Table 2 reports the outcomes of unit root tests. To confirm the stationarity properties of data, the study has employed structural break unit root tests and without structural break unit root tests. Both test results confirm that all the variables are stationary at their first difference except government size that is stationary at level. However, none of the variables is stationary at the second difference. Table 3 reports the findings of the BDS test. BDS test confirms the non-linearity in CO2 emissions, government size, and country size.
Table 2: Unit root testing
|
Unit root without structural break
|
Unit root with structural break
|
|
I(0)
|
I(1)
|
Decision
|
I(0)
|
Break date
|
I(1)
|
Break date
|
Decision
|
CO2
|
-1.521
|
-4.406***
|
I(1)
|
-3.347
|
2001
|
-5.387***
|
2013
|
I(1)
|
CSIZE
|
-1.739
|
-4.272***
|
I(1)
|
-1.565
|
1990
|
-4.967***
|
1990
|
I(1)
|
Gsize
|
-2.608*
|
|
I(0)
|
-4.692*
|
1996
|
|
|
I(0)
|
Trade
|
-1.621
|
-5.052***
|
I(1)
|
-2.354
|
1990
|
-6.675***
|
2009
|
I(1)
|
EC
|
-0.312
|
-4.775***
|
I(1)
|
-3.456
|
2002
|
-6.489***
|
2015
|
I(1)
|
Note: *** p<0.01, ** p<0.05, * p<0.1, respectively.
Table 3: BDS test
|
CO2
|
|
|
Csize
|
|
|
Gsize
|
|
|
Dimension
|
BDS Stat
|
S.E
|
z-Stat
|
BDS Stat
|
S.E
|
z-Stat
|
BDS Stat
|
S.E
|
z-Stat
|
2
|
0.196***
|
0.006
|
32.58
|
0.199***
|
0.006
|
33.40
|
0.135***
|
0.007
|
19.80
|
3
|
0.329***
|
0.010
|
33.95
|
0.334***
|
0.010
|
34.80
|
0.214***
|
0.011
|
19.51
|
4
|
0.420***
|
0.012
|
35.99
|
0.428***
|
0.012
|
36.91
|
0.260***
|
0.013
|
19.78
|
5
|
0.482***
|
0.012
|
39.12
|
0.494***
|
0.012
|
40.42
|
0.277***
|
0.014
|
20.01
|
6
|
0.525***
|
0.012
|
43.69
|
0.542***
|
0.012
|
45.37
|
0.284***
|
0.013
|
21.06
|
Note: *** p<0.01, ** p<0.05, * p<0.1, respectively.
The study makes an effort to investigate the effect of government size and country size on carbon emissions in the case of China. The study has executed both symmetric and asymmetric effects by employing ARDL and NARDL estimation techniques. Table 4 reports the outcomes of short-run and long-run relationships along with the findings of other diagnostic tests for both regressions. The long-run coefficient estimates of ARDL demonstrate that government size exerts a significant and negative impact on pollution emissions which states that 1 percent increase in government size results in decreasing pollution emissions in China by 0.041 percent. However, country size, trade, and energy consumption result in significantly increasing pollution emissions in the long-run. The coefficient estimates show that a 1 percent increase in country size, trade, and energy consumption leads to increase pollution emissions by 0.281, 0.007, and 0.715 percent, respectively. The short-run findings of ARDL demonstrate that government size has a significant and negative effect on pollution emission, but, country size and trade have a significant and negative effect on pollution emissions. However, energy consumption has no effect on pollution emissions in the short run as the associated coefficient estimate is statistically insignificant.
The findings of necessary diagnostic tests for ARDL suggest that F-stat is statistically significant that is confirming the presence of cointegration among variables. The coefficient estimate of ECM is also significant and negative confirming that about 45 percent convergence towards equilibrium takes place in a year in China. The coefficient estimates of LM test and BPG confirms the absence of serial correlation and heteroskedasticity. The findings of Ramsey RESET test also confirm the correct specification of the model. CUSUM test confirms the stability of model; however, according to CUSUMsq test the model is unstable as denoted by “US”.
Table 4: ARDL and NARDL estimates
|
ARDL
|
|
|
|
|
|
NARDL
|
|
|
|
Variable
|
Coefficient
|
S.E
|
t-Stat
|
Prob.
|
|
Variable
|
Coefficient
|
S.E
|
t-Stat
|
Prob.
|
Short-run
|
|
|
|
|
|
Short-run
|
|
|
|
|
D(GSIZE)
|
-0.019**
|
0.008
|
2.439
|
0.021
|
|
D(GSIZE_POS)
|
0.007
|
0.012
|
0.604
|
0.551
|
D(CSIZE)
|
0.540**
|
0.227
|
2.379
|
0.024
|
|
D(GSIZE_NEG)
|
-0.089***
|
0.027
|
3.242
|
0.003
|
D(TRADE)
|
0.007***
|
0.002
|
3.755
|
0.001
|
|
D(CSIZE_POS)
|
0.902***
|
0.261
|
3.450
|
0.002
|
D(TRADE(-1))
|
-0.004**
|
0.002
|
2.313
|
0.028
|
|
D(CSIZE_POS(-1))
|
0.324
|
0.283
|
1.142
|
0.262
|
D(EC)
|
0.015
|
0.142
|
0.103
|
0.919
|
|
D(CSIZE_NEG)
|
0.019
|
1.196
|
0.016
|
0.987
|
D(EC(-1))
|
-0.550***
|
0.186
|
2.952
|
0.006
|
|
D(TRADE)
|
0.001
|
0.002
|
0.361
|
0.721
|
D(EC(-2))
|
0.696***
|
0.19
|
3.658
|
0.001
|
|
D(EC)
|
0.254*
|
0.133
|
1.915
|
0.065
|
D(EC(-3))
|
-0.365***
|
0.161
|
2.266
|
0.031
|
|
D(EC(-1))
|
-0.488**
|
0.189
|
2.574
|
0.015
|
Long-run
|
|
|
|
D(EC(-2))
|
0.284*
|
0.151
|
1.877
|
0.07
|
GSIZE
|
-0.041**
|
0.017
|
2.403
|
0.022
|
|
Long-run
|
|
|
|
|
CSIZE
|
0.281***
|
0.086
|
3.26
|
0.003
|
|
GSIZE_POS
|
0.013
|
0.021
|
0.615
|
0.543
|
TRADE
|
0.007**
|
0.003
|
2.437
|
0.021
|
|
GSIZE_NEG
|
-0.159***
|
0.037
|
4.234
|
0.000
|
EC
|
0.715***
|
0.14
|
5.096
|
0.000
|
|
CSIZE_POS
|
-0.171*
|
0.093
|
1.838
|
0.074
|
C
|
8.460***
|
0.535
|
15.82
|
0.000
|
|
CSIZE_NEG
|
0.034
|
2.134
|
0.016
|
0.987
|
Diagnostic
|
|
|
|
|
|
TRADE
|
-0.004**
|
0.002
|
2.000
|
0.045
|
F-test
|
4.433***
|
|
|
|
|
EC
|
0.998***
|
0.138
|
7.255
|
0.000
|
ECM(-1)
|
-0.455***
|
0.102
|
-4.439
|
0.000
|
|
C
|
7.606***
|
0.858
|
8.861
|
0.000
|
LM
|
0.175
|
|
|
|
|
Diagnostic
|
|
|
|
|
BGP
|
1.169
|
|
|
|
|
F-test
|
11.91***
|
|
|
|
RESET
|
0.332
|
|
|
|
|
ECM(-1)
|
-0.561***
|
0.137
|
-4.088
|
0.000
|
CUSUM
|
S
|
|
|
|
|
LM
|
0.445
|
|
|
|
CUSUMsq
|
US
|
|
|
|
|
BGP
|
1.203
|
|
|
|
|
|
|
|
|
|
RESET
|
0.948
|
|
|
|
|
|
|
|
|
|
CUSUM
|
S
|
|
|
|
|
|
|
|
|
|
CUSUMsq
|
S
|
|
|
|
|
|
|
|
|
|
Gsize-LR
|
7.764***
|
|
|
|
|
|
|
|
|
|
Gsize-SR
|
1.235
|
|
|
|
|
|
|
|
|
|
Csize-LR
|
0.009
|
|
|
|
|
|
|
|
|
|
Csize-SR
|
3.565*
|
|
|
|
Note: *** p<0.01, ** p<0.05, * p<0.1, respectively.
The long-run coefficient estimates of asymmetric effects of government size and country size on carbon emissions in China have been derived from NARDL estimation technique. The long-run findings of government size show that positive shock of government size does not have a significant effect on pollution emissions. However, the negative shock of government size has a significant and negative effect on pollution emissions in the long run. The coefficient estimate infers that 1 percent increase in government size tends to decrease pollution emission by 0.159 percent. In the case of country size, the positive shock of country size in the long-run results in decreasing pollution emission significantly, however, the negative shock of country size has no effect on pollution emission as the coefficient value of a variable is statistically insignificant. The 1 percent increase in positive shock of country size leads to reducing pollution emissions by 0.171 percent in the long-run.
This finding is also consistent with Ullah et al. (2020), who noted that government size is matter in carbon emissions. This finding infers that a large size of government promotes economic growth with greater usage of energy consumption, hence increased environmental pollution. While the small size of government has a negative impact on carbon emissions. This finding is inconsistent with Ullah et al. (2020), who reported that positive shock of economic size also positively affects environmental pollution. They also noted that most of the developing countries increase the economic size by affecting the environment quality; therefore, economic size has a positive significant factor in environmental pollution. This finding is inconsistent with Meadows et al. (1972), who argue that large size of economies uses larger inputs of materials and energy uses, adverse they generate larger quantities of waste and produce more environmental pollution. A positive change in country size is statistically negative significant on environmental pollution in China and implies that China is used advanced technologies for green productivity and environmental sustainability. This also means that the China economy increases the environmental quality by using the green GDP. From the supply side, the large size of the economy is consumed more clean energy in the industrial sector as well as the transport sector. This is also a basic source of environmental quality in large economies. Another possible reason is that the large size of the economy is mostly producing clean production. On the demand side, consumer of large economies has more incomes and spends on clean and green economic activities, and positively affect on environmental pollution. This means that China is producing less environmental pollution due to income and technology innovation. Large economies are mostly doing energy-efficient production with also mitigates environmental pollution.
In the long-run, an increase in trade results in reducing pollution emissions as due to 1 percent increase in trade the pollution emissions significantly reduced by 0.004 percent. But, the energy consumption effect on pollution emissions is significant and positive in the long-run. The value of coefficient estimates of energy consumption infers that in response to 1 percent increase in energy consumption pollution emission increases by 0.998 percent. The short-run findings of NARDL infer that positive shock of government size does not exert a significant impact on pollution emissions, however, the negative shock of pollution emissions results in significantly reducing pollution emissions in China. The positive shock of country size has a positive and significant impact on pollution emissions; however, the negative shock of country size does not exert any impact on pollution emissions due to insignificant value of coefficient estimate. Among control variables, trade variable has no impact on pollution emissions in the short-run. However, energy consumption's impact on pollution emissions is significant and positive.
To confirm the findings of NARDL estimates the study has performed various diagnostic tests. The coefficient estimate of F-statistics is statistically significant and endorses the existence of cointegrating relationship among variables of the model. The coefficient estimate of the error correction term is also significant and negative confirming that the speed of adjustment towards achieving stability is about 56 percent in a year in China. The coefficient estimates of LM test and BPG also confirms the absence of serial correlation and heteroskedasticity in the model. The result of Ramsey RESET test is statistically insignificant as required that confirms the correct specification of the model. CUSUM test and CUSUMsq test results confirm the stability of the model. The Wald test establishes the long-run asymmetry for government size and short-run asymmetry for country size. The dissimilarity between negative and positive shocks is shown by an asymmetry line in fig (1) and (2), which infers the non-linearity in dynamic multiplier in government size and country size on CO2 emissions.