Heteroskedasticity and Autocorrelation

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Literature review

A government-provided supporting schemes encourages the production of RE through technology. A study on wind capacity in OECD, by Jaraite, Karimu, Kažukauskas and Kazukauskas (2015), shows that renewable energy schemes promote the production of RE and impact on the economic growth in the short-run. In contrast, the study finds no support for the long-run and considers that this is due to insufficient development of the wind and solar technology. A study by Lam, Woo, Kahrl and Yu (2013) provides supporting arguments regarding supporting schemes to promote wind technology. The study focuses on the role of the government of China to promote investment in wind energy development. The data were collected through a survey in Mainland China and the Hong Kong Special Administration Region. The study found that wind energy developers are more interested in cash flow supporting schemes, such as high feed-in tariff, government financial assistance, and inexpensive transmission access. These schemes enable wind energy developers to reduce cost. As a result, the government provided supporting schemes encourage to enhance production of RE. Johnstone, Hascic and Popp (2008a) studied the role of supporting schemes to promote technological development with special reference to renewable energy (RE). The study uses the fixed effects model to analyse the data. The data contain a panel of twenty-five OECD countries over the period 1978-2003. The empirical results confirm the positive role of supporting schemes regarding developing new technologies, except for biomass. Furthermore, the study adds that different types of supporting schemes are helpful for the promotion of RE. For example, investment incentives encourage technological development in solar and waste-to-energy technologies. Similarly, feed-in tariff encourages biomass and trade certificates to support wind technology. According to the International Science Panel on Renewable Energy (ISPRE, 2009), the improvement in technology has a causality relationship with research and development (R&D) in RE technology. A study by Garces and Daim (2010) examines the investment in R&D to promote RE technology in the US economy. The study uses 33 years of data for the estimation. The cointegration technique is used to analyse the dynamic relationship of the variables in the short-run as well as the long-run. The study finds that investment in R&D to promote RE technology has a positive impact on the economy in the short-run and the long-run.
In like manner, a study by Popp, Newell and Jaffe (2010) finds that investment in R&D to promote RE technology has a positive role in energy production. Furthermore, the study confirms that investment in R&D reduces the cost of output as well as environmental pollution. In addition, the study shows the significant role of R&D in terms of reducing innovation costs for wind turbine farms in Denmark, Germany, and the United Kingdom (UK). The study finds that investment in R&D reduces the cost related to technological development and converts the technology into carbon-free wind turbines. The study uses time series data for the countries organised as a panel dataset. The study uses two techniques to investigate the R&D impact on innovation for wind energy in Denmark: firstly, the study uses a survey of the literature, and, secondly, the study uses the two-factor learning curve (2FLC) model based on knowledge stock. The study finds that, in Denmark, the role of R&D to reduce the cost of wind energy is more successful compared to the other two countries – Germany and the United Kingdom (UK). A study by Armeanu, Vintila and Gherghina, (2017) include research and development expenditure as a control variable in renewable energy in EU-28 countries. For econometric model, the study uses panel cointegration test, unit root test and panel error correction model for the period 2003-2014. The study concludes that R&D consumption in renewable energy has a positive effect in the short-run as well as in the long-run. However, a study by Lam et al. (2013) finds that international R&D cooperation is less important for RE technology to generate wind energy output. A study by Doner (2007) suggests that among the available options for encouraging the development of renewable energy technology, the correct policy decision might be helpful to achieve sustainable growth as well as RE technologies in the US. The bottom line is that EU countries should be rational in the allocation of investment subsidy between supporting schemes and R&D to promote renewable technologies effectively.
A study by Van (2016) shows the impact of energy on the economic development and RE. According to him, the strong correlation exists between energy with economic development. Later, he divides the energy into two separate inputs, i.e. RE and conventional energy. Hence, the study concludes that RE is weakly correlated with economic development when conventional energy used as a control variable. In respect to finding the relationship of production of RE with economic development, a study by Armeanu et al. (2017) finds the contribution of RE in economic development. The study used cointegration regression set on panel fully modified and dynamic ordinary least square regression technique for 28 EU countries. Based on the techniques, the results confirm the positive influence related to the production of RE on GDP. According to them, a 1 per cent increase in RE increases GDP per capita by 0.05 – 0.06 per cent. However, the result based on Granger causality (panel vector error correction model) confirms the unidirectional causal relationship exists in both the short run and the long run from economic growth to the production of RE. Contrary to that, a study by Shafiei, Salim and Cabalu (2014) finds the bidirectional causality relationship between the production of renewable energy (RE) on economic activities. Further, the study investigates whether economic growth stimulates from RE sources. According to them, RE energy stimulates economic growth in OECD countries. Moreover, the study confirms that there is bidirectional causality between economic activities and RE consumption in short- and long-run. The study confirms that high level of economic growth leads to high level of RE consumption and vice versa.
Similarly, to identify the bidirectional relationship between economic development and renewable energy (RE) in the long-run, a study by Apergis and Danuletiu (2014) uses the data from eighty countries. The study uses the causality test of Canning and Pedroni, which confirms the causality relationship between economic growth and RE. Furthermore, the empirical findings confirm the interdependent relationship of RE and economic development, which implies that economic development encourages the use of renewable energy. Another study by Apergis and Payne (2010, 2010b), provides the supporting arguments that economic development encourages the use of RE. The study uses data from 13 Eurasian countries over the period 1992-2007 to confirm the bidirectional (interdependency) causality relationship between RE and economic development by applying panel error correction model (PECM). Besides, their study uses the heterogeneous panel cointegration test to determine the long-run relationships among the variables: RE, real gross fixed capital formation, and labour force. By using the same variables and estimation technique, Apergis and Payne (2010a) identify the relationship between renewable energy consumption and economic development for a panel of twenty OECD countries over the period 1995-2005. The Granger causality test confirms the positive bidirectional causality between RE consumption and economic development in both the short-run and the long-run.

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Theoretical Framework

Neoclassical Growth Model

In 1930’s, Wassily Leontief presented input-output model (Bjerkholt, Olav, & Heinz, 2006). He raised a question regarding production and demand. According to him, « what is the optimal level of production that satisfies the total demand for the product »? Based on the Leontief production technology, the Roy Harrod (1939) and Evsey Domar (1946) developed the first and simplest economic growth model. According to them, the growth model has two main components: saving-investment ratio and capital-output ratio. The model is positively related to its saving-investment ratio and negatively related to its capital-output ratio. Moreover, the capital factor is a crucial factor in economic development, but since it remains constant in the short-run, the rate of growth of a nation depends largely on the rate of saving. In addition, they focus on the possibility of steady growth through adjustment of supply of demand for capital. They assume that only capital and labour had a perfect substitute and used in the same proportion. Bottom line, the model concludes that the higher the saving-investment ratio and the lower the capital-output ratio, the faster an economy grows.
However, shortly after, the neoclassical growth model explains the major drawbacks of the Harrod-Domar’s growth model. For example, the Harrod-Domar growth model mainly focuses on savings and capital as the main factors of economic growth but ignores the idea of the diminishing returns as being a factor. This idea was criticised on assumption of labour surplus countries that could replaced with capital and vice versa. In addition, the lower growth rate may be the reason of lower productivity of capital rather than the availability of capital (saving), i.e., for the developing countries, it is not easy to increase saving, particularly when they are fighting for enough food to eat. The model explains the boom and bust cycles through the importance of capital. They assume the linear relationship between capital to output ratio and capital to labour ratio. It implies that to reach equilibrium, both capital to output ratio and fixed capital to labour should grow at the same rate, which is not possible.
In summary, following are the very remote assumptions in the long run. Then, Solow-Sawn (1956) published their articles and replaced Leontief production function with the neoclassical growth theory. In neoclassical growth model theory, total production is a function of labour, capital, and technology over a period.
Where Y represents output, K is capital and L is labour, and A is a measure of technology at time t. Also, Solow discussed the idea of constant returns on capital, labour and technology.
Further, Solow assumed that the rate of saving, population growth rate, and technology progress as exogenous. Solow define that labour force is coming from the population and its growth rate is equal to ( )/ ( )̇ = .
Solow considered technology as the main factor of growth, which ignored in Harrod-Domar growth model. Solow put aside the assumption of a fixed ratio between production factors and introduced a ratio variable. Furthermore, the substitution of labour by capital and, on the other hand, technological progress, which he considered to be a key determinant of growth in the long run. Solow discusses that the technology grows at the same rate as other variables in the model. Due to that, technological development occurs. According to him, ‘Technology is like manna from heaven’ (Jones, 1998; Romer, 2001). It implies that technology automatically descends from the heaven and benefitted the different sectors of the economy. Solow model does not talk about where the technology comes from. However, he considered that there is technological progress that is growing at a constant rate ̇ ( ) . ( / = Finally, the production assumes a constant return to scale feature, and the output per effective unit of labour y = Y/L, and capital per worker, k=K/L: =
This expression defines as, with more capital per labour, firms produce more output per labour. On the other hand, there are diminishing returns to capital per worker; it implies that, an additional unit of capital provided to the labour increase the output of that labour less and less.
According to the capital accumulated equation, the capital stock, is equal to the sum of investment, sY(t), less the amount of depreciation that occurs during the production process dk(t). Further, Solow assumes that worker/consumers save of their combined wage and rental income.
Furthermore, conventional energy sources (fossil oil, gas and coal) are included into the basic Solow growth model with technological progress.
Hence, Solow growth production function looks like = − − Equation 2
Where Y represents the total amount of production of the final good, in the continuous time. K is capital stock, L is labour, E represents the energy input into production, and A is exogenous technological progress, which assumes the technology index multiplies the entire production function rather than just labour and/or capital. The study assumes that is between zero and one and that + are less than 1. Hence, this production function exhibits a constant return to scale in capital, energy, technology, and labour, reflecting the standard replication argument.
The dynamics of capital, labour and the technology are the same as above: ̇ ( )= sY- dK, ̇ ̇ In-addition, the new assumption concerns energy ( ) = ( ) ( ) = ( ). resources.
Further, the study assumes that denotes the initial stock of natural energy resources that depletes when E amount of energy is used in production function. Moreover, it is assumed that the natural resource stock obey the differential equation similar to capital accumulation equation, only it dissipates.
E can be determined: it is the amount of energy used in production each period. For example, a firm/industry would demand energy until the marginal product of energy fell to the price of energy, and other firm/industry would supply energy based on the market price.
On simple assumption is that in the long-run, a fixed share of the remaining stock of energy is used in production each period1, = ⁄ . Let is some number falls between zero and one. Dividing the equation 2 by R, the total stock of energy remaining in the economy declines over time at the rate :
The solution to this differential equation is an equation defining the behaviour of the stock over time:
The stock exhibits the negative exponential growth at rate .

Table of contents :

1. Introduction
1.1 Objectives of the Study
1.2 Hypotheses
2. Literature review
3. Theoretical Framework
3.1 Neoclassical Growth Model
3.2 The Balance Growth Path
4. Methodology
4.1 Estimated Model
4.2 Data
5. Panel data
5.1 Unit Root Test
5.2 Cross-Sectional Dependence
5.3 Heteroskedasticity and Autocorrelation
5.4 Co-integration Test
5.5 Estimation Technique
6. Results and Discussion
6.1 The Hausman Test
6.2 Long-run Estimation
6.3 Panel Granger Causality
7. Conclusion
References
Appendix A
Appendix B
Appendix C

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