Descriptive Statistics
Analysis of the study begins with descriptive statists. It summarizes the large pool of data systematically. Results of the descriptive statistics are reported in Table 2. The table shows the mean, median, and standard deviation of the data and the minimum and maximum values of the chosen variables for the selected four regions (i.e., Central, Northern, Western, and Southern). The results of the Jarque-Bera test are also reported in the table. The insignificant probability value of Jarque-Bera indicates the normal distribution of the data.
Unit Root Test
Table 3 report the results of the ADF and PP unit root test, which has been applied to test the stationarity properties and order or integration of the modeled variables. Both tests are applied for two cases, i.e., with intercept and with the trend and intercept for the selected four regions. Results imply that the modeled variables of the selected four regions are integrated into the mix order, i.e., some variables are stationary at a level. In contrast, others are stationary at the first difference by rejecting the null hypothesis of non-stationary series at 5% and 1% significance levels. The Jarque-Bera values indicates the data was normalized. There was no problem of data homogeneity in the data sets for run the functions.
Table 2
Variables
|
Regions
|
Mean
|
Median
|
Maximum
|
Minimum
|
Std. Dev.
|
Jarque-Bera
|
Probability
|
WPRD
|
Central
|
8.982
|
9.0733
|
9.2944
|
8.3987
|
0.2705
|
3.9672
|
0.1375
|
Northern
|
6.138
|
6.1717
|
6.5311
|
5.3552
|
0.2632
|
1.2302
|
0.1060
|
Western
|
7.251
|
7.4100
|
7.7008
|
6.2168
|
0.4370
|
5.7897
|
0.1553
|
Southern
|
7.846
|
7.8886
|
8.2116
|
7.3479
|
0.2758
|
3.9207
|
0.1408
|
WCLA
|
Central
|
8.118
|
8.1034
|
8.2327
|
7.9986
|
0.0763
|
3.8358
|
0.1469
|
Northern
|
5.841
|
5.8318
|
6.2936
|
5.61487
|
0.1174
|
1.6564
|
0.1000
|
Western
|
6.484
|
6.5525
|
6.7175
|
6.0495
|
0.2259
|
1.3260
|
0.2422
|
Southern
|
6.969
|
6.9768
|
7.0886
|
6.8404
|
0.0677
|
1.9145
|
0.3839
|
TMEAN
|
Central
|
2.928
|
2.9326
|
2.9858
|
2.8300
|
0.0311
|
2.4372
|
0.1659
|
Northern
|
2.863
|
2.8634
|
2.9644
|
2.7715
|
0.0438
|
0.0984
|
0.9519
|
Western
|
2.908
|
2.9051
|
3.0182
|
2.8269
|
0.0389
|
1.5339
|
0.4644
|
Southern
|
2.945
|
2.9519
|
3.0470
|
2.6791
|
0.0558
|
2.3804
|
0.1000
|
TMAX
|
Central
|
3.229
|
3.2268
|
3.3099
|
3.1973
|
0.0196
|
0.5204
|
0.1000
|
Northern
|
3.229
|
3.2317
|
3.2976
|
3.1591
|
0.0333
|
1.0649
|
0.5871
|
Western
|
3.251
|
3.2498
|
3.3077
|
3.2065
|
0.0220
|
1.4243
|
0.4905
|
Southern
|
3.293
|
3.2900
|
3.3750
|
3.2381
|
0.0306
|
1.0447
|
0.5931
|
TMIN
|
Central
|
2.510
|
2.5106
|
2.5888
|
2.4150
|
0.0414
|
0.1119
|
0.9455
|
Northern
|
2.276
|
2.2950
|
2.4807
|
2.0149
|
0.1035
|
0.6620
|
0.7181
|
Western
|
2.380
|
2.3892
|
2.5700
|
2.1810
|
0.0887
|
0.2597
|
0.8782
|
Southern
|
2.416
|
2.4268
|
2.5556
|
1.9606
|
0.0979
|
194.53
|
0.1000
|
WND
|
Central
|
-0.196
|
-0.1924
|
0.3123
|
-0.8754
|
0.2699
|
1.9692
|
0.3735
|
Northern
|
-0.468
|
-0.4849
|
0.6061
|
-1.4552
|
0.4471
|
0.2946
|
0.8630
|
Western
|
0.419
|
0.4448
|
0.7143
|
-0.3298
|
0.2088
|
1.4212
|
0.3002
|
Southern
|
0.865
|
0.9162
|
2.9159
|
0.0488
|
0.4349
|
2.0952
|
0.1000
|
RNF
|
Central
|
5.320
|
5.3122
|
5.9801
|
4.39829
|
0.3585
|
2.1764
|
0.3369
|
Northern
|
5.259
|
5.2105
|
6.0665
|
4.59510
|
0.3810
|
1.8955
|
0.3879
|
Western
|
5.0712
|
5.1150
|
5.8074
|
4.25959
|
0.3892
|
2.1627
|
0.3391
|
Southern
|
3.833
|
3.7716
|
4.6011
|
2.89792
|
0.4578
|
0.8656
|
0.6486
|
TSA
|
Central
|
15.707
|
15.7114
|
15.8039
|
15.6243
|
0.0449
|
1.7378
|
0.4194
|
Northern
|
11.515
|
11.5050
|
11.6345
|
11.4520
|
0.0378
|
2.3749
|
0.1092
|
Western
|
13.579
|
13.5537
|
13.7442
|
13.4777
|
0.0711
|
2.8308
|
0.2428
|
Southern
|
14.781
|
14.7806
|
14.8215
|
14.4013
|
0.0196
|
1.0755
|
0.5840
|
TUIRA
|
Central
|
12.461
|
12.4625
|
12.6189
|
12.1952
|
0.0973
|
1.2777
|
0.5278
|
Northern
|
11.198
|
11.2056
|
11.3354
|
11.0542
|
0.0583
|
0.4246
|
0.8087
|
Western
|
11.538
|
11.5593
|
11.7598
|
11.3286
|
0.1073
|
1.7297
|
0.4210
|
Southern
|
10.089
|
10.1960
|
10.8382
|
8.47886
|
0.4665
|
1.2673
|
0.1000
|
TIRA
|
Central
|
15.669
|
15.6730
|
15.7670
|
15.5940
|
0.0410
|
1.0880
|
0.5804
|
Northern
|
10.189
|
10.2371
|
10.5178
|
9.89963
|
0.1933
|
4.3404
|
0.1141
|
Western
|
13.438
|
13.4134
|
13.6507
|
13.2970
|
0.0816
|
3.5973
|
0.1655
|
Southern
|
14.771
|
14.7712
|
14.0594
|
14.7347
|
0.0183
|
1.7930
|
0.4079
|
Table 3
|
Level
|
First difference
|
Variables
|
Regions
|
Test-statistic
|
With intercept
|
With intercept and trend
|
With intercept
|
With intercept and trend
|
|
Central
|
ADF
|
-1.3821
|
-1.8831
|
-11.1816***
|
-11.178***
|
|
Central
|
PP
|
-1.9028
|
-2.1537
|
-14.6424***
|
-19.787***
|
|
Northern
|
ADF
|
-4.8991***
|
-5.0722***
|
-9.0533***
|
-8.9689***
|
|
Northern
|
PP
|
-4.6942***
|
-5.4847***
|
-16.9609***
|
-17.702***
|
|
Western
|
ADF
|
-2.2003
|
-1.8042
|
-8.3506***
|
-8.443***
|
WPRD
|
Western
|
PP
|
-0.7274
|
-2.9834
|
-9.9271***
|
-35.154***
|
|
Southern
|
ADF
|
-0.6448
|
-2.9146
|
-12.0885***
|
-11.925***
|
|
Southern
|
PP
|
-1.0439
|
-2.1695
|
-14.6551***
|
-14.448***
|
|
Central
|
ADF
|
-1.3342
|
-2.8112
|
-5.7357***
|
-5.715***
|
|
Central
|
PP
|
-1.0887
|
-2.9223
|
-8.0292***
|
-7.835***
|
|
Northern
|
ADF
|
-4.829***
|
-5.7708***
|
-11.0077***
|
-11.052***
|
WCLA
|
Northern
|
PP
|
-5.1036***
|
-5.8781***
|
-11.6844***
|
-11.816***
|
|
Western
|
ADF
|
-2.1123
|
-0.9146
|
-5.5714***
|
-5.974***
|
|
Western
|
PP
|
-2.2293
|
-0.8026
|
-5.5546***
|
-6.9046***
|
|
Southern
|
ADF
|
-2.6999
|
-2.2231
|
-5.7208***
|
-5.5877***
|
|
Southern
|
PP
|
-2.5649
|
-2.9842
|
-14.2962***
|
-16.809***
|
|
Central
|
ADF
|
-4.4715***
|
-4.4353***
|
-9.0611***
|
-8.939***
|
|
Central
|
PP
|
-4.4768***
|
-4.4309***
|
-13.9541***
|
-13.569***
|
|
Northern
|
ADF
|
-3.3281**
|
-3.1422**
|
-11.1813***
|
-11.034***
|
|
Northern
|
PP
|
-4.2049***
|
-5.3161***
|
-13.7438***
|
-13.572***
|
|
Western
|
ADF
|
-2.0938
|
-2.2897
|
-10.8426***
|
-10.527***
|
TMEAN
|
Western
|
PP
|
-3.4751**
|
-4.2686***
|
-10.8906***
|
-10.795***
|
|
Southern
|
ADF
|
-5.3341***
|
-6.2205***
|
-7.6436***
|
-7.533***
|
|
Southern
|
PP
|
-5.5719***
|
-6.2312***
|
-34.0501***
|
-33.621***
|
|
Central
|
ADF
|
-6.6335***
|
-6.4643***
|
-10.1758***
|
-15.521***
|
|
Central
|
PP
|
-7.1764***
|
-6.9032***
|
-13.2097***
|
-12.831***
|
|
Northern
|
ADF
|
-5.8379***
|
-6.0752***
|
-10.8227***
|
-10.678***
|
|
Northern
|
PP
|
-5.8362***
|
-6.0797***
|
-20.4506***
|
-20.105***
|
TMAX
|
Western
|
ADF
|
-4.8889***
|
-4.7943***
|
-8.5256***
|
-8.411****
|
|
Western
|
PP
|
-4.9579***
|
-4.8733***
|
-8.3985***
|
-8.8453***
|
|
Southern
|
ADF
|
-4.6183***
|
-4.8283***
|
-9.7462***
|
-9.6220***
|
|
Southern
|
PP
|
-4.6892***
|
-4.9024***
|
-14.8795***
|
-14.909***
|
|
Central
|
ADF
|
-3.4796**
|
-3.4331**
|
-7.3862***
|
-7.291***
|
|
Central
|
PP
|
-3.4796**
|
-3.4331**
|
-9.5739***
|
-9.508***
|
|
Northern
|
ADF
|
-1.5835
|
-2.0912
|
-10.3672***
|
-10.239***
|
TMIN
|
Northern
|
PP
|
-2.4828
|
-2.7062
|
-10.3672***
|
-10.239***
|
|
Western
|
ADF
|
-1.4671
|
-2.1895
|
-9.6849***
|
-9.5587***
|
|
Western
|
PP
|
-2.0214
|
-1.1993
|
-9.5344***
|
-9.0036***
|
|
Southern
|
ADF
|
-5.2472***
|
-6.2952***
|
-7.3886***
|
-7.2839***
|
|
Southern
|
PP
|
-5.3694***
|
-6.2952***
|
-38.0372***
|
-37.167***
|
|
Central
|
ADF
|
-4.2225***
|
-4.5738***
|
-8.7339***
|
-8.6452***
|
|
Central
|
PP
|
-3.9923**
|
-4.3695**
|
-12.7148***
|
-12.856***
|
|
Northern
|
ADF
|
-3.8485**
|
-3.8837**
|
-8.6495***
|
-8.6730***
|
WND
|
Northern
|
PP
|
-3.8224**
|
-3.8269**
|
-12.4226***
|
-20.579***
|
|
Western
|
ADF
|
-4.8923***
|
-4.9541***
|
-6.4802***
|
-6.3181***
|
|
Western
|
PP
|
-4.7553***
|
-4.7975***
|
-19.6361***
|
-19.918***
|
|
Southern
|
ADF
|
-5.1051***
|
-5.1393***
|
-9.2076***
|
-9.3743***
|
|
Southern
|
PP
|
-5.1051***
|
-5.1393***
|
-9.2076***
|
-9.3743***
|
|
Central
|
ADF
|
-3.7502**
|
-5.1368***
|
-9.6399***
|
-9.5146***
|
|
Central
|
PP
|
-3.6505**
|
-4.1985***
|
-26.7461***
|
-26.860***
|
|
Northern
|
ADF
|
-5.3712***
|
-5.3102***
|
-10.8611***
|
-10.737***
|
RNF
|
Northern
|
PP
|
-5.4165***
|
-5.3579***
|
-20.2389***
|
-21.045***
|
|
Western
|
ADF
|
-3.5375***
|
-4.7352***
|
-9.3171***
|
-9.2266***
|
|
Western
|
PP
|
-3.4876**
|
-4.3384***
|
-12.7394***
|
-12.569***
|
|
Southern
|
ADF
|
-3.7844**
|
-3.7408**
|
-8.6499***
|
-8.5384***
|
|
Southern
|
PP
|
-4.3525***
|
-4.2877***
|
-12.9816***
|
-12.870***
|
|
Central
|
ADF
|
-2.6694
|
-2.8255
|
-5.1242***
|
-5.0578***
|
|
Central
|
PP
|
-1.9114
|
-2.1942
|
-7.0126***
|
-6.9246***
|
TSA
|
Northern
|
ADF
|
-4.0679
|
-4.0233
|
-7.5588***
|
-7.4543***
|
|
Northern
|
PP
|
-4.3744
|
-4.0027
|
-6.4767***
|
-6.2361***
|
|
Western
|
ADF
|
-2.5913
|
-2.515
|
-6.9853***
|
-6.9463***
|
|
Western
|
PP
|
-3.0655**
|
-3.0944**
|
-7.2631***
|
-7.1665***
|
|
Southern
|
ADF
|
-3.8954**
|
-4.0068***
|
-8.2606***
|
-8.1484***
|
|
Southern
|
PP
|
-3.8896**
|
-4.0176***
|
-18.726***
|
-18.118***
|
|
Central
|
ADF
|
-2.8631
|
-2.808
|
-6.4497***
|
-6.3830***
|
|
Central
|
PP
|
-2.8844
|
-2.8381
|
-6.7505***
|
-6.9261***
|
|
Northern
|
ADF
|
-3.6534**
|
-3.8456**
|
-5.3645***
|
-5.8354***
|
|
Northern
|
PP
|
-3.1291**
|
-3.2139**
|
-6.0364***
|
-5.9539***
|
TUIRA
|
Western
|
ADF
|
-3.0655**
|
-3.0944**
|
-7.2631***
|
-7.1665***
|
|
Western
|
PP
|
-3.0857**
|
-3.1314**
|
-7.2731***
|
-7.1756***
|
|
Southern
|
ADF
|
-5.9451***
|
-6.2714***
|
-7.5734***
|
-7.4691***
|
|
Southern
|
PP
|
-6.0479***
|
-6.3131***
|
-13.0831***
|
-12.905***
|
|
Central
|
ADF
|
-2.2814
|
-2.3817
|
-6.3856***
|
-6.3005***
|
|
Central
|
PP
|
-1.7344
|
-2.3743
|
-5.8475***
|
-5.0384***
|
|
Northern
|
ADF
|
-2.2837
|
-2.3091
|
-6.9684***
|
-6.8805***
|
|
Northern
|
PP
|
-2.2254
|
-2.2628
|
-6.9762***
|
-6.8874***
|
|
Western
|
ADF
|
-2.4948
|
-2.4109
|
-7.3705***
|
-7.2404***
|
TIRA
|
Western
|
PP
|
-2.4623
|
-2.3767
|
-7.1105***
|
-7.2385***
|
|
Southern
|
ADF
|
-4.0873***
|
-4.1744***
|
-8.6293***
|
-8.5143***
|
|
Southern
|
PP
|
-4.0373***
|
-4.1449***
|
-21.3582***
|
-21.336***
|
Diagnostic Tests
Time series data usually suffer from auto/serial correlation, heteroscedasticity, the problem of multicollinearity, and the problem of model misspecification, which, if not detected, provide indefinite results. The study, therefore, applies some diagnostic tests to detect these problems for the case of selected regions. The study applies Breusch-Godfrey Serial Correlation to detect serial correlation, Breusch-Pagan-Godfry HSK is applied to test the problem of heteroscedasticity, and Ramsey Reset test is applied to check the model’s specification. The results of Breusch-Godfrey Serial Correlation, Breusch-Pagan-Godfry HSK, Ramsey Reset test and correlation are reported in Table 4. The insignificant p-values of Breusch-Godfrey Serial Correlation and Breusch-Pagan-Godfry HSK (see Table 4) indicate that the problem of serial correlation and heteroscedasticity does not exist in our proposed models. The insignificant p-values of the Ramsey Reset test (see Table 4) indicate that the proposed models of the study are correctly specified. Results of Table 4 show that the problem of multicollinearity does not exist in the data because all coefficient values of correlation among the modeled variables are less than 0.5.
Table 4
Correlation matrix analysis
Panel A: Central
|
|
WPRD
|
WNDS
|
WCLA
|
TUIRA
|
TSA
|
TMIX
|
TMEAN
|
TMAX
|
RNF
|
TIRA
|
WPRD
|
1
|
|
|
|
|
|
|
|
|
|
WNDS
|
0.328
|
1
|
|
|
|
|
|
|
|
|
WCLA
|
0.196
|
0.356
|
1
|
|
|
|
|
|
|
|
TUIRA
|
-0.17
|
-0.057
|
-0.193
|
1
|
|
|
|
|
|
|
TSA
|
-0.25
|
-0.173
|
-0.292
|
0.751
|
1
|
|
|
|
|
|
TMIX
|
-0.26
|
-0.106
|
-0.324
|
0.107
|
0.079
|
1
|
|
|
|
|
TMEAN
|
0.13
|
0.029
|
-0.030
|
0.071
|
0.091
|
0.239
|
1
|
|
|
|
TMAX
|
-0.19
|
-0.381
|
-0.206
|
0.198
|
0.341
|
0.284
|
0.201
|
1
|
|
|
RNF
|
-0.13
|
-0.101
|
-0.587
|
0.207
|
0.362
|
-0.057
|
-0.164
|
-0.176
|
1
|
|
TIRA
|
-0.22
|
-0.150
|
-0.264
|
0.255
|
0.985
|
0.069
|
0.096
|
0.313
|
0.387
|
1
|
Panel B: Northern
|
|
WPRD
|
WNDS
|
WCLA
|
TUIRA
|
TSA
|
TMIX
|
TMEAN
|
TMAX
|
RNF
|
TIRA
|
WPRD
|
1
|
|
|
|
|
|
|
|
|
|
WND
|
-0.098
|
1
|
|
|
|
|
|
|
|
|
WCLA
|
0.329
|
0.167
|
1
|
|
|
|
|
|
|
|
TSA
|
0.031
|
-0.156
|
0.032
|
1
|
|
|
|
|
|
|
TUIRA
|
-0.105
|
-0.030
|
0.046
|
0.191
|
1
|
|
|
|
|
|
TMIN
|
0.129
|
-0.051
|
-0.361
|
-0.182
|
0.050
|
1
|
|
|
|
|
TMEAN
|
0.205
|
-0.008
|
-0.283
|
-0.354
|
-0.19
|
0.160
|
1
|
|
|
|
TMAX
|
0.223
|
0.049
|
-0.084
|
-0.421
|
-0.48
|
0.383
|
0.199
|
1
|
|
|
TIRA
|
0.104
|
-0.113
|
-0.015
|
0.480
|
-0.38
|
-0.224
|
-0.107
|
0.088
|
1
|
|
RNF
|
-0.095
|
-0.082
|
-0.093
|
0.285
|
0.446
|
0.095
|
-0.211
|
-0.296
|
-0.150
|
1
|
Panel C: Western
|
|
WPRD
|
WNDS
|
WCLA
|
TUIRA
|
TSA
|
TMIX
|
TMEAN
|
TMAX
|
RNF
|
TIRA
|
WPRD
|
1
|
|
|
|
|
|
|
|
|
|
WND
|
-0.204
|
1
|
|
|
|
|
|
|
|
|
WCLA
|
0.163
|
-0.165
|
1
|
|
|
|
|
|
|
|
TSA
|
-0.103
|
-0.119
|
-0.118
|
1
|
|
|
|
|
|
|
TUIRA
|
0.127
|
-0.116
|
0.203
|
0.128
|
1
|
|
|
|
|
|
TMIN
|
0.755
|
-0.332
|
0.254
|
0.113
|
-0.06
|
1
|
|
|
|
|
TMEAN
|
0.211
|
-0.335
|
0.119
|
0.104
|
-0.14
|
0.814
|
1
|
|
|
|
TMAX
|
0.126
|
-0.162
|
0.171
|
0.255
|
-0.16
|
0.367
|
0.720
|
1
|
|
|
TIRA
|
0.143
|
-0.094
|
0.227
|
-0.074
|
0.27
|
-0.088
|
-0.165
|
-0.214
|
1
|
|
RNF
|
-0.218
|
0.103
|
-0.491
|
0.295
|
0.25
|
-0.310
|
-0.386
|
-0.155
|
0.161
|
1
|
Panel D: Southern
|
|
WPRD
|
WNDS
|
WCLA
|
TUIRA
|
TSA
|
TMIX
|
TMEAN
|
TMAX
|
RNF
|
TIRA
|
WPRD
|
1
|
|
|
|
|
|
|
|
|
|
WND
|
0.199
|
1
|
|
|
|
|
|
|
|
|
WCLA
|
0.164
|
0.244
|
1
|
|
|
|
|
|
|
|
TSA
|
-0.199
|
-0.086
|
-0.129
|
1
|
|
|
|
|
|
|
TUIRA
|
0.258
|
0.326
|
0.306
|
-0.008
|
1
|
|
|
|
|
|
TMIN
|
-0.146
|
0.145
|
-0.001
|
0.190
|
0.113
|
1
|
|
|
|
|
TMEAN
|
0.183
|
0.331
|
0.223
|
0.088
|
0.213
|
-0.027
|
1
|
|
|
|
TMAX
|
-0.141
|
0.168
|
0.003
|
0.348
|
0.117
|
0.285
|
-0.043
|
1
|
|
|
TIRA
|
-0.035
|
-0.039
|
-0.028
|
-0.077
|
-0.01
|
0.240
|
-0.353
|
0.280
|
1
|
|
RNF
|
0.262
|
0.298
|
0.299
|
-0.113
|
0.947
|
0.123
|
0.325
|
0.144
|
0.184
|
1
|
Diagnostic Test
|
|
Region
|
Test statistic
|
Probability
|
Breusch-Pagan-Godfrey
|
Central
|
2.8724
|
0.1963
|
Northern
|
1.3874
|
0.2048
|
Western
|
1.9937
|
0.1964
|
Southern
|
2.0362
|
0.1835
|
Breusch-Godfrey Serial Correlation LM Test
|
Central
|
2.0364
|
0.1355
|
Northern
|
0.2554
|
0.3555
|
Western
|
1.3874
|
0.1947
|
Southern
|
2.3875
|
0.3846
|
Ramsey Reset Test
|
Central
|
1.7354
|
0.1874
|
Northern
|
1.8355
|
0.1635
|
Western
|
1.2684
|
0.1774
|
Southern
|
1.3854
|
0.1964
|
Bounds Cointegration Test
The present study applies the ARDL approach to estimate the empirical results of the study. The first step of ARDL is to test the cointegrating relation between the selected variables of the study through the bounds cointegration test. The bound test is a pre-condition of applying ARDL, which tells that either the chosen variables of the study are moving together in the long run or not.
Table 5
Bounds Co-integration Test
Region
|
K
|
F. Statistics
|
Central Punjab
|
9
|
5.7344
|
Northern Punjab
|
9
|
7.9767
|
Western Punjab
|
9
|
4.3644
|
Southern Punjab
|
9
|
7.5143
|
Significance
|
Lower Bound
|
Upper Bound
|
10%
|
2.05
|
3.02
|
5%
|
2.30
|
3.33
|
1%
|
2.79
|
3.93
|
The bound test is having the null hypothesis of “no-cointegration.” The rejection of this hypothesis indicates the cointegrating relation among the modeled variables. The results of the bounds cointegration tests are reported in Table 5. The table shows that the value of F statistics is greater than the upper bound at the significance level of 10%, 5%, and 1% for the selected regions. So here, it is concluded that cointegration exists among the chosen variables and all the variables move together in the long run.
Short-run Effects Of Climate On Wheat
The results of the short run for the selected four regions in models 1–4 respectively are reported in Table 6. Results depict that in model 1, the value of ECM is -0.6845, which is negative and highly significant at the level of 1%. This shows that 68.45% of inconsistency between the long-term and short-term wheat production of the central region is corrected within a year, while the value of ECM is -0.7454 in model 2. The ECM term indicates that 74.54% of inconsistency between the long-term and short-term wheat production of the Northern region is corrected within a year at a 1% level of significance. The value of ECM in model 3 is -0.7767, which is also significant at the level of 1%. The result shows that the speed of adjustment between the short and long-run wheat production for the Western region is 77.67%. However, this value is -0.6967 in model 4, depicting that the speed of adjustment is 69.67% for the case of the Southern region.
Long Run Effects Of Climate On Wheat
Brief model descriptions
The long-run results of models 1,2,3 and 4 are presented in Table 7. Before moving towards a detailed explanation of the long-run results, this study provides a brief description of the table and its models for the readers so that they can easily understand the results. Table 7 is comprised of four models. Model 1 report the long-run coefficients of the central region, model 2 present the results of Northern region, model 3 and 4 exhibits the long-run coefficients of Western and Southern region, respectively. However, the visual representation of the proposed relationship among the modeled variables is presented in Figs. 1A, 1B, 1C, and 1D for Central, Northern, Western, and Southern regions, respectively.
Table 6
DV: WPRD
|
Models/Regions
|
Independent Variables
|
Model 1: Central
|
Model 2: Northern
|
Model 3: Western
|
Model 4: Southern
|
WPRD(-1)
|
-0.8473***
(0.0259)
|
0.1311
(0.3817)
|
0.0318
(0.8794)
|
-0.1659
(0.2856)
|
WCLA
|
2.1061***
(0.0074)
|
2.4179***
(0.0000)
|
1.4597***
(0.0012)
|
0.7449**
(0.0212)
|
WCLA (-1)
|
-1.2662**
(0.0416)
|
-1.1998**
(0.0218)
|
0.3757
(0.3474)
|
-0.1907
(0.5678)
|
WCLA (-2)
|
-1.1967
(0.1823)
|
0.8562***
(0.0091)
|
0.3355
(0.2341)
|
0.6877***
(0.0137)
|
TMEAN
|
0.4441
(0.6062)
|
-4.0384**
(0.0481)
|
0.9647**
(0.0279)
|
-0.4416
(0.7847)
|
TMEAN (-1)
|
1.5137*
(0.088)
|
-2.3465**
(0.0375)
|
0.8743
(0.2532)
|
-1.1645
(0.6355)
|
TMEAN (-2)
|
-2.0796***
(0.0073)
|
-3.3564*
(0.0765)
|
0.6237
(0.3542)
|
-1.0354
(0.4766)
|
TMAX
|
7.24843***
(0.006)
|
4.8313
(0.4985)
|
0.6163
(0.5924)
|
0.1313
(0.4362)
|
TMAX (-1)
|
2.5985***
(0.0036)
|
4.25384
(0.2433)
|
-0.0608
(0.9146)
|
0.4047
(0.1656)
|
TMAX (-2)
|
2.3746**
(0.0354)
|
3.8357
(0.1733)
|
2.4804***
(0.0015)
|
1.1227
(0.7634)
|
TMIN
|
-1.5507**
(0.0309)
|
2.6707
(0.6402)
|
-0.4165**
(0.0221)
|
0.4696**
(0.0414)
|
TMIN (-1)
|
-1.4755**
(0.0353)
|
2.4573
(0.5244)
|
-0.3754
(0.1874)
|
0.8068
(0.1874)
|
TMIN (-2)
|
-1.3758
(0.3733)
|
1.9476
(0.3584)
|
-0.2863
(0.1753)
|
0.74555
(0.2744)
|
WND
|
0.0726**
(0.0598)
|
-0.2781***
(0.0009)
|
0.0558
(0.3995)
|
-0.0637*
(0.0702)
|
WND (-1)
|
0.05674
(0.2654)
|
-0.1424*
(0.0846)
|
0.0595*
(0.0808)
|
-0.0622*
(0.0781)
|
WND (-2)
|
0.0352
(0.1654)
|
-0.12844**
(0.0364)
|
0.0887**
(0.0456)
|
-0.04653**
(0.0274)
|
RNF
|
0.2300***
(0.0299)
|
0.1885**
(0.0346)
|
0.0974
(0.4567)
|
-0.0761*
(0.0647)
|
RNF (-1)
|
0.3243***
(0.0079)
|
0.1104
(0.1571)
|
0.0351
(0.2534)
|
-0.06418***
(0.0092)
|
RNF (-2)
|
0.2725
(0.2656)
|
0.0873
(0.1446)
|
0.0223*
(0.0645)
|
-0.03455
(0.8734)
|
TSA
|
1.4948
(0.5269)
|
2.4387
(0.7472)
|
-2.9631***
(0.0315)
|
0.5023
(0.4703)
|
TSA (-1)
|
1.39835*
(0.0745)
|
2.0624*
(0.0799)
|
-2.48391
(0.0364) ***
|
7.7270*
(0.0723)
|
TSA (-2)
|
1.2036)
(0.0365)
|
2.2764**
(0.0284)
|
-3.81934***
(0.0153)
|
5.7645
(0.9622)
|
TUIRA
|
-0.29484
(0.284)
|
-1.3662
(0.8047)
|
4.3065**
(0.0344)
|
-0.0535
(0.6304)
|
TUIRA (-1)
|
-0.3771
(0.1578)
|
-10.9396
(0.1106)
|
4.2922***
(0.0418)
|
-0.15471
(0.1884)
|
TUIRA (-2)
|
-0.32078
(0.1796)
|
-1.7583*
(0.0932)
|
2.8735***
(0.0344)
|
-0.13434*
(0.0745)
|
TIRA
|
-0.6092*
(0.0825)
|
-1.2046
(0.5508)
|
2.0818***
(0.034)
|
0.7726***
(0.0007)
|
TIRA (-1)
|
-4.31381
(0.4544)
|
-3.6737**
(0.03762)
|
2.9878***
(0.0377)
|
-9.1978
(0.9417)
|
TIRA (-2)
|
-0.84789
(0.2764)
|
-2.3467
(0.1344)
|
3.5857***
(0.0010)
|
-7.3645
(0.6455)
|
ECM
|
-0.6845***
(0.0000)
|
-0.7454***
(0.0000)
|
-0.7767***
(0.0000)
|
-0.6967***
(0.0000)
|
Constant
|
3.3344**
(0.0354)
|
4.3655**
(0.0337)
|
2.3645***
(0.0264)
|
4.47566**
(0.0265)
|
Coefficient Interpretations
Wheat cultivated area
The coefficient of WCLA in model 1 is 0.4545, which is significant at the level of 10% (i.e., p-value = 0.0734). Result reveals the positive relationship between WCLA and WPRD in the long run and implies that a 1-unit increase in WLCA will increase 0.4545 units of WPRD for the central region. The coefficient of WCLA in model 2 (1.3875) is significant at the level of 1% (i.e., p-value = 0.0005) and reveals the positive affiliation between WCLA and WPRD. The result indicates that a 1-unit increase in WCLA tends to increase 1.3875 units of WPRD in the long run for the case northern region. The coefficient of WCLA in model 3 (1.8951) and model 4 (1.0652) is also significant at the level of 1 % (i.e., p-value = 0.0000 and 0.0094, respectively). Result states that in the long run, a 1-unit increase in WCLA will increase 1.8951 units of WPRD in the western region while 1.0652 units of WPRD in the southern region. The overall results suggest the positive impact of WCLA on WPRD in the long run, and thus, (H1) is supported for all the selected regions.
Mean temperature
In model 1, the coefficient of TMEAN is negative and significant at the level of 5% (i.e., β=-1.0653; p-value = 0.0255), which shows the negative relationship between TMEAN and WPRD. The result indicates that a 1-unit increase in TMEAN will reduce 1.0653 units of WPRD for the case Central region in the long run. The coefficient of TMEAN in model 2 (-1.1583) is also negative and significant at the level of 1%. The result implies that a 1-unit increase in TMEAN will reduce 1.1583 units of WPRD for the case of the northern region. The coefficient of TMEAN in model 3 (-0.9964) also reveals the negative long-run impact of TMEAN on WPRD at 5% significant level (i.e., p-value = 0.0341). Result states that a 1-unit of increase in TMEAN will reduce 0.9964 units of WPRD for the case of the Western region.
Similarly, in the southern region, there also exists a negative relationship between TMEAN and WPRD. The result shows that a 1-unit increase in TMEAN will result from a decrease of 1.3776 units in WPRD in the long run. The overall results suggest the positive impact of TMEAN on WPRD in the long run, and thus, (H2) is supported for all the selected regions.
Maximum temperature
The coefficient of TMAX in model 1 (-3.3287) reveals the significant and negative association between TMAX and WPRD at the level of 1% (i.e., p-value = 0.0006). The result portrays that a 1-unit increase in TMAX will reduce 3.3287 units of WPRD for the case of the Central region. While, in model 2, the coefficient of TMAX (1.0711) is insignificant, depicting no long-run relationship between TMAX and WPRD for the case of the northern region. In models 3 and 4, the coefficient of TMAX is -3.1324 and − 1.4222, respectively. The result shows that in the long run, a 1-unit increase in TMAX will reduce 3.1324 units of WPRD in the western region, while 1.4222 units of WPRD in the southern region. The overall result indicates the negative role of TMAX on WPRD for the case of the Central, Western and Southern regions. Hence, (H3) is rejected for the case of the Northern region.
Minimum temperature
The coefficient of TMIN is negative and significant at level of 5% in model 1 (β=-1.8413, p-value = 0.0359), at the level of 1% in model 2 (β=-2.0740, p-value = 0.0045) and at the level of 10% in model 4 (β=-1.0949, p-value = 0.078). the result reveals the negative long-run impact of TMIN on WPRD. The result implies that a 1-unit increase in TMIN will reduce 1.8413 units of WPRD in the Central region, while 2.0740 and 1.0949 units of WPRD in the western and southern regions, respectively. On the contrary, in the Northern region, the coefficient of TMIN (-2.0740) is insignificant and reveals no LR association between TMIN and WPRD for the Western region. The overall result portrays the negative impact of TMIN on WPRD for the Central, Northern and Southern regions. Therefore, (H4) is rejected for the case of the Western region.
Wind speed
The coefficient of WND in model 1 is -0.2176, which is significant at the level of 5% (i.e., p-value = 0.0269). The result portrays the negative effect of WND on WPRD in the long run. Findings indicated that a 1-unit increase in WND would reduce 0.2176 units of WPRD for the central region. However, in model 2, the coefficient of WND (1.4849) is significant, which shows that WND does not have any significant effects on WPRD for the case of the Northern region. While, in models 3, and 4 WND has a significant negative impact on WPRD in the long run. The result depicts that 1-unit of increase in WND brings − 0.2109 units of reduction in WPRD for the case of the Western region, while − 0.1085 units of reduction in Southern region at the level of 10% and 1% respectively. The overall results support (H5) for the case of the Central, Western and Southern regions.
Rainfall
The coefficient of RNF is insignificant in model 1 (i.e., β = 0.3000, p-value = 0.1254), and model 3 (β = 0.1363, p-value = 0.4548), which depicts that in the long run, any change in RNF brings no change in WPRD for the case of Central and Western region. On the contrary, the coefficient of RNF is significant at the level of 5% in model 2 (i.e., β=-0.3441, p-value = 0.0366), and at the level of 1% in model 4 (i.e., β=-0.1205, p-value = 0.0078). The negative sign with the coefficient depicts the negative effects of RNF on WPRD in the long run. However, the result portrays that 1-unit of increase in RNF brings about 0.3441 units of decrease in WPRD for the case of Northern region, while 0.1205 units of decrease in WPRD for the case of Southern region. Hence, (H6) is accepted for the case of the Central and Southern region only.
Total sown area
The coefficient of TSA is positive and significant at the level of 5% in model 1 (i.e., β = 1.0809, p-value = 0.045) and model 4 (i.e., β = 1.9664, p-value = 3.0664) and at the level of 1% in model 2 (i.e., β = 2.6908, p-value = 0.0034) and model 3 (i.e., β = 2.5443, p-value = 0.0068). The result indicates the positive impact of TSA on WPRD in the long run. The result further indicated that a 1-unit of increase in TSA would increase 1.0809, 2.6908, 2.5443, and 1.9664 units of WPRD for the case of Central, Northern, Western, and Southern region respectively. Results supported (H7) for the selected four regions. Figure 4A-4D indicates the visual expressions of the all relationships.
Total un-irrigated area
The coefficient of TUIRA is also significant and positive in model 1 – model 4, which reveals the positive long-run impact of TUIRA on WPRD. The result indicates that a 1-unit increase in TUIRA brings 1.9333 units of increase in WPRD for the case of the central region, while 2.1873, 2.8813, and 2.1784 units of increase for the case of Northern, western, and Southern region, respectively. (H8) is also supported for the selected four regions.
Total irrigated area
The coefficient of TIRA is 2.645, 2.6149, 2.3174, and 1.8034 in models 1,2,3, and 4 respectively. The positive sign and the significant p-values (i.e., 0.0041, 0.02463, 0.0071, and 0.0274, respectively) depict a positive association between TIRA and WPRD in the long run. The result portrays that 1-unit of increase in TIRA will increase 2.645 units of WPRD in the central region, 2.6149 units of WPRD in the northern region, while 2.3174 and 1.8034 units of WPRD in the Western and Southern region. The results supported (H9) for the case of selected four regions
Table 7
DV: WPRD
|
Models/Regions
|
Independent Variables
|
Model 1: Central
|
Model 2: Northern
|
Model 3: Western
|
Model 4: Southern
|
WCLA
|
0.4545*
(0.0734)
|
1.3875***
(0.0005)
|
1.8951***
(0.0000)
|
1.0652***
(0.0094)
|
TMEAN
|
-1.0653**
(0.0255)
|
-1.1583***
(0.0017)
|
-0.9964**
(0.0341)
|
-1.3776**
(0.0272)
|
TMAX
|
-3.3287***
(0.0006)
|
1.0711
(0.1244)
|
-3.1324***
(0.0379)
|
-1.4222**
(0.0281)
|
TMIN
|
-1.8413**
(0.0359)
|
-2.0740***
(0.0045)
|
-0.4301
(0.2228)
|
-1.0949*
(0.078)
|
WND
|
-0.2176**
(0.0269)
|
1.4849
(0.7354)
|
-0.2109*
(0.093)
|
-0.1085**
(0.0268)
|
RNF
|
0.3000
(0.1254)
|
-0.3441**
(0.0366)
|
0.1363
(0.4548)
|
-0.1205***
(0.0078)
|
TSA
|
1.0809**
(0.045)
|
2.6908***
(0.0034)
|
2.5443***
(0.0068)
|
1.9664**
(0.0392)
|
TUIRA
|
1.9333***
(0.0095)
|
2.1873*
(0.0934)
|
2.8813***
(0.008)
|
2.1784**
(0.0353)
|
TIRA
|
2.6645***
(0.0041)
|
2.6149**
(0.0243)
|
2.3174***
(0.0071)
|
1.8034**
(0.0276)
|
R-Square
|
0.8645
|
0.7983
|
0.7672
|
0.8745
|
Adjusted R-Square
|
0.7784
|
0.6973
|
0.6757
|
0.7653
|
Adjusted R-square
The value of the adjusted R-square of model 1 shows that 77.84% variations in WPRD are collectively explained by all the independent variables for the case of the Central region. In contrast, in model 2, the value of adjusted R-square showed that in the Northern region, all the independent variables are explained 69.73% variations in WPRD. On the contrary, these variations ate 67.57% for the case of the Western region (see model 3) and 76.53% for the case of the Southern region (see model 4). Figure 4 indicates the Visual representation of the relationship between dependent and independent variable in various regions of Punjab.
4.7. Model Stability
The present study tests the stability of models for selected four regions by applying the CUSUM and CUSUM of the square test, suggested by Brown et al. (1975). Results are presented in Fig. 5A-5D (for the CUSUM test) and Fig. 6A-6D (for the CUSUM square test). Result reveals that the models for the present study are stable correctly specified as all the plots remain in the critical bounds.