Relationship between economic diversification and CO₂ emissions: ARDL-EC modeling in South Africa

Figures & data

Figure 1. Environmental Kuznets curve model. Source: Adopted from Ngarava et al. (2019).

Table 1. Descriptive statistics for the period 1993–2020.

Variable	Economic diversification (Tress index)		CO2 emission (kilotons)	FDI inflows (current US$) (million)	GDP (current US$) (billion)	Population (million)	Trade balance (current US$) (thousand)
	10 industries	50 industries
Mean	37.80	66.45	421,475.5	3 450	251	48.91	−10.79
Minimum	35.90	64.60	321,049.5	11.29	115	39.63	−30.18
Maximum	40.90	69.20	503,112.4	9 890	416	58.56	4.23
Std. Dev.	1.38	1.54	55,629.5	2 870	102	5.56	10.53
Skewness	0.60	0.51	−0.17	0.60	0.03	0.12	−0.32
Kurtosis	2.32	1.71	1.60	2.13	1.46	1.92	1.81
Jarque-Bera	2.18	3.05	2.06	2.46	2.67	1.37	2.04

Figure 2. Tress index and CO₂ emission in South Africa (1993–2020).

Figure 3. Provincial tress indices (10 industries) between 2000 and 2020 in South Africa.

Table 2. Unit root test.

	Augmented Dickey Fuller (ADF) test		Philips-Perron (PP) test
	I (0)	I (1)	I (0)	I (1)
Tress index (TI)	0.99	−4.50***	1.18	−4.49***
CO2 emission index ($\mathrm{C}{\mathrm{O}}_2$)	−2.07	−4.97***	−2.12	−5.14***
FDI index ($\mathrm{F}\mathrm{D}\mathrm{I}$)	−4.70***	−109.30***	−145.78***	−109.30***
GDP index ($\mathrm{G}\mathrm{D}\mathrm{P}$)	−1.26	−3.77***	−1.09	−3.70**
Population index ($\mathrm{P}\mathrm{o}\mathrm{p}$)	−1.06	−1.85	−3.66**	−5.74***
Trade balance index ($\mathrm{T}\mathrm{R}\mathrm{D}$)	−2.09	−3.56**	−5.05***	−24.08***

***, **, and * indicate significance at 1%, 5%, and 10%, respectively.

Table 3. Lag order selection criteria.

Lag	$\mathrm{T}\mathrm{I}$		$\mathrm{C}{\mathrm{O}}_2$		$\mathrm{F}\mathrm{D}\mathrm{I}$		$\mathrm{G}\mathrm{D}\mathrm{P}$		$\mathrm{P}\mathrm{o}\mathrm{p}$		$\mathrm{T}\mathrm{R}\mathrm{D}$
	AIC	SC	AIC	SC	AIC	SC	AIC	SC	AIC	SC	AIC	SC
0	2.20	2.50	5.61^a	5.67^a	11.14^a	11.44^a	7.68	7.98	5.25	5.55	18.50	18.80
1	1.10	1.45	5.66	5.73	11.15	11.50	7.35^a	7.70^a	−1.95	−1.61	18.59	18.94
2	1.20	1.60	5.76	5.83	11.24	11.64	7.45	7.84	−4.06	−3.66	18.62	19.02
3	0.95	1.40	5.83	5.92	11.20	11.65	7.43	7.88	−6.02	−5.57	18.35	18.80
4	0.72^a	1.22^a	5.92	6.02	11.18	11.68	7.53	8.02	−6.23^a	−5.73	18.17^a	18.67^a

^a Indicate Lag selection.

Table 4. ARDL Bounds Test.

Variable			$\mathrm{T}\mathrm{I}$		$\mathrm{C}{\mathrm{O}}_2$		$\mathrm{F}\mathrm{D}\mathrm{I}$		$\mathrm{G}\mathrm{D}\mathrm{P}$		$\mathrm{P}\mathrm{o}\mathrm{p}$		$\mathrm{T}\mathrm{R}\mathrm{D}$
$\mathrm{T}\mathrm{I}$					−2.66		42.65		16.96**		−0.11**		−691.28
${\mathrm{T}\mathrm{I}}_{t-1}$			0.32								−0.15***		3426.55*
$\mathrm{C}{\mathrm{O}}_2$			−0.02				1.00		1.49***		−0.007		54.28
$\mathrm{C}{{\mathrm{O}}_2}_{t-1}$			0.03		0.16		3.66		−0.78
$\mathrm{F}\mathrm{D}\mathrm{I}$			0.001		0.005				−0.03		0.0004		−4.01
$\mathrm{F}\mathrm{D}{\mathrm{I}}_{t-1}$			−5.98E-05				0.02**				−1.72E-05
$\mathrm{G}\mathrm{D}\mathrm{P}$			0.02**		0.28***		−1.22				0.004**		−18.88
$\mathrm{G}\mathrm{D}{\mathrm{P}}_{t-1}$			−0.02**						0.64**
$\mathrm{P}\mathrm{o}\mathrm{p}$			−1.77*		−15.31*		199.73		51.03**				10212.76
$\mathrm{P}\mathrm{o}{\mathrm{p}}_{t-1}$			1.64		14.74*		−189.24		−47.64**		0.95***		−9682.48
$\mathrm{T}\mathrm{R}\mathrm{D}$			−1.15E-05		8.15E-05		−0.002		4.13E-05		1.13E-05
$\mathrm{T}\mathrm{R}{\mathrm{D}}_{t-1}$			−6.95E-05**						0.001				−0.177
Constant			22.36673**		75.93		−1301.01		−553.09**		8.11***		−84913.86
Model summary
Adjusted R-squared			0.95		0.92		0.41		0.94		0.99		−0.12
Durbin-Watson statistic			1.82		1.95		3.00		2.28		1.55		2.06
F-statistic			41.76		37.51		2.94		36.73		58978.83		0.72
Prob (F-statistic)			0.000		0.000		0.037		0.000		0.000		0.68
Bounds test
	Sig.	I (0)	(1)
F-statistic	10%	2.26	3.35	4.44		5.61		2482.35		2.30		72.29		4.44
	5%	2.62	3.79
	2.5%	2.96	4.18
	1%	3.41	4.68

***, **, and * indicate significance at 1%, 5%, and 10%, respectively.

Table 5. Long-run relationship.

Variable	$\mathrm{T}\mathrm{I}$	$\mathrm{C}{\mathrm{O}}_2$	$\mathrm{F}\mathrm{D}\mathrm{I}$	$\mathrm{G}\mathrm{D}\mathrm{P}$	$\mathrm{P}\mathrm{o}\mathrm{p}$	$\mathrm{T}\mathrm{R}\mathrm{D}$
$\mathrm{T}\mathrm{I}$		−3.19	42.47	47.56	−4.74***	2323.11
$\mathrm{C}{\mathrm{O}}_2$	0.02		4.74	2.01*	−0.14	46.10
$\mathrm{F}\mathrm{D}\mathrm{I}$	0.002	0.006		−0.07	0.006	−3.41
$\mathrm{G}\mathrm{D}\mathrm{P}$	−0.003	0.33***	−1.24		0.07**	−16.04
$\mathrm{P}\mathrm{o}\mathrm{p}$	−0.20***	−0.68	10.68	9.53		450.37
$\mathrm{T}\mathrm{R}\mathrm{D}$	−0.0001	9.75E-05	−0.002	0.004	0.0002

***, **, and * indicate significance at 1%, 5%, and 10%, respectively.

Table 6. Error correction model regression.

	$\mathrm{\partial }\mathrm{T}\mathrm{I}$	$\mathrm{\partial }\mathrm{C}{\mathrm{O}}_2$	$\mathrm{\partial }\mathrm{F}\mathrm{D}\mathrm{I}$	$\mathrm{\partial }\mathrm{G}\mathrm{D}\mathrm{P}$	$\mathrm{\partial }\mathrm{P}\mathrm{o}\mathrm{p}$	$\mathrm{\partial }\mathrm{T}\mathrm{R}\mathrm{D}$
$\mathrm{\partial }\mathrm{T}\mathrm{I}$					−0.11***	−691.28
$\mathrm{\partial }\mathrm{C}{\mathrm{O}}_2$	−0.02		1.00	1.49***
$\mathrm{\partial }\mathrm{F}\mathrm{D}\mathrm{I}$	0.001***				0.0004***
$\mathrm{\partial }\mathrm{G}\mathrm{D}\mathrm{P}$	0.02***
$\mathrm{\partial }\mathrm{P}\mathrm{o}\mathrm{p}$	−1.77***	−15.31***	199.73***	51.09***		10212.76***
$\mathrm{\partial }\mathrm{T}\mathrm{R}\mathrm{D}$	−1.15E-05			4.1E-05
Constant	22.37***	75.93***	−1301.01***	−553.09***	8.11***	−84913.86***
CointEq(−1)	−0.68***	−0.84***	−0.98***	−0.36***	−0.05***	−1.17***
Time to restore equilibrium (years)	1.47	1.19	1.02	2.78	20	0.85
Model summary
Adjusted R-squared	0.73	0.68	0.99	0.66	0.98	0.60
Durbin-Watson statistic	1.82	1.95	3.00	2.28	1.55	2.06
F-statistic	11.29***	24.02***	11617.67***	11.65***	400.82***	12.16***

***, **, and * indicate significance at 1%, 5%, and 10%, respectively.

Table 7. Pairwise Granger causality test.

Null hypothesis	F-statistic
$\mathrm{C}{\mathrm{O}}_2$ emissions index does not Granger cause $\mathrm{T}\mathrm{I}$	9.00***
$\mathrm{T}\mathrm{I}$ does not Granger cause $\mathrm{C}{\mathrm{O}}_2$ emissions	0.10
$\mathrm{F}\mathrm{D}\mathrm{I}$ index does not Granger cause $\mathrm{T}\mathrm{I}$	2.50
$\mathrm{T}\mathrm{I}$ does not Granger cause $\mathrm{F}\mathrm{D}\mathrm{I}$ index	4.94**
$\mathrm{G}\mathrm{D}\mathrm{P}$ index does not Granger cause $\mathrm{T}\mathrm{I}$	12.42***
$\mathrm{T}\mathrm{I}$ does not Granger cause $\mathrm{G}\mathrm{D}\mathrm{P}$ index	0.09
$\mathrm{P}\mathrm{o}\mathrm{p}$ does not Granger cause $\mathrm{T}\mathrm{I}$	10.88***
$\mathrm{T}\mathrm{I}$ does not Granger cause $\mathrm{P}\mathrm{o}\mathrm{p}$	93.24***
$\mathrm{T}\mathrm{R}\mathrm{D}$ does not Granger cause $\mathrm{T}\mathrm{I}$	2.49
$\mathrm{T}\mathrm{I}$ does not Granger cause $\mathrm{T}\mathrm{R}\mathrm{D}$	0.35
$\mathrm{F}\mathrm{D}\mathrm{I}$ index does not Granger cause $\mathrm{C}{\mathrm{O}}_2$ emissions	0.01
$\mathrm{C}{\mathrm{O}}_2$ emissions index does not Granger cause $\mathrm{F}\mathrm{D}\mathrm{I}$ Index	7.72**
$\mathrm{G}\mathrm{D}\mathrm{P}$ index does not Granger cause $\mathrm{C}{\mathrm{O}}_2$ emissions	2.06
$\mathrm{C}{\mathrm{O}}_2$ emissions index does not Granger cause $\mathrm{G}\mathrm{D}\mathrm{P}$ Index	0.11
$\mathrm{P}\mathrm{o}\mathrm{p}$ does not Granger cause $\mathrm{C}{\mathrm{O}}_2$ emissions	2.20
$\mathrm{C}{\mathrm{O}}_2$ emissions index does not Granger cause $\mathrm{P}\mathrm{o}\mathrm{p}$	0.05
$\mathrm{T}\mathrm{R}\mathrm{D}$ does not Granger cause $\mathrm{C}{\mathrm{O}}_2$ emissions	0.24
$\mathrm{C}{\mathrm{O}}_2$ emissions index does not Granger cause $\mathrm{T}\mathrm{R}\mathrm{D}$	0.49

*** and ** indicate significance at 1% and 5%, respectively.

Table 8. Diagnostic tests.

Test	$\mathrm{T}\mathrm{I}$	$\mathrm{C}{\mathrm{O}}_2$ emissions	$\mathrm{F}\mathrm{D}\mathrm{I}$	$\mathrm{G}\mathrm{D}\mathrm{P}$	$\mathrm{P}\mathrm{o}\mathrm{p}$	$\mathrm{T}\mathrm{R}\mathrm{D}$
Normality test
Jarque-Bera	0.17	2.04	0.289	0.766	4.02	83.344
	(0.916)	(0.360)	(0.865)	(0.682)	(0.134)	(0.000)
Multi-collinearity test
Breusch-Godfrey	0.05	0.02	7.72	1.01	1.19	0.135
Serial Correlation LM Test	(0.825)	(0.898)	(0.016)	(0.334)	(0.295)	(0.719)
Heteroskedasticity test
Breusch-Pagan	1.54	1.64	2.64	1.08	0.42	0.932
Godfrey	(0.224)	(0.1997)	(0.054)	(0.436)	(0.890)	(0.521)
Linearity test
Ramsey RESET	0.14	0.66	1.21	3.24	0.92	5.31
Test (t-statistic)	(0.892)	(0.518)	(0.247)	(0.007)	(0.375)	(0.000)
Stability test
CUSUM of squares

Ngarava, Saul, Leocadia Zhou, James Ayuk, and Simbarashe Tatsvarei. 2019. “Achieving Food Security in a Climate Change Environment: Considerations for Environmental Kuznets Curve Use in the South African Agricultural Sector.” Climate 7 (9): 108. doi:https://doi.org/10.3390/cli7090108.

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