Bérangère Legendre
email: berangere.legendre@univ-savoie.fr

Olivia Ricci
email: olivia.ricci@univ-reunion.fr

Measuring fuel poverty in France: which households are the most vulnerable?

Keywords: Fuel poverty, vulnerable households, poverty indicators, clog log model

Fuel poverty is a growing concern in France. Following the hike in energy prices that started in 2004, the problem of energy affordability for low-income households entered the political debate with the "Grenelle de l"environnement" in 2007. According to the standard UK definition (10% ratio) 3.8 million households were subject to fuel poverty in France in 2006. We question the way fuel poverty is currently measured and compare the impact of alternative measurement approaches on the extent and composition of fuel poverty in France. Then, we identify and characterize vulnerable households that are not ordinarily poor, but can be pushed into poverty because of their fuel bills. A logit, a clog log and a mixed effect logit model are used to analyze which factors influence the probability of vulnerable households to fall into poverty. The study indicates that the proportion of fuel poor people and their characteristics differ significantly depending on the fuel poverty measure chosen. The econometric results show that the probability of falling into poverty is higher for those who are retired living alone, rent their home, use an individual boiler for heating, cook with butane or propane and have poor roof insulation. Current French fuel poverty reduction policies appear to be inappropriate given our conclusions.

Introduction

Fuel poverty in developed countries is a serious problem from three main perspectives: poverty and reducing it; health and well-being; decreasing carbon emissions and saving energy [START_REF] Hills | Fuel Poverty: The problem and its measurement, Interim Report of the Fuel Poverty Review. Centre for the Analysis of Social Exclusion[END_REF]. These issues are quite different from those raised in developing countries, where energy poverty addresses especially the question of the access to modern energy sources [START_REF] Nussbaumer | Measuring Energy Poverty: Focusing on What Matters[END_REF]. The existing literature discussed extensively the link between energy poverty and global development issues: energy is central to eradicate poverty in the developing world, and improving human welfare (UNDP, 2000;IAEA, 2005, Pachauri et al., 2004;Pachauri andSpreng, 2004, 2011). Fuel poverty and energy poverty must consequently be distinguished [START_REF] Li | Energy poor or fuel poor: What are the differences? Energy Policy[END_REF]. We focus in this article on fuel poverty. Fuel poverty was first defined as the difficulty for households to afford adequate warmth in their home [START_REF] Lewis | Bradford: National Right to Fuel Campaign[END_REF]. [START_REF] Boardman | Fuel Poverty: From Cold Homes to Affordable Warmth[END_REF] showed that fuel poverty occurs when a household needs to spend more than 10% of its income on fuel costs in their home to maintain satisfactory indoor temperature. In France, [START_REF] Devalière | La précarité énergétique : avoir froid ou dépenser trop pour se chauffer[END_REF] showed that 3.5 million of households suffered from cold in their home in 2006 and 3.8 million spent more than 10% of their income to pay their energy bill.

Fuel poverty in developed countries has several causes which are almost always combined: low-energy efficient housing, rising fuel prices, and low incomes (EPEE, 2006;[START_REF] Iea | Evaluationg the co-benefitrs of low-incomes energy-efficiency programmes[END_REF][START_REF] Rappel | Précarité Energétique: Etat des lieux et propositions d"actions[END_REF][START_REF] Palmer | Cold and Poor: An analysis of the link between fuel poverty and low income[END_REF]. There is a considerable overlap between fuel-poor households and those with low incomes. Using a widely adopted income poverty measure (60% median equivalised income threshold), [START_REF] Palmer | Cold and Poor: An analysis of the link between fuel poverty and low income[END_REF] showed that nearly three quarters of the fuel poor in England in 2005 were also income poor. From a definition point of view, many institutions and countries showed that monetary and fuel poverty were inextricably linked, representing both an aspect of multidimensional poverty. For instance, the Energy Act 2010, which introduces the concept of reducing both the extent and the depth of fuel poverty in the UK, defines fuel poverty as a dual issue, involving households on low incomes faced with unreasonable fuel costs. In France, the current fuel poverty policy was created in 2010 during the French environment roundtables called ""Grenelle de l"environnement"", under the law "Grenelle 2" n° 2010-7881 . The law defines the concept of fuel poverty. A person suffering from fuel poverty is "anyone who encounters, in their home, particular difficulties in obtaining the energy required to meet their basic energy needs due to insufficient resources or housing conditions". The law has since been complemented by a measurement approach inspired by the United Kingdom 2 . According to the 2001 UK Fuel Poverty Strategy, a household is considered to be in fuel poverty if it needs to spend more than 10% of its total income before housing costs on fuel to heat its home to an acceptable level.

There are numerous criticisms of the current 10 % objective measure, the main one being that it fails to capture all of the main drivers of fuel poverty [START_REF] Hills | Fuel Poverty: The problem and its measurement, Interim Report of the Fuel Poverty Review. Centre for the Analysis of Social Exclusion[END_REF]. In fact, this ratio can capture households with high energy costs, but not all of these households are on low incomes. This is why significant numbers of households with relatively high incomes have been found to be fuel poor even though they should be able to absorb the cost of higher bills [START_REF] Hills | Fuel Poverty: The problem and its measurement, Interim Report of the Fuel Poverty Review. Centre for the Analysis of Social Exclusion[END_REF][START_REF] Moore | Definitions of fuel poverty: Implications for policy[END_REF]. Other households can even be pushed into poverty because of energy costs without reaching the 10% ratio.

Therefore, much debate focuses on how to measure fuel poverty given the potential difficulties in identifying one single indicator that will satisfactorily capture all of the issues. In order to target low-income households, fuel poverty can be studied from a perspective of poverty concern in general, using the after fuel cost poverty approach [START_REF] Hills | Fuel Poverty: The problem and its measurement, Interim Report of the Fuel Poverty Review. Centre for the Analysis of Social Exclusion[END_REF]. This consists in measuring residual income (i.e. after housing and fuel costs) and comparing it to an income standard such as the poverty line (threshold of 60% of the national equivalised income level). There is a clear interest in establishing whether some households may be exposed to poverty because of high fuel costs. [START_REF] Hills | Fuel Poverty: The problem and its measurement, Interim Report of the Fuel Poverty Review. Centre for the Analysis of Social Exclusion[END_REF] has also proposed an alternative measurement framework focusing directly on the overlap of high costs and low income (the Low Income-High Costs indicator).

Little empirical research has been undertaken on fuel poverty in France. The European Fuel Poverty and Energy Efficiency Project (EPEE project) in 2006 proposed a descriptive approach of fuel poverty in France using three subjective criteria (capacity to pay to keep one"s home warm, the existence of dampness, leaks, mould in the accommodation, and the arrears on electricity, gas and water bills). Depending on the subjective criteria the composition of the fuel Poor differed significantly. Therefore, this approach failed to precisely characterize fuel poverty. Although the redistributive architecture and the welfare State are known to reduce the monetary poverty quite efficiently in France [START_REF] Cazenave | La redistribution : état des lieux en 2010 et évolution depuis vingt ans. In France portrait social 2011[END_REF]. However policy makers face some difficulties to target efficiently the fuel Poor and to decrease this form of poverty. Policies attempting to reduce fuel poverty in France have been designed using only the restrictive 10% ratio, which is subject to criticisms as we have seen.

This article examines the multiple aspects of fuel poverty in France according to different existing measurement approaches: the "10% ratio approach", "the after fuel cost poverty approach", and the "Hills approach" (Low Income High Costs indicator) and proposes a complementary approach. Using those three measurement approaches do not allow identifying households that are at risk of falling below the poverty line specifically because of high fuel costs. This study represents the first attempt to define what fuel vulnerability is by studying households on the edge of poverty. Households can be classified as vulnerable in the sense that they are a priori non-poor before the fuel bills but a marginal increase in energy prices is enough to make them slip below the threshold3 . Such an approach allows us to identify the impact of high fuel costs on the margins of poverty. A specific policy targeting such households could be implemented to help them shift above the threshold and therefore reduce the extent of fuel poverty in France.

This paper attempts to provide some answers to the following question: what are key factor of fuel vulnerability and how to protect vulnerable individual from falling below the poverty line? But answering this question necessarily requires understanding why the existing measurement approaches might be inadequate.

After giving an overview of the extent of fuel poverty and the composition of the fuel poor in France using the existing measurement approaches, we conduct an income-based analysis in order to quantify and identify vulnerable households. We use the Foster, Greer and Thorbecke (FGT) (1984) indicator to calculate the incidence, depth and severity of poverty and then estimate logit and complementary log-log regression models to characterize vulnerable households that are pushed into poverty because of fuel costs. Using a less limited methodology, namely a mixed effect logistic regression model, we next assess the robustness of the econometric estimates. The database used for this study is the French housing survey "enquête logement 2006" (Insee, 2006). It is a detailed and representative survey that includes data on income and information on housing conditions. This paper is organized as follows: Section 1 presents a literature review of the different fuel poverty measures. Section 2 describes the methodology used and the data. Section 3 relates the statistics on the impact of the three objective fuel poverty approaches on the extent and composition of the fuel poor in France. Section 4 presents the empirical analysis. Section 5 shows the results and their robustness, and sets out some policy implications.

Fuel poverty measures in the literature

While there is a widespread agreement on the concept of fuel poverty, its measurement differs markedly, leading to significant implications in terms of the extent of fuel poverty and fuel-poor households characteristics.

The most common objective measure of fuel poverty, called in this paper the "10% ratio approach", is the 10% threshold, which means that households with a ratio between expenses and income in excess of 0.1 are classified as fuel poor.

This indicator uses income before housing costs (BHC) and it is not equivalised (adjusted to household size and composition). The required fuel costs are estimated based on income data and modeled physical data relating to dwelling characteristics and energy efficiency. The advantage of focusing on required, rather than actual, fuel spending is that it takes underconsumption into account [START_REF] Dubois | From targeting to implementation: The role of identification of fuel poor households[END_REF][START_REF] Fahmy | Predicting fuel poverty at a small-area level in England[END_REF]. However, this measure is open to a number of criticisms (for a detailed description of the indicator"s weaknesses, see [START_REF] Hills | Fuel Poverty: The problem and its measurement, Interim Report of the Fuel Poverty Review. Centre for the Analysis of Social Exclusion[END_REF]. Some of these criticisms relate to its intrinsic ratio form and some to the way income is calculated.

Firstly, using a ratio to determine the extent of fuel poverty does not include a cut off for households with high income. Therefore, a significant number of high-income households were found to be fuel poor with this measure [START_REF] Hills | Fuel Poverty: The problem and its measurement, Interim Report of the Fuel Poverty Review. Centre for the Analysis of Social Exclusion[END_REF][START_REF] Moore | Definitions of fuel poverty: Implications for policy[END_REF]. This is not in line with the definitions exposed in the introduction.

Secondly, income is not adjusted to account for households'different compositions and sizes. Therefore, it overestimates the incomes available to larger households to meet these domestic fuel needs. Empirical analyses suggest that income equivalence has a substantial effect on the social and demographic composition of the fuel poor [START_REF] Fahmy | Predicting fuel poverty at a small-area level in England[END_REF].

Thirdly, experts argue that income should be measured after housing costs (AHC) to give a true picture of a household"s disposal income and therefore the affordability of fuel bills, given that housing costs are usually met before other types of consumption [START_REF] Hills | Fuel Poverty: The problem and its measurement, Interim Report of the Fuel Poverty Review. Centre for the Analysis of Social Exclusion[END_REF][START_REF] Moore | Definitions of fuel poverty: Implications for policy[END_REF]. Housing costs are highly geographically variable, therefore, estimating incomes on a before housing cost (BHC) basis can produce misleading estimates of the extent and spatial distribution of fuel poverty.

In order to capture households on low income, we can use a broader measure of fuel poverty using traditional indicators from income poverty. Eurostat"s definition of poverty risk refers to individuals living in households where the equivalised income is below the threshold of 60% of the national equivalised median income. Under this approach, households whose equivalised income after housing costs (HC) and fuel costs (FC) falls below the threshold are classified as fuel poor. This approach is presented by [START_REF] Hills | Fuel Poverty: The problem and its measurement, Interim Report of the Fuel Poverty Review. Centre for the Analysis of Social Exclusion[END_REF] and it is called "after fuel cost poverty" approach. This approach successfully identifies households that are in income poverty and whose situation is worsened by fuel costs. However, within this indicator nearly all households with very low income are classified as fuel poor regardless of their fuel requirement. This approach does not properly reflect the distinct nature of fuel poverty but rather gives insights to the broader concept of poverty. The Hills's approach (2011) recommends adopting a new indicator of the extent of fuel poverty: the "Low Income-High costs" indicator (LIHC). This indicator captures households that have a combination of low income and relatively high costs by establishing two specific thresholds:

 The income threshold is the same as for the "after fuel cost poverty approach". It is consistent with official poverty measurements;  The energy cost threshold is based on the median required spending of all households. Therefore, households that are below the conventional 60% of the median income poverty line and have fuel costs above the median level are classified as fuel poor.

This indicator is consistent with the definition of fuel poverty as it takes into account the level of income as well as the relative weight of the energy spending. However, this approach will not give a precise identification of households that are pushed into poverty because of fuel costs. Moreover, fixing the energy cost threshold to the median is essentially arbitrary.

The literature shows that some individual and households characteristics are associated with difficulties facing the energy costs. Fuel poverty can be measured with objective indicators as we have seen, but some authors also use more subjective criteria. Using the ability to heat the home adequately as fuel poverty criteria, [START_REF] Healy | Fuel Poverty and Policy in Ireland and the European Union[END_REF] shows that in Ireland, family and social factors impact the probability of being fuel poor. Living alone and having dependent children is especially associated with financial difficulties and difficulties to heat the home. The EPEE project underlines some similarities across France, United Kingdom, Belgium, Spain and Italy in fuel poverty aggravating factors: being tenants, single people, among them especially pensioners. Pensioners suffer from higher risk to have a low income, which is combined with high energy needs. Housing tenure is an important dynamic of fuel poverty [START_REF] Whyley | Fuel Poverty in Europe: Evidence from the European Household Panel Survey[END_REF][START_REF] Healy | Fuel Poverty and Policy in Ireland and the European Union[END_REF][START_REF] Boardman | Fixing Fuel Poverty: Challenges and Solutions[END_REF][START_REF] Devalière | La précarité énergétique : avoir froid ou dépenser trop pour se chauffer[END_REF][START_REF] Hills | Getting the Measure of Fuel Poverty. Final Report of the Fuel Poverty Review[END_REF] since it gives households different levels of control concerning their home. Owner-occupiers are fully autonomous while tenants are more limited in their choices. However, homeowners also endure significantly higher financial burdens for their home maintenance. Using the rate of energy effort (10% approach), Devalière calculates that French fuel Poor are in majority homeowners, which contradicts the findings of the EPEE project. This contradiction comes from the differences of the approaches: the EPEE project considers a subjective indicator: the declared ability to pay to keep home adequately warm, while Devalière uses 10% objective approach. [START_REF] Devalière | De l"inconfort thermique à la précarité énergétique, profils et pratiques des ménages pauvres[END_REF] found also that pensioners exhibit high levels of fuel poverty. A third of them declare suffering from a thermal discomfort. Heating is the most important item of energy expenditure. It accounts for about 50% of the accommodation energy bill in France [START_REF] Ademe | Stratégie utilisation rationnelle de l"énergie : Chapitre 2 les bâtiments. www2.ademe.fr/servlet/getBin[END_REF]. The age of a property has also a significant influence on energy costs [START_REF] Hills | Getting the Measure of Fuel Poverty. Final Report of the Fuel Poverty Review[END_REF]. Using a subjective measure of fuel poverty, [START_REF] Devalière | La précarité énergétique : avoir froid ou dépenser trop pour se chauffer[END_REF] showed that French households who reported suffering from cold lived more often in houses built before the first thermal regulation in 1974. In France, on 25.65 million of households, 1.59 million declared having difficulties in paying to keep home adequately warm, 3.13 million declared leaking roof, damp walls/floors/foundation, or rot in window frames or floor, and 1.64 had arrears on utility bills (EPEE, 2006).

Current studies on fuel poverty use different definition and measures leading to contrasting results in terms of the composition of the fuel poor. The lack of a precise indicator does not allow designing efficient policies, which raises two main issues: a measurement problem, combining with a targeting problem ex ante and a policy evaluation issue ex post.

Methodology and data

In a first place, we propose measuring the extent and composition of fuel poverty in France using the three objective approaches described above ("10% ratio approach", "after fuel cost poverty approach" and "Hills'approach"). However, as household composition and housing costs were a main criticism of the traditional 10% ratio measure, we will adjust gross income in the three approaches to take these two aspects into account. Moreover, it is easier to compare the indicators on the same basis. In all three approaches, gross income takes households'size and composition into account and is calculated after housing costs.

To calculate the 10% ratio, we use actual spending rather than expected ones, as existing surveys do not provide indication on theoretical energy spending4 .

We assign to each member of the household an equivalent income value, calculated using the OECD equivalence scale. Economies of scale in housing and the consumption of goods and services are allowed for controlling household composition. Some existing literature underlines the potential asymmetry in the management of, and access to, household resources [START_REF] Browning | Income and outcomes: a structural model of intra household allocation[END_REF][START_REF] Roy | Tout ce qui est à moi est à toi ? Terrain[END_REF]Belleau andProulx, 2010, 2011). Nevertheless, assuming that most households share and manage their income in a fair manner, we deflate the household resources by the number of consumption units in the household. We assign a value of 1 to the first household member, 0.5 to each additional adult member and 0.3 to each child under 14 years old. This method has the advantage of showing households'standards of living more precisely.

It is often used in income poverty measurements to deduct housing expenditure (mortgage payments or rents) from income and show the share of households under the poverty line [START_REF] Hills | Fuel Poverty: The problem and its measurement, Interim Report of the Fuel Poverty Review. Centre for the Analysis of Social Exclusion[END_REF][START_REF] Moore | Definitions of fuel poverty: Implications for policy[END_REF]. In fact, the amount households must spend is only ever an imperfect measure of the standard of living they can achieve, but for many things the same cash amount can translate into similar items in a shopping basket, meeting their needs in similar ways. The greatest exception to this is housing, because of the huge variations in rents and house prices across the country and the difficulty people would face in moving. Under the after fuel cost poverty approach, we have calculated the extent of poverty with the poverty rate (headcount), but it is also possible to study the depth and severity of poverty using the poverty gap and square poverty gap indicator [START_REF] Foster | A class of decomposable poverty measures[END_REF] (see table 1). The FGT indicator has the advantage to provide three dimensions of poverty and eventually to complement the after fuel cost poverty approach. The poverty gap shows how far below the poverty line people are affected. This is an interesting indicator for ascertaining whether the situation improves, for instance, when the poor move closer to the poverty line, even when only a few of them cross it. The square poverty gap takes into account not only the distance separating the poor from the poverty line (the poverty gap), but also inequality among the poor. A higher burden is placed on those households furthest away from the poverty line.

The headcount which is similar to the after fuel cost approach, the poverty gap and the squared poverty gap are the three measures that can be obtained using the general formula of the Foster, Greer and Thorbecke indicator (FGT):

∑ ( )

is the population size, is the number of poor (those with incomes at or below the poverty line ), are individual incomes and is a sensitivity parameter. When has a value of zero, we obtain the headcount, when is equal to one, we obtain the poverty gap and when is equal to two, we obtain the squared poverty gap. In this after fuel cost poverty approach, three levels of income can be considered to capture the effect on each spending on the exposure to fuel poverty: gross income, gross income after housing costs, gross income after housing costs and fuel costs.

The definition of fuel poverty indicators raises serious questions. First, pursuing a fuel poverty reduction policy requires precisely defining who the fuel-poor are. Which population is the most vulnerable? It is vital to identify these inhabitants ex ante in order to conduct an efficient policy. Secondly, policy makers need relevant indicators to measure the efficiency of their policy ex post. Therefore, reliable tools are needed. Depending on the fuel poverty indicators chosen, the targeted population will not be the same, and the results of the policy will change. Households and individuals identified as fuel poor using the three approaches described above can suffer from different forms of precariousness, none of them being specifically and uniquely triggered by the energy bills.

For this reason we propose to target the groups in society that are most vulnerable to energy costs and at risk of falling into fuel poverty because of this burden. Our starting point is the after fuel cost poverty approach. As we have seen, the main weakness of this approach is that it does not allow us to specifically study the nature of fuel poverty because these households are concerned with much broader poverty issues and energy bills only worsen their situation. To evaluate the vulnerability aspect of this problem, we chose a sample of households that were not poverty exposed before the fuel bill.

Targeting households that are pushed into poverty because of their fuel bills is important for understanding which type of household should be prioritized for support through fuel poverty reduction policies. The aim of the following econometric analysis is to develop a model of the most influential demographic, socioeconomic and housing characteristics affecting the likelihood of a household falling into fuel poverty, for households that are not a priori poor.

We have a choice of sources for income data as well as housing and energy expenditure. The only survey in which income data is available in combination with information on housing conditions and expenditure is the French housing survey "Enquête Logement 2006" conducted by the French National Institute of Statistics and Economic Studies (Insee, 2006). In 2006, the survey sample covered over 70,000 dwellings (about 60,000 in Metropolitan France and 10,000 in the overseas departments) and a total of 43,000 households responded to the survey. Data were collected using computer-assisted personal interviews. The survey includes more than 1000 variables related to the characteristics of the housing stock, the quality of the dwellings and the expenditure associated with housing.

Housing costs in the database include rents and mortgage payments minus housing allowance. For the after fuel cost poverty and Hills approaches, fuel costs are subtracted from income. In the French Housing Survey, fuel costs comprise water, electricity and other fuel expenses.

Statistics on the extent and composition of fuel poverty

We study the extent and composition of fuel poverty in France using the "10% ratio approach", "the after fuel cost poverty approach" and the "Hills' approach".

Figure 1 shows the extent of fuel poverty in France using the different measures.

Figure 1: The extent of fuel poverty in France using different approaches Source: Enquête Logement, authors' calculations , N = 40 136 Key to read: 6.84%+7.76%+2% are fuel poor according to the 10% approach. 7.76% are fuel poor according to the three definitions, while 2% are fuel poor according to the 10% approach and the after fuel cost approach.

Fuel poverty rates vary notably for the three measures. 16.6%5 of the French population is considered as fuel poor according to the 10% ratio approach; 20.9% according to the after fuel cost poverty approach and 9.2% according to the Hills approach. Within the 16.6% of fuel poor under the 10% ratio approach, 6.84% are not exposed to poverty after housing and fuel costs under the after fuel cost poverty approach. Also, of the households that are found to be fuel poor under the after fuel cost poverty approach, 11.14% do not spend more than 10% of their income on energy expenses.

The above figure illustrates that the 10% ratio approach includes households that do not necessarily have a low income and it also demonstrates that the rate of 10% is arbitrary because a household can still be poor with lower energy expenses. We found that among the households in the last decile group (10% of the population with the highest income), 1.15% were fuel poor under the 10% ratio approach. Moreover, households' annual gross income is on average € 116816 for those who are poor according to the after fuel cost poverty approach, € 11,980 for those who are poor according to the Hills approach and € 14,128 for those who are poor according to the less restrictive 10% ratio approach.

Also, according to the after fuel cost approach only 43% of the poor spend more than 10% of their gross income on paying the energy bill. For them, the energy bill represents almost 22% of gross income. For the 57% who do not reach the 10% ratio, energy expenses represent about 6% of gross income.

The Hills approach brings out both approaches as the thresholds used ensure that only households on very low incomes with very high fuel costs are considered as fuel poor. 17.59% of the population is exposed to poverty before redistribution7 . After housing and energy bills, almost 21% of the population is exposed. This increase in poverty is associated with more inequalities: mean gross income of poor households represents 35.9% of the mean gross income within the population8 , but mean income after housing and energy costs represents 32.1% of the average. We can deduce that those expenditures weigh more heavily on poorer households.

The composition of fuel-poor households across different socio-economic and dwelling characteristics differ depending on the approach retained (appendix 1).

When looking at the professional categories of the heads of household, we note some differences between the approaches. Under the after fuel cost poverty approach a large proportion of the poor are active (40 % of the poor are employees or blue collar workers), whereas, in the two other approaches they are mainly inactive. Pensioners are more frequently energy poor. However, it appears that pensioners do not combine necessarily low incomes9 with high energy expenses, but are probably faced with significant fuel costs compared to their standard of living. Under the 10% ratio and the Hills approaches respectively 54% and 45% of the poor are pensioners, while under the after fuel cost poverty approach, which mainly targets low incomes, only 30% are pensioners. On average, pensioners represent 33% of the French population. They are consequently over-represented in the fuel poor population (according to the 10% and the Hill approaches).

We observe that the average head of household is 57 years old according to the Hills measure of fuel poverty, 60 years old according to the 10% ratio approach, but only 50 years old under the after fuel cost poverty approach. This also explains why a greater proportion of individuals are widowed in the fuel-poor population targeted by the Hills and 10% approaches (26% and 29% against 15% with the fuel poverty's broader approach). When focusing on household composition more than marital status, we observe that the poor are mainly people living alone. The poor household composition seems to be more or less the same under the three approaches.

The fuel poor are mainly homeowners for the 10% ratio approach and the Hills approach (respectively 66% and 53%) while under the after fuel cost poverty approach 63% of the fuel poor are tenants. This last approach includes a larger share of the population that was already income poor before housing and energy costs. It is therefore logical to find more tenants when using this approach. This is in line with literature on poverty in general, where the results show that the poorest are usually tenants (Insee, 2013). As the 10% ratio approach does not cut off low-income households, it is intuitive to find more homeowners than in the two other approaches. Moreover, as this approach includes a large portion of pensioners, it is consistent with the housing occupation status.

We find that 76% and 71% of the poor live in detached houses under the 10% ratio and the Hills approach respectively, while under the after fuel cost poverty approach 54% of the poor live in an apartment. The fuel poor under the 10% and Hills approaches are more likely to live in a detached house than the average population (on average, 58% of the population live in a detached house), while with the after fuel cost poor are more likely to live in an apartment than the average population (41%).

We observe that the majority of the fuel poor under the three approaches use an individual boiler as the main heating system in their house: 65% of the poor under the 10% ratio, 60% under the Hills approach, and that the number is less significant under the after fuel cost poverty approach (38%). Those living in poverty under the three approaches also more frequently use butane and propane for cooking than the average population (about 40% against only 24% on average). In contrast, the average population more frequently uses electricity to cook (27%) than the fuel poor under all three approaches. Among the after fuel cost poor, only 12% use electricity, compared to 16% among the fuel poor with both of the other approaches.

In the French housing survey, one subjective indicator relates to why respondents feel cold in their home. The main reasons for feeling cold given by the fuel poor relate to housing quality. Of the three approaches, above 40% of the fuel poor declared that they suffered from cold due to poor insulation, and more than 30% due to insufficient heating installation. Moreover, one out of three households limit their heating consumption due to its cost. In the average population, 41% said they suffered from cold due to poor insulation, and 19% due to equipment breakdowns, compared to only around 13% for the poor population (under the three approaches). Statistics on feeling cold as a result of under-consumption of heating is particularly informative: while on average 21% of respondents declared that they suffered from the cold because of under-consumption, 36% of the fuel poor gave this reason under the 10% and Hill approaches, and 29% among the after fuel cost poor. In other words, the fuel poor are constrained in their energy consumption, which might have a strong impact on their well-being.

Depending on the characteristics observed, the three indicators do not depict the same situation. It shows why leading and evaluating economic policies to reduce fuel poverty might be particularly problematic. Targeting fuel vulnerability has the virtue to identify clearly individuals for whom energy bills trigger the difficulties. Providing financial support to those populations would suppress the energy as poverty factor.

Empirical analysis

To target fuel vulnerable households we have to study households who were not poverty exposed before the fuel bills using the after fuel cost poverty approach. 26531 observations remain in our sample. Ultimately, households that became poor specifically and uniquely because of their fuel expenses represent 2.76% of our observations (See table in appendix B).

Logit and Complementary log-log models

Logistic and complementary log-log regression models have been constructed to examine the factors that influence the probability of falling into fuel poverty in France.

Using logistics allows us to verify whether the patterns commonly seen across fuel poverty are actually associated with single characteristics or a combination of several characteristics. The advantage of the logit and complementary log log models is the direct relationship between the coefficients and the hazard ratios, which provide pieces of information that are easy to interpret. By exponentiating the coefficients, we can determine the effect of each variable on the odds of a fuel-poor individual, compared to individuals possessing the baseline set of reference characteristics. The odd ratio is the ratio between the probability of "success" and the probability of "failure" 10 . Let denote a random variable representing a binary response. We define equal to 1 if the individual is pushed into poverty because of the energy cost, 0 otherwise. The probability of being fuel poor can be written as

( ) = (
) with the latent response. The outcome depends on explanatory variables, so we estimate the following model:

Where is the vector of covariates and the error term. We assume first that follows a standard logistic distribution and estimate a logit regression model.

However, the positive outcome is quite rare in our sample (2.76% of 1). Therefore, we use a complementary log-log analysis as an alternative to the logit model [START_REF] Powers | Statistical Methods for Categorical Data Analysis[END_REF] to check the robustness of our results. The complementary log-log model is derived from the hypothesis that the error distribution (or distribution of ) follows a log Weibull distribution. Unlike the logit analysis, the transformation is not symmetrical around 0: it is skewed to the right and therefore used when a positive outcome is rare 11 .

Variables

The explanatory variables have been selected on the basis of existing literature on fuel poverty. First, we introduce socio-demographic and socio-economic variables. Literature shows that some households are more poverty exposed than others. Thus, we introduce variables that characterize housing conditions to be those often associated with difficulties in heating the home adequately and thermally insulating walls and roofs, etc. We select the variables in order to avoid any multicollinearity that might occur when some explanatory variables are highly correlated. Some variables, like for example "living in a detached house" and an "individual boiler" would provide redundant information.

Rather than marital status, we focus on household composition. We assume that compared to couples, those living without a partner are more likely to be exposed to fuel poverty. Moreover, being a pensioner might also be linked with financial hardships: so we consider work status. This piece of information is combined with the household composition.

Table 1 shows that households comprising retired and single people are far more likely to be fuel poor than other household types. 6.93% of pensioners living alone are below the poverty line. People living alone also on average face a deeper poverty than couples and they suffer from a more severe poverty than other subsamples. This statistic ties in with observations made in the previous section whereby a large proportion of the poor were living alone under the three approaches.

10 Consequently, if the odd ratio is greater than 1, it expresses that there is a greater likelihood of success (dependant variable=1) than one of failure (dependant variable=0). 11 In complementary log-log models, ( ) represents a hazard ratio, or relative risk, rather than odds ratio. However, hazard ratios are equivalent to odd ratios if p, the probability of success is small, which the case in our analysis.

Educational attainment is, in general, a good indicator of household income and social class. 6.96% of people with no diploma experience fuel poverty while this proportion is less than 1% among those with an intermediate or a high educational level. The poverty gap and severity are also greater for individuals with no diploma.

Descriptive statistics on our sample do not show large differences in poverty exposure between owner-occupiers and tenants, of whom respectively 2.84% and 2.62% are exposed, while the average poverty rate is 2.76% in the sample. However, housing tenure is a key factor of our analysis as we observed previously that depending on the fuel poverty criteria chosen, result can differ significantly. Only the 10% and the Hills's approaches report that homeowners are more frequently fuel poor. But can we consider that among those who are not fuel poverty exposed before the energy bill, homeowners are more vulnerable? Many characteristics of the housing impact the exposure to fuel poverty: the location and the age of homes, the heating system, the energy used for cooking, the existence of doubleglazed windows, or the quality of insulation.

The climate zone in which the accommodation is located seems to have a strong influence on fuel poverty as it determines the temperature of homes, although this variable is rarely reported in literature. For example, in northern areas of France the poverty rate reaches 3.33%, which is higher than in the rest of the country.

The heating system and the type of energy used for the cooking affect the amount of the energy bill: collective energy sources like mains gas seem less expensive for households, while people using butane and propane bottles, whether combined with electricity or not, are more frequently poor.

Results and policy recommendations

Econometric results

Our models match the data correctly and the predictive power of the logit and complementary log log model is good (see table of results in appendix). Given the rare positive outcome, the latter will be preferred to provide analysis.

The results (See Table 1, and appendix C ) suggest that some household types are exposed to a higher fuel poverty risk. They show that none of the existing definitions should be preferred to the other to characterize vulnerability to fuel poverty. Some results confirm statistics provided by the 10% ratio and the Hills' approach, other underline on the contrary the relevance of the after fuel cost poverty approach.

These results prove that the vulnerability to energy expenses is specific and different from the picture depicted by current approaches. Key factors to achieve a better and more precise design of economic policies are presented below.

We first analyse the impact of conventional socio-economic variables on fuel vulnerability, without introducing housing characteristics (Partial results are displayed in appendix C). As far as standard characteristics are concerned, the estimates yield significant and expected results.

Then we gradually add to the standard explanatory variables specific variables characterizing the housing. These variables capture key factors that affect energy spending and consequently the exposure to fuel vulnerability. Estimates on control variables are barely affected by the introduction of these housing characteristics. It allows us to be confident that problems of collinearity do not bias our results.

Living with a partner avoid being vulnerable while living alone makes individuals more vulnerable. The hazard ratio calculated after the complementary log log model is particularly low for active couples, at 0.25112 , while it exceeds 1 for a retiree living alone (1,518). The marginal effect (See appendix C) reaches 2.66% for a pensioner living alone. This result is consistent with both the Hills's and the 10% approaches which record an overrepresentation of the pensioners among fuel Poor. Although French retirees enjoy an average standard of living similar to that of workers, they might be more frequently at the margins of poverty. Living with a partner allows benefiting from economies of scale. Once individuals may find themselves alone, they live, and support related costs, in too big homes.

The more dependent children there are in a household, the higher the likelihood of fuel poverty. Single parent families, widows and widowers are consequently a high risk population. The marginal effect for a family composed of two active adults and two children remains below 1% (0.68%) 13 , but reaches 2.21% among tenant single parent families with one child. Being a homeowner and highly educated is associated with a lower exposure to fuel vulnerability. Their hazard ratios reach respectively 0.554 and 0.408. On the contrary, a low level of education increases exposure to fuel poverty. Homeownership seems to be a key factor to avoid shifting below the poverty line especially because of the energy bill. Let us recall that Poor individuals before the energy expenses have been dropped of our sample. Consequently, those for whom fuel expenditures trigger the poverty are in average more frequently tenant than they are homeowner, which contradicts both the Hills's and the 10% approaches but is in line with the after fuel cost poverty one. This result suggests that fuel vulnerability arises more from a rented accommodation with poor energy efficiency than from the financial burdens for the home maintenance. This is confirmed by the significant and positive coefficient of the variable "living area / Consumption unities (m2)".

A high level of education might correspond to increased awareness regarding home insulation and/or energy efficiency. Marginal effects calculated within a household whose risk is limited illustrate this result: i.e. 0.62% for a family (2 active adults and 2 children) whose head has been educated to the reference educational level. It reaches 1.68% in the absence of a diploma and 0.25% for a high educational level.

Our results show clearly that the type of heating system and the energy used for cooking are key factors to explain fuel poverty. An individual boiler is associated with a high probability of being fuel poor, while collective boilers and district heating systems seem to protect more against fuel poverty. This result is in accordance with the Hills's and the 10% approaches. Households that heat their home with an individual boiler have the highest odds of being fuel poor (nearly 1.6 times that of households using other types of heating). The marginal effects are significantly higher for those using an individual boiler. For instance, as shown in the appendix, the level is 5.39% for a homeowner retiree living alone and as much as 3.63% for a single-parent family. On the contrary, the marginal effect of using a district heating system is only 0.53% for a single-parent family, and 0.2% for a family with two children.

Cooking with butane and/or propane, whether mixed with electricity or not, increases the exposure to poverty, whereas using town gas stream (natural gas) and electricity from the grid reduces the exposure.

A poor insulation increases significantly fuel vulnerability: the hazard ratio of a poor insulation of the roof reaches almost 1.29 while having double glazed windows allow to reduce the vulnerability. The hazard ratio is 0.76.

Finally, the age of the home and the climate zone also significantly impact exposure to fuel poverty. Only housing built after the first thermal regulation in 1974 is associated with a lower fuel poverty exposure. The odds of being fuel poor are lower compared to those living in a building constructed between 1950 and 1974: i.e. 0.836.

Econometric results provide a clear picture of housing characteristics increasing the exposure to fuel vulnerability. Some of them were already underlined with previous definitions. Policy options have to be confronted with such results in order to better target population in need, the one who wouldn"t be fuel poverty exposed without the energy bill. It appear to be necessary to act on the root causes at the household scale, for example by helping them to install better equipments, or to better insulate their home.

Robustness check

Optimizing energy efficiency and providing households with energy saving equipments will not have the same meaning depending on the quality of build of their housing. For this reason, we propose to take into account possible clusters in our data: we might consider housing level data, with individuals nested in types of housing, approximated by the type of heating system. As explained above, the variables were selected in order to avoid multicollinearity in the models. Nevertheless, we can consider that the type heating system is highly representative of the housing category. Having an individual boiler represents for example naturally a high probability to live within a detached house.

Because fixed effects logistic and clog log regressions might ignore the possible sources of non-independence in the data, they could be quite limited. Thus to test the robustness of our results, we estimate a further mixed effect logistic regression [START_REF] Agresti | Categorical Data Analysis[END_REF].

In addition to usual predictors used in previous models, we introduce a random varying intercept represented by the categorical variable "heating system". The two-level randomintercept model [START_REF] Powers | Statistical Methods for Categorical Data Analysis[END_REF] can be expressed as:

( )

Where denotes the probability to be fuel vulnerable for the individual j in cluster i, in other words, within a housing equipped of heating system of type i.

accounts for observed sources of variation in the response, the vector includes the usual variables used in the standard models presented above, except the type of heating system. The error term is assumed to be normally distributed with mean 0 and variance , and is independent from . To express the random varying intercept model with more clarity, we can rewrite the previous equation as: ( ) , the random intercept varies among the level-2 units, with a mean of conditional on . This random intercept represents the combined effect of potential omitted subject-specific covariates that causes some individuals to be more exposed to fuel vulnerability depending on their type of heating equipment, and indirectly their category of housing 14 .

The LR test confirms the relevance of the two-level random-intercept model. Our results appear to be robust, even after taking into account the possible non independence in the data, due to the type of heating system, or the different categories of housing. Results are reported in appendix E. Compared with results exposed above, the location appears more significant, implying that living in areas with comfortable temperatures is determinant in the exposure to fuel poverty. This last regression shows that the type of housing, and probably indirectly the quality of the build, is a factor that makes a lot of sense in some regions.

Policy implications

A policy targeting vulnerable individuals on the margin of poverty is essential to reduce the extent of fuel poverty in France and relevant because the at-risk population can be clearly identified. For the population identified in the econometric analysis, the cost of energy is the factor that triggers poverty. Therefore, a specific policy could be implemented to help households located just below the poverty line and help them shift above the threshold. However, we realize that the precise targeting of policy intervention involves trade-offs 14 The random varying intercept model has been also estimated using the type of housing as cluster variable. For reasons of clarity, results have not been reproduced here, but are available on request. Results differ only slightly for the cooking energy variable. associated with targeting support at one group of households over another. This means that the very poor households under the after fuel cost poverty approach (17.59% that were already poor only based on their income level) are not eligible for fuel poverty support policies. However, we consider that this section of the population could benefit from broader transfer policies to improve their standard of living. In this perspective, the government's role is to deliver an effective policy that focuses on the roots of fuel poverty and drives action to alleviate the problem in the long term.

Finally our results suggest the way forward for the reduction of fuel vulnerability: vulnerable individuals cumulate financial hardships and low-energy efficient housing but are not poor a priori. Consequently, providing financial support for improving the housing energy efficiency could be a relevant measure to reduce the fuel vulnerability. However, until now policies to reduce fuel poverty were based mainly on the observation of the 10% ratio. We just explained above limitations of this ratio, and exposed why targeted fuel vulnerability would be more efficient.

Three broad types of policy are usually conducted to tackle fuel poverty: price-based, income-based and energy-efficiency improvement policies.

Price-based policy consists in reducing the price paid by households for energy. This type of policy is already applied in France, for example, through the social energy tariffs for lowincome households 15 , which have opened up the right to a reduction in electricity bills since 2005 and natural gas bills since 2008. At the end of 2012, more than 1.8 million French households benefitted from this measure. These aids are funded by all energy consumers. This policy would be expected to bring some households out of fuel poverty, reducing the headcount and the poverty gap. But there are limits to the application of this policy. The eligibility criteria are only based on households' income resources and not on fuel poverty indicators. In the econometric analysis, we emphasize the fact that it is crucial to look closely at energy costs related to disposal income. Also, targeting the type of energy used, or the type of heating equipment, both of which are factors that determine fuel vulnerability, is not taken into account. Moreover, as these measures are funded by energy consumers, they can negatively impact vulnerable households in hardship situations that do not benefit from these measures. The debate on whether interventions should be funded by energy consumers or taxes is important. The tax-funded option would allow policy funding to be progressive and better protect vulnerable consumers.

Policies that increase income would lead to reduced levels of fuel poverty. However, income transfer for low-income households could be rationally spent on any other expenditure. In France, with housing allowances that tackle poverty in general, poorer households can also receive an income supplement to help them cover expenditure on energy and water. This type of policy does not specifically focus on fuel-poor and vulnerable households. Also, such payments would only have a one-off impact on fuel poverty unless repeated. With such curative measures, root causes related to housing characteristics (types of heating system, absence of double glazed windows, poor insulation of the roof) are not addressed as they are limited in scope and were not designed for fuel vulnerable households. They do not represent a sustainable answer to fuel poverty reduction in France. In addition, the amount of such aids is too small (about 10% of the total energy bill). If these types of measures are to be implemented in the short term, they should be supplemented by preventive policies that focus on improving the energy efficiency of housing.

The main focus of fuel poverty policies should be to reduce the energy consumption of housing in order to sustainably reduce vulnerable households'energy bills. This is in line with the "Grenelle de l"environnement" objective to reduce energy consumptions by 38% in the housing stock by 2020. To reach this target, the government has introduced several 15 Since December 2012 monthly income should not exceed € 967 for a single person measures to incentivize energy-efficiency. The interest-free loan (L"éco-prêt à taux zéro) and the sustainable development tax credit (crédit d"impôt développement durable) are incentives to carry out renovation work or install efficient equipment. The first of these allows homeowners, without any income conditions, to borrow up to € 30,000 for renovation work in their main residence built before 1990. The second is for all households (tax payers, non-tax payers). They can deduct a percentage of their spending on energy efficiency improvements in their principal house from their taxable income (or receive a tax credit). These two tools aim to reduce energy consumption but as they do not focus on fuel poor households they are not well suited to reducing the extent of fuel poverty in France, especially because homeowners tend to be less fuel vulnerable according to our empirical work. In many cases, fuel poor households have a borrower profile that is not reassuring for banks that provide interest-free loans. These measures tend to benefit households with higher incomes. Similarly, accessing the sustainable development tax credit is difficult for low-income households that cannot usually afford to advance funds for renovation work.

We believe that if the policy maker clearly identifies those who are exposed specifically and uniquely because of fuel costs, it would be efficient in terms of fuel poverty reduction to provide them with incentives to save energy and carry out restoration works. This could take the form of aids for natural mains gas connection, subsidies for boiler replacements and roof and wall insulation, etc. Fuel poor households can be occupied by owners, landlords or tenants, and therefore the policy should not be too restrictive, and could be in some cases unrelated to the home's ownership. If one considers that the role of the welfare State is promote wellbeing and consequently to devote public spending to reduce fuel vulnerability, one can imagine agreements between the State and some boilers providers, some buildings craftsmen, etc., in order to propose equipments at an affordable price.

Conclusion

This paper estimates the scale of fuel poverty in France under diverse measures and identifies the vulnerable households at risk of falling into poverty only because of energy costs.

The three measurement approaches selected (the 10% approach, the Hills approach and the after fuel cost poverty approach) led to contrasting results in terms of the extent of fuel poverty and the composition of the fuel poor.

Based on the results of the French housing survey (Insee, 2006), the results show that 16.6% of the French population is fuel poor under the 10% approach, 20.9% under the after fuel cost poverty approach and 9.2% under the Hills approach. 7.76% of the population emerge as fuel poor according to the three approaches.

The approaches do not depict the same fuel poverty picture. The after fuel cost poverty approach, which is a more global approach to poverty, mainly captures active individuals who are tenants and usually living alone in apartments, while the two other approaches, focusing more on energy expenditure, tend to target inactive retirees who own their homes and live in detached houses with individual boilers as their main heating systems using domestic fuel. Furthermore, we conducted an income-based analysis in order to characterize the most vulnerable households. A renewed targeting of the fuel poor households was proposed in the empirical part of the paper. We identified those below the poverty line after the fuel bill and selected a sample of households that were not poverty exposed before the fuel bill. This enabled us to put a greater focus on individuals who fall into poverty solely as a result of energy costs. Logistic, complementary log-log and mixed effect logistic models were used to analyze the impact of certain households and dwelling characteristics on the probability of falling into poverty. This detailed consideration of the characteristics is important in understanding which type of households should be prioritized for support through policies.

The study suggests that living alone is associated with a high probability of falling into fuel poverty. Moreover, retired people living alone are significantly exposed to fuel poverty. Being a homeowner and highly educated is associated with lower exposure to fuel poverty. The heating system equipment and the type of energy used for cooking are key elements that influence the probability of falling into fuel poverty. Using an individual boiler and cooking with butane/propane are associated with a high probability of being fuel poor, while collective boilers, district heating systems and cooking with city gas (natural gas) seem to protect against fuel poverty. Moreover, a low energy performance home is a significant fuel poverty factor. Only housing built after 1974 (after the first thermal regulation in France) decreases the exposure to fuel poverty.

Our study points the way towards new research avenues. For the moment, the analysis is based on actual fuel expenditure because of a lack of data in France. Yet we cannot be sure that these costs are representative of an adequate level of well-being: would a household spend more to warm their dwelling if they could? We can assume so, because 29% to 36% of the fuel poor (depending on the definition) claim that they suffer from cold due to heating limitations. These heating limitations will be taken into account in further researches by using appropriate econometric estimates. Censored regression models, namely Tobit model, are designed to estimate the relationship between variables when there is censoring in the dependent variable. Source: Enquête Logement 2006, Key to reading: the marginal effects are calculated for a retiree, living alone, who is a homeowner with no children, the other variables being set at their reference value. A retiree living alone has a probability of 3.03% of falling into fuel poverty if he has an individual boiler, compared to other heating systems.

Marginal effect after complementary log-log model, for a retiree living alone, who is not homeowner, according to each heating system Confidence Interval 95% Source: Enquête Logement 2006, Key to reading: the marginal effects are calculated for an active adult living with one child and who is not a homeowner, with the other variables being set at their reference value. This single-parent family has a probability of 3,63% of falling into fuel poverty if it has an individual boiler, compared to other heating systems.

Marginal effect after complementary log-log model, for a family (active couple + 2 children) who do not own their home, according to each heating system Confidence Interval 95%

Risk of falling below the fuel poverty line [ ]

Individual boiler Yes=1 No=0 1,39% 0,68% 2,11%

District heating Yes=1 No=0 0,20% 0,00% 0,41%

Collective boiler Yes=1 No=0 0,13% 0,00% 0,21% Mixed heating Yes=1 No=0 0,35% 0,00% 0,69%

Heating individual electric convectors Yes=1 No=1 0,97% 0,48% 1,45%

Renewable energy Yes=1 No=1 0,50% 0,00% 0,99% Source : Enquête Logement 2006 Key to reading: the marginal effects are calculated for an active couple, living with 2 children and not homeowners, with the other variables being set at their reference value. This family has a probability of 1.39% of falling into fuel poverty if it has an individual boiler, compared to other heating systems.

Table 1 :

 1 Poverty rate, gap and severity

		Povert y rate	Pov erty gap	Sev erity	Poverty line (euros per CU)	Mean CU) income (euros per	Mean (euros per CU) income under the poverty line	N
	Gross Income	17.59% 0.05028 0.02316	9869.4	19631	7048.28
	Gross
	Income -	18.94%	0.06098 0.03083	8700.6	17607.53	5899.87
	housing costs							40136
	Gross
	Income -(housing costs	20.90%	0.07273 0.03994	8215.14	16685	5356.58
	+ energy cost)

Table 1 Results of the complete estimates: probability to be fuel vulnerable in the population not poor before the energy bill

 1

	Logit	Odd ratio	C log log	Hazard ratio
	Active couple
	Yes=1 No=0

Appendix A Characteristics of the fuel poor under three different measures

  33% of the population is retired, while 54 and 45% are pensionners among fuel poor according respectively to the 10% and the Hills "approaches. They are consequently overrepresented among fuel poor defined using these definitions. On the contrary, they are only 30 among the fuel poor according to the after fuel cost approach.

		Butane, propane	2.57%	7.14%	4.82%	3.90%
		Coal	0.42%	0.46%	0.23%	0.32%
		Wood Electricity Others	1.79% Poor (after fuel cost poverty approach) 5.73% 1.48%	2.70% Poor (10% ratio approach) 3.81% 0.00%	2.15% Poor (Hills 5.19% approach) 0.00%	2.19% 4.06% Population 0.10%
		Farmers City gas	1% 20%	2% 21%	2% 25%	1% 25%
		Shopkeepers, Butane Propane	43%	39%	38%	24%
	Professional Energy used for cooking categories of the head of household	Craftspeople, entrepreneurs Electricity Electricity and City gas Managers and profess. Electricity and Butane occupations Intermediate Other occupations Employees Insufficient heating equipment	4% 12% 5% 3% 18% 8% 2% 19% 38%	4% 16% 6% 2% 17% 5% 1% 11% 30%	4% 16% 7% 3% 12% 6% 1% 14% 34%	4% 27% 11% 12% 12% 0% 16% 14% 32%
	% of respondents	Blue collar workers Equipment breakdown	21% 12%	12% 13%	16% 13%	16% 19%
	claiming to suffer from cold due	Pensioners Other inactive people Heating under-consumption	30% 14% 29%	54% 10% 36%	45% 10% 36%	33% 4% 21%
	to…	Person living alone Poor insulation	43% 45%	49% 43%	48% 47%	33% 41%
	Other reasons Multi-person households Single parent with dependent children Source: Enquête Logement 2006, 7% 11% 4% 4% 12% 8% Family (with or without children) 40% 40% Homeowner (with or without mortgage) 32% 66% Rent free 4% 5% Tenant 63% 29% Key to read: Appendix B Household composition Housing occupation status	8% 3% 10% 38% 53% 4% 43%	15% 3% 6% 58% 59% 4% 37%
		Detached house	43%	76%	71%	58%
		Flat	54%	22%	27%	41%
		Room in a collective
	Dwelling type	structure (seniors	1%	0%	0%	0%
		residence, group home)
		Farm	0%	1%	0%	0%
		Others	2%	1%	1%	1%
		Individual boiler	38%	65%	60%	47%
		District heating	2%	0%	0%	2%
		Collective boiler	21%	4%	3%	16%
		Mixed boiler
	Heating system	(collective + individual	1%	0%	0%	1%
		heating)
		Individual electric heating	30%	23%	27%	27%
		None of the above	8%	8%	5%	6%
	Energy type for	Domestic fuel	25.15%	45.92%	36.35%	30.37%
	individual boiler	City gas	62.86%	41.27%	52.87%	59.06%

Descriptive statistics of sample selected for the estimates

	District heating system Collective boiler Intercept	0,68% 0,28% -3,701*** (0,179)	0,00048 0,00038 -3,650*** (0,150)	0,00004 0,0001 -3,560*** (0,171)	-3,940*** (0,192)	-3,839*** (0,262)
	Mixed heating system N	0,15%	0,00001	26531	0
	LL	-2914.4	-2783.0	-2779.8		-2718.6	-2714.5
	Heating individual electric convectors	2,16% * p<0.1;** p<0.05; *** p<0.01. 0,00113	0,00012
		Robust standard errors are reported in brackets
	Renewable energy	0,48%	0,00073	0,00014
	Cooking : town gas stream	2,36%	0,00159	0,00023
	Appendix D:
	Cooking : butane and propane	4,95%	0,0036	0,00058
	Cooking: electricity only	1,19%	0,00073	0,00011
	Cooking :Electricity and town gas stream	1,17%	0,00082	0,0001
	Cooking: Electricity and butane/propane	3,88%	0,00346	0,00059
	Housing constructed before 1950	3,67%	0,00269	0,00041
	Housing constructed between 1950 and 1974	2,50%	0,00181	0,00025
	Housing constructed after 1974	1,92%	0,00145	0,00027
	Climate zone 1	3,33%	0,00241	0,00036
	Climate zone 2	2,25%	0,0017	0,00025
	Climate zone 3	3,34%	0,00231	0,0004
	Climate zone 4	2,70%	0,00208	0,00037
	Double glazed Poor insulation of the roof	Poverty rate 2,35% 6,50%	0,00161 Poverty gap 0,00508	0,00025 Poverty severity 0,00077
	Couple of active people	0,86%	0,00052	0,00008
	Retired couple Entire sample Lone active N	2,89% 2,76% 2,07%	0,00204 0,00203 0,00133 26531	0,00032 0,00025 0,00016
	Lone retired	6,93%	0,00562	0,00093
	Having dependant children	1,78%	0,00091	0,00013
	Homeowners	2,84%	0,00252	0,00043
	No diploma	6,96%	0,00471	0,00059
	Intermediate educational attainment	0,76%	0,00052	0,00007
	High educational attainment	0,62%	0,00053	0,00009
	Individual boiler	3,73%	0,0029	0,00048

marginal effects after complementary log-log model

  Marginal effect after complementary log-log model, for a retiree living alone, homeowner, according to each heating system

			Confidence Interval 95%
		Risk of falling below the fuel poverty line	[	]
	Individual boiler Yes=1 No=0	3,03%	1,62%	4,43%
	District heating Yes=1 No=0	0,44%	-0,04%	0,92%
	Collective boiler Yes=1 No=0	0,28%	0,05%	0,51%
	Mixed heating Yes=1 No=0	0,76%	0,08%	1,44%
	Heating individual electric convectors Yes=1 No=1	2,10%	1,16%	3,05%
	Renewable energy Yes=1 No=1	1,08%	-0,58%	2,75%

  Key to reading: the marginal effects are calculated for a retiree, living alone, who is not homeowner and has no children, the other variables being set at their reference value. A retiree living alone has a probability of 5.39% of falling into fuel poverty if he has an individual boiler compared to other heating systems.Marginal effect after complementary log-log model, for a single parent family (1 active adult) with 1 child, who are not homeowners, according to each heating system

			Confidence Interval 95%
		Risk of falling below the fuel poverty line	[	]
	Individual boiler Yes=1 No=0	3,63%	2,29%	4,97%
	District heating Yes=1 No=0	0,53%	0,00%	1,05%
	Collective boiler Yes=1 No=0	0,34%	0,13%	0,55%
	Mixed heating Yes=1 No=0	0,92%	0,00%	1,85%
	Heating individual electric convectors Yes=1 No=1	2,53%	1,54%	3,52%
	Renewable energy Yes=1 No=1	1,30%	0,00%	2,88%
		Risk of falling below the fuel poverty line	[	]
	Individual boiler Yes=1 No=0	5,39%	3,05%	7,74%
	District heating Yes=1 No=0	0,79%	0,00%	1,58%
	Collective boiler Yes=1 No=0	0,50%	0,17%	0,84%
	Mixed heating Yes=1 No=0	1,37%	0,23%	2,51%
	Heating individual electric convectors Yes=1 No=1	3,76%	1,81%	5,71%
	Renewable energy Yes=1 No=1	1,95%	-0,65%	4,54%
	Source : Enquête Logement 2006,

Loi n°

2010-788 du 12 juillet 2010 portant sur l"engagement national pour l"environnement. 2 This complementary fuel poverty measure is not included in the law.

In this study the notion of "vulnerability" does not encompass a range of wellbeing and social issues, such as older people, the long-term sick and disabled people, etc. Vulnerable households are those for which the energy cost is the triggering poverty factor.

The consequence is that energy expenditures might be under-estimated compared to those which could provide an adequate level of thermal comfort. This limitation will be treated in further works with appropriate econometric specifications.

6,84%+7,76%+2%

Household annual gross income here is not deflated by the number of consumption units in the households

According to the French Statistical Office (INSEE), the poverty rate, calculated after redistribution attained 13.1% in 2006. We calculate in this paper the poverty headcount using the gross income per consumption unit while official statistics provide poverty rate the net income per unit of consumption (after redistribution).

7048,28/19631=0,359

In France, retirees enjoy in average a standard of living close to that of workers.

Hazard ratios reported here were computed with the estimates including all variables, socio economics and characterizing the housing.

When calculating the marginal effects, the other variables not mentioned are set at their average value or at their reference value.

-1,416*** 0,243*** -1,380*** 0,251*** (0,14) (0,126) Retired couple Yes=1 No=0 -0,332* 0,717* -0,327* 0,721* (0,168) (0,135) Active living alone Yes=1 No=0 -0,208 0,812 -0,198* 0,819 (0,116) (0,110) Retired living alone Yes=1 No=0 0,444*** 1,558*** 0,417*** 1,518*** (0,114) (0,117) Children in the household 0,223*** 1,249*** 0,211*** 1,235*** (0,0526) (0,037) Homeowner Yes=1 No=1 -0,625*** 0,535*** -0,590*** 0,554*** (0,0934) (0,071) No diploma Yes=1 No=0 1,050*** 2,858*** 1,010*** 2,746*** (0,153) (0,156) Low level of diploma Yes=1 No=0 0,420*** 1,522*** 0,415** 1,514** (0,135) (0,159) A level Yes=1 No=0 Ref. Ref. Ref. Ref. Intermediate educational level -0,382 0,682 -0,372 0,688 (0,222) (0,232) Master's degree -0,910*** 0,402*** -0,896*** 0,408*** (0,240) (0,211) Individual boiler Yes=1 No=0 0,492*** 1,635*** 0,477*** 1,612*** (0,113) (0,097) District heating Yes=1 No=0 -1,492** 0,225** -1,467** 0,230** (0,448) (0,572) Collective boiler Yes=1 No=0 -1,943*** 0,143*** -1,918*** 0,147*** (0,259) (0,321) Mixed heating Yes=1 No=0 -0,934* 0,393 -0,913* 0,401* (0,445) (0,424) Active couple Yes=1 No=0 -1,336*** -1,435*** -1,433*** -1,465*** -1,465*** (0,137) (0,123) (0,124) (0,100) (0,128) Retired couple Yes=1 No=0 -0,269 -0,311* -0,325* -0,347* -0,347* (0,143) (0,134) (0,137) (0,163) (0,131) Active living alone Yes=1 No=0 -0,320** -0,230 -0,234* -0,201 -0,201 (0,115) (0,116) (0,116) (0,126) (0,143) Retired living alone Yes=1 No=0 0,475*** 0,530*** 0,508*** 0,531*** 0,531*** (0,116) (0,114) (0,122) (0,129) (0,117) Children in the household 0,228*** 0,201*** 0,200*** 0,190*** 0,190*** (0,0448) (0,0427) (0,0363) (0,0549) (0,0399) Homeowner Yes=1 No=1 -0,214* -0,499*** -0,490*** -0,587*** -0,587*** (0,0887) (0,114) (0,0810) (0,0827) (0,0847) No diploma Yes=1 No=0 1,091*** 1,157*** 1,145*** 1,035*** 1,035*** (0,141) (0,153) (0,152) (0,127) (0,170) Low level of diploma Yes=1 No=0 0,455** 0,479** 0,481** 0,397** 0,397** (0,148) (0,141) (0,155) (0,120) (0,153) Active couple Yes=1 No=0 -1,311*** -1,401*** -1,398*** -1,429*** -1,408*** (0,133) (0,146) (0,144) (0,138) (0,101) Retired couple Yes=1 No=0 -0,264 -0,305* -0,319** -0,341* -0,322** (0,155) (0,119) (0,110) (0,135) (0,121) Active living alone Yes=1 No=0 -0,312* -0,220 -0,225 -0,194 -0,172 (0,146) (0,129) (0,139) (0,154) (0,096) Retired living alone Yes=1 No=0 0,463*** 0,512*** 0,490*** 0,504*** 0,518*** (0,129) (0,123) (0,102) (0,116) (0,117) Children in the household 0,221*** 0,192*** 0,190*** 0,183*** 0,184*** (0,0425) (0,0387) (0,0407) (0,0445) (0,0407) Homeowner Yes=1 No=1 -0,206* -0,481*** -0,472*** -0,561*** -0,555*** (0,0965) (0,0645) (0,0883) (0,102) (0,0691) No diploma Yes=1 No=0 1,067*** 1,123*** 1,111*** 1,002*** 0.988*** (0,139) (0,160) (0,169) (0,140) (0,124) Low level of diploma Yes=1 No=0 0,448*** 0,471*** 0,472*** 0,392** 0,392*** (0,122) (0,134) (0,135) (0,140) (0,111) Intermediate educational level Yes=1 No=0 -0,399* -0,405 -0,406 -0,379* -0,373 (0,192) (0,245) (0,286) (0,168) (0,203) Master's degree -0,979*** -0,978*** -0.989*** -0,881*** -0,859*** (0,211) (0,192) (0,226) (0,183) (0,129) Individual boiler Yes=1 No=0 0,384*** 0,347*** 0,573*** 0,571*** (0,0879) (0,102) (0,116) (0,123) District heating Yes=1 No=0 -1,825*** -1,866*** -1,509*** -1,469*** (0,478) (0,555) (0,456) (0,532) Collective boiler Yes=1 No=0 -2.224*** -2.268*** -1,927*** -1,907*** (0,254) (0,345) (0,311) (0,331) Mixed heating Yes=1 No=0 -1.258** -1,192* -0,994** -0.963* (0,436) (0,463) (0,451) (0,445)

A level Yes=1 No=0 Ref. Ref. Ref. Ref. Ref. Intermediate educational level Yes=1 No=0 -0,403 -0,411 -0,412 -0,388 -0,381* (0,222) (0,230) (0,238) (0,211) (0,194) Master's degree Yes=1 No=0 -0,986*** -0,989*** -1,000*** -0,891*** -0,891*** (0,237) (0,277) (0,216) (0,202) (0,220) Individual boiler Yes=1 No=0 0,393*** 0,355*** 0,592*** 0,592*** (0,080) (0,102) (0,105) (0,125) District heating Yes=1 No=0 -1,857*** -1,900*** -1,536* -1,536** (0,518) (0,575) (0,744) (0,468) Collective boiler Yes=1 No=0 -2.254*** -2.301*** -1,953*** -1,953*** (0,225) (0,327) (0,254) (0,402) Mixed heating Yes=1 No=0 -1.285* -1,221** -1,017** -1,017* (0,507) (0,421) (0,366) (0,426) Heating individual electric convectors Yes=1 No=1 Ref. Ref. Ref. Ref. Other type of heating system Yes=1 No=1 0,460* 0,408* 0,273 0,273 (0,181) (0,180) (0,162) (0,163) Renewable energy Yes=1 No=1 -0,748 -0,715 -0,665 -0,665 (0,600) (0,597) (0,558) (0,574) Housing constructed before 1949 Yes=1 No=1

Appendix C: Presentation of partial results

Logit

(