The causal relationship between renewable energy and economic growth in the US

Размещено на http://www.allbest.ru

Размещено на http://www.allbest.ru

Introduction

Nowadays the renewable energy consumption continues to grow. According to the International Renewable Energy Agency (IREA), the world consumption of renewable energy increased by 206.8% from 2009 to 2018 (from 1136226 to 2350755 British Thermal Units). Renewables are assumed to have a positive effect on economic growth so that its consumption continues to be boosted by the policymakers. However, the type of relationship between renewable energy and economic growth still varies between different countries. Because of this, in the last decades there has been an increasing interest in the science community to the analysis of the relationship between renewable energy and economic growth. Researchers of this field have implemented various instruments to shed a light on this problem, but there has not been a common conclusion yet.

The transition towards renewable energy sources began at the end of the last century caused primarily by several reasons. The first reason is the growing demand for energy. The required amount of energy today is largely covered by traditional energy sources, which is why a large amount of the use falls on natural resources. Renewable energy sources, unlike traditional ones, are potentially inexhaustible and more evenly distributed across the globe, so that the energy supply may be diversified among different types of energy. The diversification of energy supply could optimize the tariff prices and make the energy more available. The second reason is that the uniform distribution of energy could solve the problem of insecure energy supply caused by centralization of energy extraction in fossil fuel-rich regions. There are also many other reasons that encouraged the transition towards the renewable energy consumption, which includes the depletion of the environment, reduced public health, balance of payments problems in different countries, etc.

The relevance of this research can be underlined by the fact that it provides an awareness about the possible effect of renewable energy consumption on economic growth and gives the rationale for the development of a suitable energy strategy for the national economy. The need for analysis for different countries with numerous methods is attributable to the requirement of the relevant conclusion about the renewable energy consumption effect in a particular country. Therefore, the aim of this work is to investigate the causal relationship between renewable energy consumption and economic growth in the US. The object of the study is the renewable energy consumption and the subject of the study is the impact of renewable energy consumption on economic growth. The difference of the current work from the previous works is the employment of the Bayesian Inference. As far as is known, there are no studies in this field that implement such a methodology.

For achieving the aim, the following tasks have been accomplished:

1) To specify the econometric model considering the data characteristics;

2) To construct the Orthogonalised Impulse Response functions on the basis of the estimated model;

3) To draw conclusions on the nature of the impact of renewable energy on economic growth.

The work is organized as follows. The first part of the study is the literature review, which gives concepts to the basic definitions, an overview of the techniques, and other theoretical aspects of the topic. In the second part of the study the research problem is stated, where the hypotheses are given. The third part of the study contains a description of the methodology used for the analysis. In the fourth part of the work obtained results are described. Finally, the last part of the work provides the conclusions of the analysis.

1. Literature review

The importance of energy is attributable to the requirement of energy to produce goods and services. Along with both increase in population and technological development, demand for energy has amplified dramatically. For instance, in 2017 the total production of energy in the world was 14034897 kilotons of oil equivalent (ktoe), whereas in 1997 there were 9?604?842 ktoe of energy produced. On the Figure 1 the dynamic of energy production is illustrated.

Figure 1. Total primary energy supply for 2001-2017, kilotons of oil equivalent (ktoe)

As shown in Figure 1, energy production has an increasing trend. Simultaneously, due to the dominance of fossil fuels in the total energy consumption, carbon dioxide (CO2) emissions have an increasing trend similarly (Figure 2).



Figure 2. CO2 emissions for 2001-2017, metric tons of CO2 equivalent

renewable energy economic

Carbon dioxide is a gas that presents in the Earth atmosphere and is involved in living activities. Its rate is regulated by photosynthetic organisms, which consume CO2 and turn it into oxygen. Since worldwide industrialization, there has been an increase of the CO2 content in the atmosphere, because of escalating manufacturing and deforestation. High concentrations of CO2 could lead to performance degradation and decreasing of the populations' health (Allen et al., 2016). Moreover, high concentrations of CO2 could also damage the natural environment by the suffocation of living creatures and depletion of nature. The detriment both of nature and population wealth have a negative influence on the country economy. The implementation of renewable sources in the energy system would curtail CO2 content in the Earth atmosphere. That is one of the reasons for the transition towards renewable energy. The other reasons for renewable energy implementation will be described further.

Since renewable energy sources were credited with growing social interest and have been experiencing a widespread introduction, the concern about the renewable energy-growth nexus has been increasing among researchers during the last decades. According to the International Renewable Energy Agency (IRENA), the worldwide consumption of renewable energy has increased by 106,8 percent from 2009 to 2018. It has been caused by the desire of Governments and social organizations to ensure the transition of the energy systems towards renewable energy sources, which are carbon-free, reliable, and sustainable. Besides, the Energy Information Administration (EIA) reported that the volume of energy gained from renewable sources had exceeded the volume of energy gained from coal in the USA in April 2019.Despite the societies' request for a `clean' energy system, economic growth is still prioritized for governments (Domac et al., 2005) and there is no chance of instantaneous shift towards clean energy due to entry barriers (Afonso et al., 2017). However, the motivation for renewable energy implementation is associated not only with ecological issues but also with economic gains, and in theory it could benefit for the national economy (Domac et al., 2005).

There is still no common definition for the term `renewable energy'. However, there are possible definitions for this term:

1) Renewable energy is energy from sources that are naturally replenishing but flow-limited; renewable sources are virtually inexhaustible in duration but limited in the amount of energy that is available per unit of time (EIA);

2) Renewable energy is defined as the contribution of renewable energy to total primary energy supply. Renewable energy includes the primary energy equivalent of hydro (excluding pumped storage), geothermal, solar, wind, tide, and wave sources. Energy derived from solid biofuel, biogasoline, biodiesels, other liquid biofuels, biogases and the renewable fraction of municipal waste is also included (OECD);

3) Renewable energy is defined as energy that is produced by such natural resources, like sunlight, wind, rain, waves, tides, and geothermal heat and which is naturally replenished within a time span of a few years.

From the above-mentioned definitions, the common definition for the `renewable energy' can be figured, which would be the following: `Renewable energy is energy produced from self-restoring sources for the time period that is suitable for a human.'

As already has been mentioned, the one of the main reasons for transition towards renewable energy is a high concentration of CO2 in the atmosphere. The other reasons of gradual transition towards renewable energy sources are:

1) Finiteness of such a nonrenewable source, like natural gas, coal, oil, etc. The limitations are caused by the extended time required for its recreation. Growing demand for energy surpasses the rate of sources' recovery so that the fossil fuel reserves are being diminished. The scarce of fossil fuels could lead to a price boost for non-renewable energy in the future;

2) Because of ecological depletion, the health of the population decreases. Poor health causes performance degradation, so the economic growth, which relies on production efficiency, will be negatively influenced and declined. Besides, because of both environmental pollution and destruction of arable lands, the agricultural activities will be also injured, and the part of the population involved in agriculture would experience the income fall;

3) Renewable sources are distributed more evenly in comparison to fossil fuel sources (Burke and Stephens, 2017). The availability of renewable energy sources would give countries such economic gains, as job creation and low-cost energy. Due to developed technologies, a prime cost of renewable energy production is low, and the availability of sources will not demand transition costs. As a result, the cost of renewable energy can conquer the cost of fossil fuel energy;

4) The possibility of renewable power station construction, the investments in poor countries, such as some African countries, could be attracted. Consequently, the boosting of the country economy could occur (Ben Aпssa et al., 2014).

Due to the global transition to renewable energy, the implementation of renewable sources is a prime objective for countries, which tend to meet international competition. In the energy policy, the chosen strategy success relies on the primary country conditions. The politician should be aware of strategy consequences before the decision making because for different countries there would be different effects from the same strategy due to social, technical and political diversity (Xu et al., 2019).

In this section the history of renewable energy for the United States of America is overviewed, and the characteristics of energy policies are elicited. The reason for making the overview is attributable to dataset, which is containing the data of energy consumption for the USA. The observation of history could lead to better interpretation of the results.

The first reason for the US is the global trend of transition to renewable sources among leading countries. As an instance, in 2009 the participants of the European Union set a target to achieve 20% of renewable energy in total energy consumption. The second reason is the Kyoto protocol - an international treaty established in 1997 and obligating participants to reduce greenhouse gas concentration in the atmosphere. At the same time, in the USA the specific objectives regarding renewable energy were not considered. Only in 2009, when President Barack Obama was elected, the renewable energy issues were put on the agenda on the Federal level. Before that moment the states of the US were dealing with renewable energy issues in their own way, defining standards renewable energy production by themselves.

In the USA the energy industry due to government politics was in the natural monopoly condition from 1935 to 1973. It had been implemented and regulated in such a way since the entire energy infrastructure was thought to be more effective administrated by one producer rather than by many competitive producers. Then and there, the major sources of energy were oil and coil. However, in 1973 an oil embargo was imposed against Canada, Japan, the Netherlands, the United Kingdom, and the United States. In 1978 there was the second oil crisis associated with a scarce of oil supply in the wake of the Iranian Revolution. The consequences of both oil shocks were the supply reduction of oil and the increase in oil prices fourfold, and the price was seemed to continue to rise in the future. In turn, there was an increasing demand for energy year by year due to both rapid technological development and population growth. For solving that situation, the government demonopolised the energy industry and facilitated the development of such alternative energy sources, like nuclear energy and coil. It was later revealed that the costs of nuclear power stations are higher than the historical average costs for other types of plants so that the nuclear plants were not able to compete with much less expensive fossil fuel plants (Lovering et al., 2016).

At the same time, the local power and renewable energy stations, which were providing limited number of households with energy, were facilitated by ratification of specific laws. The prime example of law is PURPA (The Public Utility Regulatory Policies Act)that was adopted in 1978 to encourage fuel diversity via alternative energy sources and to introduce competition into the electric sector. It was created in response to the oil crisis, and it required utilities to purchase electricity from non-utility generators for the price equal to utilities prices, not cost price of generator. As a result, the renewable energy generators took advantage of the law and forced utilities to purchase renewable energy at inflated rates with over long contract durations. This led to the fact that the investors of renewable energy plants obtained high profit, which subsequently was directed to the development of renewable technologies. Since there was a shortfall of prices for wind energy by 80% for the next 10 years due to technology development. In addition, in California the production of wind energy was 85% of total world production, and the production of solar energy was 95% in 1990. Another key policy measure used by the government and that stimulated renewable energy development was the Renewable portfolio standard (RPS). For the first time, it has been adopted in 1983 in Iowa. According to this law, the minimal volume of energy, supplied by renewable sources, had not to be lower than a standard defined value. In case generators fail to fulfill the requirements, a penalty that serves as an enforcement mechanism must be paid by the generator to the state. Later, in the mid of 2000, similar laws have been adopted in other states to reduce the rate of unemployment and to contribute to economic development (Lyon, 2016). At present, 29 of 53 states have adopted RPS.

Along with laws, the tax incentives stimulated the local renewable energy producers for developing too, because the decreased relative cost advantages were allowing renewable energy to be competitive with the other types of energy. For instance, there is still a Renewable Electricity Production Tax Credit that allows credit amount up to 2.5 cents per kWh produced renewable energy. Another factor was the de-monopolization of the energy industry, that allowed renewable energy producers to create both investment and debt capital, which facilitated their development undoubtedly. The abovementioned factors have boosted renewable energy development so that the volume of energy supplied from renewable sources has accrued since the 1980s. In Figure 3 the dynamic of renewable energy consumption in the US from 1973-2019 is illustrated.

Figure 3. Consumption of renewable energy by type for 1973-2018, trillion Btu

As can be seen on the graph, the total renewable energy consumption has been increasing since 2001. Such a change was driven by the escalation of wind energy and biofuels consumption. Biofuels are used by public transport, and projects dealing with biofuels are actively promoted by American automakers and sponsored by the government. Solar and wind energy are more clean energy in compare to biofuels. Along with the ecological attractiveness, an appeal of them is rapid technological progress due to which the wind and solar energy are efficient. These reasons facilitate the attraction of funds for both further development and increasing of the market share for these types of renewable energy. In the Figure 4the dynamics of renewable energy share in total energy consumption is shown, and we can see that there is also an increasing trend.

Figure 4 The ratio dynamics of renewable energy consumption to total energy consumption

Overall, there is a slight rise in renewable energy share in total consumption of energy due to the fact that total energy consumption has been growing approximately at the same rate as renewable energy consumption up to 2007. From 2007 the increase in the growth rate of renewable energy consumption is observed.

In this section the costs for renewable and nonrenewable energy would be provided. It will be done because the economic benefit is a matter of cost. Therefore, the cost should be taken into consideration if a project is planned to be functioning in the long-run period. For successful implementation, renewable energy stations should have a competitive cost compared to other types of energy. Firstly, the economic reasons for belated development for renewable energy will be provided to see an overall pattern.

By the virtue of both late development and high costs, there was a belated development of the renewable energy industry. It was due to the following economic reasons. Firstly, there was a high entry barrier for renewable energy producers due to the ascendancy of the monopolistic firms, which were supplying energy from fossil fuels. Indeed, due to the availability of advanced and proved technologies for the energy of fossil fuels, there has been invested a large amount of money in the development of the nonrenewable power stations.

Secondly, at that period of time, there were exorbitant capital costs for renewable power station construction. Along with that, there were additional costs related to purchasing batteries for compensation of renewable energy variability. The variability of renewable energy is attributable to weather conditions. As an instance, when there is a strong wind, the wind station produces a greater amount of energy than essential, whereas in windless conditions the energy station underperforms. The surplus of energy produced in windy conditions could be passed to batteries, which then provide the households with energy in windless time.

Currently, the capital costs for renewable energy power stations are competitive with other types of energy thanks to the rapid development of technologies. For the comparison of construction costs for the different types of power stations, the Levelised cost of energy (LCOE) is used. LCOE is an average cost of energy production during the entire lifespan of the power plant so that it could be interpreted as the cost of the one energy unit.It is used for the analysis by such companies, as Mott McDonald, Arup, Ernst and Young (Aldersey-Williams, Rubert, 2019).

The financial advisory and asset management firm `Lazard Ltd' assesses LCOE of different energy types for the US annually. Lazard Ltd does not reveal the methodology of their analysis, but for the getting an idea of what is standing for the LCOE, the following formula, that captures the essence, is provided (Aldersey-Williams, 2019):

()

where is the capital cost for the period t (including decommissioning).

is fixed operating cost for the period t.

is variable operating costs for the period t (including fuel costs, carbon tariffs, taxes and etc.).

is produced volume of the energy for the period t.

is discount rate.

is project life in years.

There is the Lazard Ltd's analysis of LCOE on Figure 5.

Figure 5. The Levelised cost of power plants by energy type for 2019 year, $/MWh

As can be seen from the graph, the LCOE of both renewable energy and conventional energy have nearly equal values. Therefore, the cost of renewable energy station is competitive with traditional ones, and renewable energy projects could be considered ad beneficial nowadays. It is notable that in the case of renewable energy production there are no costs for fuel transportation, which in circumstances of non-renewable energy are crucial.

In conclusion, the economical obstacles and comparison of energy costs have been reviewed. Although the high costs in the past, renewable energy is quite competitive in the energy market nowadays due to the competitive costs and incentives from the government.

In this section, the review of the economic models will be provided. The aim of it is to determine the economic model, which would help with the analysis presented.

For the analysis of energy consumption and economic growth several models of economic growth could be employed, where the energy may be used as one of production factors. To start with, the core models for economic growth, such as neoclassical models and endogenous growth models, do not include energy as a production factor (Stern, 2011). For example, in the model of Solow, AK model, Shumperter model, and the Arrow model energy is not considered at all. In neoclassical models, the long-run economic growth approximately equals exogenous technologic development growth, and the economy approximates the steady-state equilibrium. In the AK model - the endogenous growth model, - the technological knowledge is anticipated as another form of capital, and the economic growth is represented as a product of technology development and capital, AK. Although energy is a necessary factor of production in modern economies, the rest of early growth models follow a similar framework and does not include the energy consumption. However, energy could be a constraining factor for production in a way similar to other factors. The limitation of energy is caused by the finiteness of the energy sources, and the lack of energy could drag on growth and devalue the positive effect of technological development for income. Due to this limitation, the long-run equilibrium does not possible. Hence, renewable sources could contribute to sustain development and facilitate the increase in income (Arbex & Perobelli, 2010).

An alternative approach for analysis of the economic growth is the biophysical framework, which was proposed in the ecological economy sphere. In the view of this approach energy is the only factor of production, and other factors are not controlled (Stern, 1993). This assumption is based on the ideas about thermodynamics laws and on the fact that the labor and the capital are a continuous process so that they are intermediate factors that started from energy consumption. There are two main thermodynamics laws: the mass-balance law and the energy efficiency law. According to the first law of thermodynamics, for the production of the particular quantity of output, the equal or greater volume of matter is needed, including the part transformed into the emissions. The energy efficiency law asserts that energy is essential for the running process of production, and under the time limitations even the greater volume of energy is required. Thus, there are minimal requirements for the production process, relating to energy limitations (Stern, 1993). Besides, in the paradigm of this model, the prices for commodities are differentiated from the energy prices. Having an assumption that a return to scale is constant, the model turns into the Leontieff model with the energy as the single factor of the production (Stern, 2011). This model is commonly used because of its simplicity and justification (Al-mulali et al., 2013; Shahbaz et al., 2011).

As has been said, in modern economy energy is an essential factor of production due to energy-dependent technologies required for the production of goods and services. Because of developed economies consuming a great volume of energy, reasoned energy strategies are needed for sustainable economic growth. The implementation of renewable energy sources is inevitable in the long-run perspective due to the finiteness of traditional energy sources. Besides, the transition towards renewable energy sources potentially could prevent the impact of both prices and supply shocks coming from the conventional energy sphere. However, the influence of renewable energy consumption for each individual country is quite different, and it could even have a negative effect on economic growth. Therefore, the analysis of renewable energy consumption impact on economic growth is necessary, because the policymakers should be aware of the potential results of introduced strategies. The awareness of renewable energy effect would allow developing of the most suitable strategy of energy sector transformation.

As has been said, renewable energy sources are distributed more evenly in comparison to nonrenewable sources (Burke, 2017). Besides, the previous studies proposed that the results of the renewable energy implementation in the main grid over a period of 1975-2010 in Bangladesh, India, Nepal, Pakistan and Sri Lanka could be (Zeb et al., 2014a):

1) The increasing of the index human development due to the technological advancement of renewable energy generation and decreasing of the environmental pollution;

2) The increasing of the net domestic product (NDP) due to lower costs for renewable energy extraction using the state-of-art technologies;

3) Decreasing the poverty rate by creating new jobs through construction of new renewable energy grids. For instance, the renewable energy industry could create more jobs potentially, than the traditional energy industry does. In fact, occupations in renewable energy industry have the fastest growth, which prevails the growth of the US economy. Although there still has been about 1 million jobs in the oil industry, the quantity of the `green workers' could predominate the employment of the oil industry in the future;

According to Ernst & Young Global Limited, there is a pursuit among the society of the US towards `clean' energy, and entities that want to operate in the long-run period should introduce innovations into their grid systems. Also the more electricity is going to be needed in the future because of the inevitable electrification of transport. Renewable energy sources are able to meet the requirements of the growing demand on electricity due to advanced technologies. However, due to the possibility to have such a renewable energy generator at home, as rooftop solar, the way energy is generated and consumed would be transformed, so that it would destabilize the electricity system. Transformation would take costs.

In addition, the dependence on nonrenewable resources could lead to decreasing of economic growth in the long-run period, causing the fall of the population wealth too. It was thought that the availability of such an energy source, as oil, coal and natural gas guaranteed sustainable and long run economic growth due to foreign trade. Besides, in the past the one unit of conventional source gave more energy than the other energy sources. However, technologies for renewable energy generation have advanced and it is inappropriate to rely solely on conventional energy. Some researcher insists that the economic activity of countries depending on the nonrenewable sources is followed by the energy source depletion and its inefficient usage (Arrow et al., 2012; Lawn, 2003). It is also confirmed by the fact that the countries depending on the non-renewable energy have costs on energy imports. The need of energy importation is followed by the dependence from the countries-exporters. In turn, it indicates about importer-country vulnerability against global energy market and exporting countries. From the fact as described above, it is more rational for countries to generate energy by themselves, using the renewable energy sources that more available. Such a shift would countries allow to make a break of inevitable bond between economic growth and environmental pollution.

Aside from pollution, the catastrophes occurring on the factories also cause losses of funds. Thus, the means that are directed on the neutralization of ecological problems could be redirected to country development if renewable energy was widely adopted. Besides, there are 4.2 million death per year from air pollution. To compare, there was 9.6 million deaths due to cancer .These all causes instability of the economic growth.

The first research dedicated to casual energy-growth nexus was published in 1978, and the unidirectional causation running from GNP to energy consumption was found by the implementation of the Granger causality (Kraft & Kraft, 1978).Since then a bunch of research, studying the energy-growth nexus, has been performed. Although, there has not been consensus about the relationship between the mentioned variables. The reason for the controversial results lies in the diversity of both research design and samples. Due to the variety of the results, the following four groups of hypothesis have been distinguished:

1) The first group is related to `the growth hypothesis', indicating that energy consumption influences the economic growth in a direct and indirect way. The idea behind this hypothesis is that energy is the essential factor of the production, and change of its consumption rate would influence the economic growth (Hajko et al., 2018). The growth hypothesis is supported if there is unidirectional causality running from energy consumption to economic growth (Apergis & Payne, 2010).

2) The second group of the research confirms the `the conservation hypothesis'. This hypothesis describes the unidirectional influence, going from economic growth to the consumption of energy. Due to the accruement of the commodities and the assets, there is a greater demand for energy. Besides, such a causal relationship allows reducing the energy consumption so that the environment would benefit. In the case of this theory the energy conservation strategy would be beneficial only if resources will be distributed effectively (Apergis&Payne,2011).

3) The third group results confirm `the neutrality hypothesis', according to which there is no relationship between energy consumption and economic growth. The neutrality hypothesis is supported by the absence of a causal relationship between energy consumption and economic growth. It is explained by the fact that there are other factors of production, and the energy consumption could have a scarce influence (Apergis &Payne, 2011). In this case any energy strategy could be implemented.

4) The last group of research describes the bidirectional nexus between those two factors, according to which the energy consumption has an influence on economic growth, and vice versa. The idea of the hypothesis is that these factors are the complements in the long-run period (Apergis & Payne, 2011; Григорьев & Кудрин, 2013). According to this hypothesis, the constraints on both factors would lead to a change in them simultaneously. This hypothesis is called `the feedback hypothesis'.

In line with the studies, investigating the relationship between total energy consumption and economic growth works dedicated to renewable energy also appeal to the same four hypotheses, because the consumption of renewable energy is the part of total energy consumption. As well as in the previous studies about total energy consumption, the results for renewable energy-growth nexus research is ambiguous, and this diversity is caused again by the various design of research and country samples.

The growth hypothesis has been confirmed for the majority of the 38 major renewable energy-consuming countries, where along withthe renewable energy, the labor force, non-renewable sources and capital formation were controlled (Bhattacharya et al., 2016). In this study `the growth hypothesis' has been confirmed for the US, but the renewable energy effect has occurred to be negative. The same result has been obtained for other 85 countries (Bhattachary et al., 2017). It is noteworthy that the factor of institutions was considered along with renewable energy consumption and CO2 emissions, and the positive effect of the institutions on the economic growth was revealed. Also Menegaki has confirmed the growth hypothesis for 27 European countries by implementing random effect model for cointegration (Menegaki, 2011).

`The conservation hypothesis' has been confirmed for a sample of 51 Sub-Sahara African countries (Ozturk & Bilgili, 2015). Along with renewable energy consumption, the authors investigated the influence of economic openness and population, which occurred to have a positive effect on economic growth. Another study, which has corroborated `the conservation hypothesis' and controlled for the countries' cross-dependence, was carried out for the 10 countries of Sub-Saharan Africa producing the greatest volume of electricity (Inglesi-Lotz & Dogan, 2018).Notably, in this research trade openness has been revealed to cause the rise in consumption of renewable energy and the income increase in the countries of Sub-Saharan Africa.

The confirmation of `the neutrality hypothesis' has been provided in previous research for renewable energy consumption too. The random effect model for the cointegration and panel cointegration model have been estimated for 27 Europian countries and a weak causal relationship running from renewable energy to economic growthhas been validated (Menegaki, 2011).However, the panel cointegration model used in the work did not reveal either short and long period Granger causality for the investigated variables. As the authors assume, such a result is incited by the sample size due to the early stages of renewable energy. For Turkey also the neutrality hypothesis has been confirmed (Bulut & Muratoglu, 2018). According to the author, there are two possible reasons for `the neutrality hypothesis'. The first is the idea that renewable energy consumption has a little share of total energy consumption. The second idea is the fact that non-energy intensive sectors (e.g. services) are prevailing in the economies of developed countries, and due to it the stimulating factors for economic growth are technologies and information.

The last hypothesis - `the feedback hypothesis', - has been revealed by Salim and Rafiq for Brazil and China (Salim & Rafiq, 2012). Omri has found bidirectional causality for Argentina, Brazil, France, Pakistan and the USA (Omri et al., 2015). Along with that, Narayan and Doytch using the GMM methods with fixed effects have settled the bidirectional causality for 89 countries (Narayan & Doytch, 2017).

Others studies for causal relationship between economic growth and renewable zenergy are listed inTable 1.For the US data many research for renewable energy and the economic growth also were conducted. The literature dedicated to US are listed in Table 2.

Table 1. The studies dedicated to the relationship between renewable energy consumption and economic growth

Authors	Sample	Period	Methodology	Findings
Belaпd and Zrelli (2019)	9 Mediterranean countries	1980-2014	Pooled Mean Group (PMG) estimator; Autoregressive Distributed Lag (ARDL)	REC Y
Kahia et al. (2017)	11 MENA countries	1980-2012	Panel Granger causality tests; vector error correction	REC Y
Koзak and Sё arkgьnesёi (2017)	10 Balkan and Blacksea countries	1990-2012	Panel cointegration; Heterogeneous panel causality	REC Y (5 countries) REC Y (3 countries) RECY (Turkey)
Lin &Mubarek (2014)	China	1977-2007	Cointegration tests; Granger causality	REC Y
Magnani & Vaona (2013)	Italian regions	1997-2007	System GMM	REC Y
Chen et al. (2020)	103 countries	1995-2015	Dynamic panel error correction threshold regression model; Linear GGM; Sup-Wald test (Seo & Shin, 2016)	REC Y (if developing country or non-OECD countries surpass a certain threshold of renewable energy consumption) REC Y (if developing country or non-OECD countries renewable energy consumption is below a threshold level) REC Y (developed countries) REC > Y (OECD countries)

Table 2. The literature for the relationship between renewable energy consumption and economic growth in the US

Authors	Period	Methodology	Findings
Ewing et al., 2007	2001:1-2005:6	Generalized forecast error variance decomposition
Payne, 2009	1949-2006	Toda-Yamamoto causality	?
Bowden & Payne, 2010	1949-2006	Toda-Yamamoto causality
Yildirim et al., 2012	1949-2010	Toda-Yamamoto causality
Menyah & Wolde-Rufael, 2010	1960-2007	Modified Granger causality test
Omri et al., 2015	1990-2011	Simultaneous equations GMM estimation

Most of the techniques used in research listed in Table 2 are the causality tests. Indeed, the results of research are different due to various methods used, and even for the US there are no mutual conclusion about effect of renewable energy consumption on economic growth. Besides, there is no research implementing Bayesian inference.

In conclusion, the literature overview of the previous research has been provided. Many of the latest research were analyzing the renewable energy consumption controlling for the other factors of production. Moreover, a bunch of methodologies have been implied for the analysis of mentioned problem, and different aspects relied have been considered. In spite of the numerous research in this field, the common result has not been still obtained.

2. Research question

In this work the casual relationship between renewable energy and economic growth for the US quarterly data is analyzed. Following the previous research, the other variables, such as non-renewable energy consumption, labour and capital have been included (Apergis, 2011). For the investigation of the casual relationship for the short-run period, the orthogonal impulse response functions have been constructed on the base of Bayesian Vector Error Correction Model (Koop et al, 2009). The four following hypothesis have been tested: H1: There is an absence of a causal relationship between energy consumption and economic growth (the neutrality hypothesis). H2: There is unidirectional causality running from energy consumption to economic growth (the growth hypothesis). H3: There is unidirectional causality running from economic growth to energy consumption (the conservation hypothesis). H4: There is bidirectional causality between energy consumption and economic growth (the feedback hypothesis).

The Bayesian Vector Error Correction Model is implied by several reasons. Firstly, the number of observations is only 187, that insufficient for getting unbiased coefficients in the case of employment of the frequentist methods. Secondly, Bayesian inference allows researchers to implement their beliefs or expectations in the analysis. For example, in case of VECM, we can set priors for coefficients from cointegration equation to be negative. Secondly, the Bayesian inference has been confirmed to provide researcher with more precise forecast results (Koop, 2009).As far as is known, this approach has not yet been applied for this problem.

3. Data description

All variables are employed with their natural logarithms in accordance with previous studies (Wolde-Rufael, 2014; Ozturck, 2015). The quarter data for GDP, the labor force and capital was obtained from Federal Reserve Economic Data (FRED) for the period starting from 1973Q1to 2018Q3. The data for energy consumption was collected from U.S. Energy Information Administration for the same period, and from the Fig.8we can see that the consumption of non-renewable energy is much more than that of renewable energy.The descriptive statistics could be seen in the Appendix.



Figure 6. The Dynamics of GDP, Q1/1973-Q3/2019

Figure 7. The Dynamics of Capital and Labor Force, 1Q/1973-3Q/2018

Figure 8. The Dynamics of Consumption of the Renewable and Nonrenewable Energy,1Q/1973-3Q/2018

In Fig.9 and Fig. 10 the seasonal Box Plot for renewable and Nonrenewable consumption are shown. The rest of the variables - GDP, capital, and labor force, - do not have seasonal components at quarter frequency. As can be seen from both graphs, the seasonality of variables is inversely dependent: in the second quarter the consumption of renewables is the highest, whereas for the nonrenewable energy consumption the same quarter has the lowest value. Besides, for renewable energy consumption there are several outliers in Fig.9 and no outliers for Nonrenewable energy in Fig. 10.The reasons for such volatility could be the variability of weather conditions, which directly influence the volume of energy produced. This factor also could explain the inverse relationship between variables: when there is a lack of renewable energy, households began to consume energy from nonrenewable sources.

Figure 9. The seasonal Box Plot for Consumption of Renewable Energy

Figure 10. The seasonal Box Plot for Consumption of Non-renewable Energy

The histograms for variables in the first difference are shown. The first difference is taken due to the fact that the model used in this work is calculated on the basis of the first differences too. As can been seen

4.Methodology

In the analysis, the characteristics of the time series should be obtained in the first place so that the appropriate model would be chosen. These characteristics are stationarity and cointegration. For the testing on stationarity the augemented Dickey-Fuller test has been implied (Mirza& Kanwal, 2017; Bhattacharya, 2016). The Johansen cointegration test has been used for revealing the cointegration relationships between the variables (Bhattacharya, 2016).

In this analysis I has implied the Bayesian Vector Error Correction model (BVECM)(Koop et al, 2009). For the calculation of BVECM the R package called «bvartools» by F.H. Mohr was used. To start with, consider the following VECM specification:

(2)

where denotes the lag length set , which is chosen via the minimization of Akaike information and Schwarz information criterias (Brini et al, 2017); is a constant term; denotes the dummies for quarters; the error term follows the distribution . The specification is similar to one from the previous research, where VECM had been implied for the set of countries (Apergis & Payne, 2009). is an error correction term and denotes the cointegration equation, which shows the long-run relationship between the variables. In the and are the deterministic components; are the long-run coefficients.

The intuition behind the system of equation is the following. The mutual impact of variables could be divided into two categories: the impact in the long-run period and in the short-run period. In the long-run period, the variables are supposed to approximate the equilibrium since they are cointegrated. The deviations from the long-run equilibrium are corrected with the error correction term, which estimates the speed of the dependent variable to return to equilibrium after the change of independent variables. In the short-run period the variables are linked in the following way:

1) GDP influence the capital through the changing of the investment; the labor force is dependent on the number of jobs that rely indirectly on the GDP growth rate. The energy consumption is also influenced by GDP, because the GDP requires more energy in the case of its increase;

2) The capital is an essential element for production and GDP. In the case of non-renewable energy, the more capital accrued, the more energy is needed for accrued capital maintaining. The same pattern is specific for labor. As for renewable energy consumption, capital stimulates renewable energy consumption in the way that on-site renewable generators can be used to provide with energy new units of capital and it would be cheaper than costs from long-term contracts with energy suppliers;

3) In the case of the labor force, it is also a vital element for production. If the number of workers goes up, such appropriate conditions, like buildings and instruments, are needed so that the capital is accumulated. Concerning non-renewable energy consumption, in the modern economy labor process requires energy constantly so energy consumption is also intensified. As for renewable energy, unemployment rates could stimulate the US government to develop new jobs in the renewable energy sphere.;

4) GDP growth is dependent on energy supply because services and factories nowadays consume a great amount of energy due to the technical processes prevailing. Hence, the less energy is supplied, the lest resources are available for the GDP growth. The same pattern is specific for labor and capital because they are energy-dependent. For renewable energy, the consumption of non-renewable energy has a negative effect on renewables.;

5) The development of renewable energy attracts new investments so that more capital is created. In the case of labor, the creation of renewable energy objects requires new specialists for its construction and maintenance. The consumption of renewable energy decreases the consumption of other types of non-renewable energy.

The system of the equations (2) could be written in the following matrix form:

, (3)

where ,,,,,is a matrix of coefficients for lagged endogenous variables; '; is the matrix of coefficients for seasonal dummies ;;.Then this equation could be written as:

, (4)

where ,,, ,, , . Matrix is a loading matrix, which contains adjustment coefficients with dimension and matrix is a cointegration matrix, which contains cointegration vectors, with dimension. Both and are of rank r, where .

In the Bayesian Inference, the Bayes' theorem is a fundamental rule of the analysis. According to the Bayes' theorem, there is an initial opinion on the model parameters in the form of a `priordistribution', which in the combination with the information from data yields the conditional distribution, which is called a `posteriordistribution':

, (5)

where - theposterior distribution for the model parameters, , having the dataset ; - the likelihood function, obtained from the dataset; - the prior distribution, or initial considerations on the model parameters; denotes the proportionality between the equation parts.

The difficulty of VECM estimation is the fact that is a product of parameters. To proceed with further Bayesian analysis of the multivariate linear models, the restriction on the cointegration vectors, , must be applied. As the restriction is implemented, the posterior distribution could be simulated by algorithms, based on a collapsed Gibbs sampler - a Markov chain Monte Carlo algorithm for obtaining a sequence of observations under the proposedprior and obtained likelihood distribution (Koop et al.,2009).

The first step is to impose the restrictions on the parameter so that it could be estimated. In previous research linear normalization for , , was associated with several drawbacks, so the cointegration space was proposed for to be identified, not particular cointegrating vectors. The cointegration space for cointegrating vectors has a notation (Kleibergen & van Dijk ,1994; Strachan & Inder, 2004). The is not constrained, and for its approximation the restrictions should be proposed so the non-informative or informative priors would be obtained. The non-informative prior is employed when any restrictions on the cointegration space are not required by researcher.A non-informative distribution on is the Uniform distribution. Due to the fact that the cointegration space is an element of the Grassmann manifold, a Uniform prior for is defined by the Uniform distribution on the Grassmann manifold. The semiorthogonal restriction that does not put bounds to the are the following:

, (6)

Such a condition restricts the matrix of cointegrating vectors to the Stiefel manifold.

The prior distribution for is defined as the matricvariate-Normal distribution:

, (7)

where, G is a matrix that could be chosen to be equal , is a scalar controlling the degree of shrinkage, that could be chosen subjectively or be treated as a hierarchical prior with as unknown parameter . For is the standard non-informative prior is used:

, (8)

Draws for can be obtained from an inverted Wishart:

, (9)

Priors (7)-(9), give an opportunity for simplified and efficient computation with the collapsed Gibbs sampler.

Now the can be generated from Gaussian conditional posterior, but for the transformation in the first place is needed, because the semiorthogonality restrictions make the conditional posterior of nonstandard, andits estimation is difficult to accomplish. Therefore, the following transformation is carried out:

, (10)

where is semiorthogonal and is a positive definite matrix. In the left part of the (9) equation is semiorthogonal while is unrestricted. In the right part of the same equation is unrestricted and is semiorthogonal. Such a parameterization allows collapsed Gibbs sampler to proceed by switching between these two parts of the equation.

The last step is to set priors for and , so that the collapsed Gibbs sampler could generate the sequence using the (10) equation. According to Koop, there are following parameterization for which in combination with the likelihood yields a Normal conditional posterior of (Koop et al., 2009):

(11)

Finally, after choosing an initial value , MCMC algorithm proceeds with the following steps for iterations:

Generate from and transform this to obtain a draw ;

1. Draw from and then transform this to obtain and .

The initial values are taken from the previous study (Apergis & Payne, 2009). They are shown in Table 3.

Table 3. Initial values for

	1	-5.18	-4.37	-6.37	-3.15

Others coefficients in the model are estimated directly as the part of multivariate linear model by the collapsed Gibbs sampler. The transformations for and is needed to just make them linear, so the Monte Carlo integration for multivariate linear model could be applied.

...