Adel Ben Youssef
email: adel.ben-youssef@gredeg.cnrs.fr

Laurence Lannes
email: llannes@worldbank.org

Christophe Rault
email: christophe.rault@univ-orleans.fr

Agnès Soucat
email: soucata@who.int

Energy Consumption and Health Outcomes in Africa 1

Keywords: JEL Classification: Q43, Q53, Q56 Energy consumption, Electricity, Health, VAR

Agnes Soucat is the Director for Health Systems, Governance and Financing at the WHO in Geneva. Until recently she was Global Leader Service Delivery and Lead Economist at the World Bank. She previously was the director for Human Development for the African Development Bank, where she was responsible for health, education, and social protection for Africa, including 54 countries in sub-Saharan Africa and the Maghreb. She has over 25 years of experience in health and poverty reduction, covering Africa, Asia and Europe. She was a pioneer

Introduction

Economic growth in industrialized countries has historically gone hand-in-hand with increasing energy intensity [Reference]. This is also the case for developing countries where impacts of energy consumption and use on economic development and the progress are increasingly significant [reference]. Africa is following the same trend andthe intensity of energy consumption is increasing rapidly with the economic growth in the last decade.

Africa is experiencing recent rapid economic development and an increasing demand on energy supply. The Continent presents mixed situation with large energy producing countries relying on oil and gas (mainly in North Africa); other countries largely relying on coal (South Africa); and Sub-Saharan Africa havingstrong dependence on biomass. The expected boom of the African population with an increase from 1 billion to 2.3 billion people by 2030 makes it necessary to consider the sustainability of energy use in order to mitigate environmental and public health damages.

Threemain problems can be identified when discussing the energy-health nexus in Africa. Firstly,many African citizens have insufficient access to modern energy sources and largely rely on biomass. This causes health problems due to indoor air pollution caused by the use of traditional fuels. In fact, a large majority of the population is facing problems with access to energy due tounavailability and unaffordability of modern energy sources. Energy poverty and insecurity are major components of poverty [Reference]. Secondly, increasing urbanization, in particular in big cities, seems to present serious negative effects on health when the populations in the new urban areas are lacking access to clean and affordable energy sources [reference]. The combustion of biomass and the coal in urban areas leads to high levels of indoor and outdoor air pollution. This air pollution is exacerbated by the use of "non-clean" technologies by industries and inefficient transports. Thirdly, global warming is modifying Africans life style with deep impact on their health. Global warming and the desertification of certain areas result in the depletion of some traditional energy sources like biomass.

Several papers reported positive effects of energy consumption on economic growth [START_REF] Arouri | Energy use and Economic Growth in Africa: A Granger Causality Panel investigation[END_REF], Adom, 2013), education (Ben Abdelkarimet al. 2014 b) andemployment (Adom,2014) in Africa. However, less is known about the effects of energy consumption on health in Africa. Researchers report balanced effects: while for some of them each further increase in energy consumption produces ever-smaller health gains, others have shown that energy use engender indoor and outdoor pollutions with significant impacts on environment and public health. Pollutants, such as Inhalable Particulate Matter (PM), Methane, micro metal elements, and SO2 have been destroying the environment and affecting public health negatively. Respiratory infections caused by air pollution from energy incomplete combustion are the main threat to the health in developing countries. [START_REF] Wang | The analysis of the impacts of energy consumption on environment and public health in China[END_REF] reports that 43 millions people would die of respiratory infection each year. However, global studies showing the long-run effects are lacking.

The objective of this paperis to address this gap in knowledge by (i) proposing an analytical framework to discuss the health effect of energy and electricity consumption in Africa; (ii) empirically identifyinghowincreased energy consumption (especially electricity) can improve health outcomes in Africa; and (iii) exploringdirect causality between energy consumption, under-5 child mortality and life expectancy as well as indirect causality between energy consumption, greenhouse effect (air pollution) and government health expenditure. The analysis focuses on 16 African countries.

The first part of the paperdiscusses the positive and negativeimpacts of energy consumption on health. The second part presents the methodology, parameters, and data used.

A policy discussion is engaged in the third section followed by recommendations.

Expected Health impacts of Energy use and electricity consumption

Energy and public health have not been analyzed together in a single framework until recently, and environment is usually looked as the media in the chain of energy, emission, environment, and human health. We propose in this section to identify the main health problems in Africa and to identify how provision of clean energy can improve Africa's health outcomes.

What are the main health problems due to insufficient energy consumption?

Energy consumption and electricity consumption have several direct and indirect impacts on health. This section summarizes the main effects and discusses the channels through which energy consumption (electricity consumption) can affect negatively or positively a population"shealth. We restrict ourselves to the channels that are the most pertinent in the African context.

Indoor pollution due to use of biomass

Energy is essential for cooking and heating. It permits access to cooking and hot meals. Evidence on link between good nutrition in children and good health outcomes (also education outcomes) is well established.Lack ofaccess to modern energy sources lead to the usage of biomass energy (mainly woods) as the principal source of energy. The World Health Organization (WHO) estimates that 3 billion people in the World are using Biomass for cooking (2006). While biomass permits access to hot meals and heating, the inefficient burning of solid fuels on an open fire or traditional stove indoors creates a dangerous cocktail to hundreds of pollutants, primarily carbon monoxide and small particles, but also nitrogen oxides, benzene, butadiene, formaldehyde, polyaromatic hydrocarbons and many other health-damaging chemicals. Where coal is used we can add to this list of pollutants sulfur, arsenic and fluorine. The problem of indoor air pollution still fail to mobilize the international community while the WHO estimates also that 4.3 million people a year die prematurely from illness attributable to the household air pollution caused by the inefficient use of solid fuels (WHO, 2014). Indeed, several diseases are associated with indoor pollution such as acute infections of the lower respiratory tract, chronic obstructive pulmonary disease, lung cancer, asthma, cataracts and tuberculosis. In 2002, in Sub-Saharan Africa 396 000 deaths were due to indoor smoke (WHO, 2006).In context of the contribution of energy technologies, [START_REF] Ezzati | Evaluating the health benefits of transitions in household energy technologies in Kenya[END_REF] studied the effect of indoor air pollution on the residents' health during the two years after advanced energy technologies were introduced. The result showed that stove efficiency innovation could significantly decrease mortality and acute respiratory infections in children.

The indoor pollution problem has a gender bias aspect since women and young girls in developing countries are particularly affected by the negative health outcomes of indoor air pollution (IAP) from the use of solid fuels. Since women are usually responsible for cooking while taking care of children, women and children are most exposed to IAP from the use of solid fuel and its subsequent health impacts. This activity has also an impact in matter of time spent by children and women in order to collect woods and biomass sources of energy. This time devoted to collecting woods and biomass sources of energy is taken from the time devoted to education or other productive activities.Young children living in households exposed to biomass indoor pollution have a two to three time greater risk of developing an acute lower respiratory infection (ALRI) than others. They are more susceptible than adults to absorb pollutants, since their lungs are not fully developed until they reach their late teens. A study in rural Kenya found that the amount of pollution a child is exposed to correlates to the risk of developing pneumonia [START_REF] Ezzati | Evaluating the health benefits of transitions in household energy technologies in Kenya[END_REF].

Outdoor Pollution

Air pollution has several adverse health effects such as asthmatic, cardio-vascular and other related health outcomes. In spite of an increasing awareness about these effects and "better" legislated air pollution policies in many countries, recent studies estimate that 80% of the world"s population continue to be exposed to ambient pollution that far exceeds the WHO recommended Air Quality Guideline (AQG) of 10mg/m3 for long-term PM2.5 concentration levels (particulate matter with aerodynamic diameter smaller than 2.5 mm) [START_REF] Van Donkelaar | Global estimates of ambient fine particulate matter concen-trations from satellitebased aerosol optical depth: development and application[END_REF][START_REF] Rao | Environ-mental modeling and methods for estimation of the global health impacts of air pollution[END_REF][START_REF] Brauer | Exposure assessment for estimation of the global burden of disease attributable to outdoor air pollution[END_REF].

Moreover, the increasing urbanization of the African continent and the emergence of megacities like Cairo, Casablanca, Lagos, Kampala has been shown to be associated with air pollution and public health issues [Ref]. Inefficient means of transport, usage of "non-clean" technologies and inefficient ways of cooking have engendered important air pollution and concentration of PM. Estimates indicate that outdoor and household air pollution are globally among the leading causes of mortality and morbidity related outcomes in developing countries [START_REF] Lim | A comparative risk assessment of burden of disease and injury attributable to 67 risk factors and risk factor clusters in 21 regions, 1990-2010: a systematic analysis for the Global Burden of Disease Study[END_REF]. Emissions from cooking stoves continue to be a major component of global anthropogenic particulate matter (e.g., (UNEP/WMO, 2011)) in particular in Africa and South Asia where emissions from cooking stoves are well over 50% of anthropogenic sources (Bond et al., 2004a[START_REF] Bond | Bounding the role of black carbon in the climate system: a scientific assessment[END_REF]. [START_REF] Smith | Health impacts of household fuel wood use in developing countries[END_REF] studied air pollution situation in China by referring to the theory of ''Total exposure assessment'', in which he reviewed the relationship between energy consumption and air pollution, introduced the exposure assessment method, and analyzed the impact of air pollution on public health. Kunzliet al. (2000) analyzed the contributions of air pollution to mortality and morbidity resulted from outdoor and traffic-related air pollution in Austria, France, and Switzerland based on the ''Epidemiology-based exposure-response functions''.

Climate change and energy efficiency related policies are additionally being undertaken in many countries and these are likely to cause energy transformations that will impact air pollution and health related outcomes in the future. There is a growing body of research focusing on the public health and potential climate co-benefits of improving access to modern cooking fuels and stoves in developing countries [START_REF] Bond | Global atmospheric impacts of residential fuels[END_REF]Haines, 2007;[START_REF] Smith | Mitigating Climate, Meeting the MDGs and Blunting Chronic Disease: The Health Co-benefits Landscape[END_REF].

Cold related diseases due to lack of energy access

Living in cold homes has been linked to excess winter deaths, Chronic Obstructive Pulmonary Disease (COPD), and respiratory tract infections, as well as increased risk of heart attacks and strokes due to raised blood pressure [START_REF] Marmot | The Health Impacts of Cold Homes and Fuel Poverty[END_REF]. The damp or mould that can accumulate in cold homes has been shown to affect allergic or respiratory conditions including asthma [START_REF] Fisk | Meta-analyses of the associations of respiratory health effects with dampness and mold in homes[END_REF] and, in general, stress, depression, and low levels of wellbeing have all been linked with cold or damp housing [START_REF] Shortt | The walls were so damp and cold, Fuel poverty and ill health in Northern Ireland: results from a housing intervention[END_REF]. Given the evidence linking cold housing to poor health, it could be assumed that energy efficiency measures should beneficially affect the health of householders. Consistent with this idea, household energy efficiency interventions have been shown to result in a diverse range of positive health impacts [START_REF] Thomson | The health impacts of housing improvement: a systematic review of intervention studies from 1887 to 2007[END_REF][START_REF] Thomson | Housing improvements for health and associated socio-economic outcomes[END_REF], including children's respiratory health, weight and susceptibility to illness, the mental health of adults [START_REF] Liddell | Fuel poverty and human health: A review of recent evidence[END_REF], better self-reported health, and reduced respiratory symptoms and school absences due to asthma (PHIS, 2006).

Africa is generally associated with warm and several areas have extreme temperatures like deserts where the temperature is very high during the day and very low at night. Without access to energy there is no way of regulating the temperature and bodies are exposed to several dangers (skin cancer…).

There is also evidence that improved domestic space heating can reduce school absences and health service use for children with asthma (Preval et al., 2010). Given that financial strain may worsen both mental and physical health improving the energy efficiency of homes can also contribute to a better quality of life by reducing energy bills. infants are often carried on their mother"s back while she is cooking, or kept close to the warm hearth. Consequently, they spend many hours breathing polluted air during their first year of life when they are developing airways and their immature immune systems make them particularly vulnerable. More than half of deaths among children under 5 from acute lower respiratory infections are due to indoor air pollution from household solid fuels (WHO).

Child mortality and inefficient provision of energy

These deaths are not equally distributed throughout the world: more than one third of the child deaths due to indoor smoke occur on the African Continent.

Thus, energy affects positively and negatively health. The sign of the total effect is not clear and needs to be discussed at continental level as well as over sub-regions. Improved energy services can reduce child mortality, improve maternal health, reduce the time and transport burden on women and young girls, and lessen the pressure on fragile ecosystems.

Availability of clinics, care centers and disincentive for doctors and nurses

Another important aspect of energy provision and especially electricity availability is the fact that those facilities are important for health care services. Without electricity most of basic medicine acts cannot be done. Provision of electricity makes it possible to use more sophisticated materials and to act at the nearest place of ill persons, avoiding for them long distance travel and transport which may complicate their initial injuries or diseases. Doctors and nurses are more motivated to access clinics and care centers where energy provision (especially electricity) is available. Lack of electricity is also a disincentive for doctors and nurses to live in those areas and can impact their absence at work. It is obvious that energy and electricity access decreases doctors and nurses absence. Modern energy provision also reduces child mortality, improves maternal health and combats HIV/AIDS, malaria and other diseases. Electricity-access strategies should target public facilities such as health clinics, which benefit the whole population in an area, so that they can provide essential services needed to improve life quality and generate income.

How can provision of modern energy sources improve population's Health?

Increasing the availability of energyaffects directly the health of humans. We discuss in this section five channels through which access to modern energy can improve population"s health.

Revenue generation of energy sector can be used for the health sector

Energy is a special service. Governments generally include several taxes in the energy market. Most of these taxes are settled in order to internalize the externalities of energy. By this mechanism, selling energy generates revenues that can be used to cover hospitals and care centers costs. In some cases, revenue generated from energy improves health services.

For example, these revenues can serve to build health centers in rural areas. They can also serve to build medical schools or finance research centers or to strengthen other aspects of the health system including human resources for health and supply chains.

Better refrigeration of basic medicines

Lack of energy is also associated with lack of hygiene conditions and inability to conserve medicines. Sterilized supplies, clean water supply and refrigeration of essential medicines are impaired in health facilities without adequate electricity. Access to modern energy permits the households to buy refrigerators and to keep the medicines available for a long time. Lack of electricity implies also less efficiency in cold chains and distribution of medicines and vaccines.\

Energy consumption can also reduce child mortality

The WHO (2006) shows three main channels through which improvement of energy practices can reduce child mortality. Firstly, reducing indoor air pollution will prevent child morbidity and mortality from acute lower respiratory infections. Secondly, protecting the developing embryo from indoor air pollution can help avert stillbirth, perinatal mortality and low birth weight. Thirdly, getting rid and open fires and kerosene wick lamps in the home can prevent infants and toddlers being burned and scalded.At the same time refrigeration permits medicines conservation and better conservation of food. By this means several diseases can be avoided.

Energy consumption can improve maternal health

Better energy practices can improve maternal health through three channels. Firstly, curbing indoor air pollution will alleviate chronic respiratory problems among women.

Secondly, a less polluted home can improve the health of mothers who spend time close to the fire after giving birth. Thirdly, a more accessible source of fuel can reduce women"s labor burden and associated health risks such as prolapse due to carrying heavy loads.Lowering levels of indoor air pollution could help prevent tuberculosis cases. Moving up the energy ladder and using improved stoves can increase energy efficiency and decrease greenhouse gas emissions.

Electricity consumption permits access to ICT and to e-Health applications

While there is a consensus about the potential effects of ICT on health in Africa little is said about the access to and consumption of electricity and energy by ICT devices. The health related benefits from ICT are not possible without resolving issues related to energyaccess and consumption , in particular electricity. Alternative solutions, like electricity out of the grid or solar batteriesare partially resolving the problem.

In this section we have seen that poor energy consumption has a negative impact on health outcomes. Increasing the provision of cleaner energy (especially electricity) can substantially improve health outcomes in Africa. Next section proposes the methodology used to identify the long-term relationship between energy consumption and health outcomes.

Methodology, data and econometric model

This paper contributes to the literature with a bootstrap panel analysis of causality relationships between energy consumption or electricity consumption and health for a sample of 16 African countries: Algeria, Benin, Cameroon, Democratic Republic of Congo, Egypt, Ethiopia, Ghana, Kenya, Morocco, Mozambique, Nigeria, Senegal, South Africa, Tanzania, Tunisia and Zambia.

Three main reasons justify our sample. Firstly, the availability of data for all our variables. Secondly, the selected countries cover the heterogeneity of Africa since they cover all parts of Africa (South, North East, West and Central Africa). Thirdly, our sample contains the three types of African countries: Fragile States, Middle OncomeCountries and Low Income Countries. We willthus be able to test whether those countries have the same trends.

Data are annual over the period 1991-2010 and sourced from the World Development Indicators. We first estimate a panel Vector AutoRegressive (VAR) model and then implement the panel-data approach of [START_REF] Kónya | Exports and growth: Granger causality analysis on OECD countries with a panel data approach[END_REF], based on Seemingly Unrelated Regressions (SUR) system and Wald tests with country specific bootstrap critical values. In the specific framework we use, we allow for cross-country correlation, without the need of pretesting for unit roots and cointegration (as in [START_REF] Phillips | Fully Modified Least Squares and Vector Autoregression[END_REF].

We propose to apply a bivariate finite-order vector autoregressive model to energy use or electricity consumption (E) and health (HEALTH): 3

                                 i i i i p j p j t i j it j i j it j i i it p j p j t i j it j i j it j i i it b N i T t HEALTH E HEALTH a N i T t HEALTH E E 1 , 2 1 , 2 1 1 , , 2 , , 2 , , 2 1 1 1 , , 1 , , 1 , , 1 1 ) 1 ( ,..., 1 ,..., 1 ) 1 ( ,..., 1 ,..., 1        
where the index i denotes the country, the index t the period, j the lag, and p 1i , p 2i and p 3i , indicate the longest lags in the system. The error terms, and , are supposed to be white-noises (i.e. they have zero means, constant variances and are individually serially uncorrelated) and may be correlated with each other for a given country, but not across countries. 3 We are grateful to L. Kónya for providing his TSP codes, which we have adapted for our analysis. This procedure has several advantages. First, it does not assume that the panel is homogenous, so it is possible to test for Granger-causality on each individual panel member separately. However, since contemporaneous correlation is allowed across countries, it makes it possible to exploit the extra information provided by the panel data setting and therefore country-specific bootstrap critical values are generated. Second, this panel approach which generalizes the methodology developed by [START_REF] Phillips | Fully Modified Least Squares and Vector Autoregression[END_REF] that tests for non-causality in levels VARs, in a time series context, does not also require pretesting for unit roots and cointegration, though it still requires the specification of the lag structure (which is determined here using the Akaike Information Criterion (AIC) and the Schwarz Information Criterion (SIC)). This is an important feature since the unit-root and cointegration tests in general suffer from low power, and different tests often lead to contradictory outcomes.

 

N i ,..., 1    T t ,..., 1  1, , it  2, , it  System (1a,
Thirdly, this panel Granger causality approach allows the researcher to detect for how many and for which members of the panel there exists one-way Granger-causality, two-way Granger-causality or no Granger-causality.

Data and variables choices

Four indicators were chosen in order to discuss the health outcomes. Firstly, life expectancy at birth as the most common health outcome indicator containing all information about health impacts. Improvements in health are translated in additional years of living. Secondly, under- 4 This assumption is very likely to be relevant for many macroeconomic time series for African countries for which strong economic links exist. 5 As stressed by [START_REF] Kónya | Exports and growth: Granger causality analysis on OECD countries with a panel data approach[END_REF] this definition implies causality for one period ahead.

1,i  2,i  1,i  2,i  2,i  1,i  2,i  1,i
 5 child mortality since the most important effects isexpected for children. Under-5 child mortality is one of the most important health outcomes. Thirdly, energy causes pollution and pollution causes health damage. We have tried to examine this indirect causality by considering air pollution. Finally we have examined a possible positive effect through the budget allocated to energy. As energy consumption and production grow, it may allow government to strengthen their health system by allocating more available revenue for health.

For energy we use energy consumption and electricity consumption. Energy consumption is an indicator of energy supply. It varies from a country to another mainly because the productive sector varies and its consumption varies. We would like to catch these differences in our analysis. At the same time we refine our analysis by examining the electricity consumption as a consumption of high-quality energy. Since Africa is increasing its access to electricity, one can expect to see some significant effects on health outcomes. In fact, as electricity consumption is more related to household energy consumption it has more important effects on health outcomes.

Empirical evidence of Energy Health nexus in Africa

In order to show the evidence of energy health nexus, we will start by discussing the link between energy consumption and the main health outcomes (direct and indirect links) before refining the analysis and focus only on electricity consumption effect on health outcomes.

Energy consumption and health outcomes in Africa

The links betweenenergyconsumptionand Mortality rate, under-5 Tables1a and 1b contain the results of the causality tests between energy consumption and mortality rate under-5 for a sample of 16 African countries for the period 1971-2010.

Our results show a unidirectional Granger causality from energy consumption to mortality rate under-5 for Algeria, Democratic Republic of Congo, Egypt, Ethiopia, Senegal, South Africa, and Zambia. For these seven countries, we found strong links between energy consumption and one of the main health outcomes (children mortality). This result confirms our analytical discussion about the potential positive effect of energy use on Health. One plausible explanation is that in those countries there is a substitution between the sources of energy. People are using more high-quality energy and less low-quality energy like biomass.

Since ten, citizens are less exposed to indoor pollution, are benefiting from more heating, warm food and better sanitation conditions. Our result shows that energy consumption is a good leverage for better health in Africa. It can be used in order to shortcut children mortality in Africa. We can remember that 80% of world child mortality isin Africa (AfDB, 2014 -HCS).

We further find a bidirectional Granger causality for Cameroon and Ghana at the 10%.

The explanation of energy consumption effect on under-5 children mortality in these two countries relies on the same arguments than those previously explained. However, the retroaction effect is a novelty. One possible explanation is the fact that children mortality decrease indicates a change in the nature of the human capital in these countries and allows better production and growth for the country. As a consequence the energy consumption grows. It can be noticed that a unidirectional Granger causality from mortality rate under-5 to energy consumption for Kenya, Mozambique, and Tanzania is also found. We can also advocate the same explanations. Tables2a and 2b report the results of the causality tests between energy and life expectancy for a sample of 16 African countries for the period 1971-2010.

The links between energy consumptionand life expectancy at birth

Our results show a unidirectional Granger causality from energy consumption to life expectancy for Algeria, Benin, Cameroon, Democratic Republic of Congo, Egypt, Ethiopia, Kenya, and Senegal. Half of our sample confirms our analytical discussion about the possible impact of energy consumption on health assessed here by life expectancy. As Africa is growing, the income per capita increases allowing more per capita energy consumption.

Energy consumption permits better sanitation, more heating and warm food, less indoor pollution and better medicines conservation. Our result is a strong result strengthened by the finding of a bidirectional Granger causality for Tanzania. For this country, the same arguments are valid for the link between energy consumption andlife expectancy. However, the retroaction effect is also found. It is an expected result, since as life expectancy increases, the energy use need to be increased.

Evidence of a unidirectional Granger causality from life expectancy to energy consumption is found only for Mozambique. One plausible explanation is the fact that as life expectancy increases, energy consumption increases. While this result is expected for the entire sample, it was but found only in the case of Mozambique (and Tanzania). It may be explained by the fact that Mozambique has shown the most important impact in recent years. 3a and3b show the results of the causality tests between energy and greenhouse effect.

The links between energy consumption and air pollution

Our results show that energy consumption is causing air pollution in Algeria, Tunisia and Ghana. Per capita consumption of energy is among the highest in the Continent in Tunisia and Algeria. Those economies are transforming and the demand for energy is fast growing implying air pollution. One plausible explanation is that those countries are in the first phase of the Kuznets curve where economic growth is accompanied by pollution (Arouri et al. 2012). One can also note that these two countries are among the most urbanized in Africa and that urbanization foster air pollution [Ref]. Ghana is fast growing and its per capita energy consumption is also fast growing implying air pollution. The same explanation than Tunisia and Algeria is valid while the per capita income is different. What is happening in Tunisia, Algeria and Ghana is expected also to happen to the other African countries.

Our results show also bidirectional Granger causality for Tanzania, at the 10% or lower level of significance. While the link between energy consumption and air pollution can be easily explained by economic growth and perhaps the use of biomass as main source of energy; the reverse link is less easily explained. Greenhouse effect may lead some counties to use more the air conditioning and by this increase their energy consumption. The evidence of a unidirectional Granger causality from greenhouse to energy consumption for Kenya,and Zambia can also be explained by the same fact.

The links between energy consumption and government health expenditure per capita

Tables4a and 4b report the results of the causality tests between energy and Government health expenditure. There is no evidence of Granger causality from government health expenditure to energy consumption, of Granger causality from energy consumption to government health expenditure for Algeria, Morocco, Nigeria, and of a bidirectional Granger causality for Ethiopia, at the 1% level of significance.

As energy consumption grows, the revenue generated (directly: through production of energy or indirectly through taxation of energy consumption) allows more government expenditure on health in Algeria, Morocco, and Nigeria. Algeria and Nigeria are big oil producers. The domestic consumption of energy and the government health expenditure are strongly linked to the oil production rent and the better awareness of those countries about the health investment. Investing in health and energy consumption is expected to help the countries to invest in human capital and making the necessary economic transformation of the countries.

While for the case of Morocco, the relation seems more correlated to the increasing income per capita and better fiscal policies allowing increasing the health expenditure. For the case of Ethiopia, we found a feedback effect. In fact, as the energy consumption grows, the economic activities grows and allows more resources for the government that re-invest them in public expenditures in matter of health allowing better human capital. People are becoming more educated and in better health increasing their productivity which increase their revenues and as a consequence their energy consumption. Ethiopia is perhaps the virtue circle that may occur in different parts in Africa in the next decade.

Electricity consumption and health outcomes

The links between electricity consumption and child mortality under-5 As expected, there is no evidence of a unidirectional Granger causality from health to electric consumption. There are no or few arguments explaining this link.

In contrast, there is as expected evidence of a unidirectional Granger causality from electric consumption to under-5 child mortality for Cameroon, Egypt, Ethiopia, Ghana, Morocco, Senegal, and Zambia. As we have largely argued in our theoretical framework, increasing the electricity access has strong effect on child mortality. Access to electricity allows better conditions for cooking and heating and avoiding by this indoor-pollution and associated diseases.

There is evidence of a bidirectional Granger causality for Nigeria, at the 10% or lower level of significance. While the same arguments occur for the link between electricity consumption and under-5 child mortality.Electricity consumption has differentiated effects on Life expectancy at birth in Africa. Our results show contrasted results in matter of electricity consumption and health.

The links between electricity consumption and Life expectancy at birth in Africa

Two sub-groups of countries have significant links between electricity consumption and life expectancy at birth. In fact, It can be noticed no unidirectional Granger causality from health to electricity consumption, a unidirectional Granger causality from electricity consumption to health for Benin, Cameroon, Democratic Republic of Congo, Egypt, Ghana, Morocco, Senegal, and South Africa, and a bidirectional Granger causality for Nigeria,at the 10% or lower level of significance.

We found negative unidirectional causality from electricity consumption to life expectancy for South Africa, Nigeria, Ghana, Morocco, and Egypt. This finding is surprising! As electricity consumption increases the life expectancy at birth decreases? However, we found positive unidirectional causality from electricity consumption to life expectancy for Benin, Cameroon, DRC and Senegal (West and Central Africa). As electricity consumption increases the life expectancy increases. Most of these countries have very low per capita consumption of electricity and poor coverage of the grid. Most rural areas are lacking access to electricity.

Two plausible explanations may be presented. Firstly, the consumption of electricity has raised the budget allocated to energy and lower the budget for health. If we consider that electricity is subsidized like in some countries (Tunisia, Egypt…). As consequence, the energy poverty acted in a way that lowered life expectancy at birth. Secondly, as the consumption of electricity increased, the production has followed the same trends. The problem comes from the technologies used for the production of electricity. Electricity provision can be based on several types of technologies with differentiated effects ion health.

While green technologies like wind power and hydropower have (no) or small health impacts, other technologies based on Coal, Gasoil, etc....have deep impacts on health. Several reports show local air pollution due to SO2 emissions, NOx emissions and others GHG. The combined effect may be negative in the short run. Other explanations rely on the fact that electricity consumption may led to harmful behaviors: watching TV for hours, less sport activity and more time spent on screens, etc… Tables7a and 7b report the results of the non-causality tests between electricity consumption and Government health expenditure per capita for a sample of 16 African countries for the period 1971-2010. Evidence of a unidirectional Granger causality from health to electricity consumption is found for Benin.Evidence of a unidirectional Granger causality from electric consumption to health for Algeria, and a bidirectional Granger causality for Ethiopia, at the 10% or lower level of significance.

The links between electricity consumption and Government health expenditure per capita

Discussion

Our results show that there is strong impact of energy use in Africa on under-5 children mortality and life expectancy. The evidence is found for at least eight countrieshaving different levels of income per capita. The results are robust in fragile states like DRC and Côte d"Ivoire and Middle Income Countries like Tunisia and Morocco. One can expect that the effect of increasing energy consumption will be strengthened in the near future given the currentlow level of energy consumption. As per capita electricity consumption represents in SSA 1% of the European consumption level, there is an expected "health effect" in the near future of energy consumption. Moreover, we found an evidence of the link between energy consumption and Government health expenses. The revenues generated by the domestic consumption of energy are partially recycled in health care and medicines. Our results did not show significant trends between energy use and electricity consumption.

Policy implications

Increasing access to modern sources of energy and electricity implies an improvement in cooking conditions and heating (lowering the risk associated with indoor air pollution), in health centers" infrastructure (improving child and maternal health), in medicinesconservation, and provides more incentives for health workers. The overall effect of such improvement is a healthier workforce, and an increase in life expectancy.

Recent economic growth in Africa allows more investment in health, education, infrastructure, and electrification. With increasing per capita income Africanscan invest more in energy use and electricity and substitute their energy sources from pollutant ones (biomass) to less pollutant ones (Electricity, GPL). At the same time, Africa is benefitting from the technological latter comer effect. Africa is benefitting from latest technologies for provision of electricity (more efficient and cheaper technologies), especially in matter of renewable energies. While this "market dynamic" seems important, it will not be sufficient to help Africa bridge its divide in energy use and electrification. There is a strong need that must be fulfilled with Global initiatives, local and regional policies especially to improve the health impacts of energy access.

The most prominent global initiative for the provision of energy for African is the newly launched initiative of the Secretary General of the United Nations toward ""Sustainable Energy for All"" (http://www.sustainableenergyforall.org/).The UN and most of development agencies have putt African households high in their agenda.

Energy poverty seems one of the majorcomponents of poverty nowadays and even in developed countries, millions of people are facing this kind of poverty, which impacts their health, education and labor performances. This initiative targets universal access to electricity in Africa by 2025. The seventh goal of the Sustainable Development Goals (SDG) also aim to ensure universal access to affordable, reliable and modern energy services by 2030 6 .

Initiatives in matter of improving the cooking stoves like the Global Alliance for Clean Cookstoves (http://www.cleancookstoves.org/) are innovative solutions in order to decrease health risks due to indoor pollution. Switching the cooking stoveshas agreat potential toreduce the risk of death and chronic diseases associated to indoor air pollution.Improved 6 7.1: By 2030, ensure universal access to affordable, reliable and modern energy services 7.2: By 2030, increase substantially the share of renewable energy in the global energy mix 7.3: By 2030, double the global rate of improvement in energy efficiency 7.4: By 2030, enhance international cooperation to facilitate access to clean energy research and technology, including renewable energy, energy efficiency and advanced and cleaner fossil-fuel technology, and promote investment in energy infrastructure and clean energy technology 7.5: By 2030, expand infrastructure and upgrade technology for supplying modern and sustainable energy services for all in developing countries, in particular least developed countries, small island developing States, and land-locked developing countries, in accordance with their respective programmes of support access to modern energy services including cleaner-combusting and more efficient cooking fuels like LPG, biogas, natural gas and an advanced biomass stove reduce the health risks.It also has an impact on reducing carbon emissions in developing countries [START_REF] Bond | Bounding the role of black carbon in the climate system: a scientific assessment[END_REF][START_REF] Shindell | Simultaneously mitigating near-term climate change and improving human health and food security[END_REF]. Several measurement campaigns have evaluated the performance of improved stoves and fuels, including the evaluation of climate relevant species [START_REF] Maccarty | Laboratory Comparison of the Global-Warming Potential of Six Categories of Biomass Cooking Stoves[END_REF][START_REF] Maccarty | Fuel use and emissions performance of fifty cooking stoves in the laboratory and related benchmarks of performance[END_REF], and the potential health benefits of their introduction [START_REF] Anenberg | Global air quality and health co-benefits of mitigating near-term climate change through methane and black carbon emis-sion controls[END_REF].

In addition to resulting in significant health benefits, recent assessments suggest that such residential cooking fuel and stove switching, may also have a greater potential to curb global warming by reducing black carbon emissions. The major challenge in Africa is the access to these technologies at an affordablecost.

Last mile policies need also to be strengthened. Most of African infrastructure projects especially in of the area of transport, energy and water need to consider the last mile to health care, schools and public facilities as part of the projects. In fact, several schools, health care and public facilities (especially in rural Africa) lack electricity despite the proximity of an electricity grid. Insufficient resources and non-consideration of health and education aspects in infrastructure projects lead to a situation where people have no access to basic health services because of lack of electricity. For instance, maternal health services need to be close to the population but are often not available due to absence of electricity and energy sources.

Concluding remarks

The objective of this articlewas to discuss the causality links between energy consumption and health outcomes in Africa. We proposed an analytical framework to identify the expected causality links and an econometric analysis of this causality for 16 countries during the period 1971-2010.

Our analysis suggests a strong link between energy consumption and decreasing under-5 child mortality on the one hand and increased life expectancy on the other hand. The causality is well-established for more than half of the countries under study in several regions of Africa and at different levels of development.

The examination of the same causality for electricity consumption and health outcomes confirms the previous results, while showing surprising links for life expectancy.

There is a negative effect in the case of five large African countries: South Africa, Nigeria, Ghana, Morocco, and Egypt. We found also the evidence of a causality link between energy use, electricity consumption and government spending in health.

Our results advocate for improving electricity provision for Africans. Health externalities (considered as positive externalities) can balance the potential environmental negative externalities. Africa contribution to Greenhouse effect is very limited (less than 5%) and is marginal compared to countries such China and United States. While it is important that Africa grows using cleaner technologies and fosters the use of renewable energies (following a sustainable pathway), there is also urgency for Africans to use more energy (especially electricity) to reverse the dramatic health and sanitation situation leading tomaternal and child morbidity and mortality. It is also urgent to implement new technologies based on electricity out of the grid in rural Africa, wheremost important problems are reported.

H 0 :

 0 Electric Consumptiondoes not cause Mortality under-5.Table 5b Granger non-causality tests from Electric Consumption to Child Mortality under-5 model Tables5a and 5b show the results of the non-causality tests between electric consumption and under-5child mortality for a sample of 16 African countries for the period 1971-2010.

  Tables6a and 6b contain the results of the non-causality tests between electricity consumption and health (Life expectancy at birth).

  1b) is estimated by the Seemingly Unrelated Regressions (SUR) procedure, since possible links may exist among individual regressions via contemporaneous correlation 4 within the two equations. Wald tests for Granger causality are performed with country specific bootstrap critical values generated by simulations.

		With respect to system (1a, 1b), in countryi there is one-way Granger-causality from
	HEALTHto E if in the first equation not all are zero but in the second all	are zero; there
	is one-way Granger-causality from E to HEALTH if in the first equation all	are zero but in
	the second not all	are zero; there is two-way Granger-causality between E to HEALTH if
	neither all	nor all	are zero; and there is no Granger-causality between E to HEALTH if
	all	and	are zero. 5

Table 1a -

 1a Granger causality tests from Health to Energy consumption, bivariate (Energy, Mortality Under-5) model

		Estimated	Test Statistic Bootstrap critical values
		coefficient		1%	5%	10%
	Algeria	-0.0154	-6.7666**	6.9266 5.5803 4.5913
	Benin	0.0020	1.5761	3.9096 3.1560 2.5219
	Cameroon	0.0094	6.3312***	5.5186 4.6401 3.9559
	Democratic Republic of Congo -0.0258	-5.4216*** 4.3222 3.5030 2.7821
	Egypt	0.0073	6.3197*	8.3779 6.7680 5.5949
	Ethiopia	0.0162	3.7154**	4.2307 3.3893 2.7735
	Ghana	0.0149	4.6325***	4.4847 3.6093 2.9318
	Kenya	-0.0045	-.21473	4.3337 3.4443 2.8657
	Morocco	0.0043	2.9869	8.2193 6.7830 5.6088
	Mozambique	0.0064	3.3924	11.0358 9.5019 8.2426
	Nigeria	0.0248	4.1523	10.4573 8.7712 7.5523
	Senegal	-0.1335	-13.124*** 6.2304 5.0157 4.1383
	South Africa	-0.0071	-6.2283*** 4.2208 3.3716 2.7011
	Tanzania	-0.0124	-4.9785	9.9277 8.4917 7.1904
	Tunisia	-0.0001	-.11920	6.3549 5.1053 3.9867
	Zambia	0.0222	5.4244*	7.0726 5.8578 5.0060
	***. **. *: significance at the 1%. 5% and 10% levels respectively.
	H 0 : Energydoes not cause Mortality Under-5.

Table 1b -

 1b Granger causality tests from Energy consumption to Health, bivariate (Energy, Mortality Under-5) model

Table 2a -

 2a Granger causality tests from Life Expectancy at Birthto Energy consumption model

	Morocco	-0.0004	-3.5866	6.5486 5.4826 4.5393
	Mozambique	0.0005	5.3356	12.2049 10.3832 8.8010
	Nigeria	-0.0025	-9.8306	15.8256 14.3201 13.0581
	Senegal	0.0046	19.310***	5.8636 4.8950 4.0417
	South Africa	-0.0001	-2.6351	5.7361 4.6255 3.7424
	Tanzania	0.0046	40.180***	16.2130 14.8707 13.5920
	Tunisia	-0.0011	-1.4840	3.1921 2.5665 2.1053
	Zambia	-0.0007	-1.3371	9.8478 8.3028 6.9503
	***. **. *: significance at the 1%. 5% and 10% levels respectively.
	H 0 :Energy does not cause Life Expectancy at Birth.
		Estimated	Test Statistic Bootstrap critical values
		coefficient		1%	5%	10%
	Algeria	0.0011	16.469***	11.0248 9.7769 8.7914
	Benin	0.0008	11.094***	4.1493 3.3412 2.7477
	Cameroon	-0.0011	-5.2056*** 3.6968 3.0184 2.5491
	Democratic Republic of Congo 0.0094	15.363***	5.5294 4.4466 3.7054
	Egypt	-0.0009	-14.303*** 4.9001 4.0157 3.2943
	Ethiopia	-0.0011	-4.2125*** 4.0844 3.2658 2.6409
	Ghana	0.0010	1.8613	5.6523 4.5122 3.7206
	Kenya	0.0201	10.261***	7.4824 6.3867 5.4427

Table 2b -

 2b Granger causality tests from Energy consumption to Life Expectancy at Birthmodel

Table 3a -

 3a Granger causality tests from Greenhouse to Energy consumption model

		Estimated	Test Statistic Bootstrap critical values
		coefficient		1%	5%	10%
	Algeria	0.00091	3.4335***	1.9443 1.5514 1.2557
	Benin	-0.00029	-1.6961	3.8325 3.0870 2.4335
	Cameroon	0.00040	.37132	3.8015 2.9706 2.3826
	Democratic Republic of Congo 0.00017	2.1289	4.3261 3.4543 2.7978
	Egypt	0.00087	2.9162	9.4349 8.1525 7.0484
	Ethiopia	0.00009	1.6495	3.8558 3.1515 2.5475
	Ghana	0.00100	5.4220***	3.1129 2.5230 2.0541
	Kenya	0.00080	1.7277	3.7496 3.0272 2.4121
	Morocco	0.00107	1.6115	10.6206 9.2137 7.7765
	Mozambique	-0.00003	-.32141	5.2126 4.3583 3.6068
	Nigeria	-0.00085	-2.0137	5.8873 4.7023 3.8401
	Senegal	0.00039	1.2716	2.0552 1.6665 1.3398
	South Africa	0.00059	1.3352	3.9152 3.2859 2.6758
	Tanzania	0.00042	4.7859*	5.7094 4.6977 3.8633
	Tunisia	0.00146	5.2926**	6.3266 5.1848 4.1940
	Zambia	-0.00025	-.95378	6.8369 5.6581 4.7463
	***. **. *: significance at the 1%. 5% and 10% levels respectively.
	H

0 : Energydoes not causeGreenhouse.

Table 3b -

 3b Granger causality tests from Energy consumption to Greenhouse model

	Tables

  Government healthexpenditure per capita does not cause Energy.

		Estimated	Test Statistic Bootstrap critical values
		coefficient		1%	5%	10%
	Algeria	0.2250	1.16078	31.5603 24.1557 19.0303
	Benin	4.4351	6.86810	27.5836 21.4818 16.8741
	Cameroon	-1.4985	-2.82614	35.4122 27.0757 20.7601
	Democratic Republic of Congo 0.4627	.773530	35.5358 26.4677 20.3036
	Egypt	-1.0411	-1.66078	30.8394 23.6045 18.6338
	Ethiopia	6.8039	16.8518*	33.0780 24.7014 14.8476
	Ghana	-0.5306	-3.55917	26.8016 20.1940 16.1548
	Kenya	1.2757	3.02414	43.3785 32.9441 25.8460
	Morocco	1.0578	2.48531	39.8954 31.3489 24.3084
	Mozambique	3.0208	11.8271	38.1888 30.0408 23.7969
	Nigeria	0.4513	2.70139	17.8765 14.5432 11.0987
	Senegal	3.1396	5.97976	19.9071 15.2771 12.1574
	South Africa	-0.5580	-2.36808	29.1143 22.3234 17.4075
	Tanzania	0.2250	11.14249	30.4655 22.2426 18.1762
	Tunisia	4.4351	9.10458	17.2637 14.1151 11.0764
	Zambia	-1.4985	7.3426	28.3812 25.2205 19.1641
	***. **. *: significance at the 1%. 5% and 10% levels respectively.
	H 0 :

Table 4a -

 4a Granger causality tests from Government healthexpenditure per capita to Energy

	Ghana	0.0631	1.71180	41.8271 32.9599 25.6130
	Kenya	0.1132	3.90737	9.6338 7.4824 5.9461
	Morocco	0.1167	6.70038*	23.3377 13.1529 6.5095
	Mozambique	0.0354	1.79486	41.7964 32.4499 25.3856
	Nigeria	0.0779	3.89060*	5.0191 4.0666 3.2699
	Senegal	-0.0044	-.201174	38.9076 22.0789 14.0938
	South Africa	0.0438	3.20691	27.2186 21.8501 17.4535
	Tanzania	0.3287	2.13476	23.1643 19.5056 15.8260
	Tunisia	0.0107	5.86543	17.3406 15.9603 14.9666
	Zambia	-0.0156	3.09865	38.1667 27.0705 16.0961
	***. **. *: significance at the 1%. 5% and 10% levels respectively.
	H 0 :Energy does not cause Government healthexpenditure per capita)
	consumption model
		Estimated	Test Statistic Bootstrap critical values
		coefficient		1%	5%	10%
	Algeria	0.3287	9.23906*	31.3104 24.2821 9.1911
	Benin	0.0107	1.37080	27.4500 20.5580 15.6580
	Cameroon	-0.0156	-1.58181	23.1895 17.9419 13.6062
	Democratic Republic of Congo 0.0110	2.18518	25.0483 19.4576 14.9910
	Egypt	0.0236	6.16102	38.0513 27.5071 19.0758
	Ethiopia	-0.0310	-16.0195*	34.9817 27.9748 12.0003

Table 4b -

 4b Granger causality tests from Energy consumption Government healthexpenditure

	per capita model

  : significance at the 1%. 5% and 10% levels respectively. H 0 : Child Mortality under-5 does not cause Electric Consumption.

		Estimated	Test Statistic Bootstrap critical values
		coefficient		1%	5%	10%
	Algeria	0.3138	1.2673	6.2883 5.1104 4.2314
	Benin	-0.0899	-2.6585	10.7969 9.4348 8.2539
	Cameroon	-0.1390	-1.0128	9.5972 8.3618 7.3932
	Democratic Republic of Congo 0.1448	1.5035	6.4916 5.4421 4.5232
	Egypt	0.0008	.73312	4.3154 3.5576 2.8902
	Ethiopia	0.0017	.18262	3.0056 2.4021 1.9544
	Ghana	0.1961	.75527	3.7728 2.9722 2.3359
	Kenya	-0.0664	-1.5163	5.4289 4.5317 3.7025
	Morocco	-0.0545	-.47071	7.1190 5.9510 5.0396
	Mozambique	-0.6531	-3.7959	10.6425 8.8989 7.6470
	Nigeria	-0.4823	-5.2859*** 4.7055 3.6224 2.9585
	Senegal	-0.0902	-1.9145	8.8678 7.6787 6.5624
	South Africa	-4.7735	-2.3154	7.6241 6.3484 5.2870
	Tanzania	-0.1064	-2.6116	5.8902 4.6894 3.7010
	Tunisia	-0.1089	-.61200	6.6711 5.6962 4.7469
	Zambia	0.0356	.13819	3.6759 2.9481 2.3659
	***. **.

*

Table 5a -

 5a Granger non-causality tests from Child Mortality under-5 to Electric Consumption model

		Estimated	Test Statistic Bootstrap critical values
		coefficient		1%	5%	10%
	Algeria	0.0040	1.5855	7.5674 6.0284 4.9644
	Benin	0.0030	.74265	3.6752 2.9910 2.3797
	Cameroon	-0.0073	-6.2015*** 1.8555 1.4809 1.1765
	Democratic Republic of Congo -0.0078	-1.9993	8.9473 7.5185 6.5549
	Egypt	0.0062	9.4544***	6.4583 5.1216 4.1407
	Ethiopia	0.2118	5.9007**	6.1666 5.1067 4.1770
	Ghana	0.0033	3.1369*	4.4879 3.5102 2.8194
	Kenya	0.0360	1.7378	7.1101 5.8552 4.7369
	Morocco	0.0067	6.2858**	6.7409 5.4880 4.5323
	Mozambique	0.0032	2.2127	4.9570 4.1199 3.3122
	Nigeria	0.0709	7.1768**	8.1650 6.7646 5.6090
	Senegal	-0.0789	-5.6725**	5.8768 4.8717 4.0309
	South Africa	0.0003	.51312	5.5049 4.4679 3.6767
	Tanzania	-0.0490	-2.7879	6.0762 4.8094 3.9432
	Tunisia	0.0002	.69591	5.9257 4.7682 3.8647
	Zambia	0.0083	6.6783***	4.3276 3.5546 2.8859
	***. **. *: significance at the 1%. 5% and 10% levels respectively.

Table 6a -

 6a Granger non-causality tests from Life Expectancy at birthto Electric Consumption model Electric Consumptiondoes not cause Life Expectancy at birth.

	Benin	0.0032	12.164***	5.1562 4.3235 3.6238
	Cameroon	0.0011	2.9750**	3.1627 2.5440 2.1017
	Democratic Republic of Congo 0.0012	3.9945***	3.9734 3.2048 2.6206
	Egypt	-0.0012	-8.9471*** 8.7046 7.5388 6.5467
	Ethiopia	-0.0014	-.82955	8.8356 7.5850 6.6644
	Ghana	-0.0004	-6.5374*** 4.2630 3.3866 2.7887
	Kenya	-0.0051	-5.9395	9.1998 7.8263 6.8357
	Morocco	-0.0006	-9.8376*** 9.4096 8.1676 7.1513
	Mozambique	0.0001	1.9715	5.6865 4.6380 3.8156
	Nigeria	-0.0066	-9.2836*	11.5142 10.3395 9.1729
	Senegal	0.0031	10.235***	4.0868 3.3227 2.7214
	South Africa	-0.0003	-10.608*** 6.0586 4.9651 4.0556
	Tanzania	0.0039	4.7617	9.1095 7.9267 7.0043
	Tunisia	-0.0004	-.93995	4.9187 4.0493 3.3819
	Zambia	0.0006	4.9866	8.1255 6.7444 5.6374
	***. **. *: significance at the 1%. 5% and 10% levels respectively.
	H 0 :
		Estimated	Test Statistic Bootstrap critical values
		coefficient		1%	5%	10%
	Algeria	0.0002	3.4796	6.1314 5.2088 4.4440

Table 6b

 6b Granger non-causality tests from Electric Consumption to Life Expectancy at birth model

  Health expenditure per capitadoes not causeElectric Consumption.

		Estimated	Test Statistic Bootstrap critical values
		coefficient		1%	5%	10%
	Algeria	0.2250	1.1607	26.9015 21.1294 17.0864
	Benin	4.4351	6.8681*	12.8411 10.2525 6.1209
	Cameroon	-1.4985	-2.8261	43.6980 35.7427 29.5664
	Democratic Republic of Congo 0.4627	.77353	30.6792 22.9657 17.6127
	Egypt	-1.0411	-1.6607	23.2006 18.5671 14.7963
	Ethiopia	6.8039	16.851*	23.3752 18.5415 14.7213
	Ghana	-0.5306	-3.5591	5.2224 4.2231 3.4805
	Kenya	1.2757	3.0241	32.1537 25.1697 19.2141
	Morocco	1.0578	2.4853	29.7854 23.4288 18.5749
	Mozambique	3.0208	11.827	29.7471 23.5034 18.6776
	Nigeria	0.4513	2.7013	21.3035 16.4112 13.3047
	Senegal	3.1396	5.9797	13.0377 10.3030 8.1585
	South Africa	-0.5580	-2.3680	20.2443 15.6382 12.0435
	Tanzania	0.2250	-3.3546	9.3456 8.1873 7.8765
	Tunisia	0.3924	2.2346	11.5123 9.1265 6.9086
	Zambia	0.2454	1.9876	16.9216 14.9654 11.4567
	***. **. *: significance at the 1%. 5% and 10% levels respectively.
	H 0 :

Table 7a -

 7a Granger non-causality tests from expenditure per capitato Electric Consumption model Electric Consumptiondoes not cause Health expenditure per capita.

	Nigeria	0.0779	3.8906	51.7398 41.4223 32.9166
	Senegal	-0.0044	-.20117	28.4903 22.2955 17.2014
	South Africa	0.0438	3.2069	53.1188 42.7987 35.0586
	Tanzania	0.0456	4.4567	38.1786 34.6578 29.6543
	Tunisia	-0.0324	3.6543	45.6754 38.1765 31.4567
	Zambia	0.0235	1.5487	23.8796 19.8976 16.0098
	***. **. *: significance at the 1%. 5% and 10% levels respectively.
	H 0 :
		Estimated	Test Statistic Bootstrap critical values
		coefficient		1%	5%	10%
	Algeria	0.3287	9.2390*	17.7488 9.6706 7.0807
	Benin	0.0107	1.3708	26.4519 20.0469 16.1444
	Cameroon	-0.0156	-1.5818	24.1989 19.0736 15.1717
	Democratic Republic of Congo 0.0110	2.1851	24.6775 19.3065 15.2766
	Egypt	0.0236	6.1610	41.4677 29.4222 16.0679
	Ethiopia	-0.0310	-16.019*	37.1127 28.5266 12.5332
	Ghana	0.0631	1.7118	43.0568 34.3979 27.2814
	Kenya	0.1132	3.9073	9.3856 7.3393 5.8544
	Morocco	0.1167	6.7003	49.7991 32.2589 20.4923
	Mozambique	0.0354	1.7948	41.3394 32.1611 25.2466

Table 7b

 7b Granger non-causality tests from Electric Consumption to Health expenditure per capitamodel

Authors are grateful to helpful comments and discussions with Professor Mohamed Arouri, Professor HatemMhenni, Doctor Caroline Jehu-Appiahand Doctor Ute Dubois.

Dr. Ben Youssef has coordinate several research projects in multiis a Full Professor of Economics. He has also been a Senior Expert for the European Central Bank (since 2007), for «l"EcoleNationaled'Administration Work for Poor People" and of the Lancet Commission report "Global Health 2035: a world converging within a generation". She recently was commissioner of the recentLancet and Rockefeller Commission on Planetary Health. DrSoucat did also extensive work on the health labor market dynamics in Africa. DrSoucat holds an MD and a Masters in Nutrition from the University of Nancy in France as well


V Schmitt

X Zhou

K Juliusson

A Blais

P Bertet

D Vion

D Esteve

Multiplexed Readout of Transmon Qubits with Josephson Bifurcation Amplifiers

Achieving individual qubit readout is a major challenge in the development of scalable superconducting quantum processors. We have implemented the multiplexed readout of a four transmon qubit circuit using non-linear resonators operated as Josephson bifurcation amplifiers. We demonstrate the simultaneous measurement of Rabi oscillations of the four transmons. We find that multiplexed Josephson bifurcation is a high-fidelity readout method, the scalability of which is not limited by the need of a large bandwidth nearly quantum-limited amplifier as is the case with linear readout resonators.

Since the demonstration of quantum coherence in single Cooper pair boxes [1,2], the coherence time of superconducting quantum bits (qubits) has increased by orders of magnitude [3][4][5], and high-fidelity operation has been achieved [6,7]. Quantum speedup of the Deutsch-Josza [8], Grover search [9] and Shor's factorization [10] algorithms, as well as deterministic teleportation [11] and measurement-based entanglement [12,13] protocols, were recently demonstrated in circuits with few (2)(3)(4)(5) qubits. Nevertheless, no superconducting quantum processor able to run algorithms demonstrating the power of quantum computation [START_REF] Nielsen | Quantum Computation and Quantum Information[END_REF] has been operated yet. Making operational processors with a large number of qubits faces the challenge of maintaining quantum coherence in complex circuits, of implementing multiple individual qubit readout, and of performing high-fidelity gates in parallel with quantum error correction. Much effort is presently devoted to solving these different scalability issues [START_REF] Devoret | [END_REF].

We address here the problem of simultaneous readout of transmon qubits [3] in a single shot. Readout of Josephson qubits is commonly performed by coupling each of them to a linear microwave resonator whose resonance frequency is shifted by a qubit-state dependent value ±χ [16]. Measuring the reflection or the transmission of a microwave pulse by the resonator then reveals the qubit state [17]. High-fidelity readout has been reached in several experiments [20,21] by using quantumlimited Josephson parametric amplifiers [18]. Besides, simultaneous readout of several qubits was achieved by using resonators with staggered frequencies, all coupled to a single line on which microwave readout pulses were frequency multiplexed [19]. However, reaching single-shot fidelity in this case requires parametric amplifiers with both large bandwidth to accommodate all of these frequencies, and large saturation power to linearly amplify all simultaneous pulses. The recent implementation of this method in a four-transmon circuit [22] achieved fast readout with a fidelity compatible with surface-code error correction.

An alternative method for transmon readout that does not require a Josephson parametric amplifier consists in turning each readout resonator into a non-linear one, operated as a Josephson bifurcation amplifier (JBA) [24][25][26]. Indeed, driving a JBA with a suitable microwave pulse yields a fast and hysteretic transition between dynamical states with widely different field amplitude and phase, which can discriminate with high fidelity the transmon ground state |0 from its excited states |i = |1 , |2 . The determination of the dynamical state then requires a subsequent longer measuring time at a lower power level [27]. In this work, we demonstrate multiplexed high-fidelity single shot readout of four transmons using the circuit described in Fig. 1.

The chip consists of four cells, labeled i = 1 -4, coupled to a single transmission line that carries the multiple qubit control and JBA signals. The sample is fabricated on a sapphire substrate as indicated in the supplemental material [28]. It is measured in a dilution refrigerator with base temperature 30 mK. Each transmon B i includes a superconducting quantum interference device (SQUID) -see Fig. 1(d) -that makes its |0 ↔ |1 transition frequency f 01 Bi tunable with magnetic field [START_REF]B3 has one of its two Josephson junctions open and is consequently not tunable[END_REF]. In this experiment dedicated to readout, only a global magnetic field produced by a single coil can be applied to all transmons simultaneously. Each qubit is coupled to its JBA with a coupling constant g i /2π 85 MHz. The JBAs have staggered frequencies f Ri around 7.75 GHz separated by 61, 69, and 96 MHz, and quality factors of 2500, 2550, 2650, and 2200. All have the same Kerr non linearity K/2π -310 kHz [START_REF] Ong | [END_REF].

The qubits are controlled resonantly and we note θ kl i a rotation of qubit i by an angle θ between its states |k and |l . The microwave control pulses at frequencies f kl Bi as well as the readout pulses at frequencies f Ri are obtained by single sideband mixing as explained in the SI [see also Fig. 1(a)]. Driven at frequencies f Ri chosen 9 MHz below their bare frequencies, the JBAs switch at bifurcation from a state with average photon number 11±1 to 100±5 [START_REF] Ong | [END_REF]31].

The transmon-JBA detuning ∆ i /2π = f 01 Bi -f Ri determines both the readout sensitivity (through χ i ) and the coil current (mA) frequency (GHz) Purcell energy relaxation rate T -1

(d) B 1 B 2 B 3 B 4 R 1 R 2 R 3 R 4 01 4 f 02 4 / 2 f (b) cell 1 cell 1 cell 2 cell 2 cell 3 cell 3 cell 4 cell 4 (a) AWG HEMT 4K, +36 dB cell i ADCs 0 B f 0 R f kl Bi δ Σ Ri δ Σ 500µ (c) R 1 R 1 B 1 B 1 i B i R i φ ( ) , I Q ( ) , i i I Q
P,i 2πf Ri /Q i (g i /∆ i ) 2
of the qubit through the resonator input line [3]. The readout pulses have a first short 25 ns long step [see Fig. 2(b)] and a longer 2 µs latching step at 85% of the peak power. In practice, bifurcation develops (or not) between 50 ns and 500 ns, whereas I and Q are averaged between 325 ns and 1325 ns. Readout pulses can over- lap in time [see for instance Fig. 4(a)] so that the output signal contains contributions of different JBAs. In order to extract these contributions, an analog and a digital demodulation at the readout carrier frequency f R0 are performed as indicated in [28]. The outcome of a readout sequence is thus four points (I i , Q i ) in the in-phase and quadrature plane.

Spectroscopic data of the qubits and readout resonators as a function of the coil current are displayed in Fig. 1(d). This data was recorded at high excitation power to show spectroscopic lines at both f 01

Bi and f 02 Bi /2.

Frequencies f 01

Bi of tunable qubits B 1,2,4 peak at about 0.7-1 GHz below the frequency of their respective JBA, and the anharmonicity α = f 12 Bi -f 01

Bi

-434 ± 2 MHz. The measured relaxation times of all transmons are found to be in the range T 1 = 1.7 -3.2 µs for |∆ i /2π| 1 GHz. This is significantly below the Purcell limit T P > 8 µs and shorter than in comparable 2D transmon circuits [22], probably due to dielectric losses [23].

All qubit-readout cells yielded similar performances at equal detuning ∆ i . Performance of cell 1, operated at a qubit-JBA detuning ∆ 1 /2π = -1.08 GHz, is summarized in Fig. 2. All qubit control pulses have 3σ long Gaussian rises and falls with σ = 4 ns, as shown in Fig. 2(a). Numerical simulations of the transmon dynamics including its three lowest levels show that such control pulses do not introduce preparation errors larger than 0.1% [33]. Readout is performed either immediately after applying a θ 01 1 Rabi pulse, or after a subsequent π 12 1 pulse that shelves the excited qubit in state |2 , as in [25]. This shelving decreases the error made in measuring the excited qubit by blocking its relaxation down to state |0 before the measurement is completed [32].

The density plot of (I 1 , Q 1 ) obtained from 10 5 repetitions of the readout after a (π/2) 01 1 pulse is shown in the left inset of Fig. 2(b). The two clouds with a small relative overlap of order 10 -5 (estimated from the corresponding histogram in the right inset) reveal an excellent discrimination of the JBA states. The fidelity of the qubit to JBA mapping is investigated by measuring the variations of the switching probability p 1 as a function of the peak readout power P R . These so-called S-curves are shown in Fig. 2(d) in three different cases: when the qubit is left in its ground state |0 with no applied control pulse (blue), after a π 01 1 pulse aiming at preparing state |1 (red), and after a π 01 1 pulse followed by a π 12 1 shelving pulse (magenta). One observes that the S-curves for the two states |0 and |1 are separated in P R by about 5.5 dB (or equivalently by 2χ = 3.4 MHz in resonator or drive frequency), which is much larger than the 2.4 dB (1.5 MHz) width of the ground state S-curve, defined here by 1% < p < 99%. This result implies that, in absence of preparation errors and relaxation before and during measurement, readout errors would be negligible.

In practice, at the optimal powers P R [see Fig. 2(d)], the measured total errors are 1.1% for |0 , and 3.1 % and 2.2% for |1 without and with shelving, respectively. These errors result from two effect. First, the 1.1% error in the ground state is due to a residual thermal excitation of the qubit (corresponding to a qubit temperature of 70 mK), as evidenced by the flat shoulder on the ground state S curve at low power. This spurious excitation is also responsible for the same absolute 1.1% error in preparing state |1 . Remaining errors in |1 are thus 2.0 % and 1.1 % without and with shelving. Second, numerical simulations including relaxation during the control pulses, using the independently measured relaxation time Γ 10 1 -1 = 2.0 µs, accounts for absolute errors of 0.6% and 1.1% without and with shelving. The shelving case is thus fully understood: errors in |1 are only due to thermal population and relaxation at preparation, and relaxation to |0 during readout is efficiently blocked as proven by the horizontal plateau at p 1 (P R ) 0.98. The intrinsic readout fidelity with shelving is thus excellent.

Without shelving, the remaining readout error is 1.4% at the optimal P R , but with a slow increase of p 1 (P R ) as it approaches 1. This behavior is not understood and quantum simulation of the JBA + excited qubit dynamics is needed to address this question. Nevertheless, to infer what would be the intrinsic readout fidelity in absence of preparation errors and extra relaxation at readout, we reconstruct ideal S-curves: for the ground state, the lower part p 1 ≤ 0.5 is replaced by the S-curve measured for the qubit excited state and shifted in power to remove the effect of residual thermal excitation; for the excited state, its upper part p 1 > 0.5 is replaced by the one measured in the ground state and shifted in power to remove the effect of relaxation at readout. These ideal S-curves, illustrated by thin solid and dotted lines Fig. 2(d), give intrinsic readout errors lower than 2 × 10 -3 both for the ground and excited states.

We now discuss the simultaneous readout of the four qubits. Given the lack of individual transmon tunability, a magnetic field leading to not too large detunings ∆ i /2π = (-1.2, -1.76, -3.12, -2.06) GHz was applied. In addition, longer readout pulses with 50 ns measurement step and 2 µs latching step are used, as shown in Fig. 4(a). The measurement outcomes for the four qubits prepared with control pulses close to (π/2) 01 , and with π 12 shelving only for B 2 and B 4 [34] are shown in Fig. 3. The density plots in the (I i , Q i ) planes are shown with their best separatrix between switching and nonswitching events. As illustrated in Fig. 3(c), the switching histograms measured along an axis perpendicular to the separatrix show a good separation, albeit smaller than obtained at the optimal working point of each cell.

Having characterized simultaneous readout of the four qubits, we now include qubit drive (see Fig. 4). For simplicity, the control pulses are not applied simultaneously in order to avoid having to take into account the qubit ac-Stark shift resulting from other qubit drives. The control and readout pulses are shown in Fig. 4(a). The switching curves of the four JBAs are shown in Fig. 4(b) after no qubit pulse, and after a π 01 i pulse without or with shelving. Rabi oscillations of the four qubits, measured at the optimal powers indicated in Fig. 4(b) are shown in Fig. 4(c). This data shows that JBA readout is compatible with qubit driving and simultaneous multiplexed operation. The overall performance of our multiplexed JBA is thus comparable with that achieved using linear dispersive readout and parametric amplifiers [22], albeit with larger errors not due to the readout method itself.

A natural question that arises is the maximum number of transmons that multiplexed JBA could handle. Indeed, due the non-linear character of JBAs, bifurcation of a given JBA can be affected by the dynamics of other JBAs that are close in frequency. How close their frequencies can be without inducing readout crosstalk is not known. In the present setup, this phenomenon was quantified by preparing B 1 in |0 or |1 and B 2 in a superposition

(|0 + |1 )/ √ 2.
The difference between the Simultaneous readout of the four qubits at a magnetic field such that ∆1-4/2π = (-1.2, -1.76, -3.12, -2.06) GHz.

(a) Switching probabilities pi of the four readouts as a function of readout power PR, after no control pulse (right curves in each panel), and after a π 01 i pulse without (middle) and with shelving (left curves for B1,2,3). Dashed vertical lines indicate the optimal readout powers used in (b-c) and in Fig. 4 (shelving used only for B2 and B4). (b) Density plots of the four (Ii, Qi) obtained from 10 5 measurements (see also [28]). Segments indicate the separatrices between switching and non-switching events. (c) Corresponding histograms along the lines perpendicular to separatrices.

values of p 2 for the two B 1 states gives a crosstalk of only 0.2%±0.05%. This low value shows that a JBA frequency separation of 60 MHz is conservative, and therefore that more qubits could be read out in parallel.

In conclusion, multiplexed JBA readout of transmons has an excellent intrinsic readout fidelity when shelving is used, and is compatible with driving and reading transmons in a small qubit register. Its scalability, limited by the interactions between JBAs with close frequencies, is still under investigation, but the present results suggest that reading out a ten-qubit register is possible. [32] This blockade occurs because the direct relaxation from state |2 to |0 involves a very small matrix element; consequently, the decay to |0 results from to the two relaxation processes |2 → |1 and|1 → |0 in series, and varies quadratically at short time, as 1 -Γ ef f t 2 with

Γ ef f = Γ 21 1 Γ 10 1 ∼ √ 2Γ 10
1 . Note however that shelving takes the qubit out of the computational Hilbert space and thus makes the readout destructive.

[33] Consequently, we do not use the DRAG correction technique used in J. M. Chow, L. DiCarlo, J. M. Gambetta, F. Motzoi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Phys Rev A 82, 040305 (2010).

[34] Shelving was neither used for qubit B1 because f 12 1 being too close from f 01 4 , it would have driven qubit B4, nor for qubit B3 whose frequency f 12 3 was outside the bandpass of the driving line.

Supplemental Information

I. SAMPLE FABRICATION

The sample is fabricated on a sapphire substrate in a two-step lithography process. The transmission line and the readout resonators are first patterned in a Niobium film using optical lithography and reactive ion etching. The transmons and JBA junctions are then fabricated by electron lithography and double-angle evaporation of aluminum through a suspended shadow-mask, with intermediate oxidation.

II. GENERATION OF CONTROL AND READOUT PULSES

The microwave control pulses at frequencies f kl Bi are obtained by translating the frequency f B0 of a single carrier using the technique of single sideband mixing: using an IQ mixer, the carrier is multiplied by two signals I and Q delivered by an arbitrary waveform generator (AWG). I and Q are a sum of signals at frequencies δ kl Bi = f kl Bi -f B0 , with suitable envelopes and phases. Another mixer is used to produce the JBA drive signals in the same way, that is by IQ mixing a carrier f R0 with a sum of signals at frequencies δ Ri = f Ri -f R0 . Figure 1(a) of the main text illustrates the setup used.

III. DEMODULATION SCHEME

The four JBA's contributions to the output readout signal are obttained by the following demodulation scheme. An analog demodulation at the readout carrier frequency f R0 is first performed. The resulting signal is then digitized at 2 GSample/s with a 1 GHz analog bandwidth that widely covers the 250 MHz frequency range spanned by the four JBAs; it is then demodulated numerically by a dedicated PC that direct multiplies it with cosine functions at frequencies δ Ri and average the result. The outcome of a readout sequence is four points (I i , Q i ) in the in-phase and quadrature plane (one for each JBA frequency f Ri ), as shown in Fig. 3(b).

IV. CHARACTERIZATION OF SIMULTANEOUS READOUT

The pairs of (I i , Q i ) clouds of the four JBAs, shown in Fig. 3 of the main text, are displayed in Fig. 2 in separated frames for clarity. In addition, the standard deviation of the switching probability for all cells [see panel (e)] is shown to decrease as expected for independent events. Simultaneous readout of the four qubits at a magnetic field such that ∆i/2π = (-1.2, -1.76, -3.12, -2.06) GHz.

Qubits are prepared with control pulses close to (π/2) 01 1 , with shelving only for B3 and B4, and with measurement powers corresponding to the maximum contrast. (a-d) Density plots of (Ii, Qi) obtained from 10 5 sequences. Segments indicate the separatrices between switching and non-switching events. (f) Corresponding histograms along the lines perpendicular to separatrices. (e) Experimental (dots) and theoretical (black and white dashed line) standard deviation of the switching probability pi ∼ 0.5 measured over n shots.

Figure 1 :

 1 Figure 1: Readout of transmon qubits based on multiplexed JBAs. (a) Schematic electrical circuit. Four qubit-readout cells i (only one shown) are capacitively coupled to a microwave transmission line (black central line). Each cell is made of a tunable transmon qubit Bi [29] of transition frequencies f kl Bi , capacitively coupled to a JBA resonator Ri of frequency fRi. Control and readout pulses are produced and analyzed as described in [28]. (b-c) Optical micrographs showing (b) the measured chip with four cells, (c) cell 1 with transmon B1 and lumped element JBA R1. (d) Spectroscopy of the four qubits Bi and readouts Ri as a function of the coil current inducing a global magnetic field. Frequencies fRi are indicated by lines, whereas qubit spectra are obtained by exciting the qubits with a 4 µs long single frequency control pulse, reading out simultaneously the four JBAs, and color plotting their switching probabilities.

Figure 2 :

 2 Figure 2: Characterization of cell 1 at detuning ∆1/2π = 1.08 GHz. (a) Microwave control pulse envelopes for π 01 1 , π 12 1 , and (2π) 01 1 rotations (see text). The dotted line shows the maximum amplitude used. (b) Beginning of the microwave readout pulse envelope (solid green line). Left inset: density plot of (I1, Q1) obtained from 10 5 repetitions of a (π/2) 01 1 pulse [purple dot P in (c)] followed by a readout pulse. Right inset: corresponding histogram (population in 10mV wide bins) along the direction I joining the two cloud centers. (c) Rabi oscillation of p1 as a function of the equivalent control pulse length (duration of a rectangular pulse with maximum amplitude), without (red) and with (magenta) shelving (see text). (d) Probability p1 with no qubit control pulse (blue) and after a π 01 1 pulse alone (red) or with shelving (magenta). Solid lines represent p1 on a linear scale (left axis) whereas dashed and dotted lines show it using a double logarithmic scale below and above 0.5 (right axis). Thin solid and dotted lines represent 'ideal' S-curves (see text). The vertical dashed lines indicate the pulse power yielding the highest readout contrasts with (left) and without (right) shelving.

 1 =

 1 -1.20 GHz  2 =-1.76 GHz  4 =-2.06 GHz  3 =-3.12 GHz

Figure 3 :

 3 Figure 3:Simultaneous readout of the four qubits at a magnetic field such that ∆1-4/2π = (-1.2, -1.76, -3.12, -2.06) GHz.(a) Switching probabilities pi of the four readouts as a function of readout power PR, after no control pulse (right curves in each panel), and after a π 01

Figure 4 :

 4 Figure 4: Simultaneous measurement of Rabi oscillations of the four qubits at readout powers indicated in Fig. 3. Microwave control (a) and readout (b) pulse envelopes used at 5 ns equivalent Rabi pulse duration. Only B2 and B4 are shelved on their second excited levels before readout. (c) Simultaneous Rabi oscillations of p1-4 as a function of the equivalent control pulse duration.

Figure 5 :

 5 Figure 5: Optical micrographs showing (a) the measured chip with four cells, (c) cell 1 with transmon B1 and lumped element JBA R1, (b) the SQUID of B1, and (d) the Josephson junction inserted in R1.

  Figure 6:Simultaneous readout of the four qubits at a magnetic field such that ∆i/2π = (-1.2, -1.76, -3.12, -2.06) GHz.Qubits are prepared with control pulses close to (π/2)01 1 , with shelving only for B3 and B4, and with measurement powers corresponding to the maximum contrast. (a-d) Density plots of (Ii, Qi) obtained from 10 5 sequences. Segments indicate the separatrices between switching and non-switching events. (f) Corresponding histograms along the lines perpendicular to separatrices. (e) Experimental (dots) and theoretical (black and white dashed line) standard deviation of the switching probability pi ∼ 0.5 measured over n shots.

We gratefully acknowledge discussions within the Quantronics group, and technical support from P. Orfila, P. Senat, J.C. Tack, and Dominique Duet. This work was supported by the European FP7 QIPC project ScaleQIT, by the CCQED network, and by the NSERC of Canada.