Non-parametric research methods to measure energy efficiency and renewable energy nexus: evidence from emerging economies

Figures & data

Table 1. Variables specifications and sources.

Variable	Specification	Source
$\mathit{REC}$	The proportion of gross inland REC to total (primary) gross inland energy consumption estimated over a calendar year and measured as % of total energy consumption.	https://databank.world-bank.org/source/world-development-indicators
$\mathit{GDP}$	The gross domestic product (GDP) is a financial measure of the market value of all final services and products made over a specific time period and measured as constant US$ 2015.	https://databank.world-bank.org/source/world-development-indicators
${CO}_2$	The release of CO2 into the atmosphere due to combustion of fossil energy and measured as kiloton (kt).	https://databank.world-bank.org/source/world-development-indicators
$\mathit{ENEF}$	Using less energy to accomplish the same task and is measured GDP per unit of energy use (PPP $ per kg of oil equivalent).	https://databank.world-bank.org/source/world-development-indicators
$TI$	The number of patents by non-residents and residents.	https://databank.world-bank.org/source/world-development-indicators

Source: collected by the authors.

Table 2. Descriptive and normality statistics.

	$\mathit{REC}$	$\mathit{GDP}$	${CO}_2$	$\mathit{ENEF}$	$TI$
Mean	1.285179	12.02869	5.859259	0.791935	4.180236
Median	1.383857	11.99486	5.677518	0.861725	4.189616
Maximum	1.768289	13.15522	7.013404	1.192992	6.188085
Minimum	0.502495	11.43123	5.143702	0.103363	2.922725
Std. Dev.	0.390032	0.346430	0.478638	0.262637	0.644145
Skewness	−0.655101	1.090950	0.741007	−1.063910	0.772699
Kurtosis	2.290813	4.633790	2.662172	3.563654	4.214440
Jarque-Bera	19.42127	65.01215	20.21680	42.39661	33.80228
Probability	0.000061	0.000000	0.000041	0.000000	0.000000

Source: calculated by the authors.

Table 3. Slope heterogeneity.

Slope heterogeneity test	Statistics
$\stackrel{\sim }{\Delta }$	17.019***
${\stackrel{\sim }{\Delta }}^{\mathrm{Adjusted}}$	19.028***

Note: Significance level is denoted by *** for 1%, ** for 5% and * for 10%.

Source: calculated by the authors.

Table 4. Cross-section dependence.

Cross-section dependence
$\mathit{REC}$	$\mathit{GDP}$
17.321***	23.141***
${CO}_2$	$\mathit{ENEF}$
14.22***	22.828***
$TI$
17.847***

Note: Significance level is denoted by *** for 1%, ** for 5% and * for 10%.

Source: calculated by the authors.

Table 5. Unit root testing (Pesaran, 2007).

Variables	$\text{Intercept and trend}$
	$\mathrm{I}(0)$	$\mathrm{I}(1)$
$\mathit{REC}$	−2.152	−4.761***
$\mathit{GDP}$	−1.620	−3.613***
${CO}_2$	−1.976	−4.764***
$\mathit{ENEF}$	−1.232	−4.564***
$TI$	−2.505	−5.406***

Note: Significance level is denoted by *** for 1%, ** for 5% and * for 10%. I(0) is for level, and I(1) is for the first.

Source: calculated by the authors.

Table 6. Cointegration results (Westerlund, 2007).

Statistics	Value	Z-value
$G_{\tau }$	−6.786***	−12.367
$G_a$	−18.212***	−3.100
$P_{\tau }$	−19.071***	−11.676
$P_a$	−23.025***	−6.120

Note: Significance level is denoted by *** for 1%, ** for 5% and * for 10%.

Source: calculated by the authors.

Table 7. Westerlund and Edgerton panel cointegration analysis with structural breaks.

Test		No break	Mean shift	Regime shift
${\mathrm{Z}}_{\mathrm{\phi }}(\mathrm{N})$		−6.43***	−6.09***	−5.04***
$p_{\mathrm{value}}$		(0.000)	(0.000)	(0.000)
${\mathrm{Z}}_{\mathrm{\tau }}(\mathrm{N})$		−6.25***	−6.01***	−5.08***
$p_{\mathrm{value}}$		(0.000)	(0.000)	(0.000)
Detected break years
1998	2002	2008	2010	2014

Note: Significance level is denoted by *** for 1%, ** for 5% and * for 10%, while () contains P-value.

Source: calculated by the authors.

Table 8. Estimates of quantile regression – MMQR.

Variable	Location	Scale	Quantiles
			Q0.25	Q0.50	Q0.75	Q0.90
$\mathit{GDP}$	1.382*** [0.224]	−0.706*** [0.101]	2.076*** [0.263]	1.274*** [0.251]	0.613*** [0.226]	0.396* [0.223]
${CO}_2$	−0.138 [0.122]	0.287*** [0.055]	−0.420*** [0.143]	−0.094 [0.129]	0.174 [0.123]	0.262** [0.124]
$\mathit{ENEF}$	0.012 [0.143]	0.321*** [0.064]	−0.304* [0.167]	0.061 [0.151]	0.361** [0.144]	0.459*** [0.146]
$TI$	−0.790*** [0.116]	0.137*** [0.052]	−0.924*** [0.137]	−0.769*** [0.117]	−0.640*** [0.117]	−0.598*** [0.122]
$\mathit{Constant}$	−11.234*** [0.012]	6.268*** [0.907]	−17.401*** [2.361]	−10.277*** [2.245]	−4.407** [2.024]	−2.483 [2.009]

Note: REC is dependent variable. Significance level is denoted by ***, ** and * for 1%, 5% and 10%.

Source: calculated by the authors.

Figure 1. Graphical representation of quantiles.

Source: drawn by the authors.

Table 9. Robust test results – BSQR.

Variable	Coefficient	Standard error	T-statistics	p > |t|
$\mathit{GDP}$	2.270***	0.532	4.26	0.000
${CO}_2$	0.237***	0.018	12.554	0.000
$\mathit{ENEF}$	0.114***	0.018	6.33	0.000
$TI$	−1.193***	0.281	−4.24	0.000
$\mathit{Constant}$	−19.565***	5.317	−3.68	0.000

Note: REC is dependent variable. Significance level is denoted by ***, ** and * for 1%, 5% and 10%.

Source: calculated by the authors.

Table 10. Dumitrescu-Hurlin panel causality.

${\mathrm{H}}_0$	${\mathrm{Wald}}_{\mathrm{Stats}}$	${\overline{\mathrm{Z}}}_{\mathrm{stats}}$	$p-\mathrm{value}$
$\mathit{GDP} \nRightarrow \mathit{REC}$	2.913***	2.96348	0.0030
$\mathit{REC} \nRightarrow \mathit{GDP}$	3.615***	4.10177	4.E-05
${CO}_2\nRightarrow \mathit{REC}$	2.394**	2.12302	0.0338
$\mathit{REC}\nRightarrow {CO}_2$	4.061***	4.03571	0.0000
$\mathit{ENEF} \nRightarrow \mathit{REC}$	3.837***	4.46030	8.E-06
$\mathit{REC} \nRightarrow \mathit{ENEF}$	2.938***	3.00421	0.0027
$TI \nRightarrow \mathit{REC}$	5.349***	4.43000	0.0000
$\mathit{REC} \nRightarrow TI$	5.847***	7.71644	1.E-14

Note: Significance level is denoted by *** for 1%, ** for 5% and * for 10%.

Source: calculated by the authors.

Pesaran, M. H. (2007). A simple panel unit root test in the presence of cross‐section dependence. Journal of Applied Econometrics, 22(2), 265–312. https://doi.org/10.1002/jae.951

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Westerlund, J. (2007). Testing for error correction in panel data. Oxford Bulletin of Economics and Statistics, 69(6), 709–748. https://doi.org/10.1111/j.1468-0084.2007.00477.x

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