Date: 05/04/15 Time: 12:50
Sample (adjusted): 1994 2013
Included observations: 20 after adjustments
Trend assumption: Linear deterministic trend
Series: LNY LNX1 LNX2 LNX3
Lags interval (in first differences): 1 to 2
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.936457 134.8779 47.85613 0.0000
At most 1 * 0.882918 79.75705 29.79707 0.0000
At most 2 * 0.717742 36.85937 15.49471 0.0000
At most 3 * 0.439000 11.56068 3.841466 0.0007
Trace test indicates 4 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.936457 55.12085 27.58434 0.0000
At most 1 * 0.882918 42.89767 21.13162 0.0000
At most 2 * 0.717742 25.29869 14.26460 0.0006
At most 3 * 0.439000 11.56068 3.841466 0.0007
Max-eigenvalue test indicates 4 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
LNY LNX1 LNX2 LNX3
-25.75089 -3.751776 35.58520 4.038372
2.785985 5.596671 -38.95409 5.976931
29.90738 -1.663514 14.84602 -4.685181
-13.83319 -0.927744 9.540318 -2.082763
Unrestricted Adjustment Coefficients (alpha):
D(LNY) 0.012062 -0.001067 -0.016061 0.013703
D(LNX1) -0.002166 -0.125168 0.001734 -0.097727
D(LNX2) -0.011048 -0.006625 0.001630 0.000530
D(LNX3) 0.021064 -0.066075 0.096757 0.127404
1 Cointegrating Equation(s): Log likelihood 139.2499
Normalized cointegrating coefficients (standard error in parentheses)
LNY LNX1 LNX2 LNX3
1.000000 0.145695 -1.381902 -0.156825
(0.02165) (0.16945) (0.02391)
Adjustment coefficients (standard error in parentheses)
D(LNY) -0.310598
(0.23008)
D(LNX1) 0.055766
(1.61851)
D(LNX2) 0.284493
(0.06429)
D(LNX3) -0.542419
(1.90961)
2 Cointegrating Equation(s): Log likelihood 160.6987
Normalized cointegrating coefficients (standard error in parentheses)
LNY LNX1 LNX2 LNX3
1.000000 0.000000 -0.396595 -0.336849
(0.03713) (0.02443)
0.000000 1.000000 -6.762803 1.235625
(0.17480) (0.11499)
Adjustment coefficients (standard error in parentheses)
D(LNY) -0.313570 -0.051223
(0.23126) (0.06016)
D(LNX1) -0.292951 -0.692402
(1.26458) (0.32896)
D(LNX2) 0.266037 0.004372
(0.03517) (0.00915)
D(LNX3) -0.726505 -0.448830
(1.84293) (0.47941)
3 Cointegrating Equation(s): Log likelihood 173.3481
Normalized cointegrating coefficients (standard error in parentheses)
LNY LNX1 LNX2 LNX3
1.000000 0.000000 0.000000 -0.145838
(0.02159)
0.000000 1.000000 0.000000 4.492772
(0.53658)
0.000000 0.000000 1.000000 0.481627
(0.07102)
Adjustment coefficients (standard error in parentheses)
D(LNY) -0.793914 -0.024505 0.232326
(0.29052) (0.05096) (0.40248)
D(LNX1) -0.241096 -0.695286 4.824502
(1.93153) (0.33882) (2.67584)
D(LNX2) 0.314773 0.001662 -0.110886
(0.04971) (0.00872) (0.06887)
D(LNX3) 2.167244 -0.609787 4.759934
(2.54151) (0.44582) (3.52087)


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