Causality between Energy Consumption and GDP: Evidence from ...

∆etm∑i=1it−in∑= α2+ γ ∆e+ δ ∆y+ ε(4)j=1jt−jtwhere ∆ is the first difference operator, so that the terms are introduced in differences to ensurethat they are stationary or I(0). Here the concept of causality is formulated in terms of changesto the variables and the presence of Granger-causality depends on the significance of the ∆e t-jterms and ∆y t-j terms in equations (3) and (4) respectively.Furthermore, if it is found that the two integrated variables co-integrate, then equations (3) and(4) can be augmented as follows:∆ytt−1m∑i=1it−in∑= α1+ σ1EC+ β ∆y+ λ ∆e+ υ(5)j=1jt−jtand∆etmn2+ σ2ECt−1+ ∑γi∆et−i+ ∑δj∆yt−jεt(6)i=1j=1= α +where EC is the error correction term from a cointegrating equation of the form yt = βet + ECtand hence is I(0). In essence, if a pair of I(1) series are co-integrated, there must be Grangercausalityin at least one direction (either e to y and/or y to e) hence it is necessary to add the ECterm to equation (3) and equation (4) to avoid miss-specifying the model and missing onesource of causation. Hence, in this formulation there are two possible sources of Grangercausality;for the ∆y t equation causality arises either through the lagged ∆e terms if λ j ≠ 0 orthrough the EC t-1 term, if σ 1 ≠ 0 (implying a long run relationship); and for the ∆e t equation itarises either through the lagged ∆y terms if δ j ≠ 0 or through the EC t-1 term, if σ 2 ≠ 0. 3Inessence, if a pair of I(1) series are co-integrated, there must be Granger-causality in at least onedirection so it is necessary to add the EC term in the model otherwise the model will miss onePage 6 of 58