Null Hypothesis: LRGDP has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.939876 0.7633
Test critical values: 1% level -3.632900
5% level -2.948404
10% level -2.612874
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LRGDP)
Method: Least Squares
Date: 03/11/25 Time: 20:04
Sample (adjusted): 1988 2022
Included observations: 35 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
LRGDP(-1) -0.009598 0.010212 -0.939876 0.3543
D(LRGDP(-1)) 0.424619 0.158925 2.671823 0.0118
C 0.125952 0.107892 1.167394 0.2517
R-squared 0.208010 Mean dependent var 0.044427
Adjusted R-squared 0.158511 S.D. dependent var 0.035170
S.E. of regression 0.032262 Akaike info criterion -3.948022
Sum squared resid 0.033307 Schwarz criterion -3.814707
Log likelihood 72.09039 Hannan-Quinn criter. -3.902002
F-statistic 4.202288 Durbin-Watson stat 2.155405
Prob(F-statistic) 0.023961
Null Hypothesis: D(LRGDP) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.570873 0.0117
Test critical values: 1% level -3.632900
5% level -2.948404
10% level -2.612874
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LRGDP,2)
Method: Least Squares
Date: 03/11/25 Time: 20:04
Sample (adjusted): 1988 2022
Included observations: 35 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(LRGDP(-1)) -0.565171 0.158273 -3.570873 0.0011
C 0.024898 0.008953 2.780920 0.0089
R-squared 0.278706 Mean dependent var -0.000484
Adjusted R-squared 0.256849 S.D. dependent var 0.037358
S.E. of regression 0.032205 Akaike info criterion -3.977934
Sum squared resid 0.034227 Schwarz criterion -3.889057
Log likelihood 71.61385 Hannan-Quinn criter. -3.947254
F-statistic 12.75113 Durbin-Watson stat 2.139949
Prob(F-statistic) 0.001116
Null Hypothesis: LTCEX has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.711072 0.8310
Test critical values: 1% level -3.632900
5% level -2.948404
10% level -2.612874
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LTCEX)
Method: Least Squares
Date: 03/11/25 Time: 20:04
Sample (adjusted): 1988 2022
Included observations: 35 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
LTCEX(-1) -0.041290 0.058067 -0.711072 0.4822
D(LTCEX(-1)) -0.407800 0.159485 -2.556984 0.0155
C 0.352389 0.178338 1.975957 0.0568
R-squared 0.195315 Mean dependent var 0.177879
Adjusted R-squared 0.145022 S.D. dependent var 0.737433
S.E. of regression 0.681867 Akaike info criterion 2.153852
Sum squared resid 14.87817 Schwarz criterion 2.287168
Log likelihood -34.69242 Hannan-Quinn criter. 2.199873
F-statistic 3.883557 Durbin-Watson stat 2.050006
Prob(F-statistic) 0.030904
Null Hypothesis: D(LTCEX) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -9.105636 0.0000
Test critical values: 1% level -3.632900
5% level -2.948404
10% level -2.612874
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LTCEX,2)
Method: Least Squares
Date: 03/11/25 Time: 20:05
Sample (adjusted): 1988 2022
Included observations: 35 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(LTCEX(-1)) -1.424869 0.156482 -9.105636 0.0000
C 0.257954 0.118131 2.183635 0.0362
R-squared 0.715303 Mean dependent var -0.010591
Adjusted R-squared 0.706676 S.D. dependent var 1.249533
S.E. of regression 0.676740 Akaike info criterion 2.112387
Sum squared resid 15.11325 Schwarz criterion 2.201264
Log likelihood -34.96677 Hannan-Quinn criter. 2.143067
F-statistic 82.91261 Durbin-Watson stat 2.068221
Prob(F-statistic) 0.000000
Null Hypothesis: LTCRX has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.267099 0.1877
Test critical values: 1% level -3.626784
5% level -2.945842
10% level -2.611531
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LTCRX)
Method: Least Squares
Date: 03/11/25 Time: 20:05
Sample (adjusted): 1987 2022
Included observations: 36 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
LTCRX(-1) -0.142607 0.062903 -2.267099 0.0299
C 0.439538 0.168559 2.607625 0.0134
R-squared 0.131318 Mean dependent var 0.190305
Adjusted R-squared 0.105768 S.D. dependent var 0.810721
S.E. of regression 0.766649 Akaike info criterion 2.360377
Sum squared resid 19.98352 Schwarz criterion 2.448350
Log likelihood -40.48679 Hannan-Quinn criter. 2.391082
F-statistic 5.139738 Durbin-Watson stat 2.513172
Prob(F-statistic) 0.029859
Null Hypothesis: D(LTCRX) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -7.998798 0.0000
Test critical values: 1% level -3.632900
5% level -2.948404
10% level -2.612874
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LTCRX,2)
Method: Least Squares
Date: 03/11/25 Time: 20:05
Sample (adjusted): 1988 2022
Included observations: 35 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(LTCRX(-1)) -1.292397 0.161574 -7.998798 0.0000
C 0.215336 0.134609 1.599716 0.1192
R-squared 0.659726 Mean dependent var -0.033034
Adjusted R-squared 0.649415 S.D. dependent var 1.308695
S.E. of regression 0.774881 Akaike info criterion 2.383230
Sum squared resid 19.81454 Schwarz criterion 2.472108
Log likelihood -39.70653 Hannan-Quinn criter. 2.413911
F-statistic 63.98078 Durbin-Watson stat 2.085439
Prob(F-statistic) 0.000000
Null Hypothesis: INTR has a unit root
Exogenous: Constant
Lag Length: 3 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.362093 0.1598
Test critical values: 1% level -3.646342
5% level -2.954021
10% level -2.615817
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(INTR)
Method: Least Squares
Date: 03/11/25 Time: 20:09
Sample (adjusted): 1990 2022
Included observations: 33 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
INTR(-1) -0.563482 0.238552 -2.362093 0.0254
D(INTR(-1)) -0.094292 0.229311 -0.411197 0.6841
D(INTR(-2)) -0.099638 0.207997 -0.479037 0.6356
D(INTR(-3)) -0.071386 0.161764 -0.441299 0.6624
C 20.12186 8.357453 2.407655 0.0229
R-squared 0.352564 Mean dependent var 0.530303
Adjusted R-squared 0.260074 S.D. dependent var 12.36542
S.E. of regression 10.63660 Akaike info criterion 7.705207
Sum squared resid 3167.845 Schwarz criterion 7.931950
Log likelihood -122.1359 Hannan-Quinn criter. 7.781499
F-statistic 3.811887 Durbin-Watson stat 1.701075
Prob(F-statistic) 0.013497
Null Hypothesis: D(INTR) has a unit root
Exogenous: Constant
Lag Length: 2 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -5.175126 0.0002
Test critical values: 1% level -3.646342
5% level -2.954021
10% level -2.615817
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(INTR,2)
Method: Least Squares
Date: 03/11/25 Time: 20:09
Sample (adjusted): 1990 2022
Included observations: 33 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(INTR(-1)) -2.062076 0.398459 -5.175126 0.0000
D(INTR(-1),2) 0.589389 0.299277 1.969376 0.0585
D(INTR(-2),2) 0.230220 0.158317 1.454170 0.1566
C 0.874961 1.999627 0.437562 0.6649
R-squared 0.715620 Mean dependent var 0.374242
Adjusted R-squared 0.686201 S.D. dependent var 20.43220
S.E. of regression 11.44566 Akaike info criterion 7.826311
Sum squared resid 3799.093 Schwarz criterion 8.007706
Log likelihood -125.1341 Hannan-Quinn criter. 7.887345
F-statistic 24.32537 Durbin-Watson stat 1.784828
Prob(F-statistic) 0.000000
Null Hypothesis: EXCR has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic 2.065378 0.9998
Test critical values: 1% level -3.626784
5% level -2.945842
10% level -2.611531
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(EXCR)
Method: Least Squares
Date: 03/11/25 Time: 20:11
Sample (adjusted): 1987 2022
Included observations: 36 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
EXCR(-1) 0.063463 0.030727 2.065378 0.0466
C 3.915123 5.097001 0.768123 0.4477
R-squared 0.111478 Mean dependent var 11.78460
Adjusted R-squared 0.085345 S.D. dependent var 21.23982
S.E. of regression 20.31326 Akaike info criterion 8.914377
Sum squared resid 14029.37 Schwarz criterion 9.002351
Log likelihood -158.4588 Hannan-Quinn criter. 8.945082
F-statistic 4.265785 Durbin-Watson stat 1.750730
Prob(F-statistic) 0.046578
Null Hypothesis: D(EXCR) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -4.378278 0.0014
Test critical values: 1% level -3.632900
5% level -2.948404
10% level -2.612874
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(EXCR,2)
Method: Least Squares
Date: 03/11/25 Time: 20:11
Sample (adjusted): 1988 2022
Included observations: 35 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(EXCR(-1)) -0.732008 0.167191 -4.378278 0.0001
C 8.886142 4.064558 2.186250 0.0360
R-squared 0.367444 Mean dependent var 0.225957
Adjusted R-squared 0.348276 S.D. dependent var 26.02127
S.E. of regression 21.00683 Akaike info criterion 8.983017
Sum squared resid 14562.46 Schwarz criterion 9.071894
Log likelihood -155.2028 Hannan-Quinn criter. 9.013697
F-statistic 19.16932 Durbin-Watson stat 1.920074
Prob(F-statistic) 0.000114
Dependent Variable: LRGDP
Method: ARDL
Date: 03/11/25 Time: 19:48
Sample (adjusted): 1987 2022
Included observations: 36 after adjustments
Maximum dependent lags: 1 (Automatic selection)
Model selection method: Akaike info criterion (AIC)
Dynamic regressors (1 lag, automatic): LTCEX LTCRX LINTR LINFR LINTR
Fixed regressors: C
Number of models evalulated: 16
Selected Model: ARDL(1, 0, 1, 0, 1)
Variable Coefficient Std. Error t-Statistic Prob.*
LRGDP(-1) 0.927846 0.022226 41.74595 0.0000
LTCEX -0.001627 0.008078 -0.201390 0.8418
LTCRX 0.011396 0.007562 1.506991 0.1430
LTCRX(-1) 0.009795 0.006441 1.520698 0.1395
LINTR -0.002980 0.008462 -0.352161 0.7274
LINFR -0.023066 0.009339 -2.469930 0.0199
LINFR(-1) 0.011769 0.008185 1.437817 0.1616
C 0.805102 0.226235 3.558706 0.0014
R-squared 0.998115 Mean dependent var 10.50168
Adjusted R-squared 0.997644 S.D. dependent var 0.549276
S.E. of regression 0.026660 Akaike info criterion -4.218177
Sum squared resid 0.019901 Schwarz criterion -3.866284
Log likelihood 83.92719 Hannan-Quinn criter. -4.095357
F-statistic 2118.424 Durbin-Watson stat 1.361145
Prob(F-statistic) 0.000000
*Note: p-values and any subsequent tests do not account for model
selection.
ARDL Long Run Form and Bounds Test
Dependent Variable: D(LRGDP)
Selected Model: ARDL(1, 0, 1, 0, 1)
Case 3: Unrestricted Constant and No Trend
Date: 03/11/25 Time: 19:50
Sample: 1986 2022
Included observations: 36
Conditional Error Correction Regression
Variable Coefficient Std. Error t-Statistic Prob.
C 0.805102 0.226235 3.558706 0.0014
LRGDP(-1)* -0.072154 0.022226 -3.246376 0.0030
LTCEX** -0.001627 0.008078 -0.201390 0.8418
LTCRX(-1) 0.021191 0.006854 3.091989 0.0045
LINTR** -0.002980 0.008462 -0.352161 0.7274
LINFR(-1) -0.011297 0.009148 -1.234935 0.2271
D(LTCRX) 0.011396 0.007562 1.506991 0.1430
D(LINFR) -0.023066 0.009339 -2.469930 0.0199
* p-value incompatible with t-Bounds distribution.
** Variable interpreted as Z = Z(-1) + D(Z).
Levels Equation
Case 3: Unrestricted Constant and No Trend
Variable Coefficient Std. Error t-Statistic Prob.
LTCEX -0.022546 0.116637 -0.193301 0.8481
LTCRX 0.293693 0.131124 2.239815 0.0332
LINTR -0.041301 0.118038 -0.349893 0.7290
LINFR -0.156566 0.132006 -1.186050 0.2456
EC = LRGDP - (-0.0225*LTCEX + 0.2937*LTCRX -0.0413*LINTR -0.1566
*LINFR )
F-Bounds Test Null Hypothesis: No levels relationship
Test Statistic Value Signif. I(0) I(1)
Asymptotic:
n=1000
F-statistic 4.558137 10% 2.45 3.52
k 4 5% 2.86 4.01
2.5% 3.25 4.49
1% 3.74 5.06
Finite Sample:
Actual Sample Size 36 n=40
10% 2.66 3.838
5% 3.202 4.544
1% 4.428 6.25
Finite Sample:
n=35
10% 2.696 3.898
5% 3.276 4.63
1% 4.59 6.368
t-Bounds Test Null Hypothesis: No levels relationship
Test Statistic Value Signif. I(0) I(1)
t-statistic -3.246376 10% -2.57 -3.66
5% -2.86 -3.99
2.5% -3.13 -4.26
1% -3.43 -4.6
Null Hypothesis: ECT has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=9)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.115293 0.0343
Test critical values: 1% level -3.626784
5% level -2.945842
10% level -2.611531
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(ECT)
Method: Least Squares
Date: 03/11/25 Time: 20:19
Sample (adjusted): 1987 2022
Included observations: 36 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
ECT(-1) -0.444848 0.142795 -3.115293 0.0037
C -0.001920 0.028154 -0.068189 0.9460
R-squared 0.222058 Mean dependent var -0.002636
Adjusted R-squared 0.199177 S.D. dependent var 0.188758
S.E. of regression 0.168917 Akaike info criterion -0.664863
Sum squared resid 0.970123 Schwarz criterion -0.576889
Log likelihood 13.96753 Hannan-Quinn criter. -0.634158
F-statistic 9.705051 Durbin-Watson stat 2.196594
Prob(F-statistic) 0.003720
Dependent Variable: D(LRGDP)
Method: Least Squares
Date: 03/11/25 Time: 20:31
Sample (adjusted): 1987 2022
Included observations: 36 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.048620 0.005947 8.175236 0.0000
D(TCEX) 1.59E-05 0.000252 0.063231 0.9500
D(TCRX) -8.86E-05 0.000423 -0.209523 0.8355
D(INFR) -0.000481 0.000375 -1.282663 0.2098
D(INTR) -0.000138 0.000419 -0.329651 0.7440
D(EXCR) -0.000346 0.000239 -1.447019 0.1586
ECT(-1) -0.086065 0.026431 -3.256139 0.0029
R-squared 0.395770 Mean dependent var 0.044135
Adjusted R-squared 0.270757 S.D. dependent var 0.034708
S.E. of regression 0.029639 Akaike info criterion -4.026784
Sum squared resid 0.025476 Schwarz criterion -3.718878
Log likelihood 79.48211 Hannan-Quinn criter. -3.919316
F-statistic 3.165833 Durbin-Watson stat 1.291143
Prob(F-statistic) 0.016359
LRGDP LTCEX LTCRX LINTR LINFR LEXCR
LRGDP 1.000000 0.935841 0.865213 0.402150 -0.281002 0.910727
LTCEX 0.935841 1.000000 0.926345 0.389016 -0.251600 0.916608
LTCRX 0.865213 0.926345 1.000000 0.410056 -0.259392 0.948317
LINTR 0.402150 0.389016 0.410056 1.000000 -0.607387 0.356685
LINFR -0.281002 -0.251600 -0.259392 -0.607387 1.000000 -0.223522
LEXCR 0.910727 0.916608 0.948317 0.356685 -0.223522 1.000000
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 2.954412 Prob. F(6,29) 0.0225
Obs*R-squared 13.65721 Prob. Chi-Square(6) 0.0337
Scaled explained SS 8.927084 Prob. Chi-Square(6) 0.1777
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 03/11/25 Time: 20:45
Sample: 1987 2022
Included observations: 36
Variable Coefficient Std. Error t-Statistic Prob.
C 0.000792 0.000177 4.477366 0.0001
D(TCEX) -1.62E-06 7.50E-06 -0.216038 0.8305
D(TCRX) -4.01E-07 1.26E-05 -0.031892 0.9748
D(INFR) -2.78E-05 1.12E-05 -2.490736 0.0187
D(INTR) 7.49E-07 1.25E-05 0.060110 0.9525
D(EXCR) -4.28E-06 7.11E-06 -0.601598 0.5521
ECT(-1) -0.001670 0.000786 -2.123533 0.0424
R-squared 0.379367 Mean dependent var 0.000708
Adjusted R-squared 0.250960 S.D. dependent var 0.001019
S.E. of regression 0.000882 Akaike info criterion -11.05693
Sum squared resid 2.25E-05 Schwarz criterion -10.74903
Log likelihood 206.0248 Hannan-Quinn criter. -10.94947
F-statistic 2.954412 Durbin-Watson stat 2.304355
Prob(F-statistic) 0.022471
7
Series: Residuals
6 Sample 1987 2022
Observations 36
5
Mean -1.54e-18
4 Median 0.001806
Maximum 0.056552
3 Minimum -0.068226
Std. Dev. 0.026979
2 Skewness -0.227432
Kurtosis 3.014590
1
Jarque-Bera 0.310671
0 Probability 0.856128
-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06
