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2.1.Không hạn chế VECTOR AUTOREGRESSIONS Các lỗi dự báo sai trong q1t do để đổi mới trong q2t được đưa ra bởi các yếu tố chéo Þrst tổng kết thứ hai (có nhãn b). | 2.1. UNRESTRICTED VECTOR AUTOREGRESSIONS 31 is labeled a in 2.12 . The forecast error variance in q1t attributable to innovations in q2t is given by the first diagonal element in the second summation labeled b . Similarly the second diagonal element of a is the forecast error variance in q2t attributable to innovations in q1t and the second diagonal element in b is the forecast error variance in q2t attributable to innovations in itself. A problem you may encountered in practice is that the forecast error decomposition and impulse responses may be sensitive to the ordering of the variables in the orthogonalizing process so it may be a good idea to experiment with which variable is q1t and which one is q2t. A second problem is that the procedures outlined above are purely of a statistical nature and have little or no economic content. In chapter 8.4 we will cover a popular method for using economic theory to identify the shocks. Potential Pitfalls of Unrestricted VARs Cooley and LeRoy 32 criticize unrestricted VAR accounting because the statistical concepts of Granger causality and econometric exogeneity are very different from standard notions of economic exogeneity. Their point is that the unrestricted VAR is the reduced form of some structural model from which it is not possible to discover the true relations of cause and effect. Impulse response analyses from unrestricted VARs do not necessarily tell us anything about the effect of policy interventions on the economy. In order to deduce cause and effect you need to make explicit assumptions about the underlying economic environment. We present the Cooley-LeRoy critique in terms of the two-equation model consisting of the money supply and the nominal exchange rate m 61 2.13 s ym 62 2.14 where the error terms are related by 62 Ă61 63 with 61 N 0 ơ2 63 zẩ N 0 nj and E 6163 0. Then you can rewrite 2.13 and 2.14 as m 61 2.15 32 CHAPTER 2. SOME USEFUL TIME-SERIES METHODS s ym A61 63. 2.16 m is exogenous in the .
