NAME: ABDINASSER AHM
MATRIC NUMBER: 200137
LECTURER: PROF LAW S. H.
ARDL Assignment
ECN4234
Data file: ARDL BC HOC.xls
Estimate the below model using the ARDL method:
GDPt = 0 + 1 BCt + 2 HOCt +  3 Kt + 4 PGt + 5 HCt + t
Where
GDP = gross domestic product
BC = business credit
HOC = household credit
K = physical capital
PG = population growth
HC = human capital
[All datasets are in natural log]
a. Test the unit root tests
Table 1 Results of Unit Root Tests
Augmented Dickey Fuller (ADF) Test
Philip-Perron (PP) Test
Level
GDP
Constant without
trend
Constant with
Trend
Constant without
Trend
Constant with
Trend
-2.770244
-2.089077
-1.516240
-2.207672
-287.2451
-249.1804
-249.1804
-5.833511
.995740
-4.703442
HC
HOC
-3.119343
KA
Unit Root Test on D(LHC)
-4.833511 Phillips-Perron
-4.781920
-0735585
PG
Near Singular
Matrix
-148.9231
-3.263730
-8.051349
-14.21099
-6.034675
-6.718961
-6.798578
-148.9231
-148.9231
-578.8751
First Difference
GDP
-5.263137
HC
HOC
-3.119343
-6.017038
-9.718612
-9.706381
KA
-3.842697
-3.982223
-8.814971
-8.733460
PG
Near Singular
Matrix
-11.65184
-18.12822
b. Formulate the model in UECM
Model
ΔGDPt = 0 + 0GDPt-1 + 1HCt-1 + 2HOCt-1 + 3KAt-1 + 4PGt-1 + 5KAt-1 +
ΔGDPt-i+
ΔHCt-i+
ΔKAt-I+
c. Estimate the Bounds cointgration test
ΔHOCt-I+
ΔPGt-I+et
Engle-Granger Cointegration Test
Date: 01/06/22 Time: 22:33
Series: LGDP LHC LHOC LKA LPG
Sample: 2002Q4 2018Q2
Included observations: 63
Null hypothesis: Series are not cointegrated
Cointegrating equation deterministics: C
Automatic lags specification based on Akaike criterion (maxlag=10)
Dependent
LGDP
LHC
LHOC
LKA
LPG
tau-statistic
-4.455486
-3.464071
-2.437115
-3.327444
-1.652190
Prob.*
0.0789
0.3807
0.8421
0.4452
0.9777
z-statistic
23.91682
-294.5019
100.6427
-63.44635
-13.64889
Prob.*
1.0000
0.0000
1.0000
0.0000
0.7159
LGDP
-1.118319
0.250998
3.79E-06
5.95E-07
8
54
5
LHC
-0.562011
0.162240
1.35E-07
1.14E-05
5
57
5
LHOC
-0.774929
0.317970
0.008512
0.049236
8
54
5
*MacKinnon (1996) p-values.
Intermediate Results:
Rho - 1
Rho S.E.
Residual variance
Long-run residual variance
Number of lags
Number of observations
Number of stochastic trends**
**Number of stochastic trends in asymptotic distribution
LKA
-0.430105
0.129260
0.001528
0.010237
5
57
5
LPG
-0.192231
0.116349
6.04E-05
0.000108
9
53
5
Augmented Dickey-Fuller Unit Root Test on RESIDUAL
Null Hypothesis: RESIDUAL has a unit root
Exogenous: Constant
Lag Length: 8 (Automatic - based on AIC, maxlag=10)
Augmented Dickey-Fuller test statistic
Test critical values:
1% level
5% level
10% level
t-Statistic
Prob.*
-4.556261
-3.557472
-2.916566
-2.596116
0.0005
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(RESIDUAL)
Method: Least Squares
Date: 01/06/22 Time: 22:45
Sample (adjusted): 2005Q1 2018Q2
Included observations: 54 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
RESIDUAL(-1)
D(RESIDUAL(-1))
D(RESIDUAL(-2))
D(RESIDUAL(-3))
D(RESIDUAL(-4))
D(RESIDUAL(-5))
D(RESIDUAL(-6))
D(RESIDUAL(-7))
D(RESIDUAL(-8))
C
-1.195775
1.128747
0.469488
0.505581
0.682674
0.211137
0.282932
0.104719
0.389948
0.000118
0.262447
0.236464
0.243625
0.214690
0.177535
0.189454
0.166696
0.134677
0.135209
0.000271
-4.556261
4.773436
1.927095
2.354932
3.845301
1.114449
1.697292
0.777561
2.884032
0.436953
0.0000
0.0000
0.0604
0.0231
0.0004
0.2711
0.0967
0.4410
0.0061
0.6643
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
d. Estimate the long-run estimation
0.718587
0.661025
0.001985
0.000173
264.9115
12.48374
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
9.10E-06
0.003409
-9.441166
-9.072835
-9.299115
1.875634
Dependent Variable: LGDP
Method: ARDL
Date: 01/10/22 Time: 03:38
Sample (adjusted): 2003Q2 2018Q2
Included observations: 61 after adjustments
Dependent lags: 2 (Fixed)
Dynamic regressors (2 lags, fixed): LHOC LKA LPG
Fixed regressors: C @TREND
Variable
Coefficient
Std. Error
t-Statistic
LGDP(-1)
LGDP(-2)
LHOC
LHOC(-1)
LHOC(-2)
LKA
LKA(-1)
LKA(-2)
LPG
LPG(-1)
LPG(-2)
C
@TREND
0.732632
-0.385633
0.005194
0.000394
0.000510
0.006424
-0.005256
-0.015030
-3.695333
6.351692
-2.750628
1.789576
0.000818
0.125058
0.120336
0.003156
0.003688
0.003444
0.006767
0.007425
0.006426
9.116182
15.15402
6.181691
0.303643
0.000446
5.858342
-3.204637
1.645839
0.106843
0.147987
0.949404
-0.707858
-2.339109
-0.405360
0.419142
-0.444964
5.893692
1.834624
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.994655
0.993318
0.002320
0.000258
290.8019
744.3325
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Prob.*
0.0000
0.0024
0.1063
0.9154
0.8830
0.3472
0.4825
0.0235
0.6870
0.6770
0.6583
0.0000
0.0728
2.503908
0.028378
-9.108260
-8.658401
-8.931956
1.555833
*Note: p-values and any subsequent tests do not account for model
selection.
e. Estimate the short-run dynamic model
Dependent Variable: D(LGDP)
Method: Least Squares
Date: 01/10/22 Time: 03:23
Sample (adjusted): 2003Q1 2018Q2
Included observations: 62 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
D(HC)
D(HOC)
D(KA)
D(PG)
ECT(-1)
0.041352
1.21E-05
1.44E-07
-0.011302
-0.486429
0.017714
0.000338
1.40E-07
0.026443
0.104878
2.334450
0.035765
1.026600
-0.427418
-4.638039
0.0231
0.9716
0.3089
0.6707
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.310267
0.261865
0.002704
0.000417
281.2466
1.539457
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
0.001588
0.003147
-8.911181
-8.739638
-8.843829
Dependent Variable: D(LGDP)
Method: Least Squares
Date: 01/07/22 Time: 01:05
Sample (adjusted): 2003Q3 2018Q1
Included observations: 59 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
D(LGDP(1))
D(LBC)
D(LBC(-1))
D(LBC(-2))
D(LHC)
D(LHC(-1))
D(LHOC)
D(LHOC(-1))
D(LHOC(-2))
D(LKA)
D(LKA(-1))
D(LKA(-2))
D(LPG)
D(LPG(-1))
D(LPG(-2))
RESIDUAL(-1)
-1.246719
0.152906
0.001231
-0.000877
-0.001488
-713253.7
712527.9
-0.002834
8.81E-06
0.003001
0.012229
0.005115
-0.028782
72.16822
-102.1872
34.42204
-0.239305
1.982509
0.187545
0.002655
0.002653
0.002533
1142356.
1141134.
0.004073
0.003723
0.003802
0.006558
0.008061
0.007180
82.02642
116.1280
39.42392
0.154567
-0.628859
0.815302
0.463552
-0.330569
-0.587590
-0.624371
0.624403
-0.695752
0.002368
0.789431
1.864609
0.634566
-4.008469
0.879817
-0.879953
0.873126
-1.548234
0.5328
0.4195
0.6454
0.7426
0.5600
0.5358
0.5357
0.4904
0.9981
0.4343
0.0692
0.5292
0.0002
0.3840
0.3839
0.3876
0.1291
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.619875
0.475065
0.002317
0.000225
284.3001
4.280615
0.000077
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
0.001629
0.003197
-9.061022
-8.462409
-8.827348
1.390498