The effect of renewable energy on carbon dioxide emission in Taiwan: Quantile mediation analysis

Abstract

In this paper, we propose an integrated method, called quantile mediation analysis, which combines quantile regression and mediation analysis, to examine the impact of renewable energy on carbon dioxide emissions, whether connected to or separate from through economic growth, from 1990 to 2018 in Taiwan. The results of this novel approach indicate that Taiwan's renewable energy did not affect carbon dioxide emissions through the mediation effect of economic growth from the period of 1990 to 2018, and that there is only a direct effect from renewable energy to carbon dioxide emissions at any distribution. Moreover, this result is remarkably different from the result of the traditional ordinary least square approach, which shows that Taiwan‘s renewable energy affects carbon dioxide emissions through the partial mediation effect of economic growth. In conclusion, we suggest that the Taiwanese government should increase the use of renewable energy in reducing local and global carbon dioxide emissions.

Keywords

Quantile mediation analysis carbon dioxide emission economic growth renewable energy

Introduction

Reducing global carbon dioxide (CO₂) emissions has been a core subject of researchers and government concern.^1,2 Due to the low CO₂ emissions of renewable energy sources, renewable energy plays an important role in reducing global CO₂ emissions. Indeed, some empirical studies concluded that renewable energy improves environmental quality.^3–5 For instance, Baek³ used the USA data to examine the effects of renewable energy on CO₂ emissions. The author found that renewable energy consumption only has a negative impact on reducing CO₂ emissions in the short run. However, according to Panayotou,⁶ renewable energy also results in environmental costs through the impact of economic activities which use more energy resources, that is, causing more carbon emission given a certain level of technology. This perspective concludes that increased economic activities stimulated by renewable energy worsens environmental quality. For example, Grossman and Krueger⁷ provided a systematic explanation for the relationship between gross domestic product (GDP) and environmental pollutants. They divide the economic development stage into three parts: scale effect, composition effect, and technique effect. The scale effect asserts that an increase in production impedes environmental quality; therefore, economic growth causes a data negative effect on environmental quality. Several empirical studies demonstrated that economic growth correlates with CO₂ emissions.^8–14

On the other hand, some empirical studies have found a favorable linkage between renewable energy consumption and economic growth.^15–22 For instance, Yao, Zhang, and Zhang²² found that there exists a long-run relationship between renewable energy, CO₂ emissions, and economic growth for 17 major developing and developed countries and for six geo-economic regions in the world. In summary, previous literature reflects an emphasis on renewable energy consumption and CO₂ emissions, economic growth and CO₂ emissions, and renewable energy consumption and economic growth. Therefore, there is an apparent scarcity of empirical evidence on the relationship amongst renewable energy consumption, economic growth and CO₂ emissions. This knowledge gap provides stronger motivation for investigating the interaction among these factors in the context of Taiwan. The purpose of this paper is to investigate whether there is a direct relationship between renewable energy and CO₂ emissions in Taiwan, or an indirect relationship between renewable energy and CO₂ emissions, via economic growth in Taiwan; or if there exist both direct and indirect relationships.

To decrease CO₂ emissions, the Taiwanese government issued the Renewable Energy Development Act in 2009, and actively promotes the use of renewable energy, from sources such as biomass and waste, solar thermal, conventional hydropower, geothermal, solar photovoltaic, and wind energy. Table 1 shows renewable energy supplies in Taiwan from 1990 to 2018. According to the statistics of the Taiwan Bureau of Energy, Ministry of Economic Affairs, biomass and waste energy are widely used and accounted for approximately 63.88% of Taiwan‘s total renewable energy supply in 2018. Since 2009, the use of geothermal, solar photovoltaic, and wind energy supply has rapidly increased from 3.48% of total renewable energy supply to 16% in 2018.

Table 1.

Renewable energy (RENEW) supply in Taiwan (1990–2018) unit: 10³ KLOE.

Year	Biomass and waste	Solar thermal	Conventional hydropPower	Geothermal, solar photovoltaic, and wind energy
1990	50.0	19.6	610.0	2.7
1991	67.9	24.9	368.4	1.7
1992	90.2	32.0	626.8	1.8
1993	81.9	38.7	392.8	1.3
1994	125.6	46.5	483.9	0.0
1995	192.9	54.6	462.7	0.0
1996	261.4	60.4	453.4	0.0
1997	465.4	66.0	501.5	0.0
1998	568.8	70.1	592.9	0.0
1999	781.5	73.2	482.9	0.0
2000	943.6	77.3	435.9	0.1
2001	1205.8	81.1	486.6	1.2
2002	1304.3	84.3	265.7	1.6
2003	1567.3	87.9	290.1	2.3
2004	1599.5	92.7	306.9	2.5
2005	1595.0	97.5	381.1	8.8
2006	1628.1	102.4	390.8	26.5
2007	1689.0	105.5	422.3	42.2
2008	1729.8	109.5	411.6	56.7
2009	1638.0	113.2	358.3	76.1
2010	1706.9	114.3	401.0	100.6
2011	1732.4	113.2	382.4	149.4
2012	1758.9	114.0	542.0	151.7
2013	1764.0	112.8	518.4	189.1
2014	1730.1	112.2	412.8	196.2
2015	1743.4	113.5	427.3	229.5
2016	1686.0	112.1	627.3	247.5
2017	1621.9	113.1	520.7	326.4
2018	1689.3	104.7	427.2	423.1

Note: KLOE = kiloliter of oil equivalent.

Source: The statistics of the Taiwan Bureau of Energy, Ministry of Economic Affairs (2020).

Moreover, in this study, we propose an innovative methodology that is totally different from past research studies. We combine mediation analysis and quantile regression, proposed by Koenker and Bassett²³ to investigate the dynamic short-run causal impact of renewable energy on CO₂ emissions, whether connected to or separate from through economic growth, across different conditional CO₂ emissions from 1990 to 2018 in Taiwan. The main advantage of using this quantile regression model is that it does not require strong assumptions for error terms and is generally considered more robust^24,25 because it estimates the median and the full range of the conditional distribution of the explained variables, rather than traditional ordinary least squares (OLS) regression to simply analyze the conditional expectation of the explained variables. Moreover, the effects of explanatory variables on the explained variables are different across quantiles. Certain studies^26–28 used a panel quantile regression approach to analyze CO₂ emissions. For example, Cheng et al.²⁶ propose panel quantile regression to explore technological innovation to mitigate CO₂ emissions in 35 OECD countries. The authors found out that technological innovation directly reduces CO₂ emissions, but it is significantly heterogeneous and asymmetric across quantiles.

Literature review

In line with rapidly increasing levels of renewable energy consumption, many studies have examined the impact of renewable energy consumption on CO₂ emissions. They conclude that increasing renewable energy consumption mitigates CO₂ emissions for the economies of the USA³; China⁴; and OECD economies.⁵ For instance, Baek³ used the US data to examine the effects of renewable energy on CO₂ emissions and found that renewable energy consumption only has a negative impact on reducing CO₂ emissions in the short run.

On the other hand, many researchers have studied the relationship between economic growth and CO₂ emissions. For instance, Balsalobre-Lorente et al.¹⁴ explores the relationship between economic growth and CO₂ emissions in countries in the European Union – Germany, France, Italy, Spain, and the United Kingdom – between 1985 and 2016. They found that economic growth has a positive impact on CO₂ emissions.

In addition to the above factors affecting CO₂ emissions, many recent studies^29–39 propose other factors, including innovation shocks, higher education, fiscal policy, monetary policy, commercial policy, eco-innovation, foreign direct investment, etc., as having an effect. For instance, Ahmad et al.³³ explored the relationship between innovation shocks and CO₂ emissions in the OECD economies. The results indicated that positive shocks to innovation improve environmental quality. However, the negative innovation shocks disrupt environmental quality. The authors suggested that the government should adopt innovation shocks as a policy instrument to formulate better environmental policies for a sustainable future. Chishti et al.³⁴ discovered a novel predictor of CO₂ emissions, namely fiscal and monetary policies, in BRICS economies. The authors found that the expansionary fiscal policy intensifies the harmful repercussions of CO₂ emissions. However, the contractionary fiscal policy serves as an effective measure to mitigate the detrimental effects of CO₂ emissions. Similarly, expansionary monetary policy also deteriorates CO₂ emissions and contractionary monetary policy mitigates environmental quality.

Methodology

This paper integrates quantile regression and mediation analysis to examine the impact of renewable energy on CO₂ emissions, whether through economic growth or not, from 1990 to 2018 in Taiwan. Through this novel methodology, the results can be provided as a reference for Taiwan‘s government to make policy decisions regarding the promotion of renewable energy supplies.

Quantile regression

Quantile regression is a statistical technique intended to estimate and conduct inference about a conditional quantile function. Koenker and Bassett²³ proposed the quantile regression approach as an alternative to ordinary least squares regression in a wide range of applications. This approach takes into consideration the skewness of distributions and gives a more complete picture of the performance affected by various independent variables. This technique was further developed by Koenker, and Hallock and Koenker.^24,25

According to Koenker,²⁵ quantile regression is used when an estimate of the various quantile of a population is desired. One of the advantages of using quantile regression to estimate the median and the full range of other conditions, rather than ordinary least squares regression to estimate the mean, is that a quantile regression will be more robust in response to large outliers. Like the least absolute deviations, the quantile regression objective function is a weighted sum of absolute deviations, which gives a robust measure of location, so that the estimated coefficient vector is not sensitive to outlier observations on the dependent variable. Moreover, a quantile regression also provides a more efficient approach than the ordinary least squares method when the disturb term is non-normal. A quantile regression can be considered as a natural analog in regression analysis to the practice of using different measures of central tendency and statistical dispersion to obtain a more comprehensive and robust analysis. Lastly, a further advantage of quantile regression is that any quantile can be estimated when we have enough data.

According to Koenker and Bassett‘s method,²³ we first let y_t, t = 1,2,…,T be a random sample on the following regression process:

y_{t} = u_{t} + x_{t} β

(1)

Equation (1) has a conditional distribution function as equation (2).

F_{y / x} = F (Y_{t} \leq y) = F (y_{t} - x_{t} β)

(2)

where x_t, t = 1,2,…,T denote a sequence of (row) k-vectors of a known design matrix.

The θ^th regression quantile, Q_y/x (θ), 0 ＜ θ ＜ 1 is defined as any solution to the following minimization problem:

\begin{aligned} \underset{β}{m i n} [θ \sum | y_{t} - x_{t} β | + (1 - θ) \sum | y_{t} - x_{t} β |] \\ {t : Y_{t} \geq X_{t} β} {t : Y_{t} < X_{t} β} \end{aligned}

(3)

The resulting solution to equation (3) is denoted as β_θ, from which we obtain the θ^th conditional quantile Q_y/x (θ) = xβ_θ

Meditation analysis on economic growth

We can use mediation analysis to investigate the causality from renewable energy to CO₂ emissions through economic growth and the direct relation between renewable energy and CO₂ emissions in equations (4) to (6). The most common approach to examine mediation effect is the causal steps procedure popularized by Baron and Kenny.⁴⁰ This analysis involves the following set of regression equations relating to the independent variable, mediator variable, and dependent variable:

C O 2 = b_{0} + b_{1} RENEW + e_{1}

(4)

GROW = c_{0} + c_{1} RENEW + e_{2}

(5)

C O 2 = d_{0} + d_{1} RENEW + d_{2} GROW + e_{3}

(6)

Here, the degree of renewable energy (RENEW) is measured as solar photovoltaics energy, solar thermal energy, wind energy, hydropower, geothermal energy; as well as renewable biomass energies, such as waste energy, biogas electrification, biofuel, and so on in kiloliter of oil equivalent. The variable of CO2 is per capita carbon dioxide emissions in metric tons. Economic growth (GROW) is measured as the real Gross Domestic Product. Technically, e_i, i = 12,3 is the stochastic error term. According to Baron and Kenny,⁴⁰ meditation analysis on economic growth processes comprise the following procedures:

Procedure 1: The independent variable RENEW should relate to the dependent variable CO2, such that b₁ in equation (4) is significant. This condition is used to establish that there is a relationship between RENEW and CO2to be mediated.

Procedure 2: The independent variable RENEW should relate to the mediator variable GROW, such that c₁ in equation (5) is significant. This condition establishes the first stage of the mediated effect.

Procedure 3: The mediator variable GROW should relate to the dependent variable CO2, such that d₂ in equation (6) is significant. This condition establishes the second stage of the mediated effect.

Procedure 4: The independent variable RENEW should no longer relate to the dependent variable CO2 after the mediator variable GROW is controlled, such that d₁ in equation (6) is not significant. This condition shows that the relationship between RENEW and CO2 examined under the first condition disappears when the mediated effect transmitted through GROW is considered.

Satisfying all four steps provides evidence for complete mediation, whereas satisfying the first three steps indicates partial mediation if d₁ in equation (6) is still significant and is smaller than b₁ in equation (4).

Quantile meditation analysis

An integrated method proposed by Hsu⁴¹ combines quantile regression and meditation analysis, which substitutes equation (3) into equations (4) to (6) and can be described to equations (7) to (9). This analysis provides a useful supplement to the standard constant-parameter regression estimate (only one b or c or d) for studying all possible parameters (for all quantiles) varying across high dependent variable and low dependent variable. This novel method also leads to a more dynamic and complete understanding of what might really underlie the stories of great effect or non-effect for renewable energy on CO₂ emissions. The quantile regression minimizes a weighted sum of the positive and negative error terms in equations (7) to (9).

\underset{b}{m i n} θ \sum^{|} CO 2_{t} - b_{0} - b_{1} RENE W_{t} | + (1 - θ) \sum^{|} CO 2_{t} - b_{0} - b_{1} RENE W_{t} |

(7)

\underset{c}{m i n} θ \sum^{|} GRO W_{t} - c_{0} - c_{1} RENE W_{t} | + (1 - θ) \sum^{|} GRO W_{t} - c_{0} - c_{1} RENE W_{t} |

(8)

\begin{aligned} \underset{d}{m i n} θ \sum^{|} CO 2_{t} - d_{0} - d_{1} RENE W_{t} - d_{2} GRO W_{t} | \\ + (1 - θ) \sum^{|} CO 2_{t} - d_{0} - d_{1} RENE W_{t} - d_{2} GRO W_{t} | \end{aligned}

(9)

Results

This study uses annual official Taiwan data that covers the period 1990–2018. The data on carbon dioxide emissions (CO2) and renewable energy (RENEW) are from the governmental Bureau of Energy, a branch of the Ministry of Economic Affairs. The variable of GROW is compiled from the Taiwan Economic Journal. All variables are in logarithmic form.

Before estimating equations (7) to (9), we use the augmented Dickey–Fuller⁴² (ADF) unit root test to determine the order of integration of these three variables. Table 2 shows the unit root test results in levels and first differences with trend and intercept. The results demonstrate that we cannot reject the null hypothesis of the unit root for three variables in levels. However, we reject the null hypothesis of a unit root at the 1% significance level for the first difference of these three variables. Based on the results from the ADF test, these three data series are integrated into order one.

Table 2.

Results from the augmented Dicker–Fuller (ADF) unit root test.

	Level	P-value	First difference	P-value
RENEW	−0.545	0.974	−14.041	0.000*
CO₂	−1.398	0.839	−4.520	0.007*
GROW	−1.928	0.613	−5.297	0.001*

*Indicates the parameter is significant at the 1% level.

CO₂: carbon dioxide; RENEW: renewable energy; GROW: economic growth.

Regarding the causal relationship between renewable energy and CO₂ emissions, and renewable energy and economic growth in equations (7) and (8), we demonstrate the causality test results in Table 3. The notation of RENEW ≠> CO2 means that the variable renewable energy does not affect the variable CO₂ emissions. Similarly, RENEW ≠> GROW means that the variable renewable energy does not affect the variable economic growth.

Table 3.

Results from RENEW to CO₂ and from RENEW to GROW at different quantiles.

Quantile	RENEW ≠> CO₂		RENEW ≠> GROW
Quantile	b ₁	P-value	c ₁	P-value
0.20	−1.035	0.001*	0.987	0.000*
0.40	−0.932	0.000*	1.072	0.000*
0.50	−0.923	0.000*	0.941	0.000*
0.60	−0.879	0.000*	0.888	0.000*
0.80	−0.888	0.000*	0.968	0.000*
OLS	−0.972	0.000*	0.949	0.000*

*Indicates the parameter is significant at the 1% level.

CO₂: carbon dioxide; RENEW: renewable energy; GROW: economic growth; OLS: ordinary least squares.

We found the following results. First, there is the causal relationship from renewable energy to CO₂ emission by using the traditional ordinary least square method (OLS) and using a quantile approach at any distributions of CO2 emissions. In other words, there is a direct relationship between renewable energy and CO2 emissions by using a quantile regression. This result shows that the negative effects of renewable energy on the low quantile CO₂ emissions are greater than those of the high quantile CO₂ emissions (see Table 3 and Figure 1). Moreover, there exists causality running from renewable energy to economic growth by using the traditional OLS method and using a quantile approach at any distributions of CO₂ emissions in Table 3. In other words, this result shows that the positive effects of renewable energy on the low quantile economic growth are closer than those of the high quantile economic growth. In summary, these results establish the first stage of the mediated effect.

Figure 1.

Changes in quantile regression coefficients.

Table 4 and Figure 2 show that d₂ is significant when using traditional OLS in equation (9); that is, the mediator variable GROW relates to the dependent variable CO2. This result establishes the second stage of the mediated effect. However, d₂ is not significant when using a quantile approach at any distribution of CO2 emissions. It means that the second stage of the mediated effect is not established by using a quantile approach.

Figure 2.

Changes in quantile regressions coefficients.

Table 4.

Results from RENEW and GROW to CO₂ at different quantiles.

Quantile	RENEW ≠> CO2		GROW ≠> CO₂
Quantile	d ₁	P-value	d₂	P-value
0.20	−0.511	0.107	0.427	0.194
0.40	−0.750	0.000*	0.181	0.246
0.50	−0.708	0.000*	0.203	0.256
0.60	−0.822	0.000*	0.058	0.738
0.80	−0.874	0.000*	0.016	0.916
OLS	−0.638	0.000*	0.351	0.011**

*Indicates the parameter is significant at the 1%.

**Indicates the parameter is significant at the 5%.

CO₂: carbon dioxide; RENEW: renewable energy; GROW: economic growth; OLS: ordinary least squares.

Moreover, through the OLS method, the variable RENEW relates to the dependent variable CO2 after the mediator variable GROW is controlled for, such that d₁ is significant in equation (9) and is smaller than b₁ in equation (7). This result illustrates partial mediation because of satisfying three steps in equations (7) to (9).

Third, through a quantile method, although the variable RENEW still relates to the dependent variable CO2 after the mediator variable GROW is controlled for at higher than 0.2 distributions of CO2 emissions in Table 4, the mediator variable GROW does not correlate to the dependent variable CO2. In other word, these results show that the negative effects of renewable energy on the high quantile CO₂ emissions are greater than those of the low quantile CO₂ emissions. These results are similar to Cheng et al. ^26,43 findings that renewable energy supply reduces CO₂ emissions with the strongest effect at the high quantile even though the authors used panel quantile regression to examine the impact of renewable energy on CO₂ emissions in OECD countries and the six developing countries, respectively. However, this condition suggests that the relationship between RENEW and CO2 examined under the second condition disappears when the mediated effect transmitted through GROW is considered. This result evidences no mediation effect because of not satisfying all four steps in equations (7) to (9).

Applying the traditional OLS method, we found that not only does renewable energy affect CO₂ emissions through the partial mediation effect of economic growth for the period of 1990–2018, but there is also a direct relationship between renewable energy and CO₂ emissions. Moreover, by utilizing quantile mediation regression, we demonstrate that renewable energy does not affect CO₂ emissions through the mediation effect of economic growth at any distributions of CO₂ emissions, which contrasts with previous empirical findings. However, there is only a direct effect from renewable energy to CO₂emissions at any distributions of CO₂ emissions in Taiwan. In summary, compared with the OLS regression results, we can assert that the quantile model provides much more useful and complete information on the impact of renewable energy on CO₂ emissions in Taiwan.

To test the stability of the estimated parameters obtained from quantile mediation regression, we applied the export variable which has a high correlation with economic growth, to rerun the regressions. Estimation results of this robust check are consistent with that of quantile mediation regression. Therefore, we conclude that the parameters of our models acquired from quantile mediation regression are stable.

Conclusion and policy recommendations

This study examines the effect of renewable energy consumption on CO₂ emissions in Taiwan. Economic growth is considered as a moderating variable. To require more robust results and obtain more information about impacts, this study utilized quantile mediation regression to estimate the median and the full range of the conditional distribution of the explained variables. Moreover, the direct and indirect impacts of renewable energy consumption on CO₂ emissions in Taiwan are analyzed.

The main conclusions of this study are threefold. First, the results of the quantile mediation regression indicated that there is a direct negative effect from renewable energy to CO₂ emissions in Taiwan. This indicates that renewable energy consumption has contributed to mitigating CO₂ emissions in the country. Second, the empirical result reflects that economic growth does not play a mediatory role in CO₂ emissions. Third, the negative effects of renewable energy on the high quantile CO₂ emissions are greater than those of the low quantile CO₂ emissions in Taiwan.

The key contribution of this paper is that we propose an innovative methodology that combines mediation analysis and quantile regression – this allows for obtaining the full characterization of the conditional distribution of the dependent variable, rather than its conditional mean only. That is, we provide a comprehensive picture of renewable energy to CO₂ emissions in Taiwan over the period of 1990 to 2018. The result of this innovative analysis indicates that Taiwan‘s renewable energy directly mitigates CO₂ emissions at any distribution. In accordance with this result, this paper recommends that the Taiwanese government should increase the use of renewable energy to reduce CO₂ emissions. First, the Taiwanese government can provide tax relief or investment incentives for manufacturers using renewable energy e.g. biomass and waste, solar thermal, conventional hydropower, geothermal, solar photovoltaic, and wind energy. Second, the Taiwanese government should adopt either contractionary fiscal policy or contractionary monetary policy or contractionary commercial policy to reduce CO₂ emissions.

The findings of this study must be considered some to have limitations which necessitates further research. Its main limitation is that it only focused on a single economy. Future studies can use a panel of other CO₂ emission nations for comparative analysis. Moreover, this study mainly considers aggregate renewable energy consumption, therefore, researchers can explore a disaggregated level analysis of renewable energy consumption.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

ORCID iD

Tzu-Kuang Hsu

Author biography

Tzu-Kung Hsu received his PhD degree in Economics in 1994. He is an Associate Professor in the Department of Business Administration at Chung Hua University, Hsinchu, Taiwan, ROC. His research interests include economic analysis and innovation, financial analysis, and energy management.

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