differences and including the ECT in the systems. In our case, the VEC
multivariate systems take the following forms:
Δcot
Δect
Δyt
Δy2t
Δopt
Δf dt
2
6666664
3
7777775
¼
μ1
μ2
μ3
μ4
μ5
μ6
2
6666664
3
7777775
þ
π11;1 π12;1 π13;1 π14;1 π15;1 π16;1
π21;1 π22;1 π23;1 π24;1 π25;1 π26;1
π31;1 π32;1 π33;1 π34;1 π35;1 π36;1
π41;1 π42;1 π43;1 π44;1 π45;1 π46;1
π51;1 π52;1 π53;1 π54;1 π55;1 π56;1
π61;1 π62;1 π63;1 π64;1 π65;1 π66;1
2
6666664
3
7777775
Δcot−1
Δect−1
Δyt−1
Δy2t
−1
Δopt−1
Δf dt−1
2
6666664
3
7777775
þ…
þ
π11;k π12;k π13;k π14;k π15;k π16;k
π21;k π22;k π23;k π24;k π25;k π26;k
π31;k π32;k π33;k π34;k π35;k π36;k
π41;k π42;k π43;k π44;k π45;k π46;k
π51;k π52;k π53;k π54;k π55;k π56;k
π61;k π62;k π63;k π64;k π65;k π66;k
2
6666664
3
7777775
Δcot−k
Δect−k
Δyt−k
Δy2t
−k
Δopt−k
Δf dt−k
2
6666664
3
7777775
þ
ψ1
ψ2
ψ3
ψ4
ψ5
ψ6
2
6666664
3
7777775
ECTt−1 þ
ε2t
ε3t
ε4t
ε5t
ε6t
ε7t
2
6666664
3
7777775
:
ð3Þ
Residual terms, ε2t,ε3t, ε4t,ε5t,ε6t and ε7t, independently and normally
distributed with zero mean and constant variance.
The VEC modeling approach allows us to distinguish between
“short-run” and “long-run” Granger causality. The Wald-tests of the
“differenced” explanatory variables give us an indication of the
“short-term” causal effects, whereas the “long-run” causal relationship
is implied through the significance or other wise of the t test(s) of the
lagged error-correction term that contains the long-term information
since it is derived fromthe long-run cointegrating relationship. Nonsignificance
or elimination of any of the “lagged error-correction terms” affects
the implied long-run relationship and may be a violation of theory.
The nonsignificance of any of the “differenced” variables that reflects
only short-run relationship, however, does not involve such violations
because; theory typically has little to say about short-termrelationships
(see Masih and Masih, 1996).
Using Eq. (3), causal relationships can be examined in two ways:
i) Short-run or weak Granger causalities are detected through the
F-statistics or Wald test for the significance of the relavant π coefficients
on the first differenced series. Masih and Masih (1996) and
Asafu-Adjaye (2000) interpreted the weak Granger causality as
‘short run’ causality in the sense that the dependent variable responds
only to short-term shocks to the stochastic environment. ii) Masih
and Masih (1996) point out that another possible source of causation
is the ECT in equations. The coefficients of the ECTs represent how fast
deviations from the long run equilibrium are eliminated following
changes in each variable. The long-run causalities are examined
through the t-test or Wald test for the significance of the relavant ψ
coefficients on the lagged error‐correction term. For example if ψ1
is zero, per capita carbon emissions does not respond to the deviations
from the long-run equilibrium in the previous period. ψi=0, i=1,
2, …, 6 for all i is equivalent to both Granger non-causality in the
long-run and the weak exogeneity (
النتائج (
العربية) 1:
[نسخ]نسخ!
differences and including the ECT in the systems. In our case, the VECmultivariate systems take the following forms:ΔcotΔectΔytΔy2tΔoptΔf dt2666666437777775¼μ1μ2μ3μ4μ5μ62666666437777775þπ11;1 π12;1 π13;1 π14;1 π15;1 π16;1π21;1 π22;1 π23;1 π24;1 π25;1 π26;1π31;1 π32;1 π33;1 π34;1 π35;1 π36;1π41;1 π42;1 π43;1 π44;1 π45;1 π46;1π51;1 π52;1 π53;1 π54;1 π55;1 π56;1π61;1 π62;1 π63;1 π64;1 π65;1 π66;12666666437777775Δcot−1Δect−1Δyt−1Δy2t−1Δopt−1Δf dt−12666666437777775þ…þπ11;k π12;k π13;k π14;k π15;k π16;kπ21;k π22;k π23;k π24;k π25;k π26;kπ31;k π32;k π33;k π34;k π35;k π36;kπ41;k π42;k π43;k π44;k π45;k π46;kπ51;k π52;k π53;k π54;k π55;k π56;kπ61;k π62;k π63;k π64;k π65;k π66;k2666666437777775Δcot−kΔect−kΔyt−kΔy2t−kΔopt−kΔf dt−k2666666437777775þψ1ψ2ψ3ψ4ψ5ψ62666666437777775ECTt−1 þε2tε3tε4tε5tε6tε7t2666666437777775:ð3ÞResidual terms, ε2t,ε3t, ε4t,ε5t,ε6t and ε7t, independently and normallydistributed with zero mean and constant variance.The VEC modeling approach allows us to distinguish between“short-run” and “long-run” Granger causality. The Wald-tests of the“differenced” explanatory variables give us an indication of the“short-term” causal effects, whereas the “long-run” causal relationshipis implied through the significance or other wise of the t test(s) of thelagged error-correction term that contains the long-term informationsince it is derived fromthe long-run cointegrating relationship. Nonsignificanceor elimination of any of the “lagged error-correction terms” affectsthe implied long-run relationship and may be a violation of theory.The nonsignificance of any of the “differenced” variables that reflectsonly short-run relationship, however, does not involve such violationsbecause; theory typically has little to say about short-termrelationships(see Masih and Masih, 1996).Using Eq. (3), causal relationships can be examined in two ways:i) Short-run or weak Granger causalities are detected through theF-statistics or Wald test for the significance of the relavant π coefficientson the first differenced series. Masih and Masih (1996) andAsafu-Adjaye (2000) interpreted the weak Granger causality as‘short run’ causality in the sense that the dependent variable respondsonly to short-term shocks to the stochastic environment. ii) Masihand Masih (1996) point out that another possible source of causationis the ECT in equations. The coefficients of the ECTs represent how fastdeviations from the long run equilibrium are eliminated followingchanges in each variable. The long-run causalities are examinedعن طريق اختبار t أو اختبار والد لأهمية relavant ψمعاملات في فترة تأخر error‐correction. فعلى سبيل المثال إذا ψ1هو صفر، وكل نصيب الفرد من انبعاثات الكربون لا تستجيب للانحرافاتمن التوازن الطويل الأجل في الفترة السابقة. Ψi = 0، أنا = 1،2,..., 6 لكل ما المكافئ لكل المزارع غير السببية فيالطويل و (اكسوجينيتي ضعيفة
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