Output Analisis Structural VAR

Lampiran 4: Output Analisis Structural VAR

*********************** Structural VAR analysis ***********************

Structural model: A.u = C.e, where C is a diagonal matrix, u is the vector with components u(1) = PPOP u(2) = GDP u(3) = LN[EC] u(4) = LN[CO] and e is a vectors of innovations. Variance matrix of u =

4.20049E-06 -1.76569E-03 -2.63894E-05 -7.71072E-05 -1.76569E-03 7.04729E+00 4.59582E-02 1.56817E-02 -2.63894E-05 4.59582E-02 7.02439E-04 3.46600E-04 -7.71072E-05 1.56817E-02 3.46600E-04 2.59014E-03

= LL', where L = 2.04951E-03 0.00000E+00 0.00000E+00 0.00000E+00 -8.61519E-01 2.51099E+00 0.00000E+00 0.00000E+00 -1.28759E-02 1.38851E-02 1.85433E-02 0.00000E+00 -3.76223E-02 -6.66298E-03 -2.44329E-03 3.35311E-02

(C^-1)A = B is a matrix with elements b(1) 0 0 0 b(2) b(3) 0 0 b(4) b(5) b(6) 0 b(7) b(8) b(9) b(10)

Identification of the structural model can be verified from the moment conditions: B'B =

b(1)b(1)+b(2)b(2)+b(4)b(4)+b(7)b(7) b(3)b(2)+b(5)b(4)+b(8)b(7) b(6)b(4)+b(9)b(7) b(10)b(7) b(3)b(2)+b(5)b(4)+b(8)b(7) b(3)b(3)+b(5)b(5)+b(8)b(8) b(6)b(5)+b(9)b(8) b(10)b(8) b(6)b(4)+b(9)b(7) b(6)b(5)+b(9)b(8) b(6)b(6)+b(9)b(9) b(10)b(9) b(10)b(7) b(10)b(8) b(10)b(9) b(10)b(10)

= 6.67192E+05 3.72480E+01 1.38538E+04 1.77826E+04 3.72480E+01 2.50825E-01 -1.58561E+01 1.71205E+00 1.38538E+04 -1.58561E+01 2.92366E+03 1.17190E+02 1.77826E+04 1.71205E+00 1.17190E+02 8.89412E+02

= inverse of the variance matrix of u(t)

This is a system of quadratic equations in the non-zero elements of B: b(1)b(1)+b(2)b(2)+b(4)b(4)+b(7)b(7) = 667191.9 b(3)b(2)+b(5)b(4)+b(8)b(7) = 37.24802 b(3)b(3)+b(5)b(5)+b(8)b(8) = .2508251 b(6)b(4)+b(9)b(7) = 13853.83 b(6)b(5)+b(9)b(8) = -15.85605 b(6)b(6)+b(9)b(9) = 2923.658 b(10)b(7) = 17782.62 b(10)b(8) = 1.712048 b(10)b(9) = 117.1904 This is a system of quadratic equations in the non-zero elements of B: b(1)b(1)+b(2)b(2)+b(4)b(4)+b(7)b(7) = 667191.9 b(3)b(2)+b(5)b(4)+b(8)b(7) = 37.24802 b(3)b(3)+b(5)b(5)+b(8)b(8) = .2508251 b(6)b(4)+b(9)b(7) = 13853.83 b(6)b(5)+b(9)b(8) = -15.85605 b(6)b(6)+b(9)b(9) = 2923.658 b(10)b(7) = 17782.62 b(10)b(8) = 1.712048 b(10)b(9) = 117.1904

Solution: b(1) = 487.921666354298

b(2) = 167.405698267693 b(3) = .398249392297348 b(4) = 213.447333321701 b(5) = -.29820624605022 b(6) = 53.9278852150879 b(7) = 596.271679343742 b(8) = .0574069364400237 b(9) = 3.92952875397241 b(10) = 29.8230162793772

Recall that the following matrices should be approximately equal: B'B:

66.71919E+004 37.24802E+000 13.85383E+003 17.78262E+003 37.24802E+000 25.08251E-002 -15.85605E+000 17.12048E-001

13.85383E+003 -15.85605E+000 29.23658E+002 11.71904E+001 17.78262E+003 17.12048E-001 11.71904E+001 88.94123E+001

Inverse of Var(u): 66.71919E+004 37.24802E+000 13.85383E+003 17.78262E+003 37.24802E+000 25.08251E-002 -15.85605E+000 17.12048E-001 13.85383E+003 -15.85605E+000 29.23658E+002 11.71904E+001 17.78262E+003 17.12048E-001 11.71904E+001 88.94123E+001

Structural model:

PPOP = +0.0020 x Innovation (5.2062) [0.00000]

GDP = -420.3539 x PPOP (-1.2821)

+2.5110 x Innovation (10.8834) [0.00000]

LN[EC] = -3.9580 x PPOP (-2.0583) +0.0055 x GDP (2.1361) +0.0185 x Innovation (7.2472) [0.00000]

LN[CO] = -19.9937 x PPOP (-4.2698) -0.0019 x GDP (-0.2902) -0.1318 x LN[EC] (-0.2207) +0.0335 x Innovation (6.1252) [0.00000]

(t-values in parenthesis) [p-values in parenthesis (two-sided, based on the normal approximation)]

The t-values and p-values have been calculated on the basis of the limiting normal distribution of the nonzero elements of the matrix L, ignoring overidentifying restrictions.

B^-1 =

2.04951E-003 0.00000E+000 0.00000E+000 0.00000E+000 (5.17) -8.61519E-001 2.51099E+000 0.00000E+000 0.00000E+000 (-1.29) (10.73) -1.28759E-002 1.38851E-002 1.85433E-002 0.00000E+000 (-2.26) (2.26) (7.25) -3.76223E-002 -6.66297E-003 -2.44329E-003 3.35311E-002 (-3.40) (-0.48) (-0.22) (6.13) (t-values between brackets)

Log-likelihood: 24.418282E+001

There are two methods available to compute the standard errors of the nonzero elements of the matrix B^-1: (1) Compute these standard errors on the basis of the limiting normal distribution of the nonzero elements of the matrix L, ignoring overidentifying restrictions. This method has been used to compute the t-values of the nonzero elements of the structural model. (2) Compute these standard errors on the basis of the limiting normal distribution of the maximum likelihood estimators of the nonzero elements of the matrix B. However, if the structural model is overidentified you may get slightly different results if you re-estimate the model with the same options. If so, this may be due to the build-up of the start simplex via random variation of the start values. Since your model is just-identified, methods 1 and

2 are asymptotically equivalent. Therefore method 1 is recommended.

Method 1 has been chosen.

x(2,1)=PPOP x -420.3539 (-1.2821) x(3,1)=PPOP x -3.9580 (-2.0583) x(3,2)=GDP x +0.0055 (2.1361) x(4,1)=PPOP x -19.9937 (-4.2698)(*) x(4,2)=GDP x -0.0019 (-0.2902)(*) x(4,3)=LN[EC] x -0.1318 (-0.2207)(*)

Test of the null hypothesis that the parameters indicated by (*) are jointly zero: Wald test: 25.53 Asymptotic null distribution: Chi-square(3)

p-value = 0.00001 Significance levels: 10% 5% Critical values: 6.25 7.81 Conclusions: reject reject

x(2,1)=PPOP x -420.3539 (-1.2821) x(3,1)=PPOP x -3.9580 (-2.0583)(*) x(3,2)=GDP x +0.0055 (2.1361)(*) x(4,1)=PPOP x -19.9937 (-4.2698) x(4,2)=GDP x -0.0019 (-0.2902) x(4,3)=LN[EC] x -0.1318 (-0.2207)

Test of the null hypothesis that the parameters indicated by (*) are jointly zero: Wald test: 25.93 Asymptotic null distribution: Chi-square(2)

p-value = 0.00000 Significance levels: 10% 5% Critical values: 4.61 5.99 Conclusions: reject reject

x(2,1)=PPOP x -420.3539 (-1.2821)(*) x(3,1)=PPOP x -3.9580 (-2.0583) x(3,2)=GDP x +0.0055 (2.1361) x(4,1)=PPOP x -19.9937 (-4.2698) x(4,2)=GDP x -0.0019 (-0.2902) x(4,3)=LN[EC] x -0.1318 (-0.2207)

Testing the significance of one parameter can be done by t-test!

Response of GDP to a unit shock in PPOP Horizon Innovation response Standard error

0 -86.15193E-002 67.03175E-002 1 -91.27813E-002 60.78443E-002

2 14.66725E-001 66.74685E-002 3 59.84475E-002 56.26612E-002 4 54.70395E-002 59.20813E-002 5 12.27728E-001 60.80315E-002 6 34.77400E-002 53.34662E-002

7 -71.10616E-003 52.12929E-002 8 -71.83473E-003 50.12986E-002

9 -36.11630E-002 46.46469E-002 10 32.36730E-002 40.44983E-002 11 55.21910E-002 42.92497E-002 12 33.64753E-002 46.99588E-002 13 60.31256E-002 47.21146E-002 14 36.42264E-002 50.17328E-002

15 -73.56986E-003 48.18516E-002 16 -13.36136E-002 46.98845E-002

17 -37.72285E-002 47.24379E-002 18 -44.84257E-002 59.86460E-002 19 -34.71834E-002 57.09413E-002 20 -46.66289E-002 60.84425E-002

Response of LN[EC] to a unit shock in PPOP Horizon Innovation response Standard error

0 -12.87595E-003 56.86099E-004 1 -93.76194E-004 80.83174E-004 2 -62.31257E-004 95.99887E-004 3 -14.79513E-003 93.60270E-004 4 -19.15661E-003 10.26680E-003 5 -20.15828E-003 11.72356E-003 6 -21.05189E-003 11.44222E-003 7 -18.38670E-003 10.31877E-003 8 -18.55665E-003 10.43065E-003 9 -15.74330E-003 10.70936E-003

10 -95.80310E-004 10.28494E-003 11 -77.43389E-004 96.45308E-004 12 -50.54448E-004 93.51272E-004

13 78.22684E-005 91.05480E-004 14 55.29512E-004 88.41936E-004 15 10.95322E-003 94.72632E-004 16 16.27137E-003 10.15337E-003 17 20.34293E-003 10.80947E-003 18 24.54600E-003 11.94453E-003 19 26.92982E-003 13.39599E-003 20 27.55715E-003 14.54014E-003

Response of LN[EC] to a unit shock in GDP Horizon Innovation response Standard error

0 13.88507E-003 61.44937E-004 1 15.40681E-003 77.44081E-004 2 88.14772E-004 63.32204E-004 3 54.38929E-004 59.73826E-004 4 69.88906E-004 63.66096E-004 5 84.74032E-004 69.62610E-004 6 22.14945E-004 75.80258E-004 7 17.35853E-004 70.93772E-004 8 72.38944E-004 59.31235E-004 9 77.42041E-004 56.61466E-004

10 65.96554E-004 58.70301E-004 11 75.59636E-004 55.44874E-004 12 69.83965E-004 47.46404E-004 13 57.65217E-004 44.13870E-004 14 39.99506E-004 45.26659E-004 15 24.93663E-004 45.44482E-004 16 23.88458E-004 46.28821E-004 17 12.58658E-004 46.28075E-004

18 -66.88662E-005 42.84809E-004 19 -17.34540E-004 46.54767E-004 20 -32.80195E-004 47.21439E-004

Response of LN[CO] to a unit shock in PPOP Horizon Innovation response Standard error

0 -37.62231E-003 11.06528E-003 1 -14.10649E-004 11.02820E-003 2 -72.34807E-004 12.97443E-003 3 -30.98839E-003 15.04023E-003 4 -16.07353E-003 14.59441E-003 5 -82.25771E-004 14.36940E-003 6 -40.37098E-004 12.65968E-003 7 -29.96508E-003 13.24188E-003 8 -23.55767E-003 13.26366E-003 9 -17.54553E-003 12.36937E-003

10 -24.36248E-003 13.35803E-003 11 -10.88046E-003 13.95605E-003

12 59.68742E-004 12.59170E-003 13 19.54878E-003 11.28252E-003

14 22.79226E-003 12.39211E-003 15 20.37429E-003 12.80536E-003 16 26.08092E-003 13.49849E-003 17 27.59793E-003 14.51252E-003 18 25.62110E-003 14.64148E-003 19 30.55002E-003 15.10187E-003 20 36.28630E-003 15.74349E-003

Response of LN[CO] to a unit shock in GDP Horizon Innovation response Standard error

0 -66.62975E-004 13.91370E-003 1 12.58007E-003 95.31336E-004 2 28.11133E-003 13.20803E-003 3 10.15948E-003 92.74108E-004 4 74.02690E-004 10.69228E-003

5 -96.49638E-004 10.37232E-003 6 69.18858E-004 10.77104E-003 7 36.34811E-004 94.95494E-004 8 19.87655E-004 97.56245E-004 9 14.29205E-003 99.97165E-004

10 14.46979E-003 93.31126E-004 11 71.85007E-004 84.78919E-004 12 18.40322E-004 96.33690E-004 13 36.42687E-004 85.73367E-004 14 94.82180E-004 74.20395E-004 15 57.17678E-004 66.60451E-004

16 -55.45603E-005 61.68628E-004 17 -18.03345E-004 67.90469E-004 18 -38.71741E-004 62.77337E-004 19 -85.09702E-004 71.94335E-004 20 -86.83994E-004 85.11751E-004

Response of LN[CO] to a unit shock in LN[EC] Horizon Innovation response Standard error

0 -24.43293E-004 11.06647E-003 1 -70.32217E-004 56.51489E-004

2 11.10307E-004 82.93931E-004 3 21.82377E-004 47.06804E-004

4 -43.47612E-004 49.05971E-004 5 -30.49062E-004 40.48353E-004 6 -54.67834E-005 48.11687E-004 7 -34.98279E-005 42.53464E-004 8 -24.95864E-004 38.87059E-004

9 19.98734E-004 41.93724E-004 10 67.41494E-004 35.29711E-004 11 17.45305E-004 32.64391E-004

12 -16.45056E-004 32.57979E-004 13 -53.65891E-005 32.60151E-004 14 -13.02948E-005 33.49764E-004 15 -71.37869E-005 32.79513E-004 16 -82.88982E-006 34.64079E-004

17 21.39842E-004 30.15233E-004 18 25.64349E-004 28.79843E-004 19 13.49501E-004 34.26185E-004 20 24.67626E-004 36.39596E-004

Column 1: Horizon Column 2: Contribution (%) of the innovation in PPOP Column 3: Contribution (%) of the innovation in GDP Column 4: Contribution (%) of the innovation in LN[EC] Column 5: Contribution (%) of the innovation in LN[CO]

Forecast error variance decomposition of PPOP

1 2 3 4 5 -------------------- 1 100 0 0 0 2 100 0 0 0 3 100 0 0 0 4 100 0 0 0

Forecast error variance decomposition of GDP

1 2 3 4 5 -------------------- 1 20 80 0 0 2 36 64 1 0 3 38 61 1 0 4 39 59 2 0 5 46 52 2 0 6 46 52 2 0 7 45 51 4 0 8 45 51 4 0 9 46 51 4 0

Forecast error variance decomposition of LN[EC]

1 2 3 4 5 -------------------- 1 18 30 52 0 2 18 31 52 0 3 26 28 46 0 4 37 25 39 0 5 45 23 32 0 6 52 20 28 0 7 57 18 25 0 8 59 18 23 0 9 61 18 21 0

Forecast error variance decomposition of LN[CO]

1 2 3 4 5 -------------------- 1 48 7 2 44 2 34 23 1 42 3 45 20 1 34 4 46 20 1 33 5 46 21 1 32 6 45 21 1 32 7 52 18 1 28 8 55 17 1 26 9 55 18 1 25

12 57 19 2 23 13 58 18 2 22 14 60 18 1 21 15 61 18 1 20 16 63 17 1 19 17 66 16 1 17 18 67 15 1 16 19 69 14 1 15 20 71 14 1 14