Gauging Energy Poverty in Developing Countries through Electricity Access

Energy poverty is a crucial development issue though is ambiguously conceived. In many parts of the world, energy poverty is a severe problem, particularly amongst the vulnerable and developing countries. When impoverished people do not have adequate access to energy, they will not be able to generate the power they need to lift themselves out of poverty and often get proper food, education, health and sanitation, infrastructures and basic daily and development needs. With the advantage of interval-based composite indicators and triplex representations of the intervals as a sensitivity analysis, we measure and assess developing countries’ electricity access as a proxy of energy poverty. The proposed quantitative approach is particularly innovative because it adequately gauges robust measures of electricity access and the level of resilience and vulnerability of energy access in the developing world. Our conclusion based on the comparison of the different representations allows identifying a cluster of developing countries showing higher international vulnerability, whilst other countries display higher electricity access resilience.


Introduction
Energy poverty is a severe development issue in many areas of the globe, especially amongst the poor and vulnerable and in the developing world. The phenomenon is multidimensional and alarming, becoming progressively more so to many extents (Alem and Demeke 2020). Ensuring energy security to all crucially in uences one country's development pattern and sustainability outcomes (Groh 2014). As a result, alleviating energy poverty is on the top of the domestic and international development agendas (Sagar 2005). Generally speaking, it is understood that if poor people do not have su cient access to energy, they will be unable to produce the electricity they need to lift themselves out of poverty and often get proper food, education, health and sanitation, infrastructures and basic daily and development needs (Indrawati 2015).
In spite of its centrality within the energy and development policy debate, energy poverty has not yet reached a univocal de nition. Authors have different interpretations of what constitutes energy poverty. However, a standard de nition given by the World Economic Forum sees energy poverty as the inaccessibility to environmentally friendly, technologically advanced "energy services and products" (World Economic Forum 2002; Robic et al. 2010).
Families experiencing energy poverty cannot get enough energy services for their homes (Bouzarovski 2014;Fahmy 2011;Buzar 2007). The ndings are essential since they demonstrate that disadvantaged populations are at a greater risk of falling into fuel poverty. This vulnerability is often likely to become even a trap (Bouzarovski 2014).
The notion of energy poverty is hugely similar to the concept of fuel poverty and the two concepts are frequently used interchangeably (Li et al. 2014;Bouzarosvski 2014). Even if there are differences, energy poverty may be de ned as the insu ciency of access to energy services rather than a more general problem relating to the di culty for families to pay the relevant expenses associated with maintaining a comfortable interior environment (Boardman 2013;V.A. 2009). There are signi cant measuring problems to address concerning both ideas at the same time. Thompson Snell (2013) provides information on the measurement and estimation of fuel poverty in Europe, whilst Trinomics (2013) discusses the indicators to be used to assess energy poverty (2014).
Energy poverty is a multifaceted conundrum, to be solved with a multidimensional approach (Okushima 2017). According to Gatto and Busato (2020) and Middlemiss Gillard (2014), a connection between energy poverty and energy vulnerability exists. In particular, when there is a shock in the energy price, the aspects of energy vulnerability that may be regarded as concepts in quantitative studies can be ideally identi ed and quanti ed (Renner et al. 2019; Busato and Gatto 2019). Even though fuel poverty is directly linked to social disadvantage, there are signi cant challenges in accurately de ning this connection (Fahmy 2011). According to the author, money and energy e cacy (thermal e ciency is a signi cant predictor) are essential factors determining fuel poverty. At the same time, there are substantial negative health consequences of fuel poverty, particularly for the most vulnerable, such as children (see Liddell and Morris 2010).
In order to assess the overall impact of fuel poverty on a population, it may be necessary to collect extensive data exploring the energy-development nexus and assess it by collection standards (see . In this regard, energy e ciency is expressly promoted to alleviate fuel poverty (see Sharma et al. 2019 for India and Ismail and Khembo 2015 for South Africa).
In contrast, the notion of "fuel poverty" was thoroughly researched and examined in the United Kingdom and Ireland before being adopted (Walker et al. 2014a;Walker et al. 2014b;Boardman 2013). It was deemed appropriate to alleviate poverty in Northern Ireland by using energy e ciency measures and more particularly an energy-e cient heating system. In the long term, it was feasible to combat fuel poverty by adopting a more proactive approach. Sovacool (2015) explains that the "Warm Front" initiative in England was being implemented, increased energy e ciency during the years 2000-2013 enabled the "fuel poor" to see an improvement in their health conditions. Energy e ciency can have an impact on the reduction of energy and fuel poverty directly. However, it can also indirectly impact energy and fuel poverty reduction by enhancing and boosting entrepreneurial processes, reducing energy, and fuel poverty by developing new relevant energy-e cient technologies.
At the same time, increased energy e ciency may contribute to greater energy security in this situation if appropriately performed (Selvakkumaran and Limmechokchai 2013). The concepts of energy insecurity and energy security are, in reality, another vital development issue to be considered (see Morrow et al., 2018). While discussing globalization, it is essential to remember that the distribution of energy resources across the globe necessitates a rise in security through time and an increase in insecurity or vulnerability due to energy disparities (Overland 2016). Furthermore, energy insecurity can cause health issues for the general public (Hernandez 2016).
Energy poverty has exhibited its magnitude and harm for short-and long-run development (Guruswamy 2011). To foster sustainable development outcomes, energy poverty requires private-public-third sector cooperation to jumpstart duly initiatives with the scope to tackle energy vulnerability and enhance energy resilience (Gatto and Drago 2021  ). However, there is also a problem of arbitrary assumptions to consider when constructing an indicator (see Nussbaumer et al. 2012). In this sense, the interval-based composite indicator is the most appropriate choice to take into account the different assumptions that can be considered for the construction of the same composite indicator and motivates this work's rationale. Indeed, rankings between the different countries as statistical units can be obtained using intervals (particularly assessing the different centers and upper or lower bound).
The article is organized as follows: in section 2, we describe the methodology and the data used; in section 3, we show the results of the work; in section 4, selected policy implications are elicited; nally, in section 5, the conclusions are presented. The appendix section complete this work.

Data
The article in question is concerned with the construction of a composite indicator of energy poverty via access to electricity (intended as balanced by negative polarity). We use these variables in the construction of the composite indicator as described in Table 1.
These variables contribute to the nal electricity access score for the Regulatory Indicators for Sustainable Energy (RISE) index and database (RISE 2021, see Banerjee et al. 2017). The rationale was to following the last RISE database, issued in 2020, as the score is a means of support in the attainment of Sustainable Development Goal 7, which asks for "universal access to clean and modern energy" (see also Global Off-Grid Lighting Association 2015). The RISE is a collection of indicators designed to be used to assess policy and "regulatory frameworks that countries have put in place to support the achievement of Sustainable Development Goal 7".
The data considered in our study are related to 2019, the last available year. Therefore, the initial observations are excluded; all these are characterized by missing observation (N\A). In the end, we obtain a dataset based on 54 developing countries as cross-section statistical units, characterized by eight different indicators.
Moreover, the different indicators (obtained by the same source, i.e. RISE 2021) are exhaustive of the phenomenon we are investigating because they are jointly at the same part of the scores of the electricity access in the RISE electricity access pillar. Therefore, one can conclude that both indicators are, in fact, a side of the same phenomenon.

Methodology
This work aims to construct an innovative composite indicator of electricity access to calculate energy poverty. In this respect, we also innovate the methodology because this measure is not based on a single value but an interval of values instead. The advantage of using an interval is that we explicitly have a unique measure of the composite indicator (the center) summarizing and representing a single value for the statistical units Following Gioia and Lauro (2006), an interval can be considered as: [1] Tiny intervals, also known as degenerate intervals of the type are equal to real numbers ( Here identify the variable q considered at a specific point t in time is the mean for the considered variable and is the standard deviation In order to construct the composite indicator, we identify all the variables as components. Then, the various indicators have been standardized to achieve the same scale for all indicators in use. When indications are converted to a common scale having a zero mean and a standard deviation of one, this is referred to as standardization or z-scores. [2] Then, to calculate the final composite indicator, the sorting components are combined by aggregating the different values. In this sense, we compute the composite indicators facing the existing uncertainties on constructing the composite indicators making use of interval data. The advantage of using an interval is that we have not been forced to adopt a unique specification for constructing our composite indicator. However, we can consider different assumptions and specifications (we have, indeed, not forced to either adopt an equal weighting specification). The final result is an interval of the different composite indicators obtained. Following Lauro and Palumbo (2000) and Moore et al. (2009), we can also calculate some parameterizations of our interval, allowing a comparison between the different intervals. In this way: [3] Where is the upper bound of the interval and the is the lower bound.
The center is a measure that allows summarizing the most plausible value obtained by the interval. Finally, a measure of the variability is the radius, which has the same value considering the two different radii: the radius that departs from the lower bound to the center and the radius that departs from the center and goes to the upper bound.
So the radii are: A third measure that can be computed can be the interval range , which is simply obtained by summing the two radii or subtracting from the upper bound the lower bound: Different rankings can be obtained by considering the center of the intervals (equivalent to rank classical composite indicators, which can be considered tiny intervals). However, it is also possible to rank the radii differently and upper and lower bound (see Mballo  weight. In this respect, we simulate a new preliminary weight for each component, which is not necessarily equal to the component's nal weights. So considering the simulation, the equal weighting is a plausible case but we also cover situations in which some components can be weighted more than others.
2. The composite indicator's preliminary weights should be added together to provide a value representing a theoretical total. Therefore, the various candidate weights are added together, and then each one is divided for the sum of the weighting scheme obtained to obtain the nal weight for each of the eight components considered. Thus, the result comprehends a single weight for the components of the composite indicators.
3. We repeat the procedure 100000 times, and for each simulation, we obtain repeating the procedure above a single (probabilistically different) weighting scheme. Hence, in the end, we obtain 100000 weighting schemes which are the baseline in the construction of the composite indicator based on an interval.
4. Finally, we compute the parameters of the composite indicators considering the center, the radii, and the range.
From the diverse centers and radii, we can construct the different rankings. Then, to perform a sensitivity analysis of the different results, we compute a triplex representation based on less intense assumptions (on the triplex representations see Williamson 1989; Drago 2021 on the context of the interval-based composite indicators). In this case, the sensitivity analysis is different from the classic one because we have already considered the different assumptions in our indicator, and now we compare different representations.
A triplex representation of the interval can be defined in this way: where the corresponds to the equal weighting scenario. However, it is essential to note that the radii are not symmetric but can be different. This fact is significant in interpreting the results of the analysis in which the triplex representation is involved.
The triplex representation is used to represent the intervals the quantiles 0.95 and 0.05, excluding the observations lying outside these intervals. In this respect, we are using some more reasonable intervals that exclude some extreme scenarios (namely, some weighting schemes that are particularly favorable for a country or particularly adverse). The center of the interval on the triplex representation is based on the equal weighting scenario. Therefore, it is helpful to compare the results obtained by the center of the interval with the equal weight scenario. Furthermore, the triplex representation can be used as a sensitivity analysis to compare the results obtained with the interval composite indicators with different assumptions. In order to compare these different assumptions, we subtract the triplex representation from the interval. [3] So we have two generic intervals: In this way, we elicit the relevance of the extreme scenarios. It is noticeable that the higher the difference between the two intervals, the more relevant the possibility for extreme scenarios. In this sense, the results are an interval and represent the relevance of possible extreme scenarios in the interval analysis. So, this means that to analyze policies and evaluate vulnerability (the difference between lower limits) and resilience for each nation, the ndings are critical (that is the difference between the upper bounds).

Results
It is possible at this point to interpret the different tables and results. From Table 2, we can analyze the intervalbased composite indicator ranking by the center. The center is the most representative value for the intervals considered. We can observe that Guatemala reaches the rst position, followed by Bangladesh, Tanzania, Cambodia, Ethiopia, South Africa and Kenya.
Two cases are emblematic in this group of countries: Bangladesh and Tanzania (the rst two countries in the ranking). According to Ichord (2019), Bangladesh is a "leader" in developing emerging nations, has been the rst among developing countries to expand access to electricity. According to estimates, electricity availability in Bangladesh has grown "from 55 percent in 2010 to 88 percent in 2017" (Ichord 2019), which were at the same tune rural regions accounting for 81 percent of the total.
Aiming to attain 100 percent coverage by 2021, the government of Bangladesh is attempting to accomplish this ambitious goal. However, the internal inability to provide consistent electricity has hampered growth (Ichord 2019). It shall be remarked that, according to the World Bank (2016), Tanzania's socioeconomic development goals will be impossible to attain without cheap and reliable energy. Given that just 36 percent of households have access to power, the World Bank is aiding the government with a project to increase access to cheap, e cient, and modern energy while safeguarding the sector's long-term operational and nancial viability and sustainability (World Bank 2016).
South Sudan, the Congo Republic, and Somalia perform the worst (last, penultimate and third last, respectively). The bad practice of South Sudan is emblematic because, considering the 12.5 million inhabitants in South Sudan, only 1percent have the accessibility to the electric grid (Gallucci 2020). However, after years of civil strife, the nascent nation of East-Central Africa is reviving its electrical industry. As a result, South Sudan is on the verge of building its power grid (Gallucci 2020; Hundermark 2021). Table 3 and Table 6 in the Appendix show information based on another relevant interval parameter: the radius (or radii because there are two). The radius is a way to represent the variability of the interval-based composite indicator. Here, Chad, Solomon Islands, Nepal, Zambia, and Afghanistan get the best positions. A lower variability pertains to Niger, the Philippines, Yemen, the Congo Republic and Bangladesh. In this respect, these countries show the highest level of robustness and a lower vulnerability for a single indicator. The results can be compared with a similar weighting scenario (Table 4), showing, on one hand, the robustness of the results obtained and on the other hand some relevant differences. Bangladesh is not the rst country on the ranking, the best score is achieved by Tanzania.
There are, at the same time, differences between the other positions on the ranking. This result shows the consistency of the result obtained examining the center of the interval. The radii represent a new contribution that allows discovering essential differences between the different countries. In particular, countries that are fairly robust, such as Yemen, the Philippines and Niger, also show a lower variance considering the different initial components and simultaneously very low radii. Countries such as Chad, the Solomon Islands and Nepal show a higher vulnerability because the variance of the different components of the interval-based composite indicator is higher than the international average level. Nevertheless, at the same time, these countries show a higher radius. That means they can improve their rank, but conversely, they are at risk because the different situation of the whole number of the indicator shows essential weaknesses. So in this respect, the situation should be carefully considered.
Then we can compute the triplex representation ( Table 7 in the Appendix), which allows us to observe a different type of representation. In this case, we consider two different smoother upper and lower bound with respect to the original interval computed. So the results should be based on less extreme scenarios. The difference between the two representations computed using interval algebra is obtained in Table 5. The differences between the two extremes (the lower bound and the upper bound) obtained by the difference of the two intervals represented (Table 6 and Table 7

Policy Implications
The approach presented in this work allows identifying the situations showing higher resilience and vulnerability at an international level. So in this respect, we can use this approach to evaluate situations highlighting some virtuous or vicious paths to a relevant improvement or worsening in domestic performance which may be of interest for energy and development policy. The latter may be used as alerters which may trigger in case of cautious situations. The outcomes may also be interpreted as indicators of energy resilience or vulnerability. In both cases, the computed index may return relevant development policy recommendations to be used for energy poverty assessment.
Considering all the different rankings obtained, we can evaluate and classify different situations and policy implications. The rankings assessing the center (or the classical assumption of "equal weighting", able to respond to the same question the center answer) is a general value of electricity access can be obtained examining the multitude of the scenario considered. So the center's ranking allows evaluating the general level of electricity access at the international level. More interesting and innovative are the other rankings. The radii show bene cial information, which can improve or worsen the situation on the basis of different assumptions. Enormous radii can improve or worsen the situation depending on the distribution of numbers on the various indicators. Enormous radii can be due to a higher upper bound or a lower upper bound respect other extremes at the international level.
That means, more speci cally, an intense vulnerability shall exist and on the other side, a possibility to strongly

Conclusions
This work had the mission to shed light on energy poverty by improving our understanding in terms of energy and development policy. To this end, an interval-based composite indicator on 54 developing countries, representative of the totality of the world regions has been built. Additional tests and sensitivity analyses complete the inquiry. We learnt a number of facts on the domestic energy poverty situations of the selected countries, whereby we can distinguish energy resilient and energy vulnerable countries. The explored issues returned insightful guidance to be examined for achieving sustainable development goals (SDGs).
Poor access to energy is a signi cant problem in many parts of the world, particularly amongst the vulnerable socioeconomic groups and those living in developing countries. The World Economic Forum conceives energy poverty as the inability to get environmentally friendly, technologically sophisticated "energy services and goods". Therefore, it is possible to de ne energy poverty as a lack of adequate access to energy services rather than a more general issue related to the inability of families to pay the necessary costs involved with maintaining a pleasant interior environment.
Associated energy and development policy issues have to be highlighted. Before being implemented in the United Kingdom and Ireland, the idea of "fuel poverty" was extensively studied and evaluated in both countries.
Energy e ciency has the potential to have a direct effect on the alleviation of energy and fuel poverty. While this will directly contribute to the decrease, it will also have an indirect effect by improving and promoting entrepreneurial activities, which will, in turn, contribute to the creation of new applicable energy-e cient technology.
In this study, we have approached energy poverty by measuring electricity access using a new approach based on an interval-based composite indicator. In this respect, we can consider two different representations. Based Where the difference is higher is possible to observe a higher resilience for the considered country.
The presented work is not exempt from limitations. Electricity access has been used as a proxy of energy poverty. However, this theoretical choice has been interpreted to be more solid with respect to subjective interpretations. On top of that, this option returns more extensive and reliable data. Further research can consider an exploration of fuel poverty. Another important topic to examine in the future is the difference between the notions of energy insecurity and energy security.
Appendix A