Results: multireg.sas~

The VARMAX Procedure

The Varmax Procedure

Number of Observations

Number of Observations 41
Number of Pairwise Missing 0

Summary Statistics

Simple Summary Statistics
Variable Type N Mean Standard
Deviation		 Min Max Label
ln_gdp Dependent 41 12.08651 0.63937 11.19265 13.30277 ln_gdp
export_value Dependent 41 10.44624 0.88418 8.96221 11.91551 export_value
ln_debt Dependent 41 9.19007 0.54368 8.28632 10.06017 ln_debt

The VARMAX Procedure

Estimation

Type of Model

Type of Model VECM(1)
Estimation Method Maximum Likelihood Estimation
Cointegrated Rank 2

Beta

Long-Run Parameter Beta Estimates When RANK=2
Variable 1 2
ln_gdp 4.88481 -1.90342
export_value -3.57755 1.32534
ln_debt 1.67490 1.37703

Alpha

Adjustment Coefficient Alpha Estimates When RANK=2
Variable 1 2
ln_gdp -0.01375 0.08300
export_value 0.11309 0.02569
ln_debt -0.04584 -0.05244

Coefficient of Granger Representation

Coefficient of Granger Representation
Variable ln_gdp export_value ln_debt
ln_gdp 0.41366 0.39393 0.84781
export_value 0.57390 0.54653 1.17624
ln_debt 0.01942 0.01850 0.03981

Constant

Constant Estimates
Variable Constant
ln_gdp 0.23245
export_value -4.25664
ln_debt 1.88863

Parameter Alpha * Beta' Estimates

Parameter Alpha * Beta' Estimates
Variable ln_gdp export_value ln_debt
ln_gdp -0.22515 0.15919 0.09127
export_value 0.50350 -0.37052 0.22479
ln_debt -0.12410 0.09449 -0.14898

Schematic Representation

Schematic Representation of Parameter Estimates
Variable/Lag C AR1
+ is > 2*std error,  - is < -2*std error,  . is between,  * is N/A
ln_gdp . ...
export_value - +-+
ln_debt . ..-

Model Parameter Estimates

Model Parameter Estimates
Equation Parameter Estimate Standard
Error		 t Value Pr > |t| Variable
D_ln_gdp CONST1 0.23245 1.18377 0.20 0.8454 1
  AR1_1_1 -0.22515 0.16648 -1.35 0.1847 ln_gdp(t-1)
  AR1_1_2 0.15919 0.12115 1.31 0.1972 export_value(t-1)
  AR1_1_3 0.09127 0.06886 1.33 0.1934 ln_debt(t-1)
D_export_value CONST2 -4.25664 1.47278 -2.89 0.0065 1
  AR1_2_1 0.50350 0.20713 2.43 0.0202 ln_gdp(t-1)
  AR1_2_2 -0.37052 0.15073 -2.46 0.0189 export_value(t-1)
  AR1_2_3 0.22479 0.08567 2.62 0.0127 ln_debt(t-1)
D_ln_debt CONST3 1.88863 1.48895 1.27 0.2128 1
  AR1_3_1 -0.12410 0.20940 -0.59 0.5571 ln_gdp(t-1)
  AR1_3_2 0.09449 0.15239 0.62 0.5391 export_value(t-1)
  AR1_3_3 -0.14898 0.08661 -1.72 0.0940 ln_debt(t-1)

Alpha and Beta Parameter Estimates

Alpha and Beta Parameter Estimates
Equation Parameter Estimate Standard
Error		 t Value Pr > |t| Variable
D_ln_gdp ALPHA1_1 -0.01375 0.03176 -0.43 0.6676 Beta[,1]'*_DEP_(t-1)
  ALPHA1_2 0.08300 0.03176 2.61 0.0130 Beta[,2]'*_DEP_(t-1)
  BETA1_1 4.88481       ln_gdp(t-1)
  BETA1_2 -1.90342       ln_gdp(t-1)
D_export_value ALPHA2_1 0.11309 0.03951 2.86 0.0070 Beta[,1]'*_DEP_(t-1)
  ALPHA2_2 0.02569 0.03951 0.65 0.5196 Beta[,2]'*_DEP_(t-1)
  BETA2_1 -3.57755       export_value(t-1)
  BETA2_2 1.32534       export_value(t-1)
D_ln_debt ALPHA3_1 -0.04584 0.03994 -1.15 0.2587 Beta[,1]'*_DEP_(t-1)
  ALPHA3_2 -0.05244 0.03994 -1.31 0.1976 Beta[,2]'*_DEP_(t-1)
  BETA3_1 1.67490       ln_debt(t-1)
  BETA3_2 1.37703       ln_debt(t-1)

Covariance Parameter Estimates

Covariance Parameter Estimates
Parameter Estimate Standard
Error		 t Value Pr > |t|
COV1_1 0.04034 0.00902 4.47 <.0001
COV1_2 0.02658 0.00898 2.96 0.0052
COV2_2 0.06244 0.01396 4.47 <.0001
COV1_3 0.00704 0.00810 0.87 0.3899
COV2_3 0.02722 0.01087 2.50 0.0164
COV3_3 0.06382 0.01427 4.47 <.0001

Multivariate Diagnostics

Covariances of Innovations

Covariances of Innovations
Variable ln_gdp export_value ln_debt
ln_gdp 0.04034 0.02658 0.00704
export_value 0.02658 0.06244 0.02722
ln_debt 0.00704 0.02722 0.06382

Log-likelihood

Log-likelihood 125.6914

Information Criteria

Information Criteria
AICC -215.827
HQC -220.055
AIC -227.383
SBC -207.116
FPEC 0.000146