A roadmap to a green economy in South Africa: modelling technological innovation and energy consumption in the novel dynamic ARDL simulations framework

Figures & data

Table 1. A summary of the selected articles on the innovation-CO₂ emissions nexus based on different regions.

S/N	Authors	Period/sample	Methods	Main findings
Region: EU countries
1	Anser et al. (2021)	2000–2017	PFE; PQR	Innovation reduces CO2 emissions
Region: BRICS economies
2	Khattak et al. (2020)	1980–2016.	CCEMG, AMG	Innovation increases CO2 emissions
3	Santra (2017)	2005–2012	OLS, LSDV	Innovation increases CO2 emissions
4	Rafique et al. (2020)	1990–2017	AMG	Innovation reduces CO2 emissions
5	Dauda et al. (2019)	1990–2016.	FMOLS, DOLS	Innovation increases CO2 emissions
6	Yang et al. (2021a)	1990–2016	DSUR, FMOLS	Innovation reduces ecological footprint
7	Haseeb et al. (2019)	1994–2014	DSUR, FMOLS	Innovation reduces CO2 emissions
8	Erdogan (2021)	1992–2018	DCCE, PMG	Innovation reduces CO2 emissions
Country: Turkey
9	Demir et al. (2020)	1971–2013	ARDL	Innovation increases CO2 emissions
10	Shan et al. (2021)	1990–2018	ARDL	Innovation reduces CO2 emissions
Region: African countries
11	Ibrahiem (2020)	1971–2014/Egypt	ARDL	Innovation reduces CO2 emissions
12	Asongu (2018)	2002–2012/44 SSA	GMM	Innovation reduces CO2 emissions
13	Dauda et al. (2021)	1990–2016	FE, GMM	Innovation increases CO2 emissions
Region: America
14	Dinda (2018)	1963–2010/USA	VAR and Engle and Granger	Innovation reduces CO2 emissions
15	Ahmad and Raza (2020)	1984–2018/Brazil	ARDL	Innovation reduces CO2 emissions
Region: OECD countries
16	Álvarez-Herránz et al. (2017)	1990–2014	Lagged Distributive models	Innovation reduces CO2 emissions
17	Mensah et al. (2018)	1990–2014	STIRPAT and ARDL	Innovation has different environmental effects across the BRICS economies.
18	Ahmad and Wu (2022)	1990–2017	FMOLS,PQR, DOLS	Innovation reduces CO2 emissions
19	Baloch et al. (2021)	1990–2017	PMG/ARDL	Innovation reduces CO2 emissions
Region: Asian countries
20	Zameer et al. (2020)	1985–2017/India	VECM	Innovation reduces CO2 emissions
21	Usman and Hammar (2021)	1990–2017/APEC	FGLS, AMG	Innovation increases CO2 emissions
22	Godil et al. (2020)	1995–2018/Pakistan	QARDL	Innovation reduces CO2 emissions
23	Arshad et al. (2020)	1990–2014/SSEA	DOLS, GM-FMOLS	Innovation increases CO2 emissions
24	Villanthenkodath and Mahalik (2022)	1980–2018/India	ARDL	Innovation increases CO2 emissions
25	Guo et al. (2021)	1995–2017	AMG/CS-ARDL	Innovation reduces CO2 emissions
Region: Belt and Road host countries
26	Khan et al. (2022b)	1979–2019	OLS, Fixed Effect, GMM	Innovation reduces CO2 emissions
Region: G7 countries
27	Pan et al. (2022)	2000–2014	Input-Output Model	Innovation reduces CO2 emissions
28	Sharif et al. (2022)	1995–2019	CS-ARDL technique	Innovation reduces CO2 emissions
29	Anwar et al. (2021)	1996–2018	AMG	Innovation reduces CO2 emissions
30	Khan et al. (2020)		CS-ARDL	Innovation reduces CO2 emissions
Region: BEM countries
31	Destek and Manga (2021)	1995–2016	ECM-based cointegration test	Innovation reduces CO2 emissions
32	Faisal et al. (2020)	1993–2014	FMOLS, DOLS	Innovation increases CO2 emissions
33	Altinoz et al. (2021)	1995–2014	Panel VAR/GMM	Innovation reduces CO2 emissions
34	Ibrahim and Vo (2021)	1991–2014	GMM	Innovation reduces CO2 emissions

Note: GMM: Generalized method of moments; PFE: Panel Fixed Effect; PQR: Panel Quantile Regression; OLS: Ordinary Least Squares; AMG: Augmented Mean Group; FMLS: Fully Modified Least Squares: CCEMG: Common Correlated Effects Mean Group; AMG: Augmented Mean Group; LSDV: Least Squares Dummy Variables; FMOLS: Fully Modified Ordinary Least Squares; DOLS: Dynamic Ordinary Least Squares; DSUR: Dynamic Seemingly Unrelated Cointegrating Regression; DCCE: Dynamic Common Correlated Effects; PMG: Pooled Mean Group; ARDL: Autoregressive Distributed Lag; FE: Fixed Effects; FGLS: Feasible Generalized Least Square; QARDL: Quantile Autoregressive Distributed Lag; GM-FMOLS: Group Mean-Fully Modified Ordinary Least Square; CS-ARDL: Cross-Sectionally Augmented Autoregressive Distributed Lag; FE-OLS: Fixed Effects Ordinary Least Squares; EU: European Union; BRICS: Brazil, Russia, India, China and South Africa; OECD: Organisation for Economic Co-operation and Development; BEM: Big Emerging Market; SSEA: South and Southeast Asian region; APEC: Asia Pacific Economic Cooperation. SSA: sub-Saharan Africa.

Table 2. Definition of variables and data sources.

Variable	Description	Expected sign	Source
CO2	CO2 emissions (kg per 2010 US$ of GDP)	N/A	WDI
EC	Energy consumption, million tonnes oil equivalent	Positive	BP Statistical Review of World Energy
TECH	Technological innovation measured by gross domestic spending on R&D (% GDP)	negative	WDI
OPEN	Trade openness computed as composite trade intensity introduced by Squalli and Wilson (2011) capturing trade effect	Positive or negative	WDI, Authors
SE	Real GDP per capita capturing scale effect	Positive	WDI
TE	Real GDP per capita squared capturing technique effect	Negative	WDI, Authors
FDI	Foreign direct investment, net inflows (% of GDP)	Positive	WDI
IGDP	Industry, value added (% of GDP)	Positive or negative	WDI

N/A: Not available; WDI: World Development Indicator.

Table 3. Descriptive statistics.

Variables	Mean	Median	Maximum	Minimum	Std. Dev	Skewness	Kurtosis	J-B Stat	Probability
CO2	0.264	0.238	0.477	0.084	0.120	0.217	1.652	4.682	0.196
SE	7.706	7.959	8.984	6.073	0.843	−0.511	2.156	4.102	0.129
TE	60.316	63.754	80.717	36.880	12.663	−0.387	2.082	3.422	0.181
TECH	9.360	9.255	10.545	8.210	0.766	0.082	1.634	4.499	0.105
EC	4.220	4.422	4.840	3.177	0.527	−0.558	1.921	5.621	0.160
FDI	13.203	13.286	14.659	11.913	0.738	0.056	2.463	0.702	0.704
IGDP	3.513	3.580	3.813	3.258	0.161	−0.215	1.697	4.474	0.107
OPEN	6.060	6.512	7.665	2.745	1.329	0.636	2.077	5.757	0.156

Source: Authors’ calculations.

Descriptive statistics provide a concise summary of data, and help to condense large datasets into key measures, making it easier to understand and work with the data. They are fundamental in making data more manageable and comprehensible. They are often the starting point for deeper data analysis, interpretation, and decision-making in various fields, including research, business, and public policy.

CO₂: CO₂ emissions; SE: Scale effect; TE: Technique effect; TECH: Technological innovation; EC: Energy consumption; FDI: Foreign direct investment; IGDP: Industry, value added.

Table 4. Unit root analysis.

Variable	Dickey-Fuller GLS	Phillips- Perron	Augmented Dickey-Fuller	Kwiatkowski-Phillips- Schmidt-Shin	Narayan et al. (2010) Unit Root Test
	(DF-GLS)	(PP)	(ADF)	(KPSS)	Model 1		Model 2
Level	Test – Statistics value				Break-Year	ADF-stat	Break-Year	ADF-stat
InCO2	−0.570	−0.464	−1.152	0.966	1982:1985	−3.132	1987:1994	−8.160***
InSE	−0.116**	−0.079	−1.308	0.833***	1979:1988	−2.914	1982:1990	−7.601***
InTE	−0.112*	−0.076	−1.268	0.848***	1979:1990	−1.939	1982:1994	−6.791***
InTECH	−0.254***	−0.284***	−2.999	0.255***	1995:2000	−4.318	2008:2011	−7.821***
InEC	−0.011	−0.014	−0.366	1.300***	1982:1989	−4.372**	1985:1991	−8.521***
InFDI	−0.032*	−0.001	−0.012	0.640	2001:2006	−2.021	2004:2010	−8.362***
InOPEN	−0.072	−0.082	−1.335	1.080*	1996:2001	−3.053	2003:2009	−7.318***
InIGDP	−0.046	−0.071*	−1.718	1.060**	1972:1985	−3.815	1982:1991	−7.521***
First difference					Critical value (1%, 5%, and 10%)
$\Delta$ InCO2	−0.995***	−0.996***	−7.176***	0.705***	1999:2005	−4.801**	1980:1991	−5.832***
$\Delta$ InSE	−0.695***	−0.707***	−5.319***	0.585***	1983:1997	−5.831***	1985:1995	−6.831***
$\Delta$ InTE	−0.694***	−0.707***	−5.316***	0.589***	1991:2000	−8.531***	1987:1996	−5.893***
$\Delta$ InTECH	−1.023***	−1.034***	−7.473***	0.424***	1999:2003	−4.841**	2006:2010	−5.983***
$\Delta$ InEC	−1.105***	−1.121***	−8.142***	0.586***	1985:1993	−5.921***	1989:1997	−7.942***
$\Delta$ InFDI	−0.207**	−0.209**	−6.443***	0.609***	2005:2008	−6.831***	2001:2008	−6.973***
$\Delta$ InOPEN	−0.935***	−0.938***	−6.699***	0.626***	1996:2004	−6.842**	2001:2007	−8.942***
$\Delta$ InIGDP	−0.799***	−0.801***	−5.878***	0.431***	1975:1990	−7.742***	1988:1992	−7.892***

Source: Authors’ calculations.

Note: *, ** and *** denote statistical significance at 10%, 5% and 1% levels, respectively. MacKinnon’s (1996) one-sided p-values. Lag Length based on SIC and AIC. Probability-based on Kwiatkowski-Phillips-Schmidt-Shin (1992). The critical values for Narayan-Popp unit root test with two breaks are followed by Narayan et al. (2010). All the variables are trended.

Table 5. Lag length criteria.

Lag	LogL	LR	FPE	AIC	SC	HQ
0	178.453	NA	3.2e-12	−6.594	−6.331	−6.493
1	607.095	857.28	1.5e-18	−21.195	−19.094*	−20.390*
2	661.093	108	1.4e-18	−21.388	−17.448	−19.877
3	719.755	117.32	1.2e-18*	−21.759	−15.981	−19.544
4	784.113	128.72*	1.3e-18	−22.350*	−14.733	−19.430

Source: Authors’ calculations.

Note: * indicates lag order selected by the criterion.

Table 6. ARDL bounds test analysis.

Test statistics	Value	K	${\mathit{H}}_0$	$\mathrm{ }{\mathit{H}}_1$
F-statistics	14.341	7	No level relationship	Relationship exists
t-statistics	−8.752
Kripfganz &Schneider (2018) critical values and approximate p-values y
Significance	F-statistics		t-statistics p-value F
	1(0)	1(1)	1(0)	1(1)	1(0)	1(1)
10%	2.12	3.23	−2.57	−4.04	0.000***	0.000***
5%	2.45	3.61	−2.86	−4.38	p-value t
1%	3.15	4.43	−3.43	−4.99	0.000***	0.002**

Note: *, ** and *** respectively represent statistical significance at 10%, 5% and 1% levels. The respective significance levels suggest the rejection of the null hypothesis of no cointegration. The optimal lag length on each variable is chosen by the Schwarz’s Bayesian information criterion (SBIC).

Table 7. Diagnostic statistics tests.

Diagnostic statistics tests	$X^2$ (P values)	Results
Breusch Godfrey LM test	0.3812	No problem of serial correlations
Breusch-Pagan-Godfrey test	0.2610	No problem of heteroscedasticity
ARCH test	0.6837	No problem of heteroscedasticity
Ramsey RESET test	0.5183	Model is specified correctly
Jarque-Bera Test	0.2715	Estimated residual are normal

Source: Authors’ calculations.

Table 8. Dynamic ARDL simulations analysis.

Variables	Coefficient	St. Error	t-value
Cons	−1.1814	1.2878	−0.92
InSE	0.2139***	0.1829	4.56
$\Delta$ InSE	0.3962***	0.2721	2.77
InTE	−0.6657**	0.8605	−2.34
$\Delta$ InTE	−0.7441	0.1387	−1.79
InTECH	−0.7358***	0.5941	−3.24
$\Delta$ InTECH	−0.2274**	0.0738	−2.62
InEC	0.2713***	0.1762	3.98
$\Delta$ InEC	0.5906*	0.1719	1.98
InFDI	0.9064	0.0810	1.12
$\Delta$ InFDI	0.2846**	0.2657	2.59
InOPEN	0.1883***	0.0487	5.39
$\Delta$ InOPEN	−0.3043**	0.0570	−2.53
InIGDP	0.3429**	0.1577	2.17
$\Delta$ InIGDP	0.5308	0.2309	0.23
ECT(-1)	−0.8243***	0.1396	−3.04
R-squared	0.7845
Adj R-squared	0.7693
N	55
P val of F-sta	0.0000***
Simulations	1000

Source: Authors’ calculations.

Note: *, ** and *** denote statistical significance at 10%, 5% and 1% levels, respectively.

Figure 1. The impulse response plot for scale effect (economic growth) and CO₂ emissions.

It shows a 10% increase and a decrease in scale effect and its influence on CO₂ emissions where dots specify average prediction value. However, the dark blue to light blue line denotes 75, 90, and 95% confidence interval, respectively.

Figure 2. The impulse response plot for technique effect and CO2 emissions.

It shows a 10% increase and a decrease in technique effect and its influence on CO₂ emissions where dots specify average prediction value. However, the dark blue to light blue line denotes 75, 90, and 95% confidence interval, respectively.

Figure 3. The impulse response plot for trade openness and CO₂ emissions.

It shows a 10% increase and a decrease in trade openness and its influence on CO₂ emissions where dots specify average prediction value. However, the dark blue to light blue line denotes 75, 90, and 95% confidence interval, respectively.

Figure 4. The impulse response plot for energy consumption and CO₂ emissions.

It shows a 10% increase and a decrease in energy consumption and its influence on CO₂ emissions where dots specify average prediction value. However, the dark blue to light blue line denotes 75, 90, and 95% confidence interval, respectively.

Figure 5. The impulse response plot for foreign direct investment and CO₂ emissions.

It shows a 10% increase and a decrease in foreign direct investment and its influence on CO₂ emissions where dots specify average prediction value. However, the dark blue to light blue line denotes 75, 90, and 95% confidence interval, respectively.

Figure 6. The impulse response plot for technological innovation and CO₂ emissions.

It shows a 10% increase and a decrease in technological innovation and its influence on CO₂ emissions where dots specify average prediction value. However, the dark blue to light blue line denotes 75, 90, and 95% confidence interval, respectively.

Figure 7. The impulse response plot for urbanization and CO₂ emissions.

It shows a 10% increase and a decrease in urbanization and its influence on CO₂ emissions where dots specify average prediction value. However, the dark blue to light blue line denotes 75, 90, and 95% confidence interval, respectively.

Table 9. Frequency-domain causality test.

Direction of causality	Long-term	Medium-term	Short-term
	${\mathrm{\omega }}_{\mathrm{i}=0.05}$	${\mathrm{\omega }}_{\mathrm{i}=1.50}$	${\mathrm{\omega }}_{\mathrm{i}=2.50}$
InSE → InCO2	<8.31>	<8.50>	<9.96>
	(0.02)**	(0.00)***	(0.00)***
InTE → InCO2	<4.89>	<6.49>	<6.93>
	(0.07)*	(0.03)**	(0.04)**
InOPEN → InCO2	<8.94>	<8.73>	<7.28>
	(0.00)***	(0.00)***	(0.01)**
InEC → InCO2	<5.12>	<6.49>	<6.73>
	(0.08)*	(0.04)**	(0.03)**
InFDI → InCO2	<8.20>	<8.08>	<8.62>
	(0.01)**	(0.03)**	(0.00)***
InTECH →InCO2	<4.84>	<5.14>	<7.83>
	(0.06)*	(0.04)**	(0.02)**
InIGDP → InCO2	<5.46>	<8.82>	<8.89>
	(0.07)*	(0.00)**	(0.00)**

Source: Authors’ calculations.

Note: *, ** and *** denote statistical significance at 10%, 5% and 1% levels, respectively.

Figure 8. The impulse response plot for industrial value-added and CO₂ emissions.

It shows a 10% increase and a decrease in industrial value-added and its influence on CO₂ emissions where dots specify average prediction value. However, the dark blue to light blue line denotes 75, 90, and 95% confidence interval, respectively.

Figure 9. Plot of cumulative sum of recursive residuals (CUSUM).

Figure 10. Plot of cumulative sum of squares of recursive residuals (CUSUMSQ).

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Availability of data and materials

The datasets used are publicly available from the World Bank World Development Indicators, which can be accessed at https://databank.worldbank.org/source/world-develop ment-indicators