RDP 8910: An Analysis of the Determinants of Imports Appendix 3: Error Correction Models[17]

Tracey Horton and Jenny Wilkinson

December 1989

MODEL 1

  • dependent variable – ΔM
  • period of estimation – 1975:4 – 1989:3
VARIABLE COEFFICIENT STANDARD ERROR T-STATISTIC
RESIDUALt−1 −0.762 0.117 −6.513
ΔRPMt−1 0.413 0.278 1.486
ΔRPMt−3 −0.405 0.179 −2.263
ΔRPMt−4 −0.519 0.263 −1.973
ΔRPXt−1 −0.620 0.274 −2.263
ΔRPXt−2 −0.559 0.160 −3.494
ΔRPXt−4 0.379 0.232 1.634
ΔOTt−2 0.150 0.100 1.500
ΔOTt−4 0.145 0.087 1.667
CONSTANT 0.010 0.005 2.000
R2 0.616  
Adjusted R2 0.512  
DW 2.030  
Sum of squared residuals 0.051  
Standard error of estimate 0.035  
F-tests of joint significance:
Variables Test statistic Significance level
ΔRPMt−1,ΔRPMt−3,ΔRPMt−4 F(3,42) = 3.181 0.034
ΔRPXt−1,ΔRPXt−4 F(2,42) = 3.521 0.039
ΔOTt−2,ΔOTt−4 F(2,42) = 3.372 0.044
Tests for autocorrelation: Test statistic Significance level
First order Inline Equation = 0.148 0.700
Fourth order Inline Equation = 2.362 0.124
First to fourth order Inline Equation = 2.491 0.646

MODEL 2

  • dependent variable – ΔEM
  • period of estimation – 1975:4 – 1989:3
VARIABLE COEFFICIENT STANDARD ERROR T-STATISTIC
RESIDUALt−1 −0.668 0.127 −5.260
ΔEMt−4 −0.214 0.108 −1.981
ΔYt−1 0.860 0.479 1.795
ΔRPEMt−4 −0.392 0.231 −1.697
ΔRPXt−2 −0.380 0.174 −2.184
ΔRPXt−4 0.416 0.230 1.809
ΔOTt−2 0.196 0.114 1.719
ΔOTt−4 0.178 0.097 1.835
CONSTANT 0.009 0.006 1.500
R2 0.627  
Adjusted R2 0.523  
DW 1.944  
Sum of squared residuals 0.062  
Standard error of estimate 0.038  
F-tests of joint significance:
Variables Test statistic Significance level
ΔYt−1, ΔRPEMt−4 F(2,43) = 3.195 0.051
ΔRPXt−2, ΔRPXt−4 F(2,43) = 5.109 0.010
ΔOTt−2, ΔOTt−4 F(2,43) = 3.867 0.029
Tests for autocorrelation: Test statistic Significance level
First order Inline Equation = 0.857 0.354
Fourth order Inline Equation = 2.174 0.140
First to fourth order Inline Equation = 3.079 0.545

MODEL 3

  • dependent variable – ΔM
  • period of estimation – 1975:4 – 1989:3
VARIABLE COEFFICIENT STANDARD ERROR T-STATISTIC
RESIDUALt−1 −1.063 0.138 −7.703
ΔRPMt−3 −0.300 0.149 −2.013
ΔRPXt−1 −0.249 0.145 −1.717
ΔRPXt−2 −0.495 0.143 −3.462
ΔOTt−2 0.178 0.093 1.914
ΔOTt−4 0.207 0.080 2.588
CONSTANT 0.009 0.004 2.250
R2 0.637  
Adjusted R2 0.548  
DW 2.210  
Sum of squared residuals 0.048  
Standard error of estimate 0.032  
F-tests of joint significance:
Variables Test statistic Significance level
ΔRPXt−1, ΔRPXt−2 F(2,45) = 8.609 0.000
ΔOTt−2, ΔOTt−4 F(2,45) = 7.134 0.002
Tests for autocorrelation: Test statistic Significance level
First order Inline Equation= 1.426 0.232
Fourth order Inline Equation = 2.289 0.130
First to fourth order Inline Equation = 4.298 0.367

MODEL 4

  • dependent variable – ΔEM
  • period of estimation – 1975:4 – 1989:3
VARIABLE COEFFICIENT STANDARD ERROR T-STATISTIC
RESIDUALt−l −0.903 0.156 −5.788
ΔEMt−4 −0.200 0.101 −1.980
ΔDt−1 0.536 0.401 1.337
ΔDt−3 0.586 0.431 1.360
ΔRPXt−2 −0.219 0.168 −1.304
ΔRPXt−4 0.227 0.165 1.376
ΔOTt−2 0.237 0.116 2.043
ΔOTt−4 0.154 0.098 1.571
CONSTANT 0.006 0.006 1.000
R2 0.624  
R bar2 0.510  
DW 1.915  
Sum of squared residuals 0.063  
Standard error of estimate 0.038  
F-tests of joint significance:
Variables Test statistic Significance level
ΔDt−1, ΔDt−3, ΔRPXt−2, ΔRPXt−4 F(4,43) = 2.468 0.059
ΔOTt−2, ΔOTt−4 F(2,43) = 3.715 0.032
Tests for autocorrelation: Test statistic Significance level
First order Inline Equation = 0.671 0.413
Fourth order Inline Equation = 1.779 0.182
First to fourth order Inline Equation = 3.456 0.485

Footnote

For all of these results the standard errors have been adjusted to take account of the additional 4 degrees of freedom lost in estimation of the cointegrating relationships. [17]