Impact of inter-fuel substitution on energy intensity in Ghana

Abstract

Energy intensity and elasticity, together with inter-fuel substitution are key issues in the current development stage of Ghana. Translog production and ridge regression are applied for studying these issues with a data range of 2000–2015. The current energy dynamics reveal the expected inverse relationship: higher energy intensity and lower elasticity with economic growth. There are evidences of energy-economic challenges: high energy cost, inefficiency and backfire rebound effect. The implications are higher energy losses in the system, more consumption of lower-quality energy together with low energy technology innovation. Energy is wasted and directly not productive with economic activities. It is observed further that the higher energy intensity invariably increases CO₂ emission because approximately 95% of total energy is derived from hydrocarbons and biomass. An inter-fuel substitution future scenario design was further conducted and the results were positive with growth, lower energy intensity, and improved energy efficiency. Therefore, government and energy policymakers should improve energy efficiency, cost, and productiveness. That is, they should change energy compositions and augment energy technology innovation, thus, increasing renewable share to 15% by 2026, reducing wood and charcoal by about 69%, and increasing natural gas to about 776%. Energy policymakers should enhance the installation of smart energy, cloud energy solution, tokenization of energy system and storage.

Graphical abstract

Keywords

energy intensity / energy elasticity / inter-fuel substitution prospects / energy contribution / Translog production approach / ridge regression

1 Introduction

The application of energy factor input in modern economic development cannot be overvalued. Therefore, the issue of energy intensity or efficiency is apparently driven by energy technology referred to as inter-fuel substitution and related factors have almost come to stand the tests of research time. Inferentially, theories and models that abound are almost as numerous as the interpretation of the energy-economic dynamics. That is, energy consumption over the years has been the key to supporting economies as they transit from the low technology to the industrialized development stage. Energy factor input in Ghana has been found by Refs. [1,2] to have played a significant role in economic growth over the period. Therefore, energy application is seen as essential of the Ghanaian economy over the years. To that extent, Ghana is said to have lost about 1.8% of its GDP in 2007 as a result of energy or electricity crisis in Ghana [3]. Furthermore, according to the Minister of Finance and Economic Planning, in 2017 budget presentation to parliament, the “dumsor,” technically known as power rationing had negatively accounted for the lowest growth rate ever recorded in the past decades, which is leading to job losses, reduced economic output, the loss of consumer, and investor confidence in the Ghanaian economy. Therefore, the energy factor input can be seen as one of the main determinants of economic growth, besides labor and capital factors in the Ghanaian economy. And this energy is mostly obtained from petroleum, biomass, and a small amount from renewable and hydro sources. It can be observed from Table 1 that the final petroleum energy consumed is recorded as the highest (47%), followed by biomass (39%), and electricity (14%). According to Ref. [4], biomass consumption in Ghana has been seen increasing steadily by 64% in recent years. Besides, as mentioned in Ref. [5], in 2000, Ghana obtained about 75% of its commercial energy from petroleum products and has since been growing at an annual average rate of 8%.

Consequently, previous studies on energy consumption in Ghana have been conducted with diverse empirical approaches in estimating the linkage between energy consumption and economic growth hypotheses (bidirectional, conservation, growth, and neutral) with both parametric and non-parametric models. However, those causality relationship studies in Ghana over the years have not comprehensively examined the critical factors that do affect energy intensity and efficiency and possible rebound effects from other macroeconomic factors having realized the economic significance of energy. For example, how much energy intensity and elasticity are required for sustainable economic growth? How much energy consumption should be reduced in terms of conservation measure to enhance environmental sustainability, without negatively affecting economic growth? In addition, what are the substitution and contribution rates of energy and other factors in the economic growth of Ghana?

Therefore, the motivation of this paper seeks to examine energy substitution prospects or inter-fuel substitution beyond the previous causality test to further include energy output elasticity, energy intensity and contribution of input factors to economic growth. It also focuses on the current energy consumption challenges on the economic growth and environment of Ghana for the period of 2000–2015. It henceforth applies Translog production and ridge regression techniques to estimate the above objectives. These methodologies are robust in determining all those critical issues discussed above to include the residual factor contributing to economic growth. Reference [6] was the first of its kind to apply the Translog production model in Ghana in determining inter-production factors. However, it did not determine energy factor contribution, energy intensity, inter-fuel substitution and residual factor in economic growth. Eventually, the present paper is a comprehensive work contributing to the literature in terms of methodological extension on the energy-economic dynamic which is instrumental in the subject matter and the context currently. It accordingly offers academic information and policy design recommendations on energy, economic, and environment based on the findings hereafter.

2 Scientific literature review

Before the empirical test, the subject matter is scientifically tackled by a review of what has already been researched in the literature about the subject of interest in a diverse manner. Therefore, this literature review is in two subsections: a generic review based on both theory and empirical works around energy and economic growth scope, and a typical one on Ghana subject to the problem and objectives of the thereby. As this brings research transparency, clarity, replicability, and future policy design direction, the systematic review is conducted only on the Ghanaian economy to disclose the state of the art and identify research gaps in the field in order to recommend future energy policy direction and research methodology applicable to bring sustainable development in energy, economy, and the environment at large.

2.1 Energy consumption, economic and environment empirical studies and theories

Energy and economic growth causal relationship determination [7] has been a topical, theoretical, and empirical research area across the world over time and settings. Because the historical development connections of economic growth as postulated by the neoclassical economists have, since 1970s, observed that material and energy are pivotal factor inputs in economic growth and development [8,9]. The energy consumption and economic growth causality relationship have severally been investigated in Refs. [10–15] and that energy factor actually plays a crucial role in many economies in the world in terms of economic growth and development. Besides, these studies on the subject matter most probably have begun with a seminar paper in Ref. [7] which tested the energy-economic theory [16] and observed unidirectional causality relationship moving from GNP to energy consumption in the United States. Thereafter, several researchers have found that energy input had a significant contribution to economic growth besides capital and labor inputs. In general economics literature, several studies have investigated the topic with different models and found a wide range of results [17]. However, Refs. [18–21] added that macroeconomic growth theorists have had only emphasized on labor and capital at the neglect of the significant contribution of energy input in production. That is to say, energy factor input development is equally central in the determinant of economic growth just as important as labor and capital, in industrialized and emerging economies [22–24]. Subsequently, Refs. [10,25] observed that natural scientists and most ecological economists have finally placed importance on energy and its availability in the economic growth process. Consequentially, Ref. [20] suggested that energy is relevant and its intensity in the economic growth process is usually affected by the capacity to be substituted with other or within factors, technological changes, changes in energy composition, and the economic structures. References [26–28] found that energy substitution strategy, for example, has led to energy efficiency in many economies and enhanced environmental sustainability in both developed and developing countries over the years.

2.2 Energy consumption, and economic linkage, and CO₂ emission studies in Ghana

Energy consumption and economic growth relationship in Ghana begun with Ref. [1] which investigated the period of 1975–2001 with the application of the VECMG ranger causality test. The finding showed unidirectional connection running from energy consumption to economic growth, which supported the energy-led-growth hypothesis. In the following year, Ref. [2] examined the connection selecting 16 African countries plus Ghana with data for the period of 1971–2001. It estimated the relationship with the application of Toda and Yamamoto Granger Causation test. But the result contradicted the findings in Ref. [1] for Ghana. Additionally, Ref. [29] surveyed the factors influencing economic growth in Ghana by applying the ordinary least squares approach. It was found that energy price and political stability influenced economic growth besides capital, and labor, using annual data from 1966 to 2000. The results showed that the long-run economic growth was positively influenced by political stability, while the exogenous energy price was negative. The results further revealed that economic growth was not influenced by both capital and labor and therefore, suggesting that economic growth was a matter of other factors. This finding did not follow the neoclassical production model hypotheses. Furthermore, Ref. [30] was highly interested in finding a balance between the previous works, but with the data from 1980 to 2007. It applied an innovative fully-modified OLS (FMOLS) approach for some selected African countries including Ghana. The outcome revealed a bidirectional causality between energy consumption and economic growth. In a like manner, in the same year, Ref. [31] further reexamined the economic phenomenon with the VECM Granger Causation by adding five more years to that in Ref. [1]. The finding repeated the 2005 results, energy-led-growth economy of Ghana.

Subsequently, Ref. [32] was intrigued to add knowledge to the field on the same energy-economic-link. It investigated the causal relationship between energy and economic growth of seven selected Sub-Sahara African countries including Ghana by employing the threshold cointegration approach to examine the linkage for the period of 1970–2007. The finding showed that energy consumption cointegrated with economic growth in Ghana and also, with unidirectional causality moving from real GDP to energy utilization in Ghana. Moreover, Ref. [33] studied the causal relationship and the magnitude of impact between economic growth and energy consumption. It applied the test in Ref. [34] based on the theory of causality in Ref. [35] by using the quarterly data of 39 years. The results showed a unidirectional causal relationship between economic growth and electricity consumption. That is, a unit increase in economic growth would positively cause electricity to increase by two units, keeping all factors constant. It used electricity as a proxy for energy and the results showed that economic growth caused electricity consumption, which contradicted other results. Reference [36] further examined electricity consumption and economic growth linkage in Ghana for the period of 1971–2008 by applying Toda and Yamamoto Granger causality and ARDL bounds tests. The results revealed the existence of unidirectional causality moving from economic growth to electricity consumption: growth-led-electricity (energy) hypothesis. Furthermore, Ref. [37] presented a paper of West Africa Built Environment Research (WABER) Conference in Ghana on the topic “energy generation and consumption in Ghana” by applying the nonparametric test. The results showed that electricity demand and consumption was growing at 10% per annum, and the production rate was 66%. It, however, did not determine the causal relationship between economic growth and energy consumption.

Reference [38] added knowledge to the subject matter and this time around, disaggregating the consumption of energy. It investigated the causality between disaggregated energy consumption (electricity and fossil fuels) and economic growth, agriculture, and manufacturing growth in Ghana for the period of 1971–2007 by applying ARDL and Johannsen Granger Causality tests. The findings revealed a unidirectional causality moving from economic growth to electricity and fossil fuel consumption. The result further indicated a unidirectional causality from agriculture to electricity consumption and a feedback relationship between manufacturing and electricity consumption. It came to the conclusion that energy consumption seemed not an important factor in the agriculture sector. In addition, Ref. [39] contributed to electricity and economic growth nexus. It assessed the causal relations between electricity consumption and economic growth in Ghana for the period of 1970–2010 by applying the unit root and the cointegration test and considering structural breaks. The results disclosed a unidirectional causation running from economic growth to electricity consumption in support of previous works. In the ensuing year, Ref. [40] further evaluated the link between electricity consumption and economic growth with the use of ARDL bounds test and VECM for nine African countries together with Ghana for the period of 1970–2010. The outcome revealed a bidirectional causality for Ghana and some other countries.

Reference [41] revisited the field by review and empirically assessed various studies on the energy-growth relationship and energy demand in Ghana. Previous findings revealed that studies in Ghana did not reach any consensus regarding the direction of causality between energy consumption and economic growth. It, therefore, suggested that this could have been a result of some differences in sources of data and estimation methods which support Ref. [42] for some other countries. In the same year, Ref. [43] investigated the causal relationship between electricity consumption and economic growth in Ghana with the ARDL bound test method and Ref. [44] further conducted study on Ghana together with other three developing countries with the same model. In both cases, they found that economic growth drives electricity consumption which satisfied the growth-led-energy hypothesis. Furthermore, Ref. [45] conducted a similar research: the influence of electricity consumption on economic growth using the augmented Dickey-Fuller test, the cointegration test, VECM, and Granger causality test. The results show that, in the long-run, a unit increase in electricity consumption would positively cause economic growth by 0.52 unit. The results further indicate a unidirectional causality running from electricity consumption to economic growth. The results, however, show that, in the short-run, electricity consumption is negatively causing economic growth in economy. It, therefore, recommended the government to invest massively in electricity infrastructure and conservation measures to augment electricity demand and consumption. Later in the year, Ref. [46] assessed the impact of energy consumption and economic growth of ten oil-producing countries in Africa in addition to Ghana for the period of 1971–2011. It disintegrated energy consumption into renewable and non-renewable with a fixed panel effect methodology. The results showed that a unit change in both sources of energy consumption would lead to a significant increase in economic growth. It further used the VECM Granger causality test with the same data and found that both energy consumption sources had an energy-led-growth relationship only in the long-run for Ghana.

Additionally, Ref. [47] independently investigated the relationship between energy consumption, productivity, and economic growth in three selected African countries including Ghana for the period of 1985–2011. It applied the dynamic stimulation panel data model, Granger causality test, the cointegration test, and the VAR and VECM approaches. The results suggested a long-run unidirectional causality from both sources to economic growth in Ghana. Reference [48] investigated 11 selected African countries including Ghana for this linkage. It employed the cointegration and Granger causality test on the relationship between energy consumption and economic growth for the period of 1971–2010 and found a feedback hypothesis for Ghana.

Reference [6] was the first to apply the Translog model in Ghana. It determined the inter-production factors and energy substitution possibilities, and found the possibility of substitution among the factor inputs with their technological progress. It finally recommended the removal of energy subsidies as the subsidies would reduce the application of energy and thereby increase capital and labor intensiveness with their associated challenges. Moreover, Ref. [49] examined energy consumption and economic growth in Sub-Saharan African countries with Ghana for further evidence. It employed the ARDL bound test to the cointegration and Granger causality tests and found a neutrality hypothesis for the case of Ghana. Furthermore, Ref. [50] further modeled the relationship between economic growth and energy consumption and found there was a cointegration between the variables but it did not further find the causality relationship thereafter. Finally, Ref. [51] repeated the application of the Toda Yamamoto, Granger causality, and ARDL bounds test methods in the estimation process. It further employed the Johansen and Johansen-Jeselius cointegration approaches to determine the evidence of cointegration among energy consumption, carbon dioxide emission, and economic growth for the period of 1960–2015. The findings show a cointegration among the variables and a feedback relationship among variables.

In summary, a lot of studies have been conducted in Ghana with mixed methodologies in estimating the causal relationship between economic growth and energy and or electricity. The results and conclusions have equally been diverse as illustrated by Ref. [52] in the African context. A literature synthesis analysis in Ref. [50] shows that of all the works conducted in Ghana between 2005 and 2018 on the subject matter, 25% confirmed the unidirectional hypothesis, 45% observed the growth-led-energy hypothesis, 20% found the feedback hypothesis, 5% confirmed the neutrality hypothesis, and 5% did not study the theory but tested on cointegration relationship. Furthermore, a literature review reveals that 45% examined using electricity as a proxy for energy in testing the theory. And all the results in this method confirmed growth-led-energy hypothesis except Ref. [40] whose conclusion supports the feedback hypothesis. In effect, the research in Ghana has established the fact that energy and or electricity plays a significant role in the Ghanaian economy. The studies reviewed have all confirmed the four hypotheses on energy and economic growth typology. From the foregoing, all studies conducted in the field have contributed immensely to the existing literature and have offered energy policy implications to decision-makers. However, it is noted the three questions mentioned in the introduction of the present paper are not examined and hence well-intended for consideration in future works. Therefore, this paper offers both academic and policy design information subject to the previous limitations in the area of energy intensity, energy elasticity, and energy substitution prospects and contribution by use of Translog production and robust ridge regression techniques.

3 Methodology, data set and variable, and robust inference

3.1 Description of sample data set

This paper obtained secondary data from World Bank Development Indicators and Ghana National Energy Commission websites. The predictor variables included labor force (L) which was the total employment in Ghana. The other variables included capital stock accumulation (K) or gross capital formation [53]. It, however, did not consider capital depreciation because of land improvement, outlays on an addition to fixed assets, and net changes in the level of inventories as they did not undergo depreciation but rather an appreciation. It, instead, applied the accounting identity method [54] and hence did not require net capital stock adjustment of the formula: K _t = K _{t -1} (1-d) + I _t. Besides, energy input was made up of final energy consumption: biomass, petroleum, and electricity. Others were the economic growth representing the gross domestic product (Y). In addition, it measured both GDP(Y) and capital stock accumulation (K) in billions of US dollars at current market prices, and measured the labor force in the unit of millions, and energy consumption (E) in thousand kilotons of oil equivalent (ktoe). Moreover, it obtained all the data in yearly observations from 2000 to 2015.

It, then, standardized the data [55] and further took first-differenced to avoid linear trends [56]. Furthermore, it tested the stochastic process to meet all the time series data requirements. Finally, it transformed all the data to best suit the Translog model procedure.

3.2 Specification of general Translog model

This paper employed a multifaceted Translog production approach to determine energy contribution, substitution prospects and output elasticity of factor inputs in determination of economic growth. One of the advantages of this approach is that it can avoid the constant assumption of elasticity [57]. Furthermore, this approach does not assume rigid perfect substitution between production factors or perfect competition on the production function as in the case of Cobb-Douglas function [58]. The general production function can be expressed by

(1) Y=f(K,L,E),

where Y represents economic output while K, L, and E denote labor, capital stock, and energy respectively.

3.3 Specification of specific Translog production model

In general, the production function is unknown and in practice it is widely approximated by a Translog functional form

(2) \begin{array}{l}\ln {{\displaystyle Y}}_t={{\displaystyle \alpha }}_{\mathrm{0}}+{{\displaystyle \alpha }}_K\ln {{\displaystyle K}}_t+{{\displaystyle \alpha }}_L\ln {{\displaystyle L}}_t+{{\displaystyle \alpha }}_E\ln {{\displaystyle E}}_t+{{\displaystyle \alpha }}_{KL}\ln {{\displaystyle K}}_t\cdot \ln {{\displaystyle L}}_t+{{\displaystyle \alpha }}_{KE}\ln {{\displaystyle K}}_t\cdot \ln {{\displaystyle E}}_t+\\ {{\displaystyle \alpha }}_{LE}\ln {{\displaystyle L}}_t\cdot \ln {{\displaystyle E}}_t+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{{\displaystyle \alpha }}_{KK}{(\ln {{\displaystyle K}}_t)}^{\mathrm{2}}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{{\displaystyle \alpha }}_{LL}{(\ln {{\displaystyle L}}_t)}^{\mathrm{2}}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{{\displaystyle \alpha }}_{EE}{(\ln {{\displaystyle E}}_t)}^{\mathrm{2}}+{{\displaystyle \epsilon }}_t,\end{array}

where ε _t is the random error. Essentially, Eq. [2] is the second Taylor approximation to the Translog production lnY _t = f(lnK _t, lnL _t, lnE _t) and the coefficients is the partial derivatives.

Equations (3)-(5) are the output elasticity calculation as affected by the changes in the output relative to changes in factor inputs under constant technology and prices conditions.

(3) {{\displaystyle \sigma }}_{{{\displaystyle K}}_t}={\displaystyle \frac{\partial \ln {{\displaystyle Y}}_t}{\partial \ln {{\displaystyle K}}_t}}={{\displaystyle \alpha }}_K+{{\displaystyle \alpha }}_{KK}\ln {{\displaystyle K}}_t+{{\displaystyle \alpha }}_{KL}\ln {{\displaystyle L}}_t+{{\displaystyle \alpha }}_{KE}\ln {{\displaystyle E}}_t,

(4) {{\displaystyle \sigma }}_{{{\displaystyle L}}_t}={\displaystyle \frac{\partial \ln {{\displaystyle Y}}_t}{\partial \ln {{\displaystyle L}}_t}}={{\displaystyle \alpha }}_L+{{\displaystyle \alpha }}_{LL}\ln {{\displaystyle L}}_t+{{\displaystyle \alpha }}_{KL}\ln {{\displaystyle K}}_t+{{\displaystyle \alpha }}_{LE}\ln {{\displaystyle E}}_t,

(5) {{\displaystyle \sigma }}_{{{\displaystyle E}}_t}={\displaystyle \frac{\partial \ln ({{\displaystyle Y}}_t)}{\partial \ln ({{\displaystyle E}}_t)}}={{\displaystyle \alpha }}_E+{{\displaystyle \alpha }}_{EE}\ln ({{\displaystyle E}}_t)+{{\displaystyle \alpha }}_{KE}\ln ({{\displaystyle K}}_t)+{{\displaystyle \alpha }}_{LE}\ln ({{\displaystyle L}}_t).

Therefore, σ _Kt, σ _Lt and σ _Et represent the output elasticity of capital (K _t), the labor force (L _t), and energy (E _t) factor inputs respectively in time, t. Thus, α _KK, α _LL, α _EE, and α _KL, α _KE, α _LE are the second-order derivatives and cross partials respectively.

According to Ref. [59], the three-factor input contribution rates can be determined by

(6) {{\displaystyle \delta }}_{{{\displaystyle K}}_t}=({{\displaystyle \alpha }}_K+{{\displaystyle \alpha }}_{KK}\ln {{\displaystyle K}}_t+{{\displaystyle \alpha }}_{KL}\ln {{\displaystyle L}}_t+{{\displaystyle \alpha }}_{KE}\ln {{\displaystyle E}}_t){\displaystyle \frac{\Delta K/K}{\Delta Y/Y}}\times \mathrm{100}\%,

(7) {{\displaystyle \delta }}_{{{\displaystyle L}}_t}=({{\displaystyle \alpha }}_L+{{\displaystyle \alpha }}_{LL}\ln {{\displaystyle L}}_t+{{\displaystyle \alpha }}_{KL}\ln {{\displaystyle K}}_t+{{\displaystyle \alpha }}_{LE}\ln {{\displaystyle E}}_t){\displaystyle \frac{\Delta L/L}{\Delta Y/Y}}\times \mathrm{100}\%,

(8) {{\displaystyle \delta }}_{{{\displaystyle E}}_t}=({{\displaystyle \alpha }}_E+{{\displaystyle \alpha }}_{EE}\ln {{\displaystyle E}}_t+{{\displaystyle \alpha }}_{KE}\ln {{\displaystyle K}}_t+{{\displaystyle \alpha }}_{LE}\ln {{\displaystyle L}}_t){\displaystyle \frac{\Delta E/E}{\Delta Y/Y}}\times \mathrm{100}\%.

Besides, Ref. [60] denotes D A/A as the factor input comprehensive growth rate

\Delta A/A=\Delta Y/Y-{{\displaystyle \delta }}_{{{\displaystyle K}}_t}\Delta K/K-{{\displaystyle \delta }}_{{{\displaystyle L}}_t}\Delta L/L-{{\displaystyle \delta }}_{{{\displaystyle E}}_t}\Delta E/E.

But, D Y/Y is the economic output growth rate, D K/K is the capital factor input growth rate, D L/L is the labor factor input growth rate, and D E/E is the energy factor input growth rate. Reference [60] further introduces that there are other minor factors (like environmental resources or agricultural products and minerals) which contribute to economic growth and can be estimated using Eq. (9), which consists of residual factor contribution.

(9) \mathrm{Residual=}\Delta A/A÷\Delta Y/Y.

Finally, the economic growth contribution rates of all the factors together with residual factor inputs can be obtained from the estimation of Eqs. (6)-(9) and their sum must be equal to one hundred percent (100%) or one (1). In addition, the output elasticity of the factors can be estimated with the application of the Translog production methodology, Eqs. (3)-(5) [61]. Therefore, the presence of multicollinearity is mitigated with robust inference and the ridge regression technique.

Furthermore, substitution elasticity consists of relative changes in the proportion of input factors. That is, the substitution technology of the firm is the preference of the firm of an input factor relative to others due to its higher productivity or efficiency. This paper, only estimated the substitution possibility for labor and capital factors in line with Ref. [62] that energy is a complement with capital, rather than a substitute. Thus, energy enhances the output of labor [63–65]. In addition, energy and capital literature have shown that they have weaker substitution results [10,66]. Therefore, their substitution technology possibility rather depends on the factor share of labor-capital [67] which is specified in Eq. (10). Now capital and labor substitution possibility is represented by

(10) {{\displaystyle \sigma }}_{KL}={{\displaystyle \left[\mathrm{1}+{\displaystyle \frac{-{{\displaystyle \alpha }}_{KL}+({{\displaystyle \sigma }}_L/{{\displaystyle \sigma }}_K){{\displaystyle \alpha }}_{LL}}{-{{\displaystyle \sigma }}_L+{{\displaystyle \sigma }}_K}}\right]}}^{-\mathrm{1}}.

Subject to the previous studies and the objectives of this paper, the complementarity typology is, therefore, adopted for nested energy and capital (s _KE), and estimated the substitutability prospects for capital and labor (s _LE) since it is a developing economy.

3.4 Robust inference: ridge regression

According to Refs. [68,69], ridge regression is an alternative corrective measure usually applied to reduce the multicollinearity effect among regressors in a multivariate model. The presence of multicollinearity could cause serious problems in estimation and prediction of future effects. The multicollinearity might, in turn, increase the variance, which may have the tendency to generate large least squares estimators [70]. Specifically, the model specification in Eq. (2) is such a one, which could present the possibility of multicollinearity among regressors. Besides, according to Refs. [71–73], the presence of multicollinearity in an estimated coefficient could be sensitive to any change of the model specification or data and subsequently, the predicted estimate will be biased in predicting the outcome of the entire model. Because of the limitation in the model and likelihood of multicollinearity, the ridge regression analysis is applied as an alternative to enhance the parameter estimates as recommended in the literature.

Therefore, the basic theory of ridge regression is based on the simple linear regression equations given by

(11) \mathit{Y}=\mathit{\alpha }+{\mathit{\beta }}^{\mathrm{T}}\mathit{X}.

Equation (11) is an expression of the relationship between dependent and independent variables. However, for finding the regressive coefficient, b _i (i = 1, …,m), the following equation is applied Y = X β + ε, where Y and X are different in meaning from those in Eq. (11). Thus, X is a matrix composed of sample data.

The ordinary least squares estimator of b is given by

(12) \mathit{\beta }={({\mathit{X}}^{\mathrm{T}}\mathit{X})}^{-\mathrm{1}}{\mathit{X}}^{\mathrm{T}}\mathit{Y}\mathrm{.}

But X ^T X = R, where R denotes the correlation matrix of independent variables. These estimates are unbiased, and therefore, the expected value of the estimates is the observed values. That is, \mathit{E}\left(\widehat{\mathit{\beta }}\right)=\mathit{\beta }.

The variance-covariance matrix of the estimate is Var \left(\widehat{\mathit{\beta }}\right)={\sigma }^{\mathrm{2}}{\mathit{R}}^{-\mathrm{1}}, but

(13) \sigma =\mathrm{1.}

Expanding Eq. (13) yields

(14) \mathrm{Var}({{\displaystyle b}}_j)=r^{jj}=\mathrm{1}/(\mathrm{1}-{{\displaystyle R}}_j^{\mathrm{2}}),

where {{\displaystyle R}}_j^{\mathrm{2}}is the R-squared value obtained from regression X_j on other independent variables.

In solving the multicollinearity effect among independent variables, ridge regression is the most popular in producing efficient values where k is added to the diagonal elements of the correlation matrix [68,69]. This development led to the name ridge regression, since the diagonal of ones in the correlation matrix may be thought of as a ridge. The formula is

(15) \overline{\mathit{\beta }}={(\mathit{R}+k\mathit{I})}^{-\mathrm{1}}{\mathit{X}}^{\mathrm{T}}\mathit{Y},

where k takes the space between 0–n. But in most cases k is between 0 and 1 and the specific value usually depends on the actual situation. But the level of bias in the estimator is given by

(16) \mathit{E}\left(\overline{\mathit{\beta }}-\mathit{\beta }\right)=[{({\mathit{X}}^{\mathrm{T}}\mathit{X}+k\mathit{I})}^{-\mathrm{1}}{\mathit{X}}^{\mathrm{T}}\mathit{X}-\mathit{I}]\mathit{\beta }.

And the covariance matrix is given by

(17) \mathrm{Var}\left(\overline{\mathit{\beta }}\right)={({\mathit{X}}^{\mathrm{T}}\mathit{X}+k\mathit{I})}^{-\mathrm{1}}{\mathit{X}}^{\mathrm{T}}\mathit{X}{({\mathit{X}}^{\mathrm{T}}\mathit{X}+k\mathit{I})}^{-\mathrm{1}}.

From Eq. (16), the presence of k with a value for which the mean squared error (the variance plus the bias squared) of the ridge estimator is supposed to be less than that of the estimator of the least square. The appropriate value of k depends on knowing the true regression coefficients (which are being estimated) and an analytic solution has not been found that guarantees the optimality of the ridge solution which is estimated in Section 4.2.

4 Analysis of parameter results, discussion, and interpretation

4.1 Estimation procedure of Translog production model

The unit root test was undertaken after standardization and conversion of data into a logarithmic form to ensure that the data can meet the requirements of time series estimation under ordinary least squares [74]. That is, the Augmented Dickey-Fuller (ADF) test was applied and all data had a unit root at the 5% level. As discussed in Section 3.1, the introduction of the Translog production model was then tested with the specified production factors. The Translog production was estimated for the analyzed three-factor-inputs. Besides, all the results obtained are feasible and final. The respective production factors were introduced into the extended Translog production model [58] using EViews8 software, to estimate the parameters.

4.2 Procedure and analysis of ridge regression

The presence of multicollinearity was tested for applying Pearson’s correlation coefficient to compute the predictor variables before proceeding with the Translog production model estimation process as established in Section 3. Pearson’s coefficient measures the level of linearity dependence between two continuous variables with a value range of -1 to+ 1. Pearson’s correlation test results show that all variables have a higher correlation among the predictor variables with a range of 0.74 to 1 with a high significance level (see Table 2). Refs. [75,76] justified the use of Pearson’s correction test for multivariate statistics, as in this study. This test is further supplemented with the variance inflation factor (VIF) and the values of all variables show a higher than the thumb rule of 10 [77] (see Table 2). The result for R-squared is 0.99, which also indicates a higher value than the standard value of 0.90. Besides, the results demonstrate the existence of multicollinearity in the estimated model. To, therefore, avoid this limitation in the Translog model, ridge regression was employed as a more robust technique to enhance the reliability in parameter estimators. Thus, ridge regression results were then used for the analysis.

4.3 Analysis of ridge trace plot

Ridge trace is a plot of estimated standard coefficients against ridge parameters: a common graphical adjunct to determine a favorable tradeoff of bias against the precision of the estimates. It is a technical way of estimating the feasible value of k, as established in Section 3. Thus, estimated standard coefficients and or VIF (on Y-axis) are plotted against a range of specified values of k (on X-axis). The stable technical value was then chosen as k = 0.20 from Fig. 1. This is the value where the variables are observed to attain stability. Therefore, the choice of the k value equal to 0.20 is in line with that in Ref. [68]. The k value was, therefore, incorporated in the ridge regression technique to obtain the results for analysis and discussion and hence no evidence of bias in the ridge results are presented in Section 4.4 because all the model variance inflation factors are less or equal to the upper limit of 0.10, which is discussed in details in Sections 3.4 and 4.2.

4.4 Analysis of ridge regression estimates

Substituting the results from Table 3 into Eq. (2), Eq. (18) can be obtained.

(18) \begin{array}{l}\ln {{\displaystyle Y}}_t=\mathrm{23.63265}+\mathrm{0.206749}\ln {{\displaystyle K}}_t+\mathrm{0.760515}\ln {{\displaystyle L}}_t-\\ \mathrm{0.542156}\ln {{\displaystyle E}}_t+\mathrm{0.009607}\ln {{\displaystyle K}}_t\cdot \ln {{\displaystyle L}}_t+\mathrm{0.011541}\ln {{\displaystyle K}}_t\cdot \ln {{\displaystyle E}}_t+\mathrm{0.001363}\ln {{\displaystyle L}}_t\cdot \ln {{\displaystyle E}}_t+\\ \mathrm{0.009203}\times {\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{(\ln {{\displaystyle K}}_t)}^{\mathrm{2}}+\mathrm{0.046585}\times {\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{(\ln {{\displaystyle L}}_t)}^{\mathrm{2}}-\mathrm{0.062491}\times {\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{(\ln {{\displaystyle E}}_t)}^{\mathrm{2}}.\end{array}

In line with Ref. [78], the estimated energy results in Eq. (18), represented in Table 3 are technically referred to as energy intensity and not elasticity. The model results reveal reasonable and reliable approximations to the true population parameters as can be seen in Table 3 where all the VIF are less or equal to 0.10 and hence there is no evidence of multicollinearity. The result reveals the expected inverse relationship between energy intensity and economic growth. There is also high labor and low capital intensity in the economy. Currently, the economic energy efficiency or rate of return on energy consumption is negative. This is suggestive of high energy cost on the economy and hence evidence of a labor-intensive economy. This further verifies that more energy is being consumed in order to produce economic growth. In addition, energy is not directly associated with the production factors and equally not efficiently applied. That is, the implied negative energy intensity is revealed on the increased in energy cost or tariffs, which has since been subsidized by the government over the years in all the sectors on petroleum products and electricity until 2015, where the government then scraped the subsidy. The inverse relationship and negative value of energy intensity further imply that the demand side energy is mismanaged in the current energy-economic trajectory of Ghana, which has led to the evidence of energy inefficiency challenges and further complicated with higher carbon intensity since more of the energy consumed come from hydrocarbons and biomass with low technology. This is rightly so, because currently the primary energy consumption composition constitutes about 95% of petroleum and biomass (see Table 1). Evidently, according to Ghana’s Third National Communication Report to the UNFCCC (available at UNFCCC website), CO₂ emission grew from 16.87 million tons in 2000 to about 33.66 million tons in 2012 and hydrocarbon and biomass alone contributes 85.2%. In effect, the current energy consumption with economic growth does not support the Ghana’s development drive toward a sustainable development agenda. The commitment toward a safe climate would be achieved via the reduction of CO₂ emissions through the reduction of energy intensity, mainly by energy efficiency designs and management.

4.5 Estimates and analysis of total output elasticity

From the estimation of Eqs. (3)-(5), the results were obtained and listed in Table 4, which reveal labor and capital with positive and perfectly elastic outcomes and energy is inelastic over the period. The negative elasticity energy suggests high energy inefficiency. And the marginal rate of energy productivity is yet very low even beyond the zero-limit. This may be because of the high energy cost associated with energy, and hence the economy has since reverted to consuming more low-quality energy in economic activities as this is realized: biomass consumption alone composes of about 39% of the total final energy. Therefore, energy policy designs could be stimulated toward shifting away from such energy sources to enhance desirable energy marginal productivity. The negative energy elasticity is suggestive of decreasing returns to scale and evidence of backfire rebound effect, which is a policy failure. That is, as the economy designs energy policy to augment efficiency, the policy turns to trigger more energy consumption and hence ought to be addressed. This finding supports Ref. [79] where it is found that economic growth is negatively affected by energy challenges referred to as energy inefficiency. This paper further supports Refs. [80,81], as they concluded that energy-GDP elasticity in higher per capita income countries should be higher and lower for low per capita income. Therefore, the inverse relationship between energy intensity [82,83] and energy elasticity is established with the implied implication of energy inefficiency as observed. That is, twofold energy challenges are observed: energy losses from transmission, distribution, through to end-users and more consumption of low-quality energy. These identified energy challenges are certainly apparent in the Ghanaian economy [3]. The finding of Ref. [4] suggests that biomass consumption is a major source of primary energy in Ghana, accounting for about 64%. This, and many others, therefore, demonstrate that as more low-quality energy vector increases through the biomass source, it does affect economic energy efficiency and the economic outcomes thereby. Furthermore, similar energy challenges result was found by Ref. [82] in China’s economy in 1978–2009, known as the transformation period. Additionally, Refs. [83,84] suggest that energy efficiency is a core determinant in economic growth and not just the increase in consuming more energy units, which increase energy intensity. It is evident that high-quality energy complements much effect on labor and capital efficiency as well as its impact on energy required to produce a unit of economic growth [85–88]. And this low-quality energy, obviously biomass energy, has the lowest output energy content for electricity and transportation [89]. Also, there is evidence of a high level of energy loss in transmission, distribution through to final consumers. The electricity sector in Ghana alone records about a 32% transmission and distribution loss in the energy system, through GRID Co, VRA, ECG, and NED Co. The system is not efficient in transmitting and distributing final energy to consumers [90]. Moreover, Ref. [91] stated that the current ratio of distribution to transmission losses averaged 22% in the past ten years. All these suggest that the percentage of the total power generated is not utilized in Ghana for economic growth. This implies that as the country and investors invest a dollar worth in energy, approximately 32% becomes economically unproductive and this also shows why energy tariffs in Ghana are costly. And as a cumulative effect, according to the government expressed notice of Concession on ECG in 2017 and finally transferred to bulk power distributor called, PDS in 2018. The result in this paper, moreover, supports Ref. [92] on energy inefficiency challenges in Ghana in which it was found that energy inefficiency deteriorating situation started in Ghana far back from 2001 to 2013, which coincided with the study period of this paper. As a result of the energy inefficiency in 2017, the Energy Commission launched a mobile application Apps to augment energy efficiency Ghana web, 2017.

4.6 Estimation and analysis of factors contributing to economic growth

The results in Table 5 are the estimates of Eqs. (6)-(9). The presented results are the contributions of factors, including the residual factor to economic growth in the period of 2000–2015. The outcomes reveal that capital has a contribution of 174% in 2000. This apparently suggests that capital factor input contributes more, with an average contribution of 113%, to economic growth relative to the changes in the input factor, indicating that it has a higher positive impact on economic growth. This result supports Refs. [93,94] on capital which suggest that capital is the most significant contributor in economy. The finding further reveals labor with decreasing returns on the economy. That is, both capital and labor are found to be good input factors in the Ghanaian economy which hence, supports the Cobb-Douglas production theory.

However, the energy factor contribution has been found negative, which is also evident in the energy elasticity estimate above. This observation is presented in Table 5 in the energy column. The negative energy intensity and elasticity are evident in energy contribution. That is, on average, the contribution of energy factor input to economic growth is -80%. This percentage is the evidence of the backfire rebound energy effect [95], and or failed energy policy and its consequential negative impacts on economic growth. This further suggests that there is a disconnection between energy policy and the macroeconomic variables or a lack of policy integration among energy and sector variables. For instance, the energy inefficiency outcomes do affect the power sector, which also affects the industries, as a kind of energy transmission mechanism. To further clarify this observation, the economy since 2010 has lost about 24 billion dollars due to energy inefficiency or crisis [3,96], which has served as the greatest barrier and major bottleneck to economic growth in Ghana. The implication for the current energy consumption dynamics of Ghana shows that it is still at the early phase of development where the residual factor or agriculture sector contributes more than other sectors and more energy consumption turns to waste [97,98], which can be seen in Table 5 in the residual column.

Finally, referring to Ref. [99], residual is that part of output growth unaccounted for in the production model but considering only for capital and labor. The theory adds the fact that there is a variety of factors that may contribute to economic growth and hence the residual may be quite sizeable. The methodology in this paper, i.e., the Translog model, adds the residual factor to the estimation. Therefore, Eq. (9) is estimated and the results are given in Table 5. According to Ref. [60], this residual factor is denoted in Ghana to include all-natural resources with their combination technologies. These natural resources include but not limited to bauxite, manganese, gold, and forest or agriculture. And the result of residual factor, on average, is 56%, which supports Ref. [29] which suggests that economic growth in Ghana is a matter of natural resources endowment besides labor and capital. To justify the relevance of the residual factor in the economy with further evidence, Ref. [100] reports that mining and quarrying together with oil contribute to 12.2%, agriculture and forest contribute to 19%, while water and sewerage contribute to 0.6%. Therefore, the model to account for the residual factor contributing to economic growth is empirically reasonable, as it quantifies the residual relevance in the economy and shows that the Ghanaian economy is still at the first stage of development.

4.7 Elasticity substitution possibility between capital and labor factors

The results in Table 6 are obtained from the estimate of Eq. (10). Substitution possibility between capital and labor for the period are all positive and approximately equal to one, indicating a perfect substitution between capital and labor in the Ghanaian economy. This finding supports Ref. [101] on the Liberian economy and Refs. [6,79] on Ghanaian and Brazilian economy respectively. Precisely an increase in the price of capital would lead to an increase in the employment of more labor in the economy keeping other factors constant.

4.8 Inter-fuel substitution possibility and technology innovation in energy

The energy application outcomes show that the current energy consumption dynamics are highly undesirable and costly in economic growth, and therefore, require improved future energy designs to enhance energy utilization, economy, and the environment toward a sustainable development future. Therefore, in line with Ref. [102], the values of all factors are calculated in order to evaluate future energy intensity, elasticity, and substitution prospects on economic growth. That is, a robustness analysis is, therefore, designed. Thus, scenario projection analysis of inter-fuel substitution prospects is estimated in this section to determine future energy efficiency strategies. First, energy composition is estimated through a reduction in consumption of low-quality fuel biomass with an increase in natural gas. Secondly, a further improvement is made in electricity transmission, distribution, and end-user losses via energy technology innovations. And finally, the renewable energy factor share is increased.

The data in Table 7 represents the outcome of the inter-fuel substitution projection scenario in reducing biomass (wood and charcoal) consumption by 69.45% but increasing natural gas to about 776%, for their conversion difference factor is greater: natural gas energy density is about 46 MJ/Kg relative to 2.56 MJ/L of biomass. Also, the renewable energy (solar, wind and hydro) share should be increased from the current 5% to 15% and energy losses should be reduced from the current 32% to at least about 18% via energy technology. This inter-fuel substitution projection scenario proposition is followed from Refs. [20,103,104], as they have found that energy vector substitution in those contexts is practically a reliable design to improve energy efficiency, especially for countries shifting toward industrialized states.

In applying the inter-fuel substitution scenario design possibility in Table 7, the energy data has shown a significant improvement in final energy. Thus, the 2016 energy consumption of 7085.60 ktoe as a baseliner has been enhanced to11687.52 ktoe (see Table 7), as a result of the inter-fuel shift. Besides, the data for capital in 2016 is $ 9750607184, that for GDP is $ 42689783734, and that for labor is $ 13335128 [53]. Furthermore, the scenario projection is set in line with the forecasting in Ref. [102] for all the factors and GDP over the period 2016–2026. Thus, the reasonable annual alpha values were obtained for GDP, capital, labor, and energy set at 2%, 1.5%, 2%, and 14%, respectively. The data were then used to estimate again with the Translog production and ridge regression techniques, (Eqs. (2) and (17)), and the results are presented in Table 8.

The results from the inter-fuel substitution possibility estimation of Eq. (2) and the results in Table 8 reveal positive effect of energy on economic growth as compared with the original results in Table 3. This robustness check is a more informative evidence of structural validity [105] and how Ghana could design general and specific energy policies in targeting future direction. If this energy strategy design is followed, it would lead to an enhancement in energy efficiency, lower energy intensity and improve energy elasticity for economic growth, and at the same time reduce CO₂ emission in the country. That is, the reduction in energy intensity would also reduce carbon intensity, carbon monoxide and environmental deforestation that is emanating from the more consumption of biomass in Ghana, thus, boosting energy efficiency through the application of higher-quality energy, increasing renewable energy share and reducing energy losses and CO₂ through technological change [106–108]. This result is evident that the energy crisis would be averted and the economy improved. The negative energy intensity would also drastically reduce cost or tariffs and the negative environmental consequences thereafter. This, therefore, suggests that inter-fuel substitution and energy technological changing designs may reduce the current high energy cost or negative energy intensity and improve energy efficiency from the backfire rebound effect to either a full or world-wide economy effect.

5 Conclusions and targeted future energy strategies

In this study, the energy intensity and elasticity were examined together with the energy contribution to economic growth and inter-fuel substitution in Ghana in the period of 2000–2015. The previous literature reveals the state of the art with a research gap in energy intensity, energy elasticity, inter-fuel substitution possibility, and factor inputs contribution. To this end, the Translog production model was applied and ridge regression techniques were subsequently used as robust inference following the multicollinearity challenge in the Translog model to enhance the results. The ridge regression results were then used as energy intensity to compute elasticity, inter-fuel substitution prospects, and energy contributions. The results reveal that current energy consumption dynamics in energy intensity shows the expected inverse relationship with economic growth and with energy elasticity. There is an indication of high energy cost or negative energy intensity currently of $ -0.54 and negative energy elasticity of -0.80, thus suggesting energy inefficiency. There is also evidence of backfire rebound effect from the negative energy contribution of -80% and the economy is still in its first phase of development. The current energy consumption mix reveals that 95% of energy is obtained from both biomass and fossil fuels which invariably leads to an increase in CO₂ emission. These dynamics of energy, economic growth, and environmental challenges are associated with energy losses resulting from the transmission, distribution, and end-users. Besides, the results suggest that there is more utilization of lower-quality energy together with low energy technology application. That is to say, more energy is being wasted and equally directly not productive with economic activities.

For future policy design purposes, an inter-fuel substitution scenario possibility was conducted, whose result reveals positive energy outcomes with economic growth as energy intensity become lower and hence suggesting lower energy cost or tariffs and enhanced energy productivity as the result of inter-fuel substitution possibility and improving energy technology application. Therefore, twofold future energy policy designs were recommended: general energy policy and energy technology innovation. That is, substituting for higher-quality energy, thus, reducing biomass (wood and charcoal) energy by 69.45% and increasing natural gas consumption by 776%, especially in the industrial and power-generating sectors. Furthermore, policy design should be targeted to increase renewable energy (solar, wind and hydro) share from the current 0.5% to 15% by 2026. The execution of this energy design on the inter-fuel substitution policy strategy would not only lead to a lower energy intensity with an improved energy efficiency in economic growth but also reduce CO₂ emission. Secondly, VRA, GRID Co, NED Co, and the end-users electricity loss would be improved through energy technology innovation on the installation of smart energy and cloud energy solution, conducting energy audits, tokenization of the electricity sector and education programs. Finally, institutional policymakers under the residual factor agencies should be integrated effectively into natural resource management in the economy to harness more of their contribution. This methodology and policy design strategy in this paper present insightful contributions to examining energy intensity, elasticity, inter-fuel substitution prospects for policymakers and academia on energy, economic, and environment in developing Ghanaian economy and other countries with similar characteristics.

References

[1] Lee C C. Energy consumption and GDP in developing countries: a cointegrated panel analysis. Energy Economics, 2005, 27(3): 415–427

[2] Wolde-Rufael Y. Electricity consumption and economic growth: a time series experience for 17 African countries. Energy Policy, 2006, 34(10): 1106–1114

[3] ISSER. The state of the Ghanaian economy in 2011. Legon: Institute of Statistical, Social and Economic Research, 2012

[4] Duku M H, Gu S, Hagan E B. A comprehensive review of biomass resources and biofuels potential in Ghana. Renewable & Sustainable Energy Reviews, 2011, 15(1): 404–415

[5] RCEER. Guide to natural gas in Ghana. Resource Centre for Energy Economics and Regulation (RCEER) of University Ghana, 2006

[6] Lin B, Atsagli P, Dogah K E. Ghanaian energy economy: inter-production factors and energy substitution. Renewable & Sustainable Energy Reviews, 2016, 57: 1260–1269

[7] Kraft J, Kraft A. Relationship between energy and GNP. Journal of the Energy Division, 1978, 3(2): 401–403

[8] Allen R. The British Industrial Revolution in Global Perspective. Cambridge: Cambridge University Press, 2009

[9] Moe E. Energy, industry, and politics: energy, vested interests, and long-term economic growth and development. Energy, 2010, 35(4): 1730–1740

[10] Stern D I. Energy and economic growth in the USA: a multivariate approach. Energy Economics, 1993, 15: 137–150

[11] Akarca A T, Long T V. Relationship between energy and GNP: a reexamination. Journal of the Energy Division, 1980, 5: 326–331

[12] Dale M, Krumdieck S, Bodger P. Global energy modelling–a biophysical approach (GEMBA) Part 2: Methodology. Ecological Economics, 2012, 73: 158–167

[13] Özatalay S, Grubaugh S, Long T V II. Energy substitution and national energy policy. American Economic Review, 1979, 69: 369–371

[14] Stern D I, Kander A. The role of energy in the industrial revolution and modern economic growth. Energy Journal, 2012, 33(3): 127–154

[15] Csereklyei Z, Rubio-Varas M M, Stern D I. Energy and economic growth: the stylized facts. Energy Journal, 2016, 37(2): 223–255

[16] Apergis N, Payne J E. Energy consumption and economic growth: evidence from the commonwealth of independent states. Energy Economics, 2009a, 31(5): 641–647

[17] Ozturk I. A literature survey on energy–growth nexus. Energy Policy, 2010, 38(1): 340–349

[18] Stern D I. Energy and economic growth. In: Clevel C J ed. Encyclopedia of Energy. San Diego CA: Academic Press, 2004, 35–51

[19] Pirlogea C, Cicea C. Econometric perspective of energy consumption and economic growth relation in European Union. Renewable & Sustainable Energy Reviews, 2012, 16(8): 5718–5726

[20] Stern D I. Economic growth and energy. Energy Policy, 2004, 50: 518–527

[21] Stern D I. The role of energy in economic growth. Annals of the New York Academy of Sciences, 2011, 1219(1): 26–51

[22] Rafiq S, Salim R. The linkage between energy consumption and income in six emerging economies of Asia. International Journal of Emerging Markets, 2011, 6(1): 50–73.

[23] Chontanawat J, Hunt L C, Pierse R. Causality between energy consumption and GDP: evidence from 30 OECD and 78 non-OECD countries. In: Surrey Energy Economics Discussion Paper Series. Surrey Energy Economics Centre (SEEC), Department of Economics, 2006, 113

[24] Ayres R U, Warr B. The Economic Growth Engine: How Energy and Work Drive Material Prosperity. Cheltenham, Northampton: Edward Elgar Publishing, 2009

[25] Georgescu-Roegen N. The Entropy Law and the Economic Process. Cambridge MA: Harvard University Press, 1971

[26] Bloch H, Rafiq S, Salim R. Economic growth with coal, oil and renewable energy consumption in China: prospects for fuel substitution. Economic Modelling, 2015, 44: 104–115

[27] Best R. Switching towards coal or renewable energy? The effects of financial capital on energy transitions. Energy Economics, 2017, 63: 75–83

[28] Salim R A, Hassan K, Shafiei S. Renewable and nonrenewable energy consumption and economic activities: further evidence from OECD countries. Energy Economics, 2014, 44: 350–360

[29] Kwabena A A. What factors have influenced economic growth in Ghana? In: IEA Ghana, Policy Analysis. Institute of Economic Affairs, 2006

[30] Akinlo A E. Energy consumption and economic growth: evidence from 11 Sub-Sahara African countries. Energy Economics, 2008, 30(5): 2391–2400

[31] Twerefo D K, Akoena S K K, Egyir-Tettey F K, Energy consumption and economic growth: evidence from Ghana. Department of Economics, University of Ghana, Accra, Ghana, 2008

[32] Esso L J. The energy consumption-growth nexus in seven Sub-Saharan African countries. Economics Bulletin Access Economics, 2010, 30(2): 1191–1209

[33] Abaidoo R. Economic growth and energy consumption in an emerging economy: augmented granger causality approach. Research in Business and Economics Journal, 2011, 4: 1

[34] Sims C A. Role of approximate prior restriction in distributed lag estimation. Journal of the American Statistical Association, 1972, 67(337): 169–175

[35] Granger C W J. Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 1969, 37(3): 424–438

[36] Adom P K. Electricity consumption-growth nexus: the Ghanaian case. International Journal of Energy Economics and Policy, 2011, 1(1): 18–31

[37] Essah E A. Energy generation and consumption in Ghana. In: West Africa Built Environment Research (WABER) Conference, Accra, Ghana, 2011, 391–401

[38] Kwakwa P A. Disaggregated energy consumption and economic growth in Ghana. International Journal of Energy Economics and Policy, 2012, 2(1): 34–40

[39] Dramani J, Tandoh F, Tewari D. Structural breaks, electricity consumption, and economic growth: evidence from Ghana. African Journal of Business Management, 2012, 6(22): 6709–6720

[40] Bildirici M. The relationship between economic growth and electricity consumption in Africa: MS-VAR and MS-Granger causality analysis. Journal of the Energy Division, 2012, 37: 18

[41] Kwakwa P A. Energy-growth nexus and energy demand in Ghana: a review of empirical studies. Applied Research Journal, 2014, 1(1): 28–38

[42] Paul S, Bhattacharya R N. Causality between energy consumption and economic growth in India: a note on conflicting results. Energy Economics, 2004, 26(6): 977–983

[43] Odhiambo N M. Energy dependence in developing countries: does the level of income matter? Atlantic Economic Journal, 2014, 42(1): 65–77

[44] Bernard N L, Odhiambo N M. The dynamic causal relationship between electricity consumption and economic growth in Ghana: a trivariate causality model. Managing Global Transitions, 2014, 12(2): 141–160

[45] Patrick E, Dodzi K H E. Influence of the electricity consumption on economic growth in Ghana: an econometric approach. International Journal of Economics, Commerce, and Management (United Kingdom), 2014, 2(9)

[46] Ackah I, Adu F. The impact of energy consumption and total factor productivity on economic growth oil producing African countries. Bulletin of Energy Economics, 2014, 2(2): 28–40

[47] Ackah I. On the relationship between energy consumption, productivity and economic growth: evidence from Algeria, Ghana, Nigeria, and South Africa. University of Portsmouth United Kingdom, 2015, MPRA Paper No. 64887

[48] Esso L J, Keho Y. Energy consumption, economic growth, and carbon emission: cointegration and causality evidence from selected African countries. Energy Policy, 2016, 114: 492–497

[49] Zerbo E. Energy consumption and economic growth in Sub-Saharan African countries: further evidence. Economic Bulletin, 2017, 37(3): 1720–1744

[50] Samuel Y A. An econometric modelling of financial development-aggregate energy consumption nexus for Ghana. 2017

[51] Appiah M O. Investigating the multivariate granger causality between energy consumption, economic growth and CO₂ emissions in Ghana. Energy Policy, 2018, 112: 198–208

[52] Omri A. An international literature survey on energy-economic growth nexus: evidence from country-specific studies. Renewable & Sustainable Energy Reviews, 2014, 38: 951–959

[53] World Bank Development Indicators (WDI). Online database, World Bank, Washington, DC, USA. 2017

[54] Frieling J, Madlener R. Estimation of substitution elasticities in three-factor production functions: identifying the role of energy. FCN Working Paper, 2016, Paper No. 1/2016

[55] Wesseh P K Jr, Zoumara B. Causal independence between energy con-sumptionand economic growth in Liberia: evidence from a non-parametric bootstrapped causality test. Energy Policy, 2012, 50: 518–527

[56] Anderson A. Business Statistics for Dummies. Wiley, 2013

[57] Woodland A. Substitution of structures, equipment, and labor in Canadian production. International Economic Review, 1975, 16(1): 171–187

[58] Klacek J, Vopravil J. Total factor productivity in Czech manufacturing industry: the KLEM approach. Statistika, 2008, 45(5): 414–428

[59] Li X. The variation tendency analysis on contribution rate to economic growth by production factor input in China . Management Science and Engineering, 2013, 7(2): 16–23

[60] Li L, Zhu K, Guo H. The empirical studies of science and technology progress contribution rate estimation in various regions of China. China’s Population, Resources, and Environment, 2011, (4): 55–61

[61] Christensen L R, Jorgenson D W, Lau L J. Transcendental logarithmic production frontiers. Review of Economics and Statistics, 1973, 55(1): 28–45

[62] Adetutu M O. Energy efficiency and capital-energy substitutability: evidence from four OPEC countries. Applied Energy, 2014.119: 363–370

[63] Fuss M A. The demand for energy in Canadian manufacturing. Journal of Economics, 1977, 5(1): 89–116

[64] Berndt E R, Wood D O. Engineering econometric interpretation of energy-capital complementarity. American Economic Review, 1979, 69(3): 342–354

[65] Magnus J R. Substitution between energy and non-energy inputs in the Netherlands: 1950–1976. International Economic Review, 1979, 20(2): 465–484

[66] Smyth R, Narayan P K, Shi H. Substitution between energy and classical factor inputs in Chinese Steel Sector. Applied Energy, 2011, 88(1): 361–367

[67] Zha D, Zhou D. The elasticity of substitution and way of nesting CES production function with emphasis on energy input. Applied Energy, 2014, 130: 793–798

[68] Hoerl A E, Kennard R W. Ridge regression: biased estimation for non orthogonal problems. Technometrics, 1970, 12(1): 55–67

[69] Hoerl A E, Kennard R W. Ridge regression: an application to non-orthogonal problems. Technometrics, 1970, 12(1): 69–82

[70] Wetherill F G. Evaluation of ordinary ridge regression. Bulletin of Mathematical Statistics, 1986, 18: 1–35

[71] O’Mahony M, Timmer M P. Output, input and productivity measures at the industry level: the EU KLEMS database. Economic Journal (London), 2009, 119(538): F374–F403

[72] Wheeler D, Tiefelsdorf M. Multicollinearity and correlation among local regression coefficients in geographically weighted regression. Journal of Geographical Systems, 2005, 7(2): 161–187

[73] Wooldridge J M. Introductory Econometrics: a Modern Approach. South-Western College Publishing, 2006

[74] Pickup M. Introduction to Time Series Analysis, Quantitative Applications in the Social Sciences. Thousand Oaks, USA: SAGE Publications, Inc., 2015

[75] White H. Author cocitation analysis and Pearson’s r. Journal of the American Society for Information Science and Technology, 2003, 54(13): 1250–1259

[76] Bensman S J. Pearson’s r and author cocitation analysis: a commentary on the controversy. Journal of the American Society for Information Science and Technology, 2004, 55(10): 935–936

[77] Marquardt D W, Snee R D. Generalized in inverses, ridge regression, biased linear estimation. Technometrics, 1970, 12(3): 591–612

[78] van Benthem A. Energy leapfrogging. Journal of the Association of Environmental and Resource Economists, 2015, 2(1): 93–132

[79] Lin B, Ankrah I, Manu S A. Brazilian energy efficiency and energy substitution: a road to cleaner national energy system. Journal of Cleaner Production, 2017, 162: 1275–1284

[80] Burke P J, Csereklyei Z. Understanding the energy-GDP elasticity: a sectoral approach. Energy Economics, 2016, 58: 199–210

[81] Shahbaz M, Salah Uddin G, Ur Rehman I, Imran K. Industrialization, electricity consumption and CO₂ emissions in Bangladesh. Renewable & Sustainable Energy Reviews, 2014, 31: 575–586

[82] Ma C, Stern D I. China’s changing energy intensity trend: a decomposition analysis. Energy Economics, 2008, 30(3): 1037–1053

[83] Jorgenson D W. The role of energy in productivity growth. Energy Journal, 1984, 5(3): 11–26

[84] Wang Z H, Zeng H L, Wei Y M, Zhang Y X. Regional total factor energy efficiency: an empirical analysis of industrial sector in China. Applied Energy, 2012, 97: 115–123

[85] Bataille C, Jaccard M, Nyboer J, Rivers N. Towards general equilibrium in a technology-rich model with empirically estimated behavioral parameters. Energy Journal, 2006, 27(01): 93–112

[86] Sinton J E, Levine M D. Changing energy intensity in Chinese industry: the relative importance of structural shift and intensity change. Energy Policy, 1994, 22(3): 239–255

[87] Schurr S H, Bruce C, Netschert. Energy in the American Economy, 1850–1975: an Economic Study of its History and Prospects. Baltimore, MD, USA: Johns Hopkins Press, 1960

[88] Liddle B. The importance of energy quality in energy intensive manufacturing: evidence from panel cointegration and panel FMOLS. Energy Economics, 2012, 34(6): 1819–1825

[89] Kaufmann R K. The mechanisms for autonomous energy efficiency increases: a cointegration analysis of the US energy/GDP ratio. Energy Journal, 2004, 25(1): 63–86

[90] Ghana Energy Commission. National energy statistics 2000–2013. Final Draft Report 2016

[91] Acheampong T, Ankrah F. Pricing and deregulation of the energy sector in Ghana: challenges and prospects. Imani Ghana Report for Ghana’s Energy Situation, Q1. 2014

[92] Ackah I. Analysis of energy efficiency practices of SMEs in Ghana: an application of product generational dematerialization. Africa Center for Energy Policy, 2017

[93] Jorgenson D W. Productivity and Economic Growth. Chicago: University of Chicago Press, 1991: 19–118

[94] Christensen L R, Jorgenson D W. Measuring the performance of the private sector of the U.S. economy. In: Milton Moss ed. Measuring Economic and Social Performance. New York: NBER, 1973, 233–238

[95] Freeman R A. Theory on the future of the rebound effect in a resource-constrained world. Frontiers in Energy Research, 2018, 6: 81

[96] World Bank. Energizing economic growth in Ghana: making the power and the petroleum sectors rise to the challenge. Washington DC: World Bank, 2013

[97] Panayotou T. Empirical tests and policy analysis of environmental degradation at different stages of economic development, ILO: World Employment Program Research, WEP 2–22/WP, 1993, 238

[98] Mehrara M. Energy consumption and economic growth: the case of oil exporting countries. Energy Policy, 2007, 35(5): 2939–2945

[99] Solow R M. Technical challenge and the aggregate production function. Review of Economics and Statistics, 1957, 39(3): 312–320

[100] Ghana Statistical Service. Annual Gross Domestic Product. 2015

[101] Wesseh P K Jr, Lin B, Appiah M O. Delving into Liberia’s energy economy: technical change, inter-factor, and inter-fuel substitution. Renewable Sustainable Energy Reviews Journal, 2013, (24): 122–130

[102] Greene W H. Econometric Analysis. 7th ed. Boston, MA: Pearson Education, Inc., 1951

[103] Stern D I. Energy quality. Ecological Economics, 2010, 69(7): 1471–1478

[104] Zha X G, Liu P K. Substitution among energy sources: an empirical analysis on biomass energy for fossil fuel of China. Renewable & Sustainable Energy Reviews, 2013, 18: 194–202

[105] Lu X, White H. Robustness checks and robustness tests in applied economics. Journal of Econometrics, 2014, 178: 194–206

[106] Li K, Lin B. How to promote energy efficiency through technological progress in China? Energy, 2018, 143: 812–821

[107] Li K, Lin B. An application of a double bootstrap to investigate the effects of technological progress on total-factor energy consumption performance in China. Energy, 2017, 128: 575–585

[108] Liu J, Cheng Z, Zhang H. Does industrial agglomeration promote the increase of energy efficiency in China? Journal of Cleaner Production, 2017, 164: 30–37

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature