Africa Countries’ Energy Efficiency: Evidence from a Directional Distance Function Approach

Energy is recognized as the backbone of economic development while at the same time it is the most contributor to global warming. This paper aims to assess energy-efficiency of a sample of African countries over the period from 1971 to 2014. Through a directional distance function approach, we estimated both the energy efficiency and the environmental energy efficiency scores in the sample. The results showed that ignoring the undesirable output, i.e. dioxide carbon emissions associated with environmental degradation, overesti-mates countries’ energy inefficiency. Besides, from a non-parametric approach, we shed light on the sensitivity of countries environmental energy efficiency to the income level. Our findings confirmed the sensitivity of environmen-tal-energy efficiency to the Kuznets curve hypothesis. In particular, countries with high-level income are the most environmental-energy efficient in the sample over the period of study. The paper ends with some policy implications and some research perspectives.


Introduction
The debate among economists on energy efficiency originated after the 1973 oil crisis when the energy security of importing countries was threatened due to the oil embargo proclaimed by the world's major oil producers. Thus, an important concern of the public authorities is to find appropriate strategies to satisfy the energy demand which is still growing at high rates. The recent increases in global energy demand of 1.9% in 2017 and 2.3% in 2018 which is the biggest increase of the last three decades confirmed the need for countries to worry about their How to cite this paper: Alinsato, A. S., Bassongui, N., & Alakonon, C. B. (2021). Africa Countries' Energy Efficiency: Evidence from a Directional Distance Function Approach. energy security (IEA, 2018). The pioneering work of Lovins and Bethe (1977) will then distinguish three fundamental paths to achieve the energy goal of countries. First, one could increase energy production through fossil fuel sources, such as petroleum, coal, uranium. Second, countries could look for improving the rational use of available energy resources, i.e. their energy efficiency which could be defined in economics as the less use of energy for performing the maximum amount of desirable output. Recent studies in developing countries, as well as industrialized countries, found that the greater the energy efficiency is, the lower the energy demand issues are. Agyarko et al. (2020) and Van Buskirk et al. (2007) indicated that households' appliance subsidy policies electricity sector reforms, institutional quality could be used for improving countries energy efficiency.
Finally, countries could mix their energy sources by increasing the share of renewable energies, and many studies found evidence of such a hypothesis (Chang, 2020;Nieto et al., 2020;Ozoegwu & Akpan, 2021). According to these authors, increasing the share of renewable energies, such as solar, wind, biomass energies, in the countries' energy mix has significant impacts on their energy efficiency. However, with the global warming concerns, the concept of energy efficiency has moved from a purely economic concept to an economic and environmental concept. Hence, one could talk about "Eco-Energy Efficiency" or "Environmental-energy Efficiency" or "Energy and Environmental Efficiency" (EEE) for taking into account pollution issues in the energy efficiency measurement.
In order to shed light on the understanding of countries' energy efficiency, scholars have performed many studies which can be classified into generations. The first generation of studies was initially interested in examining the energy efficiency of countries around the world under the pure economic orientation of the concept of energy efficiency (Cantore, Calì, & Velde, 2016;Rajbhandari & Zhang, 2018). Throughout single input (energy) as well as multi-outputs (energy, capital, and labour) production functions, these authors tried to evaluate and explained the main drivers of countries' energy efficiency. They generally concluded that countries can improve their energy use without increasing the amount of input.
A second generation is refining the concept of energy efficiency by taking into account the environmental dimension (Djordjević & Krmac, 2019;Robaina-Alves, Moutinhob, & Macedoc, 2015). For instance, Djordjević and Krmac (2019) examined the environmental energy efficiency of the European countries' transport sector using the non-radial Data Envelopment Analysis (DEA) model. Their findings support that the road sub-sector is the most environmental energy efficient. Robaina-Alves et al. (2015) also used a stochastic frontier model to evaluate the energy and environmental efficiency of European countries during 2000-2011. Their results showed that countries are environmentally energy efficient after the implementation of the Kyoto Protocol in 2005. In the second generation of works, instead of a single output production function, they used a multi-output production function in which an undesirable output measured by pollution is taken into account. They revealed significant differences between energy efficiency and environmental energy efficiency scores. This paper contributes to existing literature on energy efficiency in Africa, especially that of the environmental-energy efficiency area by investigating the environmental-energy efficiency of African countries. The novelty of this paper is twofold. First, we use the directional distance function approach to estimate both energy inefficiency and environmental-energy efficiency scores by taking into account countries' specific effects over a long period of 44 years. Second, the paper finds out the economic impact of environmental-energy efficiency in Africa through a non-parametric approach. Finally, our results are expected to contribute to a better understanding of how policy-makers could improve the economic and environmental use of energy in Africa.
The rest of the paper is organized as follow. The second section presents the methodology and data sources. The empirical results and the analysis are presented in the third section. Finally, we conclude with some policy implications in the last section. Yet the issue of environmental energy efficiency is of great importance to African countries for several reasons. First, the continent experienced moderate rates of economic growth these last two decades. From 2000-2014 Africa recorded an average economic growth of 5% even though this performance fell smoothly to 3.1% during the period 2015-2019 (Osman, 2020). However, these three phenomena are reputed to be responsible for high energy demand. Second, Africa's energy demand increased by 2.4% per annum during the last decade against a world average of 1.6% (BP, 2020) while 45% of its primary energy con- Overall, there is a lack of empirical proof on environmental energy efficiency and its drivers in Africa. This paper contributes to fill this gap through a long series of data.

Methodology
In order to estimate countries' energy efficiency, we use the directional distance function approach. The advantage of this approach is that it allows estimating separately efficiency when desirable is considered and when both desirable and A. S. Alinsato et al. undesirable outputs are included without any transformation of undesirable outputs.

Directional Distance Function without Undesirable Outputs
Let the gross domestic product (GDP) creation within a joint production framework of desirable outputs. Let suppose N Decision Makers Units (DMUs) with ∈  inputs and d y + ∈  desirable outputs. In this paper, the vector of inputs which encompasses capital, labour, and energy consumption is transformed to produce a desirable output d y designing by GDP. Then, the production technology can be described as follows in Equation (1): In Equation (1), T describes all input-output combinations that are technologically feasible.
We can define the Pyatt (1972) output distance function to represent the technology T as follows in Equation (2): In Equation (2), the producer aims to expand the GDP production ceteris paribus. However, it is possible to expand the desirable output and reduce simultaneously the inputs used by the same proportion under the directional output distance function framework. Hence, following Chung, Färe and Grosskopf (1997), we define the directional output distance function instead of the Shephard's output distance function as follows in Equation (3) In Equation (3), D  denotes the directional technology distance function, is a non-zero directional vector through the input-output combination will be scaled.
As Färe, Grosskopf and Weber (2004), we set the observed input-output direction as follows in Equation (5): The direction g states that GDP is increased and capital, labour, and energy consumption are decreased at the same proportion. When setting the directional vector to g as specified in Equation (4), the Equation (3) becomes as follows in Equation (5): Equation (5) shows that DMUs seek to simultaneously increase GDP and get a maximum contraction in the capital, labour, and the energy consumption used by the proportion β . The value of ( ) can be obtained by solving the following linear programming problem as presented in Equation (6): In Equation (6), i λ denotes the intensity level at which countries form convex combinations of capital, labour, and energy consumption into GDP. Regarding the length of the time-space of our data, Equation (6) is estimated under variable return to scale (VRS). We also estimate an output-oriented directional distance function as suggested in the empirical literature (Bampatsou et al., 2013;Wang et al., 2013). Indeed, countries have better controls of their output than inputs such as energy. Besides, this assumption is confirmed as the conditions of isotonicity are meet, indicating that an increase in inputs (capital, labour, and energy) leads to an increase in countries' outputs (GDP). All inputs are positively correlated to outputs at a 1% level of significance (Table A1 and Table A2 in Appendix).

Directional Distance Function with Undesirable Outputs
In order to know whether there are some biases by estimating countries' energy efficiencies without considering the pollution issue, we also evaluate energy efficiency by including countries CO 2 emissions. By doing that, we estimate the environmental energy efficiency. Generally, two approaches are used for incorporating the undesirable (bad) outputs in the evaluation of efficiency (Scheel, 2001). The first approach is called the indirect approach that transforms the bad output before including it as good (normal) output in the production function. Gomes and Lins (2008) used this approach to evaluating the energy efficiency of a sample of developed and developing countries. The second approach proceeds directly by including the undesirable output in the production function without any transformation then impose the assumptions that undesirable outputs are weakly disposable and the strong disposability of desirable outputs. Many studies applied this approach for assessing countries' energy efficiency (Wang et al., 2013;Tavana et al., 2021).
We use the direct approach as it avoids potential errors in the transformation of bad outputs through the directional distance functions. This method is an additive of inefficiency measure by setting a given direction and is suitable when we face non-negative inputs or outputs (Chambers et al., 1996).
In presence of the undesirable output u y measured by the CO 2 emissions, the multiple input-output production technologies defined in Equation (1) becomes as follows: 1  2  3  1  2  3 , , , , : , , can produce , In Equation (7), T describes all input-output combinations that are technologically feasible. Thus, the output set is assumed to have the following properties (Chambers et al., 1996): 1) The assumption of null-jointness is presented in Equation ( The assumption of null-jointness implies that the production of a positive amount of desirable output (GDP) must be accompanied by some amount of undesirable one (CO 2 emissions).
2) The assumption that undesirable outputs are weakly disposable is presented in Equation ( The assumption of weak disposability states that a reduction in CO 2 emissions (undesirable output) is feasible only if GDP (good output) is proportionally reduced, given a fixed level of inputs.
3) The assumption of strong disposability of desirable outputs states that: Subsequently, the directional output distance function with undesirable output is defined as follows in Equation (8)  D x x x y y g g g g g x x x y y g g g g g T In Equation (8), the directional vector is set as follows in Equation (9): The direction g in Equation (9) indicates that the producer aims to expand the GDP production on the one hand, and reduce the CO 2 emissions, and all inputs are used proportionally and simultaneously as much as is feasible.
Finally, in order to know whether energy efficiency scores estimated from both DDF with CO 2 emissions and without CO 2 emissions are statistically different, we then performing the Wilcoxon matched-pairs signed-rank test. In both cases of energy efficiency and environmental energy efficiency, we use the non-parametric DEA approach. This latter has been widely used in the assessment of efficiency in various fields. Its main advantage is it does not require any functional form of production technology. Hence, we avoid the risk of misspecification of the production process.

Sampling and Data Sources
In this study, we use balanced panel data obtained from a sample of 21 African function. The energy consumption in the kiloton is used for measuring energy used. The gross domestic product in billion dollars constant is used to measure countries total desirable output while the pollution is captured by the Carbon emissions. All data used come from the worldwide data indicators maintained by the World Bank Group.

Descriptive Statistics
Results in Table 2  which is greater than the mean of this variable.

Energy and Eco-Energy Efficiency Scores
In this section, we present the results of both the model that takes into account the undesirable output as specify in Equation (8) and that of the model that does not include the undesirable output (Equation (9)). The model without the undesirable output (model 1) is estimated by using the capital, labour and energy consumption as inputs while the single output used is the countries' GDP. Apart from these inputs and output, the model that takes into account the undesirable output (model 2) includes a second output which is the CO 2 emissions. The results of the directional output distance function estimation based on a DEA approach of both two models (Table 3) indicate an average energy inefficiency of 5.91 (model 1) while the eco-energy inefficiency is about 0.33 (model 2). These results show that countries tend to be more inefficient when the CO 2 emissions are not taken into account in the evaluation of the energy efficiency performance.  From the results reported in Table 3, the countries' ranking indicates that Togo, Mauritius, Congo, Gabon, and Benin are the best eco-energy efficient countries, i.e. when we do not take into account the undesirable output. However, when considering the model that takes into account the CO 2 emissions, the ranking changes and Sudan, Gabon, Algeria, Egypt, and DRC become the best Eco-energy efficient countries. It can be noticed that the ranking has changed with the inclusion of CO 2 emissions, and only Gabon still been in the top five best eco-energy efficient countries. Furthermore, the rank of Gabon has shift from the fourth position in model 1 (energy efficient) to the second-best eco-energy efficiency when taking into account the CO 2 emissions. Hence, the shift in the ranking from model 1 to model 2 could be due to the inclusion of the CO 2 emissions in model 2.
To confirm whether or not that difference is driven by the inclusion of the CO 2 emissions, we run a nonparametric test imposed by the rejection of the null hypothesis of normality of the distributions through the Shapiro-Wilk test for A. S. Alinsato et al. normality (Table 4, rows 1 and 2). A one-sided Wilcoxon matched-pairs signedrank test (Table 4, row 3) supports the rejection of the null hypothesis at a 1% level of significance, implying that there is a significant difference between the inefficiency scores estimated from model 1 and model 2. In particular, the model that does not take into account the pollution issues in the evaluation of energy efficiency underestimates the energy efficiency scores. Our results are in line with previous findings that found countries with a high level of CO 2 emissions are less eco-energy efficient than those who have low environmental impact production behavior (Tachega et al., 2021;Bampatsou et al., 2013;Wang et al., 2013). Other findings outside the energy area also confirmed that efficiency models that ignore undesirable outputs tend to overestimate the inefficiency scores (Almanza et al., 2018;Liu et al., 2020). Therefore, in that follows, we interpret only the results obtained from model 2.
Results of model 2 show that the average eco-energy inefficiency score in the sample is about 0.33 during the period of analysis. Our results are in line with those of (Ohene-Asare et al., 2020) who found an average eco-energy efficiency of about 0.35 by using a slacks based model (SBM). In regard to the mean values of inputs and outputs reported in Table 2, our findings imply that countries in the sample have the potential to improve on average their GDP by 32.216 billion of dollars US while reducing the amount of labor and capital used by respectively 7,645,197 of labor force and 3.573 billion dollars US and reducing on average 9904.975 tons of CO 2 emission. These results suggest that African countries have to invest more in energy-saving potential. Especially, key economic sectors such as buildings, transports, residential sectors in cities, including energy-using products are identified as energy-saving sources in Africa (Koskimäki, 2012).
As our model that estimates energy efficiency with undesirable output is standardized for allowing countries to produce the maximum amount of GDP when minimising CO 2 emissions and inputs used, that implies if countries aim to reduce the environmental impacts of their energy consumption, they become more efficient. These results could be explained explained by the fact that most African countries have a scanty industrialised sector which is the most pollutant economic sector. Besides, one could argue that environmental energy policies have the potential to compel countries to improve their production process through their technology used and the choice for less pollutant energy sources. Figure 1 shows the growth of both energy inefficiency and eco-energy inefficiency during the period of analysis. From the left side of Figure 1, it can be seen that the energy inefficiency in the sample has increased on average overall periods, while the eco-energy inefficiency has decreased during the same period.

Trend Analysis on the Energy Efficiency
Furthermore, even though both energy inefficiency and eco-energy inefficiency in the sample have been unbalanced over time, it can be noticed that the instability in model 1 has been greater than that of model 2, supporting the view that environmental issues are matter in energy consumption. Especially, green energy policies have the potential to secure strong energy efficiency in the long term. One explanation of the improvement of African eco-energy efficiency could be that since the united nations conference on the environment, of Stockholm in 1972, African countries have ratified many international conventions and protocols agreements for the reduction on global warming such as the united nations framework convention on climate change in 1992, the Kyoto protocol in 1997, the 21 st conference of the parties in 2016.

Income Level and Environmental-Energy Efficiency
In this paragraph, we wonder if the eco-energy efficiency varies with the level of development. To know that, nonparametric tests have been used. We first split the sample into two groups according to their level of development. The choice of grouping the sample into two relies on the goal to have a sufficient number of observations in each sub-group. We used the gross domestic product per capita based on purchasing power parity (PPP) in international dollars constant 2010 in 2014 to measure the countries' level of development. The countries that GDP per capita is lower than 3996 dollars US are said to be low-income countries (Group L) and those that GDP per capita is greater or equal to 3996 dollars US are classified in Group H, and called high-income countries 1 . We then run a nonparametric test, namely the Mann whitey' test.
The results reported in Table 4, row 4 strongly support the hypothesis that the eco-energy efficiency of the high-level income countries is greater than that of the low-level income countries at a 1% level of significance. Our results are consistent with the theoretical assumptions, especially those of the environmental Kuznets curve hypothesis. Our results are also in line with some empirical evidence in Africa (Güngör et al., 2021;Liu et al., 2020). Indeed, Güngör et al. (2021) tested the environmental Kuznets curve with structural breaks and confirmed that the higher is the income level, the better the environmental quality is in South Africa during the period 1996-2016. (Liu et al., 2020) investigated the nexus between income distribution and environmental pollution using a sample of 33 countries during the period 2000-2016. They confirmed a nonlinear effect of income inequality on energy efficiency within the sample while industrialization harms countries' energy efficiency. Thus, our results could be explained by the fact that the higher is the income level, the greater are resources available to invest in innovation, green energy; and the greater are the population preferences for environmental quality. Furthermore, most of the low-income countries face a lack of access to energy; especially electricity, so that their energy supply is not able to satisfy the demand.

Conclusion and Policy Implications
Energy security, fossil fuels' price uncertainties, and the global warming concern have increased the need for countries to control their energy use. For that, energy efficiency has become one of the key instruments to evaluating energy policies which shifted into environmental energy efficiency regarding the importance of green gas emissions in industrialized countries as well as in some developing countries. This study aims to fill gaps in the literature of energy efficiency measurement by focusing on African countries. Especially, we evaluated the energy efficiency by including the environmental pillar which seems to be less investigated in the Africa region. Within a framework of a nonparametric directional output distance function with undesirable output (Chung et al., 1997) under the variable return to scales assumption (VRS), we showed that neglecting the dioxide carbon emissions in the estimation of energy efficiency leads to overestimating countries' energy inefficiency. Besides, non-parametric tests are used to find out the role of the level of income in countries' environmental energy efficiency. Our results revealed that there are significant disparities in environmental energy efficiency across income level groups. Thus, high-income level countries are more environmentally energy-efficient than those with low-income levels. This funding confirmed the environmental Kuznets curve hypothesis within the sample. Hence, energy policies should be implemented for improving countries energy savings in Africa, in particular in those with low-income levels. Future researches that investigate the divers of African countries' eco-energy efficiency should take into account the income level disparities. Modern Economy