Dorothée Charlier
email: dorothee.charlier@univ-smb.fr

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

Fuel Poverty and Health: A Shared Agenda for Policy

Keywords: Fuel poverty, Health, Poor housing Quality, Panel dataset JEL codes: C33, I14, Q41

Précarité énergétique et santé : pour un programme politique commun ?

Le changement climatique et la promotion de la santé publique sont aujourd'hui au coeur des préoccupations des citoyens et des gouvernements. Dans ce papier, nous contribuons à la littérature en évaluant le lien entre précarité énergétique et santé sur longue période. À l'aide de modèles probit dynamiques, nous examinons l'influence de la précarité énergétique sur la santé. Nous contrôlons la persistance de l'état de santé car nous considérons que l'état de santé est étroitement lié aux trajectoires de santé antérieures. L'état de santé et la précarité énergétique pouvant être affectées simultanément d'hétérogénéité non observée, nous corrigeons le biais d'endogénéité qui pourrait affecter nos résultats. Nous concluons que le fait d'être énergétiquement précaire multiplie par 7 le risque de mauvaise santé pour les individus dont la santé est déjà mauvaise et par 1,82 pour les individus en bonne santé. Lutter contre la précarité énergétique permet donc non seulement d'améliorer le bien-être des individus dans leur logement mais également leur santé, et donc d'éviter des coûts en santé.

Mots clés: Précarité énergétique; Santé; Mauvaise qualité de l'habitat; Panel dynamique Codes JEL: C33; I14; Q41 Protecting and improving health and mitigation of climate change have a shared agenda. In this paper, we contribute to the literature by assessing the link between fuel poverty and health over a lengthy recent period. Using dynamic probit models, we examine the influence of fuel poverty on health. We control for state dependency of health as we regard health status to be closely related to previous health trajectories. Considering that unobserved heterogeneity might influence health status and fuel poverty simultaneously, we have corrected for the endogeneity bias that could affect our results. We conclude that being fuel-poor increases the risk of bad health by slightly more than a factor of 7 for those whose health is already poor and by 1.82 for those in good health. For policy makers, combatting fuel poverty reduces sources of discomfort which might also severely affect the health of a dwelling's inhabitants, and reduce health spendings.

1/ Introduction

Protecting and improving health and mitigation of climate change have a shared agenda. Public policies intended to respond to climate change can help reduce health problems. Various policies can reduce greenhouse gas emissions and produce important health co-benefits [START_REF] Zivin | Environment, Health, and Human Capital[END_REF] notably through retrofitting of housing (WHO Regional Office for Europe, 2004). In northern countries, many households live in homes that have poor thermal conditions and are therefore expensive to heat, accounting for a substantial share of emissions which in turn contribute to climate change. Inadequate thermal performance and ventilation of existing buildings are two of the biggest challenges for the European housing sector with respect to the sustainability and health of the built environment. Moreover, recent research has demonstrated that it is possible to improve indoor environmental quality, health and well-being of building occupants along with improved energy efficiency [START_REF] Pampuri | Effects of buildings' refurbishment on indoor air quality. Results of a wide survey on radon concentrations before and after energy retrofit interventions[END_REF][START_REF] Prasauskas | Effects of Energy Retrofits on Indoor Air Quality in Three Northern European Countries[END_REF][START_REF] Rashid | A Review of the Empirical Literature on the Relationships Between Indoor Environment and Stress in Health Care and Office Settings: Problems and Prospects of Sharing Evidence[END_REF][START_REF] Stabile | The effect of the ventilation retrofit in a school on CO2, airborne particles, and energy consumptions[END_REF].

This paper makes three contributions to the literature. Our first objective is to contribute to the literature by assessing the link between fuel poverty and health over a lengthy recent period (2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016). Identifying a precise, direct and mid-term link between fuel poverty and health seems crucial in the design of relevant public policies. Households affected by fuel poverty are not always the same as those affected by monetary problems, even if the two phenomena are inextricably linked, representing an aspect of multidimensional poverty [START_REF] Legendre | Measuring fuel poverty in France: Which households are the most fuel vulnerable?[END_REF]. Income poverty is now much studied in the literature, but its multiple dimensions sometimes require more in-depth study of certain aspects of deprivation, such as fuel poverty or the notion of health poverty [START_REF] Clarke | Defining and measuring health poverty[END_REF]. Fuel poverty has generally been treated as a monetary poverty problem [START_REF] Charlier | A Multidimensional Approach to Measuring Fuel Poverty[END_REF]. Thus, like income poverty, energy poverty can be defined by the minimum energy consumption needed to sustain life. But unlike income poverty, which is based on the concept of a poverty line defined by the minimum consumption of food and non-food goods and services necessary to sustain a livelihood, energy poverty lacks a well-established energy poverty line to determine the minimum amount of energy needed for living. Moreover, a fuel-poor household may not be poor in monetary terms, and face difficulty in sustaining its energy needs. In that sense, energy poverty differs from monetary poverty. Low-income households may have difficulty paying for energy due to the poor thermal conditions of the buildings they occupy combined with rising energy prices, and therefore restrict their energy consumption. These households are considered to be fuel-poor [START_REF] Boardman | Fuel Poverty: From Cold Homes to Affordable Warmth[END_REF][START_REF] Boardman | Fixing Fuel Poverty: Challenges and Solutions[END_REF][START_REF] Hills | Fuel Poverty: The problem and its measurement. Interim Report of the Fuel Poverty Review, Centre for Analysis and Social Exclusion[END_REF][START_REF] Hills | Getting the measure of fuel poverty. Hills Fuel Poverty Review: Centre for Analysis and Social Exclusion[END_REF] and are subject to increased health problems due to the inferior energy performance of the buildings they live in.

Second, in this paper, we want to provide a better understanding of the profile of households in poor health in order to help policy makers prevent other households from falling into this state and reduce future health expenditures. Implementing an effective policy implies anticipating both intermediate and final objectives: tackling fuel poverty as the intermediate objective and improving public health as the final objective. The literature shows that poor material conditions can cause health degradation [START_REF] Adena | Poverty and transitions in health in later life[END_REF]. Studies also demonstrate that improving housing insulation and decreasing carbon emissions seems to be particularly important especially for public health: energy efficiency has been linked to an extensive range of health benefits and to flow on outcomes for psychosocial functioning in society [START_REF] Naess | Air Pollution, Social Deprivation, and Mortality: A Multilevel Cohort Study[END_REF][START_REF] Wilkinson | A global perspective on energy: health effects and injustices[END_REF]. [START_REF] Haines | Public health benefits of strategies to reduce greenhouse-gas emissions: overview and implications for policy makers[END_REF] examined the effect of hypothetical strategies to improve energy efficiency in UK housing stock, assuming that low energy efficiency is also correlated with higher air pollution. They conclude that such interventions were generally beneficial for health: a strategy of combined fabric, ventilation, fuel switching, and behavioral changes implied 850 fewer disability-adjusted life-years (DALYs), and a saving of 0.6 megatons of carbon dioxide (CO2), per million populations in 1 year. This result suggests that household energy interventions could allow important benefits in pursuit of both health and climate goals. Therefore, studying fuel poverty, covering issues of housing quality, income and consumption patterns, will make it possible to focus on one aspect of the material difficulties that households may experience.

Third, we explore empirically the impact of being fuel poor on health using a panel dataset controlling for endogeneity, state dependency of health and initial conditions, which is to our best knowledge relatively new in this field of literature. Indeed, the literature on the relationship between fuel poverty and health is quite limited, while research into the determinants of health is extensive. We focus on the French situation where the direct medical cost related to poor housing is estimated to be 930 million euros (Eurofound, 2016). The indirect annual costs are estimated to be 20.3 billion euros. Using a panel data (EU-SILC) lets us to consider individual health and household fuel poverty trajectories, but also to avoid obtaining results affected by 1-year climate variables. Advantages of panel dataset are numerous such as a greater capacity for modeling the complexity of human behavior than a single cross-section [START_REF] Ben-Porath | Labor force participation rates and the supply of labor[END_REF] or more accuracy of inference of model parameters [START_REF] Hsaio | Bayesian integration of end-use metering and conditional demand analysis[END_REF]. Based on the example of [START_REF] Ben-Porath | Labor force participation rates and the supply of labor[END_REF] where a woman's work status is a perfect predictor of her future work status, we consider that an individual's self-assessed health status is a good predictor of its future health status. A cross-sectional data is not able to distinguish between these two possibilities, but panel data can because the sequential observations for a number of individuals contain information about their health problems in different subintervals of their life cycle. Using dynamic probit models, so we can test the influence of fuel poverty on health. Moreover, health state dependence can also serve as an explanation for observed spending phenomena, such as the decreasing consumption path in old age [START_REF] Börsch-Supan | Life cycle savings and consumption constraints -Theory, empirical evidence, and fiscal implications[END_REF]. Thus, we controlled for state dependency of health as we consider health status to be closely related to health status in the previous year. We also controlled for initial conditions: those found to be fuel poor in the base year may be a non-random sample [START_REF] Cappellari | Modelling low income transitions[END_REF][START_REF] Heckman | The Incidental Parameters Problem and the Problem of Initial Conditions in Estimating a Discrete Time -Discrete Data Stochastic Process[END_REF] Considering that unobserved heterogeneity might have an impact on health status and fuel poverty simultaneously, we corrected for the endogeneity bias that could affect our results. In order to improve the living conditions of households in fuel poverty, both short-and long-term policies are needed. Supplementing the household income and reducing energy costs will help in the short term but improving the energy efficiency of housing (e.g. modernizing heating systems, installing thermal insulation) is the long-term solution to address fuel poverty and its health consequences. Energy-efficient housing not only has benefits for the health of occupants, but also for society as a whole. Thus, governments could see a double benefit in energy retrofitting: an environmental gain and a reduction in health care costs.

The next section presents the existing literature on the relationship between energy efficiency and health. The theoretical background is then introduced. Data are presented in the fourth section, and the empirical strategy is introduced in the fifth section. The results are presented in Section 6, along with a key policy recommendation. We conclude in Section 7.

Methods

Literature on energy efficiency and health

The literature extensively documents the impact of cold, damp housing and mold on health [START_REF] Maidment | The impact of household energy efficiency measures on health: A meta-analysis[END_REF][START_REF] Peat | Effects of damp and mould in the home on respiratory health: a review of the literature[END_REF][START_REF] Platt | Damp housing, mould growth, and symptomatic health state[END_REF]. There is much evidence that poor housing conditions, combined with financial constraints may worsen both mental and physical health [START_REF] Hills | Getting the measure of fuel poverty. Hills Fuel Poverty Review: Centre for Analysis and Social Exclusion[END_REF]Hunt, 1988;[START_REF] Maidment | The impact of household energy efficiency measures on health: A meta-analysis[END_REF][START_REF] Platt | Damp housing, mould growth, and symptomatic health state[END_REF][START_REF] University College | The health impacts of cold homes and fuel poverty[END_REF]. Persistently low temperatures in housing lead to respiratory tract infections and coronary problems, increased blood pressure, worsening arthritis, along with more frequent accidents in the home and adverse effects on children's education and nutrition (National Heart Forum, 2003). Dampness and mold that accumulate in cold homes increase respiratory symptoms including asthma, coughing and wheezing [START_REF] Dales | Respiratory Health Effects of Home Dampness and Molds among Canadian Children[END_REF][START_REF] Jaakkola | Home Dampness and Molds, Parental Atopy, and Asthma in Childhood: A Six-Year Population-Based Cohort Study[END_REF][START_REF] Peat | Effects of damp and mould in the home on respiratory health: a review of the literature[END_REF]. In their metaanalysis [START_REF] Fisk | Meta-analyses of the associations of respiratory health effects with dampness and mold in homes[END_REF] conclude that dampness and mold are associated with increases of 30-50% in respiratory and asthma-related health problems. Cold and damp housing may also affect well-being and cause stress and depression in its inhabitants [START_REF] Khanom | Cutting the Cost of Cold -Affordable Warmth for Healthier Homes[END_REF][START_REF] Lowry | Housing and Health: British Medical Journal[END_REF][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]. Poor-quality housing can expose households to cancer risks , due to exposure to radon, or to formaldehyde from combustion or off-gassing [START_REF] Braubach | Environmental burden of disease associated with inadequate housing: a method guide to the quantification of health effects of selected housing riss in the WHO European Region[END_REF]. Thus, improving housing reduces health problems. In an experiment conducted in south Devon in the UK, [START_REF] Barton | The Watcombe Housing Study: the short term effect of improving housing conditions on the health of residents[END_REF] concluded that improving heating and insulation reduces chest problems and asthma symptoms, at least in the short term. After conducting a fuel poverty program in 54 rural homes in Ireland, [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] showed that the installation of central heating systems and development of energy-efficiency awareness led to a significant decrease in both the numbers of householders reporting arthritis/rheumatism and other forms of illness. A pilot study in Cornwall established that installation of central heating was an effective measure for reducing nocturnal cough and asthma in children, and consequently time lost from school [START_REF] Sorrell | Empirical estimates of the direct rebound effect: A review[END_REF]. Other studies have demonstrated the general impact of fuel poverty on health [START_REF] Liddell | Fuel poverty and human health: A review of recent evidence[END_REF].

Public policies such as retrofitting and saving energy pursue an intermediate objective which is the reduction of fuel poverty, but also have an impact on public health as a final objective. For households, retrofitting increases comfort, as housing conditions are improved.

The literature includes many case studies which were carried out with experimental data. Some of them explore the direct impact of retrofitting plans, housing improvements and/or energy-saving programs on health3 [START_REF] Chapman | Retrofitting houses with insulation: a cost-benefit analysis of a randomised community trial[END_REF][START_REF] Howden-Chapman | Warmer houses reduce children's asthma[END_REF][START_REF] Lloyd | The efficacy of an energy efficient upgrade program in New Zealand[END_REF] [START_REF] Chapman | Retrofitting houses with insulation: a cost-benefit analysis of a randomised community trial[END_REF][START_REF] Ezratty | Liens entre l'efficacité énergétique du logement et la santé des résidents : résultats de l'étude européenne LARES[END_REF][START_REF] Thomson | Quantifying the prevalence of fuel poverty across the European Union[END_REF]. Others do not measure the impact on health but assess domestic energy use after retrofitting in order to estimate the likely health impact of an intervention from an intermediate outcome, such as temperature [START_REF] Pollard | Use of Simple Telemetry to Reduce the Health Impacts of Fuel Poverty and Living in Cold Homes[END_REF] or air quality and carbon emissions [START_REF] Rosenow | Evaluating the evaluations: Evidence from energy efficiency programmes in Germany and the UK[END_REF]. Some studies evaluate the actual impact of energy consumption and fuel poverty [START_REF] Rosenow | Evaluating the evaluations: Evidence from energy efficiency programmes in Germany and the UK[END_REF] [START_REF] Grimes | Does Retrofitted Insulation Reduce Household Energy Use? Theory and Practice[END_REF][START_REF] Webber | The impacts of household retrofit and domestic energy efficiency schemes: A large scale, ex post evaluation[END_REF].

Case studies and experiments make it possible to precisely evaluate the impact of policies on a given region at a particular point in time, thus providing useful guidance for designing or improving public policy. However, they fail to establish a clear causal relationship between fuel poverty and health in the absence of any retrofitting, energy-saving measures or housing improvements. When non-experimental studies confirm a link between fuel poverty and health [START_REF] Chaton | Does France have a fuel poverty trap?[END_REF][START_REF] Lacroix | Fuel poverty as a major determinant of perceived health: the case of France[END_REF][START_REF] Liddell | Fuel poverty and human health: A review of recent evidence[END_REF], the results are based on cross-sectional data, ignoring in most cases the effects of health trajectories and climate hazards on fuel poverty. Only [START_REF] Oliveras | Energy poverty and health: Trends in the European Union before and during the economic crisis 2007-2016[END_REF], recently provided a panel analysis to highlight the impact of the crisis on the EP-health relationship in Europe using longitudinal data. The effects of climate hazards are then determined by conducting an evaluation ex-ante, and/or ex-post and by carrying out a nonexperimental study. However, existing literature neglects the health state dependence. We propose then to use panel data in order to consider in the analysis the climate hazard and the health state dependence.

Data

In this study, we wish to shed light on the potential causal effect of energy precariousness on the health of individuals. Thus, econometric analysis was conducted using the French portion of the EU-SILC4 database (European Union -Community Statistics on Income and Living Conditions). We chose data from 2008 until 2016, which is the last survey to date. This time frame was selected since the year 2008 marked significant changes, such as improving the accuracy of household resources using data from public institutions, and specifying the type of energy used inside dwellings instead of a global indicator, which is fundamental to the construction of relevant fuel poverty indicators [START_REF] Hills | Fuel Poverty: The problem and its measurement. Interim Report of the Fuel Poverty Review, Centre for Analysis and Social Exclusion[END_REF][START_REF] Hills | Getting the measure of fuel poverty. Hills Fuel Poverty Review: Centre for Analysis and Social Exclusion[END_REF]. The database also includes some health indicators, such as self-assessed health condition, the presence of chronic diseases and handicaps, potentially unfulfilled needs to see a specialist and the reasons for this, and other health-related variables, thus providing a good set of tools for describing and controlling the effect of fuel poverty on health. The database also contains many variables characterizing socio-economic status, demographic status and living conditions related to housing and energy use of individuals, thus provides a solid basis for assessing health and fuel poverty under the many aspects and definitions reviewed in the literature. The entire sample consisted of 239,477 observations over nine years.

Fuel poverty indicators

Our health indicator is the self-assessed health status of the respondents; this will be the binary dependent variable, with 1 for poor health. Considering this indicator of self-assessed health encompasses more than just an assessment of an individuals' physical health [START_REF] Bassett | Probability Limits: Are Subjective Assessments Adequately Accurate?[END_REF]. For example, cultural differences may explain some heterogeneity between self-reported measures of health [START_REF] Meijer | Internationally comparable health indices[END_REF]. Sometimes used with more objective measures, self-assessed health has been shown to improve both inference and predictability of outcomes in a variety of situations. However, questions that rely on self-assessment are now commonplace in health surveys where researchers have demonstrated their usefulness as a proxy for objective health measures when the latter are not readily observed [START_REF] Damian | Determinants of self assessed health among Spanish older people living at home[END_REF][START_REF] Pinquart | Correlates of subjective health in older adults: A meta-analysis[END_REF]. According to [START_REF] Simon | How is your health in general? A qualitative study on self-assessed health[END_REF], 80% of respondents referred to one or more physical aspects (chronic illness, physical problems, medical treatment, age-related complaints, prognosis, bodily mechanics, and resilience) when answering the question 'How is your health in general?' They also include aspects that go beyond the physical dimension of health. Thus, self-assessed health can let us to consider several consequences of fuel poverty on health in general, physical but also mental illness. Finally, authors also demonstrate that health behaviour or lifestyle factors (behavioural dimension) are relatively unimportant in health self-assessments.

In our study, some 8.3% of individuals declared a status of poor health over the period studied. While a categorical self-assessed health variable is a wide measure of one's mental and physical condition, its reliability could be questionable [START_REF] Crossley | The reliability of self-assessed health status[END_REF]. However it remains one of the best tools available to measure health as it predicts future mortality and morbidity adequately [START_REF] Idler | Self-Ratings of Health: Do they also Predict change in Functional Ability[END_REF][START_REF] Lundberg | Assessing reliability of a measure of self-rated health[END_REF]. We also use a stated binary variable for chronic disease as a control (robustness check); 37.3% of individuals in the sample report a chronic disease. A chi square test of independence shows that having a chronic disease is not independent from declaring a status of poor health. Among people who declared a status of poor health, 94% had a chronic disease. In this study, we are interested in the possible continuity of health status. In our sample, the 95.9% of individuals who reported a status of good health, reported this over the entire period. Only 4.1% of individuals saw their health deteriorate, whereas 41% reported a status of poor health at the beginning of the period and saw their health improve.

To measure fuel poverty, we chose to apply the most common indicators of fuel poverty defined and used in the literature (which will be our main predictors): the 10% ratio 5 [START_REF] Boardman | Fuel Poverty: From Cold Homes to Affordable Warmth[END_REF] and Low Income High Costs (LIHC) 6 [START_REF] Hills | Fuel Poverty: The problem and its measurement. Interim Report of the Fuel Poverty Review, Centre for Analysis and Social Exclusion[END_REF][START_REF] Hills | Getting the measure of fuel poverty. Hills Fuel Poverty Review: Centre for Analysis and Social Exclusion[END_REF]. Both of these measures are calculated based on the standard of living 7 (SL) of the households observed rather than the disposable income of the household. When standard indicators incorporate income to measure fuel-poverty, it is necessary to define precisely what definition of income is used, standard of living (Standard of living is the material well-being of the average person in a given population) or disposable income (i.e. income minus taxes and social contributions).The 10% ratio permits comparisons and serves as a reference. We built it by aggregating electricity, natural gas and other heating expenditures whether or not included in the rent, and calculating its share of the SL which gives us the energy effort rate of individuals, and compared it to the 10% threshold, resulting in a binary variable (1=fuel poor, 0=not fuel poor). There is some criticism in the literature about this measure of fuel poverty, mainly due to the fact that high income individuals who spend a lot on energy can be considered to be fuel poor while being nowhere near fuel poverty socially speaking [START_REF] Healy | Fuel poverty in Europe A cross-country analysis using a new composite measurement[END_REF], so we have also compared our results with the LIHC indicator 8 . We did this by comparing an individual's SL to a poverty threshold 9 on the one 5 Based on the first measure used in the UK, 10% representing the ratio between the double median (we take the median value of expenditures and multiply it by two) of heating energy expenditure of the population and their income. If one's own ratio is over this threshold, then the individual is considered to be fuel poor. 6 The LIHC is used in the analysis to prove the robustness of results obtained later. 7 Disposable income / consumption unit (OECD equivalent scale) 8 Due to the cultural heterogeneity of European countries, as well as EU resistance to acknowledge a pan-European definition of fuel poverty (Thomson et al., 2017), the debate on how to measure it precisely and exhaustively is still raging. Our objective in this paper is not to discuss measurement of fuel poverty, but to determine if fuel-poor individuals have a worse health status that those who are not fuel-poor. 9 This particular threshold is fixed at 60% of the median of income after energy costs by consumption unit.

hand and then comparing the individual's fuel expenditures to an expenditure threshold 10 . If one has a SL below the poverty threshold, and spends more on energy than the expenditure threshold, the individual is then considered to be fuel poor (1=fuel poor, 0=not fuel poor). In our sample 4.78% are fuel poor according to the 10% ratio and 5.74% according to the LIHC.

We tested the independence of fuel poverty (10% definition) and health status. The chi square test allows us to reject the hypothesis of independence between fuel poverty and poor health at the 1% level. Similar results are obtained if we consider another definition of fuel poverty or another measure of health i.e. having a chronic disease. Generally speaking, although the evolution over the period does not show at first glance the dependence between fuel poverty and health status (Figure 1), more fuel-poor households are in poor health (Figure 2).

Independent variables

Finally, we introduced variables for controlling for health status: socio-demographic characteristics and local conditions (weather and pollution). Indeed, the economic and epidemiologic literature on the nexus between air pollution and health is vast (Contoyannis & Jones, 2004;[START_REF] Neidell | Air Pollution, Health, and Socio-economic Status: The Effect of Outdoor Air Quality on Childhood Asthma[END_REF]. Health status might be linked to climate (WHO, 2013) and local air quality exposure is a significant driver of health problems [START_REF] Currie | Air Pollution and Infant Health: Lessons from New Jersey[END_REF][START_REF] Jans | Economic Status, Air Quality, and Child Health: Evidence from Inversion Episodes[END_REF]. By reducing air pollution levels, countries can reduce the burden of disease from stroke, heart disease, lung cancer, and both chronic and acute respiratory diseases, including asthma [START_REF] Who | Review of evidence on health aspects of air pollution -REVIHAAP project: final technical report[END_REF][START_REF] Who | Ambient (outdoor) air quality and health[END_REF]. The relationship between socioeconomic characteristics and health is well-established. Negative health behaviors and psychosocial characteristics are clustered in low socioeconomic status groups [START_REF] Lynch | Why do poor people behave poorly? Variation in adult health behaviours and psychosocial characteristics by stages of the socioeconomic lifecourse[END_REF]. The notion that low socioeconomic status, mainly due to low income, causes poor health is widely supported by empirical research (Contoyannis et al., 2004): poverty is associated with poor health even in advanced industrial societies [START_REF] Benzeval | Income and health: the time dimension[END_REF]. Education has been also found to have a positive association with physical and mental health (the so-called education-health gradient) because individuals invest in their health more effectively and allocate their resources better [START_REF] Cutler | Education and Health: Evaluating Theories and Evidence[END_REF]. Older people are often in poor health also [START_REF] Ohrnberger | The dynamics of physical and mental health in the older population[END_REF]. Our dataset gave us access to information about the climate zone where each household is located. This was matched with meteorological data of Meteo France (unified degree days 11 ) to provide a proxy for the actual meteorological conditions and to obtain unified degree-days. Finally, we approximated the income variable with level of education to avoid multicollinearity with fuel poverty (based on income). The descriptive statistics are presented in Table 1, and all variables are defined in Appendix 1.

Empirical model

This paper presents an approach based on traditional consumer theory where representation of individual preferences is based on the bundle of goods they have chosen to maximize their utility or wellbeing.

We estimate the impact of fuel poverty on the probability of being in poor health controlling for other characteristics. We use panel probit models and propose four configurations, first to control for statedependence of health (Contoyannis et al., 2004;[START_REF] Kools | Health and consumption preferences; estimating the health state dependence of utility using equivalence scales[END_REF], and second to control for endogeneity of fuel poverty (Awaworyi [START_REF] Churchill | Energy Poverty and Health: Panel Data Evidence from Australia[END_REF].

So, we have as the first model specification (Model 1):

ℎ * 𝑖𝑡 = 𝛼𝑋 𝑖𝑡 + 𝛽𝑊 𝑖𝑡 + 𝛾𝐹𝑃 𝑖𝑡 + 𝑢 𝑖 + 𝑣 𝑖𝑡 (4)

With:

𝑖 = 1, … , 𝑁 𝑎𝑛𝑑 𝑡 = 1, … , 𝑇 ℎ 𝑖𝑡 = 1 if ℎ 𝑖𝑡 * > 0 and 0 otherwise ℎ 𝑖𝑡 represents the health status of the individual 𝑖 in 𝑡, equal to 1 for good health at time t, 𝑋 𝑖𝑡 is the vector of observed variables (including age, level of education, etc.), 𝑊 𝑖𝑗 is a vector of living conditions including local air pollution and climate, 𝐹𝑃 𝑖𝑡 is the fuel poverty regressor, equal to 1 for a fuel-poor individual, according to the 10% threshold., 𝑢 𝑖 the individual-specific effect assumed to be unrelated to control variables, and 𝑣 𝑖𝑡 the idiosyncratic error term.

However, health status has a certain degree of persistence over time (Contoyannis et al., 2004;[START_REF] Kools | Health and consumption preferences; estimating the health state dependence of utility using equivalence scales[END_REF], which leads to the first configuration being biased. To account for this state-dependence [START_REF] Carro | STATE DEPENDENCE AND HETEROGENEITY IN HEALTH USING A BIAS-CORRECTED FIXED-EFFECTS ESTIMATOR: STATE DEPENDENCE AND HETEROGENEITY IN HEALTH[END_REF][START_REF] Halliday | Heterogeneity, state dependence and health[END_REF], we include a lagged health status variable representing the health of individuals in the previous year. So, we propose a dynamic random effect model:

ℎ 𝑖𝑡 * = 𝛿ℎ 𝑖𝑡-1 + 𝛼𝑋 𝑖𝑡 + 𝛽𝑊 𝑖𝑡 + 𝛾𝐹𝑃 𝑖𝑡 + 𝑢 𝑖 + 𝑣 𝑖𝑡 (5)
ℎ 𝑖𝑡-1 representing the lagged health status.

The use of a lagged variable presents the initial conditions problem [START_REF] Heckman | The Incidental Parameters Problem and the Problem of Initial Conditions in Estimating a Discrete Time -Discrete Data Stochastic Process[END_REF]. The historic stochastic process of health status is not observed at the beginning. The initial values of this variable cannot be considered exogenous [START_REF] Akay | The Wooldridge Method for the Initial Values Problem is Simple: What about Performance[END_REF]. Health during childhood, or other exogenous parameters affect the entire health trajectory for example (Contoyannis et al., 2004;[START_REF] Halliday | Heterogeneity, state dependence and health[END_REF]. So, we can express health at the first period in the panel as following:

ℎ 𝑖0 * = 𝛾𝑍 𝑖0 + 𝜃𝑢 𝑖 + 𝜀 𝑖 (6)
With 𝑍 𝑖0 including exogenous attributes affecting health status in the first period. The initial conditions problem leads 𝑦 𝑖0 then to be correlated with the unobserved heterogeneity. Consequently, in equation ( 2) we have 𝐸(𝑢 𝑖 |𝑦 𝑖0 ) ≠ 0 when 𝜃 ≠ 0.

In order to treat the initial conditions problem, we use the inverse of Mills' ratio12 within the Orme's two-step method [START_REF] Arulampalam | Simplified Implementation of the Heckman Estimator of the Dynamic Probit Model and a Comparison with Alternative Estimators[END_REF][START_REF] Orme | The Initial Conditions Problem and Two Step Estimations in Discrete Panel Data Models[END_REF]. We estimate a probit of the probability of being in good health in the first year in the panel. The medical density13 i.e. the ratio of physicians (practitioners or specialists) to the population in a geographic area, is used as an exogenous instrument (𝑍 𝑖0 ) to explain the health status at time 𝑡 0 [START_REF] Chaix | Access to general practitioner services: the disabled elderly lag behind in underserved areas[END_REF][START_REF] Macinko | The Contribution of Primary Care Systems to Health Outcomes within Organization for Economic Cooperation and Development (OECD) Countries, 1970-1998[END_REF].

Our second specification, correcting the initial conditions problem, might be expressed as follows (Model 2):

ℎ 𝑖𝑡 * = 𝛿ℎ 𝑖𝑡-1 + 𝛼𝑋 𝑖𝑡 + 𝛽𝑊 𝑖𝑡 + 𝛾𝐹𝑃 𝑖𝑡 + 𝜎𝐸[𝑢 𝑖 |𝑦 𝑖0 ] + 𝑢 𝑖 * + 𝑣 𝑖𝑡 (7)
in which the inverse Mills ratio, 𝐸[𝑢 𝑖 |𝑦 𝑖0 ], has been estimated in the first step as:

𝐸[𝑢 𝑖 |𝑦 𝑖0 ] = 𝐸[𝑢 𝑖 |𝜃𝑢 𝑖 + 𝜀 𝑖 ≥ -𝛾𝑍 𝑖𝑡 ] = 𝜙(𝛾𝑍 𝑖𝑡 ) Φ(𝛾𝑍 𝑖𝑡 )
The inverse Mills ratio allows controlling initial conditions for health.

The third specification of the model accounts for the potential endogeneity of fuel poverty. Endogeneity occurs when a variable, observed or unobserved, that is not included in our models, is related to a variable we incorporated in our model. In this paper, we confront one potential problem of endogeneity related to unobserved heterogeneity that simultaneously affects health and fuel poverty (Awaworyi [START_REF] Churchill | Energy Poverty and Health: Panel Data Evidence from Australia[END_REF]. We adopt a two-step instrumental method [START_REF] Heckman | Sample Selection Bias as a Specification Error[END_REF] by first estimating fuel poverty.

To confirm the presence of endogeneity, we considered instruments that can explain fuel poverty and potential health problems not directly measured by the direct variables introduced in the model. A good instrument should explain fuel poverty, but not the health status. Thus, the first two instruments seem to meet this requirement are energy prices. Indeed, electricity and natural gas prices are used as instruments as they are the most commonly used sources of energy for heating [START_REF] Ambrosio | Observatoire de la Precarite Energe tique[END_REF], but intuitively, there is no reason why they should explain the state of health of the individual. Energy prices are often recognized as one of the most important determinants of residential energy demand (see [START_REF] Labandeira | A meta-analysis on the price elasticity of energy demand[END_REF][START_REF] Labandeira | A meta-analysis on the price elasticity of energy demand[END_REF] for a literature review) and as a consequence of energy expenditures. A high share of energy expenditures in the income is one of the main component of fuel poverty [START_REF] Charlier | From Residential Energy Demand to Fuel Poverty: Income-induced Non-linearities in the Reactions of Households to Energy Price Fluctuations[END_REF][START_REF] Onpe | Définitions, indicateurs, premiers résultats et recommendations -Premier rapport de l'ONPE[END_REF]. We extrapolate the fuel price rate of each individual using the surface area of their dwelling and their fuel bills.

In order to estimate fuel poverty more precisely, we also introduce another variable as instrument to consider energy efficiency from the solar exposure of the dwelling [START_REF] Charlier | From Residential Energy Demand to Fuel Poverty: Income-induced Non-linearities in the Reactions of Households to Energy Price Fluctuations[END_REF], a binary variable if the dwelling is dark. Exposure is a criterion that is taken into consideration to measure the theoretical energy efficiency of a dwelling (and therefore the energy requirement). How a house is oriented in relation to the sun can have an impact on heating and cooling expenditures which are the largest energy contributor in most homes. In a building heated by passive solar energy, glass areas are oriented and arranged so as to optimize the capture of solar light and heat. When buildings are highly insulated and energy efficient, passive solar energy can meet a substantial share of the heating demand, even in cold climates [START_REF] Laustsen | Energy Efficiency Requirements in Building Codes, Energy Efficiency Policies for New Buildings[END_REF]. However, because building's exposure can vary over the year and the day, it is necessary to store and balance solar energy. If too much solar is captured, it could require cooling that offset the efficiency gains. Thus, exposure appears to be a good explanatory factor for energy expenditure. Intuitively, however, window exposure should not have a direct impact on the health of individuals.

The predicted value of fuel poverty is thus obtained using equation 8:

𝐹𝑃 𝑖𝑡 * = 𝜃 1 𝑋 𝑖𝑡 + 𝜃 2 𝑊 𝑖𝑡 + 𝜃 3 𝐺𝑎𝑠_𝑝 𝑖𝑡 + 𝜃 4 𝐸𝑙𝑒𝑐_𝑝 𝑖𝑡 + 𝜃 5 𝐺𝑎𝑠𝐸𝑙𝑒𝑐_𝑝 𝑖𝑡 + 𝜃 6 𝐷 𝑖𝑡 + 𝑢 𝑖 ′ + 𝑣 𝑖𝑡 ′ ( 8
)
With 𝑝 𝑖𝑡 = 1 if 𝑝 𝑖𝑡 * > 0 and 0 otherwise. 𝐺𝑎𝑠_𝑝 𝑖𝑡 , 𝐸𝑙𝑒𝑐_𝑝 𝑖𝑡 are the gas price and the electricity price, 𝐺𝑎𝑠𝐸𝑙𝑒𝑐_𝑝 𝑖𝑡 the interaction parameter between both energy prices to account for potential multicollinearity between evolution of energy prices 14 and 𝐷 𝑖𝑡 , a dummy variable indicating if the dwelling is dark.

The third specification of the model is a dynamic probit model, with correction of the endogeneity bias caused by the fuel poverty variable (Model 3):

14 Before 2008, energy prices rose rapidly and fell sharply during the 2009 crisis, which explains why energy expenditures were quite low during this period compared to the previous. However, since 2010, the price of oil increased as did household energy expenditures, reaching a peak in 2013. Then, considering France had recorded several mild winters, the share of energy expenditure in the overall budget continued to grow [START_REF] Onpe | Définitions, indicateurs, premiers résultats et recommendations -Premier rapport de l'ONPE[END_REF])

ℎ 𝑖𝑡 * = 𝛿𝑦 𝑖𝑡-1 + 𝛼𝑋 𝑖𝑡 + 𝛽𝑊 𝑖𝑡 + 𝛾𝐹𝑃 𝑖𝑡 ̂+ 𝜎𝐸[𝑢 𝑖 |𝑦 𝑖0 ] + 𝑢 𝑖 * + 𝑣 𝑖𝑡 (5)
Finally, the fourth specification controls the sensitivity to the choice of health variable. We estimate the third model and replace the health variable with a binary variable for chronic disease (Model 4). Then, we apply bootstrap techniques in each step to avoid bias [START_REF] Efron | Inadequate Housing in Europe : costs and consequences[END_REF][START_REF] Horowitz | The Bootstrap in Econometrics[END_REF].

Results and discussion

The main results are reported in Table 2. For the sake of clarity, the results of the initial conditions equation and the endogeneity treatment of fuel poverty equation are reported in the Appendix (See Appendix 2).

The estimates confirm the negative impact of fuel poverty on health status, as expected in the theoretical model, and as previously established in different cross-sectional case studies. Using a dynamic probit panel model we found that being fuel poor significantly increases the probability of being in bad health (Table 2, Model 1). The marginal effect of fuel poverty on poor health reaches 1.9% 15 (Table 3, Model 1) for an individual. These results persist even after controlling for the state dependency of health and the initial conditions (Table 2, Model 2), which demonstrates the importance of health trajectories: being fuel poor increases the probability of being in bad health by 1.7% (Table 3, Model 2) for individuals in good health in the previous period, and 6.5% for those already in poor health.

However, treating the endogeneity of fuel poverty modifies the marginal effect substantially. The impact is thus strongly reinforced (Table 2, Model 3): being fuel poor increases the risk of bad health by more than a factor of 7 (Table 3, Model 3) for those already in poor health, and by a factor of 1.82 for those who were in good health in the previous year. Finally, to test the robustness of the results established by Models 1 to 3, we use an objective measure of health, the existence of chronic diseases (Model 4). This last model confirms that being fuel poor multiplies the risk of chronic disease by more than a factor of 6.14 (Table 3, Model 4) for those in good health (no chronic disease) in the previous year, and by 7.88 for those who already declared at least one chronic disease. If we account for the unobserved heterogeneity affecting exposure to fuel poverty and deteriorating health simultaneously, we can conclude there is a very strong causal relationship between both phenomena.

The empirical strategy adopted first shows that the nature of the health variable has to be accounted for, and second that neglecting endogeneity of fuel poverty would lead to a significant underestimation of the health risk. The entire health trajectory of each individual has to be controlled: the intermediate estimate consisting of the control of initial conditions shows that medical density is a good instrument to explain the health of individuals before their entry in the panel (Table 6, Appendix 2A). Medical density significantly decreases the probability of being in poor health and of having a chronic disease. The first step in Models 3 and 4 which provides the estimated fuel poverty probability also allows us to conclude that energy prices are good instruments and strongly affect exposure to fuel poverty (Table 7 in Appendix 2B). When electricity and gas prices increase, the risk of fuel poverty increases significantly for each individual. Having a dark dwelling also significantly increases the probability of being poor. This step enables us to provide a good prediction of fuel poverty: the correct prediction rate is about 87%.

To test the robustness of the results established in the Models 3 and 4, we introduced an alternative indicator of fuel poverty: the low-income high cost indicator. According to this definition, households are fuel-poor if they have an income after fuel costs that is below the poverty threshold16 as well as fuel costs above the median population fuel cost. These estimates are reported in the Appendix (Table 8 in Appendix 2C). We have validated the results and particularly the size of the effect: being fuel poor leads to an increase in the risk of 15 In the case of a dynamic random effect probit, coefficient can be directly interpreted as linear prediction.

bad health by more than a factor of 2 for a person previously in good health and by more than 8 for those already in poor health (Table 9 model 3). The risk of declaring a chronic disease increases by a factor of 4.38 for a healthy person (Table 9 Model 4). Finally, using the same methodology, we wanted to identify the threshold where the effort rate significantly increases the probability of being in poor health. Results for predictive values are presented in Figure 3 below. 4: when the effort rate increases marginally, the risk of declaring a state of poor health increases by 5.5. Our results reinforce the estimates provided by the National Housing Federation in 2010: the cost for treating ill health resulting from poor housing conditions has been estimated at GBP 2.5 billion per year in the UK. Eurofound (2016) models the cost of housing inadequacies and estimated that in France, 930 million euros in medical expenses would be saved by repairing inadequate housing. The previous reports combined with our results lead us to conclude that spillover effects exist in public policy: implementing policies which promote energy efficiency, such as encouraging investment in retrofitting are useful tools for tackling fuel poverty and also reduce medical spending.

Retrofitting policies, in this sense, go beyond the simple monetary benefits: a household could occupy an energy-inefficient dwelling and cope with it by means of a high income. Retrofitting measures would still be highly beneficial to them due to improvement of the environment. In the context of continuous increases in energy prices in Europe as shown by Eurostat (2019), investment opportunities created by the need for energy efficiency are vast and highly profitable [START_REF] Amstalden | Economic potential of energy-efficient retrofitting in the Swiss residential building sector: The effects of policy instruments and energy price expectations[END_REF]. Retrofitting plans and energy efficiency measures have an impact on fuel poverty through different channels. First, they directly and robustly improve living conditions (reduce cold, dampness, mold). Second, they lead indirectly to a decrease in energy costs, particularly because the housing becomes less energy-intensive. Finally, reducing residential energy consumption/demand reduces carbon dioxide emissions, which is an important component of the preservation of climate and natural resources, and the environment as a whole. "For example, cleaner energy systems could reduce carbon emissions, and cut the burden of household air pollution, which causes some 4.3 million deaths per year, and ambient air pollution, which causes about 3 million deaths every year" (WHO, 2018).

More broadly, our results beg the question whether it is possible to achieve energy transition without considering the impact of fuel costs on fuel poverty and the indirect impact on public health. Achieving energy transition without incurring excessive economic and social costs requires anticipating long chain reactions.

7/ Conclusion

Fuel poverty has been treated extensively in recent literature. But very few studies target the causal link between fuel poverty and poor health. Numerous papers focus on specific experiments assessing the link between some timely retrofitting policies and the health of occupants [START_REF] Chapman | Retrofitting houses with insulation: a cost-benefit analysis of a randomised community trial[END_REF][START_REF] Ezratty | Liens entre l'efficacité énergétique du logement et la santé des résidents : résultats de l'étude européenne LARES[END_REF][START_REF] Howden-Chapman | How real are the health effects of residential energy efficiency programmes[END_REF][START_REF] Howden-Chapman | Warmer houses reduce children's asthma[END_REF][START_REF] Lloyd | The efficacy of an energy efficient upgrade program in New Zealand[END_REF][START_REF] Thomson | Quantifying the prevalence of fuel poverty across the European Union[END_REF]. To the best of our knowledge only two papers [START_REF] Lacroix | Fuel poverty as a major determinant of perceived health: the case of France[END_REF][START_REF] Liddell | Fuel poverty and human health: A review of recent evidence[END_REF] describe nonexperimental and cross-sectional research on the relationship between fuel poverty and health. Our study aims to go beyond the limits of this previous work, namely the overly specific aspects of experimental studies and the non-generalizable results of cross-sectional research that neglect climate hazards and the path dependency of health.

In the present paper, we estimate the causal effect of fuel poverty on health status. To do this, we used panel data from the EU-SILC over a long recent period (2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016) and estimated probit panel models in four steps. We begin with a simple probit model without controlling for state dependency of health and endogeneity of fuel poverty, and finish with a dynamic probit model controlling for both biases.

We conclude that fuel poverty has a significant impact on health. Being fuel poor increases the risk of bad health by slightly more than a factor of 7 for those already in poor health (1.82 for those in good health) and by 7.88 the risk of having a chronic disease for those who already have a chronic disease (6.14 for those previously in good health). In terms of policy recommendations, we stress the importance of energy-efficiency retrofits. Our results allow us to make the link between experimental studies and medical literature demonstrating the effects of humidity, cold and indoor pollution on the health of individuals. Even more than underlining the importance of supporting renovations, our results show what kind of renovations could bring a double dividend, both in terms of well-being for the inhabitants of a dwelling and in terms of public health expenditures. It thus appears that public policies should allow households to improve their insulation, whether this involves roof insulation or wall insulation. At the same time, allowing households to have efficient and safe heating sources can also improve public health.

Lessons learned from our empirical strategy also allow us to conclude that neglecting path dependency of health and endogeneity of fuel poverty leads to a substantial underestimation of the impact on health. By controlling both biases, we first show that medical density must be accounted for to achieve a good understanding of the health history of each individual. Secondly, as energy prices are good instruments for controlling endogeneity, our results question the inextricably linked issues of energy transition, combatting fuel poverty and safeguarding public health. Is it possible to achieve energy transition without excessive economic and social costs, i.e. without increasing fuel poverty and damaging public health?

Appendix 2: Results

2A -Estimated results for controlling initial conditions

To ensure that medical density is a good variable to explain the initial health status, we perform a Wald test as in [START_REF] Cappellari | Modelling low income transitions[END_REF]. Based on the p value, we are able to reject the null hypothesis, indicating that the coefficient for medical density is not equal to zero, meaning that including this variable creates a statistically significant improvement in the fit of the model at the 1% level.

2B -Estimated results for binary probit regression on fuel poverty

It is quite difficult to test the consistency of instruments. But it is possible to test whether parameters are significant and significantly improve the fit of the model. In our estimates, energy prices are significant, especially the price of gas which is significant at 1%. It is also possible to perform a Wald test, and a likelihood-ratio test. The Wald test performs simple and composite linear hypotheses about the parameters of the most recently fit model. Based on the p value, we are able to reject the null hypothesis, indicating that the coefficients for gas price, electricity price and the interaction parameter for energy prices are not simultaneously equal to zero, meaning that including these variables creates a statistically significant improvement in the fit of the model. Finally, the likelihood-ratio test performs a likelihood-ratio test of the null hypothesis that the parameter vector of a statistical model satisfies some smooth constraint.

Adding the energy price parameters as predictor variables together (not just individually) results in a statistically significant improvement in the model fit.

Figure 1

 1 Figure 1 Evolution of the proportion of observations in good health and in fuel poverty (10%)

Figure 2

 2 Figure 2 Health status according to fuel poverty definition

Figure 3 :

 3 Figure 3: Predictive margins for effort ratelinear prediction

Table 1

 1 Descriptive statistics

	Variable		Mean	Std Dev	Min	Max	Observations
	Poor health	overall	0.084	0.277	0.000	1.000	N = 187817
		Between*		0.246	0.000	1.000	n = 53430

11

Unified Degree Days express the severity of cold weather in a specific time period taking into consideration actual outdoor temperature and an average reference temperature previously recorded.

Table 2

 2

	results -probability of being in poor health
		Model 1	Model 2	Model 3	Model 4
	To be in poor health		1.611***	1.609***
	(lag)
			(0.0328)	(0.0328)
	Fuel poverty 10%	0.252***	0.198***
		(0.0332)	(0.0630)
	Number of children	0.0824***	0.0353***	0.0188**	0.00461
		(0.0127)	(0.0118)	(0.00857)	(0.00607)
	Unified Degree Days	0.0527	0.0306	-0.0280	-0.0823***
	(log)
		(0.0466)	(0.0361)	(0.0371)	(0.0252)
	Age	0.0529***	0.0216***	0.00139	-0.000319
		(0.00100)	(0.00651)	(0.00272)	(0.00190)
	Pollution problem	0.186***	0.142***	0.0202	0.0708***
		(0.0247)	(0.0515)	(0.0273)	(0.0179)
	Undergraduate degree	-0.365***	-0.186***	0.0287	0.0160
		(0.0469)	(0.0718)	(0.0397)	(0.0176)
	Homeowner	-0.642***	-0.281***	-0.0208	0.00102
		(0.0274)	(0.0915)	(0.0392)	(0.0158)
	Mills' ratio		-0.0219	-0.836***	-0.895***
			(0.293)	(0.119)	(0.0994)
	Predicted fuel poverty			21.39***	25.15***
	10%
				(3.357)	(2.964)
	Chronic disease (lag)				1.548***
					(0.0210)
	Constant	-5.568***	-3.068***	-0.242	0.526*
		(0.362)	(0.828)	(0.431)	(0.286)
	Observations	173,88	122,362	122,347	122,32
	Number of individuals	49,422	37,855	37,855	37,861
		Robust standard errors in parentheses
		*** p<0.01, ** p<0.05, * p<0.1

Table 4

 4 Results -probability of being in poor health

	Poor health (lag)	1.613***

Table 6

 6 Estimated results for controlling initial conditions

			Poor health			Chronic disease
		Coef.	St.Err.	Sig	Coef.	St.Err.	Sig
	Fuel poverty 10%	0.246	0.032	***	0.170	0.027	***
	Number of Children	0.039	0.009	***	-0.038	0.006	***
	UDD (log)	-0.071	0.052		-0.053	0.037
	Age	0.027	0.001	***	0.027	0.000	***
	Pollution problem	0.203	0.024	***	0.174	0.018	***
	Undergraduate degree	-0.261	0.038	***	-0.079	0.022	***
	Homeowner	-0.382	0.019	***	-0.176	0.014	***
	Medical density	-0.001	0.000	***	-0.001	0.000	***
	Constant	-1.882	0.428	***	-0.752	0.306	**
	Observations		45918			45921
	Pseudo R-squared		0.117			0.115
	Chi-square		3249.936			6953.236
	Percent correctly predicted		90.9%			69.5%
	Wald test	chi2( 1) = 7.71 p= 0.0055		chi2( 1) = 62.54 p= 0.0000
	LR test	chi2( 1) = 7.74 p= 0.0054		chi2( 1) = 62.71 p= 0.0000
	*** p<0.01, ** p<0.05, * p<0.1-Bootstrap 5000 replications

Table 7

 7 Estimated results for binary probit regression on fuel poverty

			Fuel poverty 10%		Fuel poverty LIHC
		Coef.	St.Err. p value	Coef.	St.Err.	p
							valu
							e
	Number of Children	-0.156	0.012	***	0.049	0.010 ***
	UDD (log)	0.511	0.050	***	0.183	0.044 ***

*** p<0.01, ** p<0.05, * p<0.1 -Bootstrap 5000 replications 2C -Results : probability of being in poor health using the LIHC indicator

Table 8

 8 Results -probability of being in poor health using the LIHC indicator

		Model 1	Model 2	Model 3	Model 4
	Poor health (lag)		1.611***	1.609***
			(0.0328)	(0.0328)
	Fuel poverty 10%	0.252***	0.198***
		(0.0332)	(0.0630)
	Number of children	0.0824***	0.0353***	0.0188**	0.00461
		(0.0127)	(0.0118)	(0.00857)	(0.00607)
	Unified Degree Days (log)	0.0527	0.0306	-0.0280	-0.0823***
		(0.0466)	(0.0361)	(0.0371)	(0.0252)
	Age	0.0529***	0.0216***	0.00139	-0.000319
		(0.00100)	(0.00651)	(0.00272)	(0.00190)
	Pollution problem	0.186***	0.142***	0.0202	0.0708***
		(0.0247)	(0.0515)	(0.0273)	(0.0179)
	Undergraduate degree	-0.365***	-0.186***	0.0287	0.0160
		(0.0469)	(0.0718)	(0.0397)	(0.0176)
	Homeowner	-0.642***	-0.281***	-0.0208	0.00102
		(0.0274)	(0.0915)	(0.0392)	(0.0158)
	Mills' ratio		-0.0219	-0.836***	-0.895***
			(0.293)	(0.119)	(0.0994)
	Predicted fuel poverty 10%			21.39***	25.15***
				(3.357)	(2.964)

Table 9

 9 Marginal effects of fuel poverty (LIHC) on poor health

	Model 1	0.02***
		Good health in t-1	Poor health in t-1
	Model 2	0.02***	0.09***
	Model 3	2.30***	8.89***
	Model 4	4.38***	5.62***
	*** p<0.01, ** p<0.05, * p<0.1 -Bootstrap 5000 replications

See Maidment et al. (2014) for a meta-analysis including 36 studies which evaluate the relationship between household energy-efficiency interventions and the health of the occupants

The EU-SILC project was established in response to a request from the European Commission and is led by Eurostat. The French part of the project is called SRCV (Statistiques sur les Ressources et Conditions de Vie)

Which is a monotone decreasing function of the probability of the selection of an observation in the sample[START_REF] Heckman | Sample Selection Bias as a Specification Error[END_REF]

Data from the French Atlas of Medical Demography 13 , carried out annually by the French Medical Board, adjusted by national territory divisions have been used to construct the variable of medical density.

This poverty threshold is set at 60% of the population income, from which fuel costs have been deducted.

Appendix 1