Could Cryptocurrency Policy Uncertainty Facilitate U.S. Carbon Neutrality?

Round 1

Reviewer 1 Report

This study investigates the short-run impacts of cryptocurrency policy uncertainty on U.S. carbon emissions. To the contents and results of this paper, I propose some questions and suggestions as follows:

1.      The definition of CPU is unclear. This study should explain it a bit more.

2.      The results need to be teased out much more. Why do you get the results you do? Think more about the economic story for the results. The authors mention that some information is lost when the weekly data is averaged into the monthly sequence in the LF-VAR model, and then this study adopt the MF-VAR model with CPU1, CPU2, CPU3 and CPU4. However, this study does not explain why there are different effects of CPU1, CPU2, CPU3 and CPU4 on carbon emissions.

3.      On page 3, line 106, the abbreviation of mixed-frequency vector auto-regression should be ‘MF-VAR’.

Author Response

Reply to the Reviewer 1

This study investigates the short-run impacts of cryptocurrency policy uncertainty on U.S. carbon emissions. To the contents and results of this paper, I propose some questions and suggestions as follows:

 

1. The definition of CPU is unclear. This study should explain it a bit more.

Response: Thank you so much for your comments.

We have added the definition of CPU as follows (Pages 1 and 6):

 

1. Introduction

The study aims to probe the conduction mechanism between cryptocurrency policy uncertainty (CPU) and carbon emission (CE) and also answer whether cryptocurrency policy uncertainty could facilitate the target of U.S. carbon neutrality. ...... Further, cryptocurrency policy uncertainty means that the policies of trading platforms and governments towards cryptocurrency are volatile (Lucey et al., [8]), that is the uncertainty caused by the authority’s failure to clarify the direction and intensity of cryptocurrency policy expectations, implementation and stance changes, which may exert specific influences on carbon emissions.

 

4. Data

This exploration selects the weekly (428 weeks) and monthly (107 months) sequences of January 2014 to November 2022 to probe if cryptocurrency policy uncertainty could facilitate U.S. carbon neutrality. ...... After that, this exploration chooses the weekly cryptocurrency policy uncertainty (CPU) index to reflect the situation of cryptocurrency policy, which could be taken from the authors’ website (Lucey et al., [8]). This index is counted by the following formula:

where N_t refers to the weekly observation of news articles on LexisNexis Business Database, which covers a a wide variety of newspapers and news agencies, containing three groups about the uncertainty of cryptocurrency policy: uncertainty or uncertainty; bitcoin, Ethereum, Ripple, Litecoin, Tether, cryptocurrency or cryptocurrencies; government, regulator or central bank. Then, they set the Group Duplicate option to MODERATE to minimize duplicate outcomes. v indicates the average of these articles and  points out the standard deviation. A higher CPU indicates there is a stronger uncertainty on cryptocurrency policy, and vice versa.

 

2. The results need to be teased out much more. Why do you get the results you do? Think more about the economic story for the results. The authors mention that some information is lost when the weekly data is averaged into the monthly sequence in the LF-VAR model, and then this study adopt the MF-VAR model with CPU1, CPU2, CPU3 and CPU4. However, this study does not explain why there are different effects of CPU1, CPU2, CPU3 and CPU4 on carbon emissions.

Response: Thank you so much for your comments.

We have added more economic story for the results, especially the different effects of CPU1, CPU2, CPU3 and CPU4 on carbon emissions. These contents are shown as follows (Pages 11-13):

 

In most cases, CPU_i (i=1, 2, 3 and 4) exerts an adverse effect on CE, and the underlying causes can be demonstrated in two sides. On the one hand, a high CPU may decrease investors’ desire to hold cryptocurrencies since they intend to avert possible risks and uncertainties (Lucey et al., [8]; Elsayed et al., [9]). After that, the transactions of cryptocurrencies would decline correspondingly, reducing electricity consumption and consequent carbon emissions in the U.S. (Yuan et al., [11]). For instance, the hackers have breached the security of the Bitfinex exchange (one of the world’s largest bitcoin exchanges) in August 2016, and they initiated 2072 unauthorised transactions, resulting in the theft of nearly 120000 bitcoins. Affected by this incident, the relevant trading platforms and governments have introduced policies to strengthen supervision, increasing CPU. The rise in CPU causes the demand for bitcoin to decrease, which is reflected in its price; the bitcoin price fell from 657.975 dollars in July 2016 to 576.890 dollars in August 2016. The reduction in demand and transactions for bitcoin decreases the amount of electricity used and greenhouse gases released (Sarkodie et al., [6]; Sarkodie and Owusu, [7]), and thus there is a decline in CE. On the other hand, a high CPU may reduce the willingness to mine cryptocurrencies to avoid huge losses due to uncertainties. Depending on the efficiency of different mining machines, one bitcoin currently consumes 200000 to 300000 kilowatt-hours of electricity, which is equivalent to the annual power consumption of 66 to 100 homes. Thereupon, a reduction in cryptocurrency mining would inevitably lead to lower electricity consumption (Baur and Oll, [4]; Jana et al., [5]), which decreases CE correspondingly. For example, the bitcoin halves not only increase CPU but also lead to a bitcoin block reward halving, which means that the reward given to miners for verifying new blocks is reduced by 50% (Kim et al., [45]). The cost for miners would increase since they need more computing power to obtain the same amount of bitcoins, which may cause some small-scale miners to exit the market (Su et al., [1]). After that, the market for bitcoin mining might shrink, further reducing electricity demand and carbon emissions.

In addition, high CPU may be caused by some restrictions, which directly decreases CE. For instance, the New York Governor Kathy Hochul signed a moratorium in 2022 on using fossil fuels to power bitcoin mining. This approved bill aims at bitcoin and other cryptocurrency mining enterprises that exploit cheap energy to mine digital assets, which causes CPU to increase. At the same time, the New York state plans to reduce carbon emissions by 80% through this bill, and CE would show a downward trend accordingly. Thus, we could conclude: Cryptocurrency policy uncertainty can facilitate the progress of U.S. carbon neutrality. However, this opinion could not be held in few cases, which is primarily reflected in the short-run CPU₂ and CPU₃. High CPU might also be caused by several events that support the development of cryptocurrency market, for example, some governments have allowed cryptocurrency transactions or even accepted cryptocurrencies as legal tender (Qin et al., [2]). After that, the growing popularity of cryptocurrencies sharply increases the enthusiasm for transactions and mining in the short term, which would be diminished since the public would be more rational in the medium and long terms. Thus, there is a positive effect of CPU₂ and CPU₃ on CE in the short run. Another example is the bitcoin bubble in 2017, which caused a significant increase in CPU, and the bitcoin demand also increased obviously in the short term due to its soaring price (Li et al., [46]), increasing CE. But after the bitcoin bubble burst, its demand and mining willingness dramatically decreased, which led CE to fall accordingly in the medium and long term. Although CPU₂ and CPU₃ have a positive influence on CE in the short term, this effect is less than that of CPU₁ and CPU₄ (which is shown in Table 3). Thus, the impact of total CPU on CE is always negative, even in the short run.

 

3. On page 3, line 106, the abbreviation of mixed-frequency vector auto-regression should be ‘MF-VAR’.

Response: Thank you so much for your comments.

We have changed to ‘MF-VAR’ as follows (Page 3):

 

Therefore, this exploration considers the mixed-frequency data and performs the mixed-frequency vector auto-regression (MF-VAR) model to obtain more information.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors,

It is a good read, however lacks on specific areas.

I believe that primarily you wanted to showcase interrelationship between cryptocurrency policy uncertainty (CPU) alongside carbon emission (CE) using low frequency and mixed frequency VAR models. Although it addressed a specific gap in this field, yet there are some areas to be covered. Why not TVP-VAR or QVAR or DCC-GARCH? Is the frequency of data matched properly the two segments (namely low and mixed frequency). Carbon neutrality has two parts: A. Emitting Carbon, B. Absorbing Carbon; therefore, the literature review needs to be modified around the same. For instance, too much money chasing too few stocks creating a Carbon Credit bubble (https://doi.org/10.3390/jrfm15080367); or identifying several flaws of Carbon Trading markets (https://doi.org/10.3389/fclim.2021.686516). Further, Bitcoin Carbon footprint (https://doi.org/10.3390/e24050647)didn’t change despite procuring too much emission, unlike Ethereum(https://www.theguardian.com/technology/2022/sep/15/ethereum-cryptocurrencycompletes-move-to-cut-co2-output-by-99). These aspects aren’t addressed. Moreover, positive connection exists between EPU and carbon footprint (https://doi.org/10.1016/j.mulfin.2023.100785). I believe these gaps needs to be filled before we consider it further. Apparently, your methodology seems perfect, however, the reasoning of low & mixed frequency of VAR models needs to be established with existing literature and intuitive understanding. For instance, why a VAR model, which is typically Gaussian is chosen for investigating such a complex interrelationship. Ideally, Gaussian methods don’t work in stressed conditions. Therefore, a sound theory is required here. Is your argument and findings consistent with any other study conducted recently? 

 

Sincerely

Reviewer

 

 

 

Author Response

Reply to the Reviewer 2

It is a good read, however lacks on specific areas.

 

I believe that primarily you wanted to showcase interrelationship between cryptocurrency policy uncertainty (CPU) alongside carbon emission (CE) using low frequency and mixed frequency VAR models. Although it addressed a specific gap in this field, yet there are some areas to be covered. Why not TVP-VAR or QVAR or DCC-GARCH?

Response: Thank you so much for your comments.

Since CPU is weekly data and CE is monthly data, the mixed-frequency vector auto-regression model is a more efficient estimated technique than the conventional approaches of collecting all sequences into the least frequency sampling. However, TVP-VAR, QVAR and DCC-GARCH can only construct models with the same frequency data, such as a monthly sequence counted by averaging weekly CPU, which may lose some weekly frequency data information and result in an inaccurate result. Thus, this paper applies MF-VAR model (including mixed-frequency data) rather than TVP-VAR, QVAR and DCC-GARCH models (including same-frequency data), which may obtain a more accurate and robust conclusion. Also, this paper proves that some information is lost when the weekly data is averaged into the monthly sequence, exhibiting a relatively weak explanatory power and even an inaccurate statistical inference (we can see it in Tables 2 and 3). From Table 3, we can perceive that CPU (CPU₁+CPU₂+CPU₃+CPU₄) could account for 6.6% (short-run), 9.2% (medium-run) and 10% (long-run) of CE, which possesses a higher explanatory power than the LF-VAR model. A similar phenomenon can be observed in other sequences, further evidencing that the MF-VAR model could fully use mixed-frequency data information, which results in a more accurate conclusion. Thus, it is reasonable to perform the MF-VAR technique to identify the complicated connection between CPU (weekly data) and CE (monthly data) under the control of OP (monthly data).

 

Table 2. Prediction error variance decomposition of the LF-VAR model

Decomposition of CPUa
	CPUa	CE	OP
h=4	0.967	0.002	0.031
h=8	0.966	0.002	0.032
h=12	0.969	0.002	0.029
Decomposition of CE
	CPUa	CE	OP
h=4	0.041	0.935	0.023
h=8	0.073	0.885	0.042
h=12	0.088	0.866	0.046
Decomposition of OP
	CPUa	CE	OP
h=4	0.097	0.006	0.897
h=8	0.195	0.017	0.788
h=12	0.281	0.017	0.702

Notes: The LF-VAR model uses monthly CPU_a, CE and OP, and this exploration performs the prediction error variance decomposition at horizons are 4, 8 and 12 months respectively.

 

 

Table 3. Prediction error variance decomposition of the MF-VAR model

Decomposition of CPU1
	CPU1	CPU2	CPU3	CPU4	Sum (CPUi)	CE	OP
h=4	0.431	0.074	0.125	0.324	0.954	0.016	0.030
h=8	0.365	0.088	0.111	0.397	0.961	0.012	0.027
h=12	0.339	0.095	0.102	0.431	0.967	0.010	0.023
Decomposition of CPU2
	CPU1	CPU2	CPU3	CPU4	Sum (CPUi)	CE	OP
h=4	0.401	0.138	0.083	0.338	0.960	0.018	0.022
h=8	0.333	0.133	0.085	0.415	0.966	0.012	0.022
h=12	0.312	0.132	0.080	0.446	0.970	0.011	0.019
Decomposition of CPU3
	CPU1	CPU2	CPU3	CPU4	Sum (CPUi)	CE	OP
h=4	0.292	0.126	0.259	0.298	0.975	0.005	0.020
h=8	0.249	0.126	0.173	0.422	0.969	0.007	0.024
h=12	0.246	0.126	0.146	0.457	0.975	0.006	0.019
Decomposition of CPU4
	CPU1	CPU2	CPU3	CPU4	Sum (CPUi)	CE	OP
h=4	0.190	0.135	0.077	0.561	0.962	0.018	0.020
h=8	0.211	0.135	0.067	0.557	0.971	0.012	0.017
h=12	0.213	0.134	0.069	0.561	0.977	0.009	0.014
Decomposition of CE
	CPU1	CPU2	CPU3	CPU4	Sum (CPUi)	CE	OP
h=4	0.019	0.003	0.011	0.033	0.066	0.903	0.031
h=8	0.019	0.006	0.020	0.047	0.092	0.865	0.044
h=12	0.020	0.006	0.023	0.051	0.100	0.850	0.050
Decomposition of OP
	CPU1	CPU2	CPU3	CPU4	Sum (CPUi)	CE	OP
h=4	0.080	0.036	0.024	0.045	0.185	0.009	0.806
h=8	0.104	0.049	0.017	0.101	0.271	0.021	0.708
h=12	0.123	0.060	0.014	0.148	0.345	0.021	0.634

Notes: The MF-VAR model uses weekly CPU_i (i=1, 2, 3, 4), as well as monthly CE and OP. Also, this exploration performs the prediction error variance decomposition at horizons are 4, 8 and 12 months respectively.

 

 

Is the frequency of data matched properly the two segments (namely low and mixed frequency). Carbon neutrality has two parts: A. Emitting Carbon, B. Absorbing Carbon; therefore, the literature review needs to be modified around the same. For instance, too much money chasing too few stocks creating a Carbon Credit bubble (https://doi.org/10.3390/jrfm15080367); or identifying several flaws of Carbon Trading markets (https://doi.org/10.3389/fclim.2021.686516). Further, Bitcoin Carbon footprint (https://doi.org/10.3390/e24050647) didn’t change despite procuring too much emission, unlike Ethereum (https://www.theguardian.com/technology/2022/sep/15/ethereum-cryptocurrencycompletes-move-to-cut-co2-output-by-99). These aspects aren’t addressed. Moreover, positive connection exists between EPU and carbon footprint (https://doi.org/10.1016/j.mulfin.2023.100785). I believe these gaps needs to be filled before we consider it further.

Response: Thank you so much for your comments.

We have underlined that no actual effort analyses carbon neutrality in terms of CPU, and sorted out the extant literature from three aspects: The first is the effect of cryptocurrency mining on the environment; the second is the connection between cryptocurrency and energy; the third is the interaction between cryptocurrency and carbon markets. Also, we have cited more related papers to reflect the current progress as follows (Pages 3-4):

 

2. Literature Review

Although no actual effort analyses carbon neutrality in terms of CPU, the existing investigations pay more attention to the following three aspects. Some scholars draw various conclusions concerning the effect of cryptocurrency mining on the environment. Li et al. [21] highlight that Monero mining might consume 645.62-gigawatt hours after its hard fork, contributing to 19.12-19.42 thousand tons of carbon emissions from April to December 2018. Corbet et al. [22] demonstrate that the electricity consumption of cryptocurrency transactions has increased considerably during recent periods, primarily caused by the growing difficulty in mining, and the total CE might exceed an individually developed economy. Vries and Stoll [23] propose a novel method to evaluate bitcoin’s e-waste, discovering that it will add up to 30.7 metric kilotons per year by May 2021. Howson and Vries [24] state that the digital infrastructure behind bitcoin (the most popular cryptocurrency) requires as much energy as the entire country of Thailand, which causes an aggravated climate crisis. Jana et al. [5] point out that bitcoin mining, hosted in a blockchain network, could consume considerable energy and generate e-waste at alarming rates. Sarkodie et al. [6] suggest that a rise in bitcoin trading volume spurs the carbon and energy footprint by 24% in the long term, while a dynamic impact promotes it by nearly 50%. Tee et al. [25] underline that economic policy uncertainty has a positive relationship with the carbon footprint, and this conclusion is suitable to the total, direct and indirect carbon emission measurements. Kohli et al. [16] reveal that as of July 2021, bitcoin’s energy consumption is equivalent to the countries such as Sweden and Thailand, which emits 64.18 million tons of carbon dioxide, and this emission is close to Greece and Oman. Zhang et al. [17] evidence that there is a significant Granger causality between the energy usage of bitcoin and CE, and the hash rate passes the most obvious net spillover effect to CE and bitcoin electricity consumption. However, the above view could not always be supported. Vranken et al. [26] underline that since there is a given amount of bitcoin, its growing popularity makes the competitors adopt new technologies to boost their profits at the lowest cost, which is beneficial to decrease the concerns about sustainability. Baur and Oll [4] ascertain that adding bitcoin into a diversified equity portfolio could improve its risk-return relation and decrease its aggregate carbon emission.

Some scholars explore the connection between cryptocurrency and energy. Su et al. [1] find that bitcoin and blockchain technology are the critical drivers of the Fourth Industrial Revolution, and the branches of the technology are rapidly spreading to other areas such as the oil market. Chitkasame et al. [27] point out a significant bidirectional causal relation between renewable energy consumption and bitcoin’s activity in low and high energy consumption regimes, highlighting that bitcoin’s action can not be ignored in preparing the energy policy. Ghabri et al. [28] present that bitcoin futures and stablecoins lead West Texas Intermediate (WTI) and Brent crude oil prices. Ethereum, Litecoin and Ripple preserve their position as leaders of WTI crude oil prices. Ghosh and Bouri [29] find that the bitcoin mining process possesses a feature of energy intensive, which could hinder the much-desired ecological balance. Lu et al. [30] investigate the dynamic spillover effect among cryptocurrency, clean energy and oil during the Corona Virus Disease 2019 (COVID-19), and show that the former is a net transmitter of spillover while the latter two are the net receivers. Meiryani et al. [31] show that global prices of energy sector commodities (mainly crude oil and natural gas) positively affect the bitcoin price movement. Yuan et al. [11] employ quantile connectedness to discuss the whole situation and dynamic evolution of information spillovers in the bitcoin market and discover that the hash rate and electricity demand are the main sources of risks. Le [15] indicates that the dynamic connectedness between crypto and energy volatilities is about 25% in the short run and 9% in the long run, the uncertain incidents (e.g., the COVID-19 and the Russo-Ukrainian war) exert specific impacts on the crypto and renewable energy volatilities. Salisu et al. [32] evidence that an increase in the oil price might be inclined to raise the costs of producing bitcoin, which is a benefit to lower its return and then reduce its trading and volatility.

Other scholars focus on the interaction between cryptocurrency and carbon markets, mainly from the investment perspective. Yang and Hamori [18] suggest that the European carbon market could be considered a safe haven or a hedge to avoid the cryptocurrency market, but this quality could not be shown in the Chinese carbon market. Chen and Xu [33] reveal that cryptocurrency possesses an extremely strong explanatory power for the carbon market and is also a favourite hedge for this market. Anwer et al. [20] prove that the environmentally sustainable and cryptocurrency indices show a common movement during the COVID-19; both could be viewed as hedges against each other. But Pham et al. [19] indicate that carbon price is mainly independent of cryptocurrencies during periods of low volatility. Besides, Ghosh et al. [34] highlight that the carbon credit bubbles are social and fuelled by the newfound interest in trading carbon credits, and pricing carbon is a crucial step in the transition to the future (Miltenberger et al., [35]).

 

References

Tee, C.M.; Wong, W.K.; Hooy, C.W. Economic policy uncertainty and carbon footprint: International evidence. J. Multinatl. Financ. M. 67, 2023, 100785.

Ghosh, B.; Bouri, E. Is bitcoin’s carbon footprint persistent? Multifractal evidence and policy implications. Entropy 2022, 24, 647.

Ghosh, B.; Papathanasiou, S.; Dar, V.; Gravas, K. Bubble in carbon credits during COVID-19: Financial instability or positive impact (“Minsky” or “social”)? J. Risk Financial Manag. 2022, 15, 367.

Miltenberger, O.; Jospe, C.; Pittman, J. The good is never perfect: Why the current flaws of voluntary carbon markets are services, not barriers to successful climate change action. Front. Clim. 2021, 3, 686516.

 

Apparently, your methodology seems perfect, however, the reasoning of low & mixed frequency of VAR models needs to be established with existing literature and intuitive understanding. For instance, why a VAR model, which is typically Gaussian is chosen for investigating such a complex interrelationship. Ideally, Gaussian methods don’t work in stressed conditions. Therefore, a sound theory is required here. Is your argument and findings consistent with any other study conducted recently?

Response: Thank you so much for your comments.

Firstly, we have established the reasoning of low & mixed frequency of VAR models with existing literature and intuitive understanding as follows (Pages 4-6):

 

3. Methodology

3.1. The Low-Frequency Vector Auto-Regression Model

First, we construct the conventional low-frequency vector auto-regression (LF-VAR) model (Motegi and Sadahiro, [36]) as the following formula:

              

where CPU_a,t and CE_t refer to the monthly cryptocurrency policy uncertainty and carbon emission. Since the oil market has close relations with cryptocurrency and carbon emissions, which might impact the interrelationship between CPU and CE (Qin et al., [2, 10]; Yuan et al., [11]). Thereupon, this exploration makes oil price (OP) control series, and Equation (1) can be rewritten as follows:

      

Then, we suppose that every sequence is adequately obvious to conform the covariance stationarity (Wang et al., [37]; Hu et al., [38]). In addition, this exploration sets the lag length (k) is 4. Moreover,  refers to the corresponding coefficient, where i, j=1, 2 and 3, k=1, 2, 3 and 4. On the basis of Equation (2), CE_t could be expressed as Equation (3).

 

where CPU_a,t indicates a monthly sequence counted by averaging weekly CPU, which could be rewritten as CPU_a,t = (CPU_1t + CPU_2t + CPU_3t + CPU_4t)/4. CPU_it (i=1, 2, 3 and 4) refers to the CPU at the i-th week of month t, and then Equation (3) can be further extended to the following formula. In Equation (4), CPU_i,t-k (i and k=1, 2, 3 and 4) exerts a homogeneous effect of  on CEt.

 

3.2. The Mixed-Frequency Vector Auto-Regression Model

The LF-VAR method generally utilises time-dependent summation to deal with the different frequency data. But Silvestrini and Veredas [39] ascertain that if high-frequency variables are forcibly aggregated or averaged (e.g., LF-VAR model), the statistical inference would be inaccurate due to the loss of information. The mixed-frequency vector auto-regression (MF-VAR) model, by contrast, possesses a unique advantage in making full use of mixed-frequency data information (Miller et al., [40]), which is beneficial to capture the heterogeneous effects of high-frequency sequences on low-frequency variables (Motegi and Sahahiro, [36]; Wang et al., [37]). Thereby, applying the MF-VAR model that does not require any filtering program could acquire the influence of weekly CPU on monthly CE under the control of OP.

The MF-VAR model is a more efficient estimated technique than the conventional approaches of collecting all sequences into the least frequency sampling (Ghysels and Valkanov, [41]). This model is mainly developed to be used in small proportions of sampling frequency (Götz et al., [42]; Ghysels et al., [43]). Hence, the MF-VAR model, which consists of weekly CPU and monthly CE and OP, could be developed as Equation (5).

  

where  (i, j=1, 2, 3, 4, 5 and 6, k=1, 2, 3 and 4) is the coefficient matrix, and  (i=1, 2, 3, 4, 5 and 6) is a disturbance term. The MF-VAR model could decrease the parameters’ number by fitting the function to a parameter of a high-frequency variable (Ghysels et al., [41]; Hu et al., [38]). In the above formula, it could be observed that CPU_1t, CPU_2t, CPU_3t and CPU_4t are stacked up as one vector. Thus, in order to distinctly represent the interaction between cryptocurrency policy uncertainty and carbon emission, Equation (5) could be further expressed as the following formula:

            

where  (j=1, 2, 3, 4, 5 and 6, k=1, 2, 3 and 4) could take various values from each other, thus CPU_1,t-k, CPU_2,t-k, CPU_3,t-k and CPU_4,t-k are viewed to possess a heterogeneous effect on CEt. Following Wang et al. [37] and Hu et al. [38], we explicitly set the Cholesky order, that is CPU_t - CE_t - OP_t in the LF-VAR model, as well as CPU_1t - CPU_2t - CPU_3t - CPU_4t - CE_t - OP_t in the MF-VAR model.

There are many methods to deal with mixed frequency data of the MF-VAR model, such as Kalman filtering approach, interpolation technique and Bayesian method in state space. Among them, the Bayesian method adopts iterative technique to estimate the missing value, in order to make full use of the known sample information. Through using the Bayesian method, the loss of some information could be avoided, and the parameter estimation under the mode of full information can be carried out, which is helpful to improve the accuracy of the MF-VAR model.

 

Secondly, we have cited several papers to evidence that my argument and findings consistent with other study conducted recently. These content are shown as follows (Page 11):

 

In most cases, CPU_i (i=1, 2, 3 and 4) exerts an adverse effect on CE, and the underlying causes can be demonstrated in two sides. On the one hand, a high CPU may decrease investors’ desire to hold cryptocurrencies since they intend to avert possible risks and uncertainties (Lucey et al., [8]; Elsayed et al., [9]). After that, the transactions of cryptocurrencies would decline correspondingly, reducing electricity consumption and consequent carbon emissions in the U.S. (Yuan et al., [11]). For instance, the hackers have breached the security of the Bitfinex exchange (one of the world’s largest bitcoin exchanges) in August 2016, and they initiated 2072 unauthorised transactions, resulting in the theft of nearly 120000 bitcoins. Affected by this incident, the relevant trading platforms and governments have introduced policies to strengthen supervision, increasing CPU. The rise in CPU causes the demand for bitcoin to decrease, which is reflected in its price; the bitcoin price fell from 657.975 dollars in July 2016 to 576.890 dollars in August 2016. The reduction in demand and transactions for bitcoin decreases the amount of electricity used and greenhouse gases released (Sarkodie et al., [6]; Sarkodie and Owusu, [7]), and thus there is a decline in CE. On the other hand, a high CPU may reduce the willingness to mine cryptocurrencies to avoid huge losses due to uncertainties. Depending on the efficiency of different mining machines, one bitcoin currently consumes 200000 to 300000 kilowatt-hours of electricity, which is equivalent to the annual power consumption of 66 to 100 homes. Thereupon, a reduction in cryptocurrency mining would inevitably lead to lower electricity consumption (Baur and Oll, [4]; Jana et al., [5]), which decreases CE correspondingly. For example, the bitcoin halves not only increase CPU but also lead to a bitcoin block reward halving, which means that the reward given to miners for verifying new blocks is reduced by 50% (Kim et al., [44]). The cost for miners would increase since they need more computing power to obtain the same amount of bitcoins, which may cause some small-scale miners to exit the market (Su et al., [1]). After that, the market for bitcoin mining might shrink, further reducing electricity demand and carbon emissions.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Thank you for amending your paper correctly. Good luck!