggregate demand, and monetary shocks, v t =(z t , δ t ,v t ) 0 .The economic structure embodied in the stochastic Mundell-Flemingmodel is represented byx t =∞Xj=0(F j L j )v t = F(L)v t . (8.46)Because the underlying structural innovations are not observable, youare allowed to make one normalization. Take advantage of it by settingE(v t v 0 t = I). The orthogonality between the various structural shocksis an identifying assumption. To map the innovations ² t from the unrestrictedVAR into structural innovations v t , compare (8.45) and (8.46).It follows that² t = F 0 v t ⇒ ² t−j = F 0 v t−j ⇒ C j ² t−j = C j F 0 v t−j = F j v t−j .13 They are only identifying restrictions, however, and cannot be tested.14 Cointegration is discussed in Chapter2.6.