Table 4 Results of NARDL model Component...

Table 4

Results of NARDL model

Component	Variable	Coefficient/statistic	t- or F-statistic	p-value	Interpretation or formula
Bounds test
F-bounds statistic		5.07039***	–	–	Exceeds the 1% upper bound
Lower/upper bound, 10%		2.20/3.09	–	–	Critical values
Lower/upper bound, 5%		2.56/3.49	–	–	Critical values
Lower/upper bound, 3%		2.88/3.87	–	–	Critical values
Lower/upper bound, 1%		3.29/4.37	–	–	Critical values
Conditional error-correction coefficients
Constant	$c$	6.566331	2.447597	0.0166	Conditional estimate
Lagged CO₂ emissions	$ρ y_{t - 1}$	−0.267930	−5.972170	0.0000	Error-correction coefficient, $ρ$
Positive bank-based financial development	$λ_{f d}^{+} f d_{t - 1}^{+}$	0.025950	1.878380	0.0640	Conditional level coefficient
Negative bank-based financial development	$λ_{f d}^{-} f d_{t - 1}^{-}$	0.160244	3.219762	0.0019	Conditional level coefficient
Positive economic diversification	$λ_{div}^{+} d i v_{t - 1}^{+}$	0.007906	4.052595	0.0001	Conditional level coefficient
Negative economic diversification	$λ_{div}^{-} d i v_{t - 1}^{-}$	−0.007200	−3.645880	0.0005	Conditional level coefficient
GDP per capita	Component of $γ^{'} x_{t - 1}$	−0.003760	−0.207210	0.8364	Conditional level coefficient
Urbanization	Component of $γ^{'} x_{t - 1}$	−1.550580	−2.493450	0.0147	Conditional level coefficient
Electricity consumption	Component of $γ^{'} x_{t - 1}$	0.108279	3.623523	0.0005	Conditional level coefficient
Industrial activity	Component of $γ^{'} x_{t - 1}$	−0.006590	−0.227290	0.8208	Conditional level coefficient
Trade openness	Component of $γ^{'} x_{t - 1}$	0.050396	3.042136	0.0032	Conditional level coefficient
Long-run multipliers
Positive bank-based financial-development change	$L R_{f d}^{+}$	0.096854	–	–	$- λ_{f d}^{+} / ρ$
Negative bank-based financial-development change	$L R_{f d}^{-}$	0.598082	–	–	$- λ_{f d}^{-} / ρ$
Positive economic-diversification change	$L R_{div}^{+}$	0.029508	–	–	$- λ_{div}^{+} / ρ$
Negative economic-diversification change	$L R_{div}^{-}$	−0.026873	–	–	$- λ_{div}^{-} / ρ$
GDP per capita	$L R_{g d p}$	−0.014034	–	–	$- λ_{g d p} / ρ$
Urbanization	$L R_{u r b}$	−5.787258	–	–	$- λ_{u r b} / ρ$
Electricity consumption	$L R_{p o w e r}$	0.404132	–	–	$- λ_{p o w e r} / ρ$
Industrial activity	$L R_{i n d}$	−0.024596	–	–	$- λ_{i n d} / ρ$
Trade openness	$L R_{o p e n}$	0.188094	–	–	$- λ_{o p e n} / ρ$
Short-run coefficients
Lagged change in CO₂ emissions	$Δ y_{t - 1}$	0.591811	7.861568	0.0000	$ϕ_{1}$
Positive bank-based financial-development change	$Δ f d_{t}^{+}$	0.090972	3.396743	0.0011	$θ_{0}^{+}$
Negative bank-based financial-development change	$Δ f d_{t}^{-}$	−0.320540	−2.350200	0.0213	$θ_{0}^{-}$
Positive economic-diversification change	$Δ d i v_{t}^{+}$	−0.019970	−2.469280	0.0157	$ψ_{0}^{+}$
Negative economic-diversification change	$Δ d i v_{t}^{-}$	0.011757	1.704963	0.0921	$ψ_{0}^{-}$
Lagged change in electricity consumption	$Δ p o w e r_{t - 1}$	0.010041	0.142887	0.8867	Component of $δ_{ℓ}$
Lagged change in urbanization	$Δ u r b_{t - 1}$	−291.071	−2.4328	0.0172	Component of $δ_{ℓ}$
Lagged change in industrial activity	$Δ i n d_{t - 1}$	0.018334	0.547229	0.5858	Component of $δ_{ℓ}$
Lagged change in trade openness	$Δ o p e n_{t - 1}$	−0.008440	−0.18617	0.8528	Component of $δ_{ℓ}$
Model diagnostics and stability tests
R-squared		0.858382	–	–	Goodness of fit
Adjusted R-squared		0.824322	–	–	Goodness of fit
F-statistic		25.202080	–	–	Model statistic
Durbin–Watson statistic		2.085041	–	–	Residual autocorrelation
Serial-correlation LM test		0.860000	–	–	Reported diagnostic
Normality test		0.300000	–	0.8500	Reported diagnostic
Heteroskedasticity test		0.470000	–	–	Reported diagnostic
BDS residual diagnostic
Dimension 2		0.008955	1.201169	0.2297	Null hypothesis not rejected
Dimension 3		0.009730	0.817011	0.4139	Null hypothesis not rejected
Dimension 4		0.007029	0.493150	0.6219	Null hypothesis not rejected
Dimension 5		0.021544	1.442941	0.1490	Null hypothesis not rejected
Wald asymmetry tests
Long-run diversification asymmetry	$H_{0} : L R_{div}^{+} = L R_{div}^{-}$	$t = {4.96}^{***}$	–	0.0000	Reject symmetry
Short-run diversification asymmetry	$H_{0} : \sum ψ_{k}^{+} = \sum ψ_{k}^{-}$	$F = {24.63}^{***}$	–	0.0000	Reject symmetry
Long-run bank-based financial-development asymmetry	$H_{0} : L R_{f d}^{+} = L R_{f d}^{-}$	$t = - {2.33}^{**}$	–	0.0220	Reject symmetry
Short-run bank-based financial-development asymmetry	$H_{0} : \sum θ_{j}^{+} = \sum θ_{j}^{-}$	$F = {5.42}^{**}$	–	0.0220	Reject symmetry
Normalized Long-Run Multipliers
Variable	Raw conditional level coefficient		Formula	Normalized long-run multiplier
Positive diversification	$λ_{div}^{+} = 0.007906$		$- 0.007906 / - 0.267930$	$L R_{div}^{+} = 0.029508$
Negative diversification	$λ_{div}^{-} = - 0.007200$		$- (- 0.007200) / - 0.267930$	$L R_{div}^{-} = - 0.026873$
Positive bank-based financial development	$λ_{f d}^{+} = 0.025950$		$- 0.025950 / - 0.267930$	$L R_{f d}^{+} = 0.096854$
Negative bank-based financial development	$λ_{f d}^{-} = 0.160244$		$- 0.160244 / - 0.267930$	$L R_{f d}^{-} = 0.598082$

Component	Variable	Coefficient/statistic	t- or F-statistic	p-value	Interpretation or formula
Bounds test
F-bounds statistic		5.07039***	–	–	Exceeds the 1% upper bound
Lower/upper bound, 10%		2.20/3.09	–	–	Critical values
Lower/upper bound, 5%		2.56/3.49	–	–	Critical values
Lower/upper bound, 3%		2.88/3.87	–	–	Critical values
Lower/upper bound, 1%		3.29/4.37	–	–	Critical values
Conditional error-correction coefficients
Constant	$c$	6.566331	2.447597	0.0166	Conditional estimate
Lagged CO₂ emissions	$ρ y_{t - 1}$	−0.267930	−5.972170	0.0000	Error-correction coefficient, $ρ$
Positive bank-based financial development	$λ_{f d}^{+} f d_{t - 1}^{+}$	0.025950	1.878380	0.0640	Conditional level coefficient
Negative bank-based financial development	$λ_{f d}^{-} f d_{t - 1}^{-}$	0.160244	3.219762	0.0019	Conditional level coefficient
Positive economic diversification	$λ_{div}^{+} d i v_{t - 1}^{+}$	0.007906	4.052595	0.0001	Conditional level coefficient
Negative economic diversification	$λ_{div}^{-} d i v_{t - 1}^{-}$	−0.007200	−3.645880	0.0005	Conditional level coefficient
GDP per capita	Component of $γ^{'} x_{t - 1}$	−0.003760	−0.207210	0.8364	Conditional level coefficient
Urbanization	Component of $γ^{'} x_{t - 1}$	−1.550580	−2.493450	0.0147	Conditional level coefficient
Electricity consumption	Component of $γ^{'} x_{t - 1}$	0.108279	3.623523	0.0005	Conditional level coefficient
Industrial activity	Component of $γ^{'} x_{t - 1}$	−0.006590	−0.227290	0.8208	Conditional level coefficient
Trade openness	Component of $γ^{'} x_{t - 1}$	0.050396	3.042136	0.0032	Conditional level coefficient
Long-run multipliers
Positive bank-based financial-development change	$L R_{f d}^{+}$	0.096854	–	–	$- λ_{f d}^{+} / ρ$
Negative bank-based financial-development change	$L R_{f d}^{-}$	0.598082	–	–	$- λ_{f d}^{-} / ρ$
Positive economic-diversification change	$L R_{div}^{+}$	0.029508	–	–	$- λ_{div}^{+} / ρ$
Negative economic-diversification change	$L R_{div}^{-}$	−0.026873	–	–	$- λ_{div}^{-} / ρ$
GDP per capita	$L R_{g d p}$	−0.014034	–	–	$- λ_{g d p} / ρ$
Urbanization	$L R_{u r b}$	−5.787258	–	–	$- λ_{u r b} / ρ$
Electricity consumption	$L R_{p o w e r}$	0.404132	–	–	$- λ_{p o w e r} / ρ$
Industrial activity	$L R_{i n d}$	−0.024596	–	–	$- λ_{i n d} / ρ$
Trade openness	$L R_{o p e n}$	0.188094	–	–	$- λ_{o p e n} / ρ$
Short-run coefficients
Lagged change in CO₂ emissions	$Δ y_{t - 1}$	0.591811	7.861568	0.0000	$ϕ_{1}$
Positive bank-based financial-development change	$Δ f d_{t}^{+}$	0.090972	3.396743	0.0011	$θ_{0}^{+}$
Negative bank-based financial-development change	$Δ f d_{t}^{-}$	−0.320540	−2.350200	0.0213	$θ_{0}^{-}$
Positive economic-diversification change	$Δ d i v_{t}^{+}$	−0.019970	−2.469280	0.0157	$ψ_{0}^{+}$
Negative economic-diversification change	$Δ d i v_{t}^{-}$	0.011757	1.704963	0.0921	$ψ_{0}^{-}$
Lagged change in electricity consumption	$Δ p o w e r_{t - 1}$	0.010041	0.142887	0.8867	Component of $δ_{ℓ}$
Lagged change in urbanization	$Δ u r b_{t - 1}$	−291.071	−2.4328	0.0172	Component of $δ_{ℓ}$
Lagged change in industrial activity	$Δ i n d_{t - 1}$	0.018334	0.547229	0.5858	Component of $δ_{ℓ}$
Lagged change in trade openness	$Δ o p e n_{t - 1}$	−0.008440	−0.18617	0.8528	Component of $δ_{ℓ}$
Model diagnostics and stability tests
R-squared		0.858382	–	–	Goodness of fit
Adjusted R-squared		0.824322	–	–	Goodness of fit
F-statistic		25.202080	–	–	Model statistic
Durbin–Watson statistic		2.085041	–	–	Residual autocorrelation
Serial-correlation LM test		0.860000	–	–	Reported diagnostic
Normality test		0.300000	–	0.8500	Reported diagnostic
Heteroskedasticity test		0.470000	–	–	Reported diagnostic
BDS residual diagnostic
Dimension 2		0.008955	1.201169	0.2297	Null hypothesis not rejected
Dimension 3		0.009730	0.817011	0.4139	Null hypothesis not rejected
Dimension 4		0.007029	0.493150	0.6219	Null hypothesis not rejected
Dimension 5		0.021544	1.442941	0.1490	Null hypothesis not rejected
Wald asymmetry tests
Long-run diversification asymmetry	$H_{0} : L R_{div}^{+} = L R_{div}^{-}$	$t = {4.96}^{***}$	–	0.0000	Reject symmetry
Short-run diversification asymmetry	$H_{0} : \sum ψ_{k}^{+} = \sum ψ_{k}^{-}$	$F = {24.63}^{***}$	–	0.0000	Reject symmetry
Long-run bank-based financial-development asymmetry	$H_{0} : L R_{f d}^{+} = L R_{f d}^{-}$	$t = - {2.33}^{**}$	–	0.0220	Reject symmetry
Short-run bank-based financial-development asymmetry	$H_{0} : \sum θ_{j}^{+} = \sum θ_{j}^{-}$	$F = {5.42}^{**}$	–	0.0220	Reject symmetry
Normalized Long-Run Multipliers
Variable	Raw conditional level coefficient		Formula	Normalized long-run multiplier
Positive diversification	$λ_{div}^{+} = 0.007906$		$- 0.007906 / - 0.267930$	$L R_{div}^{+} = 0.029508$
Negative diversification	$λ_{div}^{-} = - 0.007200$		$- (- 0.007200) / - 0.267930$	$L R_{div}^{-} = - 0.026873$
Positive bank-based financial development	$λ_{f d}^{+} = 0.025950$		$- 0.025950 / - 0.267930$	$L R_{f d}^{+} = 0.096854$
Negative bank-based financial development	$λ_{f d}^{-} = 0.160244$		$- 0.160244 / - 0.267930$	$L R_{f d}^{-} = 0.598082$

Note(s): Conditional level coefficients are reported separately from normalized long-run multipliers. The latter are calculated as $- λ / ρ$ ⁠, where $ρ$ is the coefficient on lagged CO₂ emissions and $λ$ is the relevant conditional level coefficient. Raw conditional coefficients are not long-run effects. For negative partial sums, the association of a negative shock depends on the multiplier and the negative sign of the shock. Standard errors and p-values are obtained from the software's long-run form output

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