Keywords: health inequality, air pollution, political institutions, social protection JEL classification: C13, D63, I1; Q53

This paper examines the link between health inequalities, air pollution and political institutions. In health economics literature, many studies have assessed the association between environmental degradation and health outcomes. This paper extends this literature by investigating how air pollution could explain health inequalities both between and within developing countries, and the role of political institutions in this relationship. Theoretically, we argue that differential in exposition to air pollution among income classes, prevention ability against health effect of environment degradation, capacity to respond to disease caused by pollutants and susceptibility of some groups to air pollution effect are sufficient to expect a positive link between air pollution and income related health inequality. Furthermore, in democratic countries, this heterogeneity in the health effect of pollution may be mitigated since good institutions favour universal health policy issues, information and advices about hygiene and health practices, and health infrastructures building. Our econometric results

show that sulphur dioxide emission (SO 2 ) and particulate matter (PM 10 ) are in part responsible for the large disparities in infant and child mortalities between and within developing countries. In addition, we found that democratic institutions play the role of social protection by mitigating this effect for the poorest income classes and reducing the health inequality it provokes.

introduction

The importance of human capital in general and population health in particular as a component of economic development predictors, has been investigated by many scholars [START_REF] John | Assessing the Impact of AIDS on the Growth Path of the Malawian Economy[END_REF][START_REF] Caselli | Reopening the Convergence Debate: A New Look at Cross-Country Growth Empirics[END_REF][START_REF] Bhargava | Modeling the Effects of Health on Economic Growth[END_REF][START_REF] Kai | The Primacy of Institutions Reconsidered: Direct Income Effects of Malaria Prevalence[END_REF][START_REF] Sachs | Sources of Slow Growth in African Economies[END_REF]. It is recognized by economists as well as international community 1 that health contributes largely to the improvement of population welfare and economic growth through productivity and availability of healthy workforce [START_REF] Bloom | The Effect of Health on Economic Growth: Theory and Evidence[END_REF][START_REF] Weil | Accounting for the Effect of Health on Economic Growth[END_REF]. Giving this important role, researchers identified variables that may influence population health, and environment quality is commonly accepted as one of these determinants. Indeed, many studies have assessed the association between air pollution and health status through macroeconomic studies [START_REF] Gangadharan | Interrelationships between income, health and the environment: extending the Environmental Kuznets Curve hypothesis[END_REF] as well as microeconomic studies [START_REF] Burnett | Air Pollution Effects on Hospital Admission Rates: A Random Effects Modeling Approach[END_REF][START_REF] Jerrett | Particulate air pollution, social confounders, and mortality in small areas of an industrial city[END_REF]. Some authors showed that air quality degradation increases all causes mortality [START_REF] Woodruff | The Relationship between Selected Causes of Postneonatal Infant Mortality and Particulate Air Pollution in the United States[END_REF][START_REF] Gangadharan | Interrelationships between income, health and the environment: extending the Environmental Kuznets Curve hypothesis[END_REF][START_REF] Chay | The Impact of Air Pollution on Infant Mortality: Evidence from Geographic Variation in Pollution Shocks Induced by a Recession[END_REF]Aunan & Pan, 2004;[START_REF] Jerrett | Particulate air pollution, social confounders, and mortality in small areas of an industrial city[END_REF] while others confirm its impact on cause-specific mortality or morbidity (Aunan & Pan, 2004;[START_REF] Burnett | Air Pollution Effects on Hospital Admission Rates: A Random Effects Modeling Approach[END_REF][START_REF] Jerrett | Particulate air pollution, social confounders, and mortality in small areas of an industrial city[END_REF].

Moreover, other scholars investigated the heterogeneity in the health effect of air pollution according to socioeconomic status [START_REF] Charafeddine | Does income inequality modify the association between air pollution and health?[END_REF]O'Neill et al., 2003), but these studies remain theoretical or specific in a given region and focus only on health status.

In addition, international studies on this topic are based on average health in the population.

One of the drawbacks of the use of average health is its inability to take into account the extent of health disparities within a population, given the differential in policy response. This can be solved by using health distribution. In this paper, we investigate how air pollution may impact income related health inequality within a country and the role of political institutions in such relation using data from developing countries. Some theoretical arguments -namely, heterogeneity in exposition to air pollution among income classes, prevention ability against health effect of environment degradation, ability to respond to sickness caused by pollutants and susceptibility of some groups to air pollution effect -allow us to predict a larger impact of pollution on the poorest as compare to its effect on the richest class of income. Therefore, this may increase income related health disparities among the population. Good political institutions may mitigate this health inequality effect of environmental degradation through universal health policy issues, information and advices about health practices, and health infrastructures availability. This article is different from previous literature since it is the first, from our knowledge, that explicitly links air pollution to within country health inequalities. Moreover, it uses a rich database from the World Bank that allows us to take into account both within and between countries characteristics of health outcomes.

Our empirical results confirm our theoretical expectations. Indeed, air pollution degrades population health and the poorest populations suffer more from this degradation than the richest. This heterogeneity in health consequences of pollution is alleviated by good political institutions.

The rest of the paper is organized as follows. In section 2 we define and discuss the different measures of health inequalities in the literature. Section 3 develops the theoretical links between health inequalities, air pollution and political environment. In this section we explore how environmental degradation may increase this disparities and the role of institutions quality. Section 4 is devoted to the empirical design. We expose the econometric methodology and the data we use in this section. The results are presented in section 5 and section 6 presents some robustness checks. Finally section 7 concludes.

Health inequality: definition and measures

Health inequality in a population can be defined as the differences, variations, and disparities in health achievements among individuals or groups of this population. This descriptive term includes health inequity which is the normative part of health inequality since it depends on personal judgement [START_REF] Kawachi | A glossary for health inequalities[END_REF]. As argued by [START_REF] Deaton | Aging and Inequality in Income and Health[END_REF], the measurement of health inequality raises at least two important issues. First, the identification of a reliable and available measure of health status data can be considered as a challenge.

Several indicators are suggested in the literature, but all of them are source of critics or suffer from data unavailability. Fang et al. (2010) classified these indicators into two categories. The traditional one based on ill health incidents such as vital statistics, disease statistics and children growth data. The second category constituted of newer indicators focuses on healthy life span such as potential years of life lost (PYLL), life expectancy free of disability (LEFD), active life expectancy (ALE), disability adjusted life years (DALY) and disability adjusted life expectancy (DALE). Another important issue is whether the chosen indicator is qualitative or quantitative. The qualitative or categorical data prevents the straightforward use of traditional tools of distributional analysis, such as the Lorenz curve, in evaluating inequality. [START_REF] Allison | measuring health inequality using qualitative data[END_REF] present a methodology for evaluating overall inequality in health when the data are qualitative rather than quantitative in nature.

Once the appropriated measure of health is identified, the second issue is how to measure inequality in health status. In economic literature, health inequality is assessed through two different approaches. On the one hand, some scholars measure health inequality through the distribution of health status across individuals in a population, like measures of income distribution in a population (Legrand 1987;[START_REF] Kawachi | A glossary for health inequalities[END_REF]. Indicators from this approach include the lorenz curve, the gini coefficient or other measures of health dispersion [START_REF] Wagstaff | Overall versus socioeconomic health inequality: a measurement framework and two empirical illustrations[END_REF]. On the other hand researchers assess health distribution by measuring health difference across social groups (income class, social class, age, race, place or neighbouring) and these indicators include the index of dissimilarity (ID), the slope relative indices of inequality, the Index of concentration, the range, the pseudo lorenz curve, the adapted gini coefficient. Some measures that are based on both health and social position utilize the ordered nature of socioeconomic status (the slope and the concentration index) while others including the adapted Gini coefficient and the index of dissimilarity do not.

As argue by [START_REF] Kunst | Development of health inequalities indicators for the Eurothine project[END_REF], the choice of measuring method depends on the health outcomes of interest, the data sources that can be accessed, and the socioeconomic information that is available. For [START_REF] Manor | comparing measures of health inequality[END_REF], the measures based only on the distribution of health are inadequate in examining social inequalities in health. The joint distribution of both health and socioeconomic status should be considered in this context. [START_REF] Wagstaff | on the measurement of inequalities in health[END_REF] and [START_REF] Schneider | Methods for measuring inequalities in health[END_REF] detailed the calculation methods and the advantages and disadvantages of the various measurements. According to Szwarcwald (2002), the measure of variations in health status across individuals in a population depends at the same time on the performance of the health system in diminishing the socioeconomic health inequalities and the extent of the income inequalities in the population. So, it is a matter of choice whether one should or should not consider the distribution of the population across socioeconomic groups. If one considers that what is important about health inequalities is to assess the magnitude of the inter-individual differences in health status, the index of health inequalities will inevitably reflect the inequality in socioeconomic status. If the main goal is to assess the performance of health systems, this is clearly a restriction because the extent of inequalities in socioeconomic status within the population is generally outside the field of control of public health policies and actions. According to [START_REF] Levine | Black-White Inequalities in Mortality and Life Expectancy, 1933-1999: Implications for Healthy People[END_REF] inequality in health is a relative rather than an absolute concept, and ratios rather than absolute differences are a more valid measure of inequality. They calculated time series for black/white ratios of age-adjusted, all-cause mortality and life expectancy in the USA. [START_REF] Lai | Statistical Properties of Generalized Gini Coefficient with Application to Health Inequality Measurement[END_REF] used two classes of generalized Gini coefficients (G1 and G2) of life expectancy to measure health inequalities among the provinces of China and the states of the United States. G1 is the measure of individual/mean absolute differences and G2 measures inter-individual absolute differences. For China, their results indicated that there was statistically significant health inequality by both G1 and G2.

However, for the US, their results showed that there was significant health inequality by G1 but no statistical significance was found in health inequality by G2. Overall, from their study, China has higher health inequality than the United States.

Health inequality, pollution and institutions quality

A healthy labour force is essential for the development of an economy and requires a healthy environment (clean air, water, recreation and wilderness). As argue by [START_REF] Pearce | World Without End: Economics, Environment and Sustainable Development[END_REF], the immediate and most important consequences of environmental degradation are damage to human health through different forms of diseases. Many authors have assessed how air quality may be associated to population's health. On the one hand, scholars showed that air pollution may increase mortality rate [START_REF] Woodruff | The Relationship between Selected Causes of Postneonatal Infant Mortality and Particulate Air Pollution in the United States[END_REF][START_REF] Gangadharan | Interrelationships between income, health and the environment: extending the Environmental Kuznets Curve hypothesis[END_REF][START_REF] Chay | The Impact of Air Pollution on Infant Mortality: Evidence from Geographic Variation in Pollution Shocks Induced by a Recession[END_REF]Aunan & Pan, 2004;[START_REF] Jerrett | Particulate air pollution, social confounders, and mortality in small areas of an industrial city[END_REF]. Aunan & Pan (2004) propose exposure-response functions for health effects of PM 10 and SO 2 pollution in China, based on Chinese epidemiological studies. They found 0.03% (S.E. 0.01) and 0.04% (S.E. 0.01) increase in all-cause mortality per µg/m 3 PM 10 and SO 2 , respectively. Furthermore, [START_REF] Jerrett | Particulate air pollution, social confounders, and mortality in small areas of an industrial city[END_REF] investigated whether chronic exposure to particulate air pollution is significantly associated with mortality when the effects of other social, demographic, and lifestyle confounders are taken into account. Their results show substantively large and statistically significant health effects for women and men.

On the other hand, authors assess the link between pollution and particular illness, such as cardio-respiratory disease (Aunan & Pan, 2004;[START_REF] Burnett | Air Pollution Effects on Hospital Admission Rates: A Random Effects Modeling Approach[END_REF][START_REF] Jerrett | Particulate air pollution, social confounders, and mortality in small areas of an industrial city[END_REF], asthma [START_REF] Nauenberg | Effect of Insurance Coverage on the Relationship between Asthma Hospitalizations and Exposure to Air Pollution[END_REF] and congenital anomalies [START_REF] Rankin | Maternal exposure to ambient air pollutants and risk of congenital anomalies[END_REF]. [START_REF] Burnett | Air Pollution Effects on Hospital Admission Rates: A Random Effects Modeling Approach[END_REF] find strong associations between the number of daily health events (hospital admissions or emergency-room visits for respiratory illnesses) and daily levels of ambient air pollutants in the vicinity of several hospitals with data obtained from 164 acutecare hospitals in Ontario over the May-to-August period from 1983 to 1988 and a randomeffects relative-risk regression model. [START_REF] Rankin | Maternal exposure to ambient air pollutants and risk of congenital anomalies[END_REF] investigate the association between exposure to particulate matter with aerodynamic diameter less than 4 mg/m 3 (BS) and sulphur dioxide (SO 2 ) during the first trimester of pregnancy and risk of congenital anomalies through a case-control study design among deliveries to mothers resident in the UK Northern health region during 1985-1990 and logistic regression models. They found a significant but weak positive association between nervous system anomalies and BS, but not with other anomaly subtypes. For SO2, they found a significant negative association with congenital heart disease combined and patent ductus arteriosus.

In addition to the effect of air pollution on population health, this paper assesses the association between pollution and income related health inequalities within a country. At least three theoretical arguments allow the expectation of a positive association between physical environment quality and inequalities in health. Firstly, air pollution exposure is differentially distributed by income level. Indeed, poor communities are more likely to be exposed than others, since they generally live in more polluted area and they cannot afford moving from polluted area to a less polluted one. That is at the core of environment justice movement.

Moreover, poor people are more exposed to pollutants at work. Populations with less wealth are more likely to be employed in dirtier occupations and may also be more likely to be exposed to pollutants indoors from heating and cooking. That may be due to the low and less prestigious position their generally occupied. The heterogeneity of exposure over space varies by pollutant type. Fine particles are distributed fairly homogeneously over large urban areas due mostly to the contribution of small, long-range transport particles (O'Neill et al., 2003).

Secondly, at a given level of exposition, rich communities have more prevention than poor. In fact, because their parents are poor, some children do not have access to immunization against illness caused or conveyed by air pollution such as meningitis. Poor communities may also lack access to stores that sell fresh fruits and vegetables or the income to buy them, resulting in reduced intake of antioxidant vitamins that can protect against adverse consequences of air pollution exposure [START_REF] Romieu | Antioxidant supplementation and respiratory functions among workers exposed to high levels of ozone[END_REF]O'Neill et al., 2003). Another way of prevention is to respect certain rules of hygiene. For example, protection of foods by covering them and the purchase of packaged products may reduce the health consequences of exposure. But these rules are more respected by the rich than the poor because of education and financial reasons. This differential prevention deepens inequalities in health caused by pollution since it mitigates the consequences for the wealthier. Finally, differential access to medical care (because of inequalities in access to health insurance) is another fact explaining inequalities in the health effect of air pollution. Indeed, poor people may not have the appropriate prescription for a respiratory condition such as asthma. Medication can alleviate symptoms aggravated by pollution exposure, and more consistent use of corticosteroids lowers baseline inflammation, potentially lowering responsiveness to pro-inflammatory pollutants (O'Neill et al., 2003). All that arguments increase the vulnerability of income disadvantaged population as compare to the richest. [START_REF] Makri | Vulnerability to air pollution health effects[END_REF] identify and evaluate information on population characteristics associated with vulnerability to ambient air pollution from a risk analysis perspective and based on available evidence. They found higher risks for foetuses and children, the elderly, and persons with pre-existing diseases. They also found that epidemiologic evidence of higher risks for racial minorities and social economically disadvantaged populations may be partly related to physiological capacity due to pre-existing diseases as well as health status. [START_REF] Charafeddine | Does income inequality modify the association between air pollution and health?[END_REF] showed that income inequality plays a modifier role in the association between general self-reported health and particulate pollution. They hypothesize that individuals living in states with lower income inequality are significantly more likely to report fair or poor health if they lived in counties where particulate pollution is high. But, their results contradict their hypothesis.

In countries with good institutions, these disparities in health effect of air pollution could be mitigated. Institutions are understood here as democratic principles, such as regular elections, universal suffrage, representation, one person-one vote, multiparty competition, and civil liberties. Thus, good institutions might produce competition for popular support among leaders who are trying to conserve or win elected office. Democratic institutions might therefore reduce health effect of pollution of the poor through their general impact on universal health policy issues, such as universal access to high quality services and universal health insurance and accessible programs. Good institutions may in addition, provide information and advices about hygiene, good health practice, and other knowledge useful for the population in general, and the poorest in particular. Political institutions could also alleviate social disparities and income inequalities that results from greater political voice and participation. Finally, governments are likely to build infrastructures (road, hospital) that could reduce air pollution or its effect for the poor. By contrast, authoritarian regimes prevent human development, since its improvement mobilizes citizens to advocate for greater participation and more resources [START_REF] Ruger | Democracy and health[END_REF]. North America (MENA) and East Asia and Pacific (EAP) also experience high pollution level, but inter quintiles health inequality is not very large. This may be due to the fact they have the best political institutions. This statistically shows that there is a link between health inequality, air pollution and political institutions.

Empirical design a. Estimation methodology

The object of this article is to evaluate the effect of air pollution on income related health inequalities and the role of political institutions in mitigating such impact. For this purpose, three econometric models are successively estimated:

The first equation assesses the effect of air pollution on health inequality between countries, while controlling for other potential determinants of health outcomes. Based on some existing empirical works (Gwatkin et al., 2007; Berthelemy & Seban, 2009; white et al., 2003), the following model is specified:

' ijt ijt jt i ijt health X environment β δ µ ε = + + + (4.1)
Where, the variable ijt health represents the health outcomes (infant and child mortality rates)

of the i th quintile in country j in the year t. environment represents the variable of air pollution (sulphur dioxide emission per capita and particulate matter) and X is the vector of control variables (mother education, gross domestic product per capita, immunization rate against DPT, fertility rate, population density and the percentage of urban population). i µ represents the quintile fixed effect and ijt ε is the error terms. In this model, the coefficient of the environmental variable (δ ) is of special interest. We expect a positive coefficient since this expresses the deterioration of population health caused by an increasing in environment pollution (marginal effect).

This equation is estimated with the ordinary least squares since we do not expect any potential source of endogeneity of our variable of interest (environment) that may lead to biased estimate of δ . Indeed, three sources of endogeneity are generally pointed out in the literature.

Endogeneity may firstly be caused by the reverse causality between the variable of interest and the dependent variable. In our model, this is not a problem since we do not expect any mechanism through which population health may affect environment quality. One could suppose that health may impact environment through its effect on income and development level. Even though this argument seems less relevant, it can not affect our identification strategy since we control for development level.

Another source of endogeneity is omitted variables bias. This problem occurs when there is a third variable, which could simultaneously affect the environment quality and population health. In our model we control for all potential variables in this sort to avoid this problem.

Finally, endogeneity may be caused by measurement error. We do not suspect any error in the measure of our variable of interest.

In order to assess the heterogeneity in the effect of pollution on health within population, we add the interactions terms of quintile dummies and environmental variables and we obtain the following model:

5 ' 2 ( * ) ijt ijt jt i jt i i ijt i health X environment environment β δ λ µ µ ε = = + + + + ∑ (4.2)
In this model the marginal effect of air pollution on quintile i th 's health outcomes is:

( ) ( ) i i health environment δ λ ∂ = + ∂
. We expect a higher impact of environment degradation on poor income quintile as compare to richer ones ( 2 3 4 5 λ λ λ λ > > > ) and environment quality may be considered as a determinant of income related health inequality.

Finally, we assess whether political institutions may mitigate this gap in the health effect of environment among poor and rich income classes. For this aim, we include in equation (3.2)

the interaction term of environment, quintile dummies and institution variable, the interaction term of environment and institution variable, and the interaction term of institution and quintile dummies. The third model can be written as follows:

5 5 ' 2 2 5 2 ( * ) ( * ) ( * ) ( * * ) ijt ijt jt i jt i i jt i i i jt i jt i i ijt i health X environment environment institution environment institution environment institution β δ λ µ ϕ µ ψ γ µ µ ε = = = = + + + + + + + ∑ ∑ ∑ (4.3)
Where, institution denotes political institution variables. The marginal effect of environment on the health outcomes of quintile i becomes: ( ) ( ) * ( )

i i i health institution environment δ λ ψ γ ∂ = + + + ∂ .
This marginal effect depends on institutions quality, and its effect is given by:

2 ( ) ( ) ( ) i i health environment institution ψ γ ∂ = + ∂ ∂ .
Political institutions alleviate the disparities in the health effect of environment if γ is higher for rich income classes as compare to poor income quintiles, namely, 2

3 4 5 γ γ γ γ < < < .
Like the first equation (4.1), equations (4.2) and (4.3) are estimated with ordinary least squares and we make a cluster for each country and all variables are expressed in natural logarithm.

b. Data and variables

In this article, we use data from different sources and largely utilized in health economics literature.

Health outcomes: Data on health variables are taken from the study leaded by [START_REF] Gwatkin | Socio-Economic Differences in Health, Nutrition, and Population Within Developing Countries, An Overview[END_REF] on Health, Nutrition and Population in 56 developing countries, and all the data are disaggregated by income quintiles. In this database, more than half of the countries are

African. The report of [START_REF] Gwatkin | Socio-Economic Differences in Health, Nutrition, and Population Within Developing Countries, An Overview[END_REF] is based on data drawn from several demographic and health surveys (DHS) conducted in these countries. These surveys target especially maternal and child health with a standardized questionnaire. Data also include socioeconomic variables like mother education for each quintile.

The report includes several indicators of health status and utilization of health services. In this paper, we are only interested in infant and under five mortality rates. These data have already been used in the literature by [START_REF] Fay | Achieving Child-Health-Related Millenium Development Goals: The Role of Infrastructure[END_REF], [START_REF] Ravallion | Achieving Child-Health-Related Millenium Development Goals: The Role of Infrastructure -A Comment[END_REF], [START_REF] David | Achieving Health, Wealth and Wisdom: Links Between Aid and the Millennium Development Goals[END_REF] and [START_REF] Berthelemy | Dépenses de santé et équité dans l'accès aux services de santé dans les pays en développement[END_REF]. We use the logistic form of mortality rates. 2 Notes : International Reports, a weekly newsletter on international finance and economics. They produce a comprehensive system that enables various types of risk to be measured and compared between countries. The system is based on a set of components for political risk.

Each component is assigned a maximum numerical value (risk points), with the highest number of points indicating the lowest potential risk for that component and the lowest number (0) indicating the highest potential risk. Government Stability index is an assessment both of the government's ability to carry out its declared program(s), and its ability to stay in office. The risk rating assigned is the sum of three subcomponents (Government Unity, Legislative Strength and Popular Support).

Corruption index is an assessment of corruption within the political system. Such corruption is a threat to foreign investment for several reasons: it distorts the economic and financial environment; it reduces the efficiency of government and business by enabling people to assume positions of power through patronage rather than ability; and, last but not least, introduces an inherent instability into the political process.

The institutional strength and quality of the bureaucracy is another shock absorber that tends to minimize revisions of policy when governments change. Therefore, high points are given to countries where the bureaucracy has the strength and expertise to govern without drastic changes in policy or interruptions in government services. In these low-risk countries, the bureaucracy tends to be somewhat autonomous from political pressure and to have an established mechanism for recruitment and training. Countries that lack the cushioning effect of a strong bureaucracy receive low points because a change in government tends to be traumatic in terms of policy formulation and day-to-day administrative functions.

The military is not elected by anyone. Therefore, its involvement in politics is a diminution of democratic accountability. However, it also has other significant implications.

Democracy Accountability is a measure of how responsive government is to its people, on the basis that the less responsive it is, the more likely it is that the government will fall, peacefully in a democratic society, but possibly violently in a non-democratic one. The points in this component are awarded on the basis of the type of governance enjoyed by the country in question.

Law and Order are assessed separately. The Law sub-component is an assessment of the strength and impartiality of the legal system, while the Order sub-component is an assessment of popular observance of the law.

Internal Conflict is an assessment of political violence in the country and its actual or potential impact on governance. The highest rating is given to those countries where there is no armed or civil opposition to the government and the government does not indulge in arbitrary violence, direct or indirect, against its own people. The lowest rating is given to a country embroiled in an on-going civil war. The risk rating assigned is the sum of three subcomponents (Civil War/Coup Threat, Terrorism/Political Violence and Civil Disorder).

Other explanatory variables: As variables of control, we use several indicators. Schooling in the population is represented by mother education. Data about this indicator are taken from [START_REF] Gwatkin | Socio-Economic Differences in Health, Nutrition, and Population Within Developing Countries, An Overview[END_REF]. We also control for Gross Domestic Product (GDP) per capita, immunization rate against DPT, fertility rate, population density and the percentage of urban population, all taken from WDI (2007). Finally, year and quintile fixed effects dummies are used and we make a cluster for each country, given data availability. Table 1 displays the characteristics of health and education data for each quintile while table A1 summarizes the characteristics, and sources of each indicator used in this paper.

Results

a. impact of air pollution on inter countries health inequality

In this subsection, we access the effect of air pollution on health inequality between countries.

More precisely, this part presents the results obtained from the estimation of equation (4.1).

These results are summarized in table 2, with logit of infant and under five mortality rates as dependent variables, and sulphur dioxide and particulate emissions as environmental variables. Regarding the impact of our variables of interest, we find that the elasticity of infant and child mortality rates with respect to environmental variables is positive and statistically significant for each health outcome and each pollution variable. These coefficients indicate that environmental degradation worsens population health outcomes and explains in part health inequalities between countries. These results are in conformity with the literature on this topic as well as our theoretical hypothesis. Our important variables of control also present the expected signs and are statistically significant. Indeed, increasing in Gross Domestic Product per capita (GDP), mother education and immunization rate improve significantly health outcomes while fertility rate degrades them.

b. Heterogeneity in the health effect of air pollution (intra country inequalities)

In the previous subsection, we found that pollution is in part responsible to health inequality between countries. This section extends these results and explores whether environmental degradation may contribute to within country income related health inequalities. It presents the results obtained from the estimation of equation (4.2) and these results are summarized in table 3. In this table, the coefficients of interest are those of the interaction terms of environmental variables and quintile dummies ( i λ ).

These coefficients are higher for poor quintiles as compare to those of richest quintiles. In addition, they are negative and statistically significant for richest quintiles and not significant for poorest quintiles. These results show that, environmental degradation degrades more the health outcomes of poorest quintiles than it worsens those of the richest quintiles. This heterogeneity in the health effect of air pollution increases income related health inequality within country. These results are in conformity with our theoretical hypothesis and arguments.

Besides these findings, all the variables already analysed in previous subsection present the correct signs and are statistically significant.

c. Roles of political institutions in the health inequality effect of pollution

We have previously found that pollution is harmful for population health and the poorest income classes are those that suffer more from this effect. This section is devoted to the roles played by political institutions regarding this effect of air pollution on health inequality. It

shows the results obtained from the estimation of equation ( 4.3) and the findings are presented in table 4.

In this table, we are interested by the coefficients of the interaction terms of environmental variables, institutions and quintile dummies ( i γ ). These coefficients are higher for richest quintiles than poorest quintiles. That result demonstrates that good political institutions mitigate more the health effect of air pollution for the poorest quintiles than they do for richest income classes. We can conclude that political institutions contribute to reduce the health inequalities created by environmental degradation by mitigating its impact on the poor.

To test the robustness of our result to the choice of institutional indicator, we replace our institutional variable (military in politics) by successively bureaucracy quality, corruption, law and order, democracy accountability, internal conflict, and freedom status indices. The results obtained are presented in Table A6 and they remain unchanged, namely, the coefficients of the interaction terms of environmental variables, institutions and quintile dummies ( i γ ) are higher for richest income quintiles as compare to poorest ones.

Robustness checks

In the previous section we showed that air pollution is more disastrous for poor people's health (poor income quintiles health) than that of rich people (rich income quintile), and therefore increases income related health inequality within population. On could argue that these results suffer from at least three drawbacks. First, because environmental variable is not disaggregated by asset quintile, we did not take into account country fixed effects and this could bias our results. The second problem also comes from the structure of our data. In fact, the dependent variables (health variables) are more disaggregated than the variables of interest (environment and institution variables), and that may downward-bias the standard deviations because of Moulton bias [START_REF] Moulton | Diagnostics for Group Effects in Regression Analysis[END_REF][START_REF] Moulton | An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Units[END_REF]. [START_REF] Moulton | An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Units[END_REF] demonstrated that if the disturbances are correlated within the groupings that are used to merge aggregated with micro data, the standard errors from Ordinary Least Squares (OLS) are seriously biased downward. Third, one could argue that we assessed the effect of environment on health inequality, but we did not use explicitly any health inequality indicator. To solve for this, we replace health indicator by the range, more precisely we use as alternative dependent variable the logarithmic form of the ratio of the first quintile of mortality rates to those of the fifth quintile. This indicator is largely used in the literature to measure health inequality [START_REF] Wagstaff | on the measurement of inequalities in health[END_REF][START_REF] Levine | Black-White Inequalities in Mortality and Life Expectancy, 1933-1999: Implications for Healthy People[END_REF]. That is, all the variables are expressed in country level.

' jt jt jt i jt health X environment β δ µ ε = + + + (6.1)
The results obtained from the estimation of this equation with fixed effect are presented in table 5. The coefficients of environment indicators are positive and statistically significant showing that air pollution increases mortality gap between rich and poor asset groups in a given country, and this confirms our previous results. To verify the role played by institutions quality in this effect of pollution on health inequality, we add to the previous equation the interaction term of environment and institutional variables and we obtain the following equation.

β δ ψ ε = + + + (6.2)
We also estimate this equation with fixed effect and the results are summarized in table 6. The coefficients of environment indicators remain positive and statistically significant, and those of the interaction terms are negative and significant. These results confirm our previous findings, namely good political institutions contribute to reduce the health inequalities created by environmental degradation. However, as argue by [START_REF] Wagstaff | on the measurement of inequalities in health[END_REF], the range overlooks what is going on in the intermediate groups. The gap between the first and the fifth quintiles might, for example, remain unchanged, but the extent of inequality between the intermediate quintiles might well be diminishing (or increasing). In addition, it does not take into account the sizes of the indicators being compared. This can lead to misleading results when comparisons are performed over time or across countries. This can be solved by using as health inequality indicator, the concentration index of mortality rates. This indicator is commonly used to represent health inequality, because of its affinity with the Gini coefficient, its visual representation by means of the Concentration Curve and the ease with which it can be decomposed. It can be calculated at individual level as well as socioeconomic group level (income quintile level). It cannot be lower than -1 and higher than 1. A negative (positive) value of the concentration index of mortality rates designates a more concentrated mortality within poor (rich) people. A zero value indicates an equal distribution of mortality according to income quintiles. As argue by [START_REF] Erreygers | Correcting the Concentration Index[END_REF], this indicator is far from perfect. The first criticism is from Wagstaff (2005). He argues that if the health variable is binary, the bounds of the Concentration Index depend upon the mean of the health variable. The bounds turn out to be much wider for populations with a low mean than for populations with a high mean. To address this issue, he proposes to divide the health Concentration Index by its upper bound. According to [START_REF] Erreygers | Correcting the Concentration Index[END_REF] Wagstaff procedure exaggerates the correction it applies to the index and to its bounds, and an alternative solution has been formulated originally by [START_REF] Wagstaff | on the measurement of inequalities in health[END_REF]. This indicator called Generalized health Concentration Index is obtained by multiplying the health Concentration Index by the average health level.

We use in this section as alternative health inequality indicator in equations (6.1) and (6.2) the Generalized Concentration Index of mortality rates. The results obtained with fixed effects estimator are presented in Tables A3 andA4 in Appendix A. They remain similar to previous results.

Concluding remarks

This article extends economic literature on the association between environment and health by investigating the responsibility of air pollution in the explanation of health inequalities both between and within developing countries. It examines also the importance of the role played by good political institutions in this effect.

We argue that population belonging to poorest income quintiles are those likely to suffer more from environmental degradation, because they receive the highest exposure, and this exposure then exercises larger effects on their health than it does on the average population.

Furthermore, richest communities have more prevention than poorest and have more access to medical care when they are sick from pollution.

In countries with good political institutions, this heterogeneity in the health effect of pollution may be mitigated since these institutions favour universal health policy issues, information and advices about hygiene, and health infrastructures building.

Globally, our econometric results corroborate these theoretical arguments and hypothesis about the positive association between air pollution and income related health inequalities. In addition, our empirical results confirm the significant role played by democratic institutions in protecting poor population from environmental degradation. These important findings raise some policy implications. First, to be effective, health policies should not be based only on average health of a given population, but also on its distribution.

In addition, differential distribution of health effects of pollution should be considered alongside differential distribution of the benefits related to the emission sources. Indeed, those who pollute more in a population, such as car ownership may compensate those who bear the adverse effect by paying a tax. Finally, improving political institutions is not only important for economic growth, but it is also essential for population wellbeing. This study could be extended in many ways. Firstly, a limit of this work is doubtless the unavailability of environmental data varying across income quintiles. This kind of data takes into account the differential of exposure. Future works on this topic should solve for this and test our hypothesis with more accurate data. Researchers may also use other environmental and health indicators to verify our hypothesis. We focus only on developing countries. It will be interesting to extend our results by testing whether they may be generalized for developed countries or compare them across different geographical regions. APPENDICES A.

Figure 1

 1 Figure 1 depicts the inter quintiles distribution of mortality rates among regions (top graphs) as well as pollution level (bottom left) and institutional quality (bottom right). From this figure we can notice that mortality rates are more unequally distributed in Sub Saharan Africa (SSA) and South Asia (SA) than other region.

Figure 1 :

 1 Figure 1: Distributions of Mortality rates and its link to pollution and institution by region

  (a) Infant mortality: number of deaths to children under twelve months of age per 1,000 live births, based on experience during the ten years before the survey. (b) Child mortality: number of deaths to children under five years of age per 1,000 live births, based on experience during the ten years before the survey. (d) Fertility rate: average number of births a woman could expect to have during her lifetime if she followed the levels of fertility currently observed at every age. The TFR is calculated as the sum of average annual age specific fertility rates for all reproductive age groups (usually 15-49 years) in the three years before the survey. (c) Female educational attainment: percent of women aged 15-49 years who had completed the fifth grade.

Figure 2 :

 2 Figure 2: Comparison of mortality rates among asset quintiles

Table 1

 1 presents important statistics of health, education and fertility indicators. This table points out the large disparities among income classes in favor of rich people for all these variables. Figure2confirms this inequality for mortality rates.

	Table 1. Summary Statistics
	Variables	Obs	Mean	Std. Dev.	Min	Max
	Full sample
	Infant mortality (a)	380	72.13	33.75	11.90	187.70
	Child mortality (b)	380	113.80	67.00	14.20	354.90
	Fertility rate (c)	380	4.55	1.80	1.20	8.50
	Female educational attainment (d)	380	50.44	31.94	0.50	99.80
	Poorest quintile (by an "asset index")
	Infant mortality (a)	76	86.88	31.32	32.00	187.70
	Child mortality (b)	76	140.08	62.82	39.10	297.90
	Fertility rate (c)	76	5.92	1.48	2.20	8.50
	Female educational attainment (d)	76	29.15	25.98	0.50	98.70
	Second quintile
	Infant mortality (a)	76	82.62	32.71	23.80	152.30
	Child mortality (b)	76	132.33	69.25	27.30	354.90
	Fertility rate (c)	76	5.14	1.55	1.80	8.20
	Female educational attainment (d)	76	39.24	29.75	1.00	99.50
	Third quintile
	Infant mortality (a)	76	75.91	34.14	19.70	157.20
	Child mortality (b)	76	120.08	69.44	23.50	348.30
	Fertility rate (c)	76	4.68	1.65	1.40	7.80
	Female educational attainment (d)	76	48.38	30.98	1.50	99.80
	Fourth quintile
	Infant mortality (a)	76	65.64	32.17	11.90	142.00
	Child mortality (b)	76	102.63	64.63	14.20	314.90
	Fertility rate (c)	76	4.02	1.61	1.50	7.20
	Female educational attainment (d)	76	59.09	29.71	4.80	99.60
	Richest quintile
	Infant mortality (a)	76	49.58	24.51	13.80	97.20
	Child mortality (b)	76	73.88	45.93	15.80	183.70
	Fertility rate (c)	76	2.96	1.15	1.20	6.20
	Female educational attainment (d)	76	76.34	20.13	27.00	99.80

Table 2 .

 2 Impact of air pollution on health inequalities between countries

			Dependent variables
		(1)	(2)	(3)	(4)
	independent variables	child mortality infant mortality child mortality infant mortality
	Sulphur dioxide emission (SO2)	0.0861**	0.0695**
		(2.610)	(2.692)
	Particulate Matter (PM10)			0.125**	0.127**
				(2.092)	(2.254)
	fertility rate	0.521***	0.342***	0.627***	0.451***
		(5.000)	(3.233)	(5.125)	(3.530)
	schooling	-0.0661	-0.0616	-0.0211	-0.0155
		(-1.615)	(-1.564)	(-0.544)	(-0.430)
	immunization rate	-0.673***	-0.499***	-0.656***	-0.496***
		(-4.412)	(-3.611)	(-4.069)	(-3.401)
	institution quality	0.0329	0.0396	0.0279	0.0346
		(0.993)	(1.321)	(0.620)	(0.899)
	GDP per capita	-0.358***	-0.234***	-0.304***	-0.186**
		(-6.372)	(-4.134)	(-4.182)	(-2.649)
	urban population	-0.0946	-0.0950	-0.0381	-0.0409
		(-0.908)	(-0.847)	(-0.374)	(-0.381)
	population density	0.0115	0.0340	-0.0300	0.000896
		(0.390)	(1.269)	(-1.215)	(0.0355)
	Constant	3.678***	1.682**	1.173	-0.556
		(4.267)	(2.234)	(1.274)	(-0.612)
	year dummies	yes	yes	yes	yes
	quintile dummies	yes	yes	yes	yes
	Observations	300	300	330	330
	R-squared	0.87	0.78	0.86	0.79
	***significant at 1%, **significant at 5%, *significant at 10%. t-statistics enter parenthesis.

Table 3 .

 3 Impact of air pollution on health inequalities within countries

			Dependent variables
		Sulphur dioxide emission (SO2)	Particulate Matter (PM10)
		(1)	(2)	(3)	(4)
	Independent variables	Child mortality Inf. mortality	Child mortality Inf. mortality
	air pollution	0.129***	0.116***	0.208**	0.187**
		(3.395)	(3.459)	(2.352)	(2.238)
	(air pollution)x(quintile 2)	-0.0321	-0.0209	-0.0176	-0.0181
		(-1.307)	(-0.969)	(-0.412)	(-0.426)
	(air pollution)x(quintile 3)	-0.0479**	-0.0592**	-0.0511	-0.0394
		(-2.021)	(-2.268)	(-0.978)	(-0.694)
	(air pollution)x(quintile 4)	-0.0549*	-0.0591	-0.0979	-0.0794
		(-1.938)	(-1.567)	(-1.278)	(-0.938)
	(air pollution)x(quintile 5)	-0.0823*	-0.0934*	-0.192**	-0.128
		(-1.706)	(-1.680)	(-2.256)	(-1.514)
	fertility rate	0.505***	0.323***	0.665***	0.478***
		(4.884)	(3.063)	(5.086)	(3.500)
	schooling	-0.0776*	-0.0754*	-0.000414	-0.00177
		(-1.848)	(-1.928)	(-0.00939)	(-0.0425)
	immunization rate	-0.658***	-0.481***	-0.680***	-0.512***
		(-4.337)	(-3.571)	(-4.204)	(-3.470)
	institution quality	0.0321	0.0387	0.0290	0.0353
		(0.956)	(1.277)	(0.639)	(0.904)
	GDP per capita	-0.357***	-0.232***	-0.303***	-0.185**
		(-6.325)	(-4.133)	(-4.095)	(-2.586)
	urban population	-0.0978	-0.0988	-0.0313	-0.0361
		(-0.948)	(-0.893)	(-0.302)	(-0.329)
	population density	0.00958	0.0316	-0.0264	0.00340
		(0.329)	(1.202)	(-1.028)	(0.129)
	Constant	4.242***	2.286***	0.740	-0.874
		(4.871)	(2.900)	(0.737)	(-0.866)
	year dummies	yes	yes	yes	yes
	quintile dummies	yes	yes	yes	yes
	Observations	300	300	330	330
	R-squared	0.87	0.78	0.87	0.79

***significant at 1%, **significant at 5%, *significant at 10%. t-statistics enter parenthesis.

Table 4 .

 4 Social protection role of political institutions

			Dependent variable
		Sulphur dioxide emission (SO2)	Particulate Matter (PM10)
		(1)	(2)	(3)	(4)
	Independent variables	Inf. mortality Child mortality	Inf. mortality Child mortality
	air pollution	0.280***	0.319***	0.0718	0.0963
		(2.996)	(3.086)	(0.467)	(0.558)
	(air pollution)x(quintile 2)	0.0102	0.0116	0.129	0.156
		(0.180)	(0.232)	(1.431)	(1.599)
	(air pollution)x(quintile 3)	-0.140	-0.109	0.0995	0.125
		(-1.596)	(-1.418)	(1.022)	(1.307)
	(air pollution)x(quintile 4)	-0.107	-0.107	0.0323	0.0447
		(-1.157)	(-1.307)	(0.220)	(0.336)
	(air pollution)x(quintile 5)	-0.290***	-0.281***	0.0266	-0.00222
		(-3.090)	(-3.085)	(0.229)	(-0.0189)
	(institution)x(quintile 2)	-0.117	-0.162	0.241*	0.287**
		(-0.557)	(-0.788)	(1.758)	(2.072)
	(institution)x(quintile 3)	0.272	0.201	0.217	0.282*
		(1.009)	(0.829)	(1.386)	(1.903)
	(institution)x(quintile 4)	0.146	0.162	0.162	0.222
		(0.542)	(0.645)	(0.621)	(0.939)
	(institution)x(quintile 5)	0.664**	0.675**	0.219	0.285
		(2.282)	(2.265)	(0.908)	(1.209)
	(institution)x(air pollution)	-0.0388**	-0.0449**	0.0401	0.0396
		(-2.191)	(-2.274)	(0.749)	(0.685)
	(institution)x(air pollution)x(quintile 2)	-0.00852	-0.0121	-0.0585**	-0.0688**
		(-0.500)	(-0.719)	(-2.033)	(-2.255)
	(institution)x(air pollution)x(quintile 3)	0.0236	0.0179	-0.0568	-0.0710**
		(1.142)	(0.957)	(-1.636)	(-2.120)
	(institution)x(air pollution)x(quintile 4)	0.0139	0.0144	-0.0438	-0.0551
		(0.684)	(0.736)	(-0.766)	(-1.047)
	(institution)x(air pollution)x(quintile 5)	0.0543**	0.0550**	-0.0581	-0.0730
		(2.532)	(2.478)	(-1.095)	(-1.386)
	fertility rate	0.328***	0.504***	0.471***	0.661***
		(3.035)	(4.552)	(3.601)	(5.274)
	schooling	-0.107***	-0.107***	-0.0261	-0.0212
		(-2.904)	(-2.804)	(-0.613)	(-0.473)
	immunization rate	-0.538***	-0.732***	-0.542***	-0.724***
		(-4.374)	(-4.650)	(-4.176)	(-4.859)
	GDP per capita	-0.241***	-0.371***	-0.179**	-0.299***
		(-4.560)	(-6.783)	(-2.411)	(-3.841)
	institution quality	-0.434*	-0.518**	-0.110	-0.112
		(-1.945)	(-2.118)	(-0.455)	(-0.441)
	urban population	-0.0944	-0.0953	-0.0272	-0.0177
		(-0.939)	(-1.016)	(-0.238)	(-0.157)
	population density	0.0551*	0.0358	0.0137	-0.0141
		(1.765)	(1.047)	(0.487)	(-0.500)
	Constant	4.588***	6.981***	-0.318	1.295
		(3.175)	(3.996)	(-0.289)	(1.052)
	year dummies	yes	yes	yes	yes
	quintile dummies	yes	yes	yes	yes
	Observations	300	300	330	330
	R-squared	0.80	0.88	0.79	0.87

***significant at 1%, **significant at 5%, *significant at 10%. t-statistics enter parenthesis.

Table 5 :

 5 Effect of air pollution on health inequality Dependent variable: log of the Ratio of poorest quintile to

	richest quintile of infant mortality rate (Q1/Q5)

Table 6 :

 6 Role of political institutions in effect of air pollution on health inequality Dependent variable: log of the Ratio of poorest quintile to richest quintile of infant mortality rate

	(Q1/Q5)

Table A1 .

 A1 Data characteristics and sources

	variables			characteristics			sources
		number of deaths to children under twelve months of age
	infant mortality rate	per 1,000 live births, based on experience during the ten	Gwatkin et al. (2007)
			years before the survey.
		number of deaths to children under five years of age per
	child mortality rate	1,000 live births, based on experience during the ten years	Gwatkin et al. (2007)
			before the survey.
	Sulphur dioxide emission (SO2)		sulphur dioxide emission		Stern (2005)
	Particulate Matter (PM10)	particulate matter less than 10 µm aerodynamic diameter	WDI 2007
		average number of births a woman could expect to have
	fertility rate	during her lifetime if she followed the levels of fertility	Gwatkin et al. (2007)
			currently observed at every age.
	schooling	percent of women aged 15-49 years who had completed the fifth grade.	Gwatkin et al. (2007)
	immunization rate		immunization rate against DPT		WDI 2007
		corruption, bureaucracy quality, ethnic tension, military in	"International Country
	institution quality	politics, law and order, external conflict, democracy	Risk Guide" (ICRG) and
		accountability, internal conflict and freedom status	freedom house
	GDP per capita		Gross Domestic Product per capita		WDI 2007
	urban population		Proportion of urban population		WDI 2007
	population density		Population density			WDI 2007
		Table A2: Descriptive Statistics of Important variables
	Variables		mean	min	max	Coef. var. N
	Infant mortality rate	74,65	22,10	147,40	0,39	95
	Under five mortality rate	118,60 25,70	302,60	0,51	95
	Sulphur dioxide emission (SO2) 239,86 0,53	2926,53	2,18	73
	Particulate Matter (PM10)	77,99	7,30	225,86	0,62	82
	urban population percentage	38,43	11,40	80,10	0,47	95
	population density		110,19 1,85	1156,40	1,75	95
	fertility rate		5,88	2,20	8,50	0,26	95
	schooling		30,25	0,00	99,10	0,92	94
	GDP per capita		815,38 120,11	4286,50	1,03	95
	ICRG Bureaucracy quality	1,71	0,00	3,50	0,50	79
	ICRG corruption index	2,54	0,00	4,00	0,36

Table A5 .

 A5 list of countries in the regression sample

	country name	Year	country name	Year
	Armenia	2000	Madagascar	1997
	Benin	1996, 2001	Mali	1995, 2001
	Burkina Faso	1992, 1998, 2003	Mozambique	1997, 2003
	Bangladesh	1996, 1999, 2004	Mauritania	2000
	Bolivia	1998, 2003	Malawi	1992, 2000
	Brazil	1996	Namibia	1992, 2000
	Central African Republic 1994	Niger	1998
	Côte d'Ivoire	1994	Nigeria	1990, 2003
	Cameroon	1991, 1998, 2004	Nicaragua	1997, 2001
	Colombia	1995, 2000, 2005	Nepal	1996, 2001
	Comoros	1996	Pakistan	1990
	Dominican Republic	1996, 2002	Peru	1996, 2000
	Egypt	1995, 2000	Philippines	1998, 2003
	Eritrea	1995	Paraguay	1990
	Ethiopia	2000	Rwanda	2000
	Gabon	2000	Senegal	1997
	Ghana	1993, 1998, 2003	Chad	1996, 2004
	Guinea	1999	Togo	1998
	Guatemala	1995, 1998	Turkmenistan	2000
	Haiti	1994, 2000	Turkey	1993, 1998
	Indonesia	1997, 2002	Tanzania	1996, 1999, 2004
	India	1992, 1998	Uganda	1995, 2000
	Jordan	1997	Uzbekistan	1996
	Kazakhstan	1995, 1999	Vietnam	1997, 2002
	Kenya	1993, 1998, 2003	Yemen	1997
	Kyrgyzstan	1997	South Africa	1998
	Cambodia	2000	Zambia	1996, 2001
	Morocco	1992, 2003	Zimbabwe	1994, 1999

Table A6 .

 A6 Robustness checks : Social protection role of political institutions. significant at 1%, **significant at 5%, *significant at 10%. t-statistics enter parenthesis.

							Dependent variables
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
	Independent variables	inf. mort.	child mort.	inf. mort.	child mort. inf. mort. child mort.	inf. mort.	child mort.	inf. mort. child mort. inf. mort. child mort.
	air pollution	0.153**	0.153***	0.184**	0.196**	0.0339	0.0110	0.120*	0.114	0.0509	0.104	0.223**	0.259***
		(2.683)	(2.862)	(2.225)	(2.654)	(0.447)	(0.147)	(1.953)	(1.632)	(0.498)	(0.829)	(2.665)	(2.936)
	(air pollution)x(quintile 2)	0.0341	0.0290	0.0596	0.0627*	0.0984*** 0.0846**	0.0760**	0.0607*	0.119*	0.107	0.0602	0.00915
		(0.758)	(0.963)	(1.351)	(1.712)	(3.565)	(2.437)	(2.048)	(1.886)	(1.860)	(1.489)	(0.836)	(0.149)
	(air pollution)x(quintile 3)	-0.0580	-0.0320	-0.0224	0.00145	0.0447	0.0865*	-0.0640	-0.0332	-0.0908	-0.0568	-0.128*	-0.102*
		(-1.049)	(-0.621)	(-0.306)	(0.0244)	(0.801)	(1.877)	(-0.807)	(-0.500)	(-1.110)	(-0.798)	(-2.004)	(-1.772)
	(air pollution)x(quintile 4)	-0.137*	-0.0948	-0.116	-0.0940	-0.0262	0.0497	-0.150**	-0.106*	-0.119	-0.119	-0.163*	-0.151*
		(-1.842)	(-1.293)	(-0.772)	(-0.795)	(-0.420)	(0.943)	(-2.152)	(-1.964)	(-1.146)	(-1.300)	(-1.905)	(-1.859)
	(air pollution)x(quintile 5)	-0.245*** 0.0377	-0.181** 0.0153	-0.234 0.0349	-0.177 0.0132	0.00118 0.0393	0.0739 0.0377	-0.116 0.0278	-0.0857 0.00991	-0.379*** -0.317*** -0.457*** -0.417*** 0.0213 0.00474 0.0203 -0.00226
		(-3.602) (1.390)	(-2.444) (0.497)	(-1.571) (1.308)	(-1.365) (0.443)	(0.00734) (1.312)	(0.508) (1.134)	(-0.759) (1.059)	(-0.614) (0.317)	(-3.361) (0.680)	(-3.024) (0.140)	(-4.204) (0.678)	(-4.459) (-0.0690)
	(institution)x(quintile 2) Constant	-0.355 2.240*	-0.387*** 4.105***	-0.364** 2.953**	-0.430*** -0.725*** -0.694*** 4.893*** -0.0392 0.726	-0.400*** 2.121*	-0.385** 3.812***	-0.518** 1.201	-0.520* 3.752*	-0.117 3.484**	-0.0543 5.803***
		(-1.542) (1.916)	(-2.958) (3.652)	(-2.369) (2.319)	(-2.777) (3.903)	(-4.960) (-0.0349)	(-2.950) (0.609)	(-2.907) (1.878)	(-2.406) (2.964)	(-2.121) (0.779)	(-1.769) (1.987)	(-1.013) (2.632)	(-0.489) (4.056)
	(institution)x(quintile 3) Institution indicators	0.0590 Bureaucracy quality -0.0332	-0.164 corruption index -0.221	-0.605* freedom status -0.759***	0.00889 democracy accountability -0.0641	0.126 law and order 0.0423	0.115 internal conflict 0.0936
	year dummies	(0.228) yes	(-0.141) yes	(-0.585) yes	(-0.975) yes	(-1.940) yes	(-3.107) yes	(0.0352) yes	(-0.302) yes	(0.438) yes	(0.163) yes	(1.250) yes	(1.074) yes
	(institution)x(quintile 4) quintile dummies	0.623 yes	0.370 yes	0.264 yes	0.182 yes	-0.0138 yes	-0.467 yes	0.363 yes	0.199 yes	0.238 yes	0.273 yes	0.170 yes	0.162 yes
	Observations	(1.456) 300	(0.954) 300	(0.404) 300	(0.368) 300	(-0.0343) 360	(-1.523) 360	(1.403) 300	(0.972) 300	(0.627) 300	(0.866) 300	(1.328) 300	(1.350) 300
	(institution)x(quintile 5) R-squared	1.124** 0.80	0.764* 0.88	0.644 0.79	0.434 0.87	-0.445 0.74	-0.813 0.84	0.0739 0.79	0.00179 0.87	1.080** 0.79	0.900** 0.87	0.559*** 0.79	0.522*** 0.87
		(2.631)	(1.832) ***	(0.917)	(0.725)	(-0.430)	(-0.882)	(0.126)	(0.00334)	(2.608)	(2.278)	(3.398)	(3.666)
	(institution)x(air pollution)x(quintile 2)	-0.0252	-0.0265***	-0.024**	-0.0296** -0.060*** -0.0584*** -0.0312*** -0.0298**	-0.0411**	-0.0406*	-0.0103	-0.00561
		(-1.531)	(-2.956)	(-2.077)	(-2.359)	(-4.785)	(-2.907)	(-2.805)	(-2.274)	(-2.186)	(-1.782)	(-1.142)	(-0.633)
	(institution)x(air pollution)x(quintile 3)	0.0110	0.00482	-0.00615	-0.0102	-0.0507** -0.0633***	0.00237	-0.00449	0.00855	0.00225	0.00746	0.00583
		(0.562)	(0.279)	(-0.296)	(-0.584)	(-2.057)	(-3.212)	(0.124)	(-0.277)	(0.413)	(0.120)	(1.077)	(0.850)
	(institution)x(air pollution)x(quintile 4)	0.0563*	0.0380	0.0268	0.0203	-0.00539	-0.0410*	0.0300	0.0171	0.0161	0.0170	0.0115	0.0105
		(1.765)	(1.328)	(0.553)	(0.558)	(-0.180)	(-1.814)	(1.544)	(1.114)	(0.597)	(0.740)	(1.175)	(1.138)
	(institution)x(air pollution)x(quintile 5)	0.0956***	0.0678**	0.0541	0.0377	-0.0326	-0.0649	0.00793	0.000878	0.0813***	0.0666** 0.0430*** 0.0392***
		(3.081)	(2.261)	(1.006)	(0.827)	(-0.417)	(-0.927)	(0.177)	(0.0217)	(2.754)	(2.372)	(3.386)	(3.558)
	(institution)x(air pollution)	-0.0188	-0.0147	-0.0279	-0.0274	0.0344	0.0507	-0.000535	0.00673	0.0192	0.00839	-0.0109	-0.0134
		(-0.644)	(-0.538)	(-1.044)	(-1.142)	(1.032)	(1.488)	(-0.0283)	(0.326)	(0.660)	(0.248)	(-1.373)	(-1.606)
	fertility rate	0.353***	0.528***	0.336***	0.515***	0.419***	0.694***	0.338***	0.520***	0.342***	0.524***	0.360***	0.546***
		(3.085)	(4.843)	(3.108)	(4.938)	(3.540)	(5.686)	(2.937)	(4.565)	(2.977)	(4.807)	(3.542)	(5.887)
	schooling	-0.0862**	-0.0859*	-0.0744*	-0.0765*	-0.0601*	-0.0747*	-0.0833**	-0.0863*	-0.0904**	-0.0864* -0.0870** -0.0853*

The mortality indicators are limited asymptotically, and an increase in this indicator does not represent the same performance when its initial level is weak or high, the best functional form to examine is that where the variable is expressed as a logit[START_REF] Grigoriou | Essais sur la vulnérabilité des enfants dans les pays en développement: l'impact de la politique économique[END_REF].

See Dockery (2009) for a large explanation of particulate air pollution.


J R Gomez-Solano

A Petrosyan

S Ciliberto

Heat fluctuations in an out of equilibrium bath

Keywords: numbers: 05.40.-a, 05.70.-a, 05.70.Ln

We measure the energy fluctuations of a Brownian particle confined by an optical trap in an aging gelatin after a very fast quench (less than 1 ms). The strong nonequilibrium fluctuations due to the assemblage of the gel, are interpreted, within the framework of fluctuation theorem, as a heat flux from the particle towards the bath. We derive, from a simple model, an analytical expression of the heat probability distribution, which fits the experimental data and satisfies a fluctuation relation similar to that of a system in contact with two baths at different temperatures.

The heat flux between two reservoirs at different temperatures is an important and useful example of an out of equilibrium process. In small systems this heat flux is a strongly fluctuating quantity and the probability distribution of these fluctuations has been recently widely studied, within the context of fluctuation theorems [1]. These studies have been mainly devoted to the steady state, that is when the temperatures T A and T B of the two reservoirs, A and B, are kept constant. In such a case the probability distribution P (Q τ ) of exchanging with the reservoir A the heat Q τ in a time τ , is related to the that of exchanging the quantity -Q τ according:

ln P (Q τ ) P (-Q τ ) = ∆β Q τ (1)
where ∆β = (1/T B -1/T A )/k B , k B is the Boltzmann constant and k B ∆β Q τ can be easily identified as the entropy production during the time τ [1][2][3]. This equation has been derived for several theoretical models [3,4] in the stationary regime. However the non stationary case, although very useful for applications, has been studied only in some specific models [5] of systems relaxing towards equilibrium. Thus one may wonder whether a relation like Eq. ( 1) may still hold, how it is eventually modified and what kind of information on the system can be obtained [5]. These important questions have never been analyzed in any experiment. Thus the purpose of this letter is to give new insight to this problem, by measuring the energy fluctuations of a Brownian particle used as a probe inside a gelatin relaxing towards its solid-like state (gel), after a very fast quench, from above to below the gelation temperature T gel . The main result of our investigation is that these fluctuations can be interpreted as a heat flux from the particle towards the bath. The measured P (Q τ ) satisfies an equation formally equivalent to Eq. ( 1), but in this case ∆β is a decreasing function of time. The P (Q τ ) can be fitted by an analytical expression that we derive from a Langevin equation for a Brownian particle coupled with an out of equilibrium bath.

The experiment has been performed using gelatin, a thermoreversible gel obtained from denatured collagen. Above T gel an aqueous gelatin solution is in a liquid viscous phase (sol), whereas below T gel the formation of a network of cross-linked filaments leads to an elastic solid-like phase (gel) [6]. In this gel phase the gelatin viscoelastic properties slowly evolve toward equilibrium and share some common phenomenological features with glassy dynamics [7][8][9]. We are interested in this transient out-of-equilibrium regime, that we use to study the fluctuations of the energy fluxes from and to the heat bath in the nonstationary case. A similar problem has been theoretically analyzed for the first time in Ref. [5] for a model of aging spin glasses. It has been found that a relation like Eq. ( 1) can be applied to a relaxing system to obtain quantitative informations on the heat exchanges with the bath. We show in this letter that this approach, exploited only once in real experiments [10], can be indeed very useful for understanding the properties of a Brownian particle in an out-of-equilibrium bath.

In the present experiment, an aqueous gelatin solution (type-B pig skin) at a concentration of 10%wt is prepared following the usual protocol [9]. For this sample T gel = 29 • C. This solution fills a transparent cell the temperature of which is controlled by a Peltier element [Fig. 1(a)], at T 0 = 26 ± 0.05 • C < T gel . Thus the solution inside the cell is in the solid-like phase. A silica bead, of radius r = 1 µm, is kept inside the gelatin in the focal position of a tightly focused laser beam (λ = 980 nm) at a power of 20 mW. At this power the laser produces on the particle an elastic force of stiffness k = 2.9 pN/µm. Because of light absorption, the temperature of the trapped particle is T = 27 • C, which is still smaller than T gel . Therefore the bead is inside the solid gel in the beam focus at a distance h = 25 µm from the cell wall, see Fig. 1(a) [11]. Starting from this condition, the laser power is increased to 200 mW and the local temperature around the focus rises to 38 • C > T gel . As a result the gel melts and a liquid droplet of radius a = 5 µm, is formed around the trapped bead inside the the solid gel bulk, as sketched in Fig. 1(a). After 180 s, the laser power is suddenly decreased again to 20 mW so that the temperature is homogenized by heat diffusion into the bulk in less than 1 ms resulting in a very efficient quench of the droplet to the final temperature T < T gel . At T the liquid inside the droplet solidifies in about 1 hour and the particle, trapped in the center of the drop by the focused beam, is a probe of this relaxation dynamics. The quenching procedure is repeated 60 times in order to perform the proper ensemble averages.

Immediately after the quench we record the time evolution of the x position [see Fig. 1(a)] of the trapped particle measured by a position sensitive detector whose output is sampled at 8 kHz and acquired by a computer. The resolution of the measurement of x is about 1 nm [10,12]. In order to characterize the particle dynamics we measure, using active microrheology [10], the time evolution of the viscous drag coefficient γ 0 of the particle and the largest correlation time τ 0 of the fluid. This is done by measuring the response of the bead at a timedependent sinusoidal force F of amplitude 87 fN and frequency f applied to the bead. The force F = kx 0 is obtained through the modulation of the beam focus position x 0 . The results for γ 0 and kτ 0 , measured at f = 5 Hz, are shown in Fig. 1(b). First, for t 200 s after the there is a transient regime where the droplet is purely viscous, τ 0 ≃ 0, whereas γ 0 increases in time. In this regime γ 0 and τ 0 do not depend on f . For t > 200 s the liquid gelatine inside the drop has a behavior similar to that observed in macroscopic samples [6,9], i.e. the liquid drop is actually undergoing gelation. We will study the nonequilibrium statistical properties of the bead dynamics in the very first 200 s after the quench where the liquid gelatin inside the drop is mainly viscous and the elasticity is negligible with respect to k, as shown in the inset of 1(b), where we plot kτ 0 /γ 0 as a function of time.

We begin by analyzing the variance σ x (t) 2 of x at time t after the quench. σ x (t) 2 is computed over 60 independent quenches and over a short time window δt = 0.1 s around each value of t in order to improve the statistics, as depicted in Fig. 2(a). The time evolution of σ x (t) 2 is plotted in Fig. 2(b). At the beginning, σ x (t) 2 is almost three times the equipartition value k B T /k that would be obtained at equilibrium. This shows the presence of a stochastic force on the particle due to the transient formation of the gel network. This force weakens compared to the thermal fluctuations becoming negligible at ∼ 20 s so that σ x (t) 2 slowly decreases in time, reaching the equilibrium value for t 20 s. This relaxation timescale is two orders of magnitude larger than the initial viscous relaxation time of the particle: τ k = γ 0 /k = 65 ms. Finally for t 200 s, σ x (t) 2 starts again to decrease because of the appearance of a strong elastic component of the gel confirming the direct measure of γ 0 , τ 0 , shown in Fig. 1(b), and justifying that for t ≤ 200 s the gelatin elasticity is negligible. During this relaxation process x remains Gaussian as shown in the inset of Fig. 2(b).

In Fig. 2(b) we also plot the time evolution of σ x (t) 2 measured, after the same quenching procedure, in a Newtonian fluid (glycerol 60%wt in water) with the same viscosity of the initial sol phase of gelatin. In this case, the particle dynamics must settle into an equilibrium state in a time ∼ τ k after the quench [13]. Indeed in Fig. 2(b) we see that, in glycerol, σ x (t) 2 = k B T /k for all t within the experimental accuracy. This confirms that no experimental artifact is present and that the observed dependence of σ x (t) 2 in gelatin is a real non-equilibrium effect due to the sol-gel transition. We now focus on the energy fluctuations of the particle inside the droplet for t < 200 s, i.e. when kτ 0 /γ 0 ≪ 1. Thus the energy of the particle is simply

U (t) = kx(t) 2 /2.
As there is no external force acting to the particle, the energy fluctuation ∆U t,τ during the time τ is equal to the heat Q t,τ exchanged between the particle and the bath [14], specifically

Q t,τ = ∆U t,τ = k 2 (x 2 t+τ -x 2 t ). ( 2
)
The mean heat transferred during [t, t + τ ] is

Q t,τ = (k/2)[σ x (t + τ ) 2 -σ x (t) 2 ]
≤ 0, which reveals the existence of a mean heat flux from the particle to the surroundings over the timescale τ because of the relaxation of σ x . The maximum value | Q t,τ | ≈ k B T takes place at t = 0 s and for 20 s τ 200 s. Non-negligible values of the mean heat compared to k B T persist for several seconds after the quench. Nevertheless, as t increases, | Q t,τ | becoming negligible and experimentally undetectable for t 20 s .

The probability density function P t (q τ ) of the normalized heat q t,τ = Q t,τ /(k B T ) is computed over the 60 quenches and over a short time window δt = 0.1 s around each t and t + τ , as sketched in Fig 2(a). We focus on a large value of τ in order to probe timescales comparable to the relaxation of the nonthermal fluctuations. Fig. 3(a) shows P t (q τ ) at different times t after the quench for τ = 30 s. P t (q τ ) is highly non-Gaussian with a spike at q τ = 0 and slowly decaying tails for all the values of t. Immediately after the quench, P t (q τ ) is strongly asymmetric with a long tail occurring at negative fluctuations. As t increases this asymmetry decreases and P t (q τ ) becomes symmetric at t 20 s.Once again, we check that the long-lived asymmetry occurs because of the intricate nonequilibrium nature of the bath. In the inset of Fig. 3(a) we plot P t (q τ ) with τ = 30 s for the local quenches performed in glycerol. P t (q τ ) quickly converges to the equilibrium profile and it is always symmetric with respect to q τ = 0.

As in Eq.( 1), the asymmetry function ρ t (q τ ) = ln [P t (q τ )/P t (-q τ ))] is commonly used to measure the asymmetry of P (q τ ) between the positive and the negative values of the fluctuations. The function ρ t (q τ ), computed from the P t (q τ ) shown in Fig. 3(a), is plotted in Fig 3(b). It is a linear function of its argument q τ : ρ t (q τ ) = -∆β t,τ q τ . The slope ∆β t,τ decreases as t increases approaching the symmetric value ∆β t,τ = 0 as | Q t,τ | ≪ k B T . This linear relation, except for the time dependent ∆β t,τ , is formally similar to Eq.( 1), and it is the first experimental evidence of the phenomenon theoretically obtained for a relaxing spin glasses in Ref. [5]. For comparison we also plot ρ t (q τ ) for the quench in glycerol at t = 0 and τ = 30 s. In this case the heat exchange process is always symmetric, stressing that this is due to the nonequilibrium nature of the bath.

In absence of a theory for our experimental results we model the nonequilibrium dynamics of the particle by an overdamped Langevin equation for x:

γ 0 ẋt = -kx t + ζ t , for t < 200 s (3)
where -kx t is the harmonic force exerted by the optical trap, and ζ t is a random noise representing the interaction of the particle with the out of equilibrium bath, i.e. the drop undergoing gelation. Because of the outof-equilibrium state, the statistical properties of ζ are unknown, and it is in general a nonstationary and correlated process. Multiplying Eq. ( 3) by ẋt and integrating over the time interval [t, t + τ ] one obtains the energy balance Eq. ( 2) [14], where Q t,τ is

Q t,τ = - t+τ t γ 0 ẋ2 s ds + t+τ t ζ ẋs ds, (4)
which is the sum of the viscous dissipation plus the the heat injected by the bath. Notice that Q t,τ cannot be estimated directly as ζ is unknown. The only experimental way to measure Q t,τ is via Eq. ( 2). The asymmetry of P t (q τ ) can be directly linked to the nonstationarity of the aging bath through the quantity σ x . Using Eq. ( 2) and the experimental fact that x is Gaussian [Fig. 2(b)], the analytical expression of P t (q τ ) for large τ can be computed [11]:

P t (q τ ) = A t,τ π K 0 (B t,τ |q τ |) exp - ∆ t,τ A t,τ 2 q τ , (5)
where K 0 is the zeroth-order modified Bessel function of the second kind,

∆ t,τ = σ x (t) σ x (t + τ ) - σ x (t + τ ) σ x (t) , A t,τ = k B T kσ x (t)σ x (t + τ ) and B t,τ = A t,τ 1 + ∆ 2 t,τ /4
In Eq. ( 5) the asymmetry of the density is completely determined by the parameter ∆ t,τ in the exponential. At equilibrium ∆ t,τ = 0, A t,τ = B t,τ = 1 regardless of t and τ , so that one recovers the symmetric equilibrium profile P t (q τ ) = K 0 (|q τ |)/π with q t,τ = 0 [15]. In Fig. 3(a) for each experimental P t (q τ ) we plot the theoretical prediction given by the analytical formula (5) using the respective experimental values of σ x shown in Fig. 2(b). The excellent agreement confirms that the Langevin model ( 3) is suitable to describe the particle dynamics and the heat exchange with the gelatin bath after the quench. From Eq. ( 5) one obtains the explicit expression for the asymmetry function ρ t (q τ ) = -∆β t,τ q τ and ∆β t,τ

∆β t,τ = k B T k 1 σ x (t + τ ) 2 - 1 σ x (t) 2 . (6)
Hence, the linearity of ρ t (q τ ) is analytically satisfied for all the values of the heat fluctuations and for all t even when P (q τ ) is strongly non-Gaussian. In Fig. 3(b) we plot the straight lines with the slope ∆β t,τ given by Eq. ( 6) and computed using the experimental values of σ x . The good agreement with the experimental data shows that Eq. ( 5) verifies a fluctuation relation, as Eq. (1). Eq.( 6) gains a very intuitive interpretation if one introduces an equipartition-like relation for the particle motion for 0 ≤ t 60 s: k B T ef f (t) = kσ x (t) 2 . Here T ef f is the effective temperature perceived by the particle due to its coupling with the nonequilibrium gelatin environment. In this way the parameter ∆β t,τ can be written conveniently as ∆β t,τ = [1/T ef f (t + τ ) -1/T ef f (t)] T, which is formally equivalent to that of Eq. (1). Hence ∆S τ = -k B ∆β t,τ q t,τ can be naturally identified as the entropy produced by the breakdown of the time-reversal symmetry due to the the effective temperature imbalance at two different times after the quench. As the gelatin droplet ages ∆S τ slows down and the particle exhibits an equilibrium-like dynamics for the experimental timescales. We point out that unlike Eq. ( 1) derived in Refs. [3,4] for nonequilibrium steady states, Eq. ( 6) holds for a nonstationary regime created by the nonequilibrium bath.

In conclusion, we have experimentally studied the fluctuations of the heat exchanged between a trapped Brownian particle and a non-stationary bath, i.e. an aging gelatin after a very fast quench. We have shown that the distribution of the heat satisfies a fluctuation relation even when the bath is in a non-stationary state. A Langevin model justifies the observation. The analogy of our results with those obtained for spin glasses suggests that this fluctuation relation may appear as a very robust symmetry property of heat exchange processes in other kinds of relaxing systems.

FIG. 1 .

 1 FIG. 1. (a) Schematic representation of the experimental setup to perform a local quench in a sol droplet around a trapped particle in the gel bulk. (b) Time evolution of the viscous drag coefficient γ0 of the particle and the correlation time τ0 of the gelatin droplet measured after the quench at f = 5 Hz . Inset: kτ0/γ0 as a function of time.

FIG. 2 .

 2 FIG.2. (a) Time evolution of x after a quench. σx(t) 2 is computed over δt = 0.1 s and over 60 independent quenches. (b) Time evolution of σx(t) 2 (normalized by kBT /k) after the quenches performed in gelatin (•) and glycerol (dashed line). Inset: Probability density of x at t = 0.5 s and 50 s for the quench in gelatin. The solid lines are Gaussian fits.

FIG. 3 .

 3 FIG. 3. (a) Probability density Pt(qτ ) of the normalized heat qt,τ for τ = 30 s at different times t after the quench. The theoretical lines are computed using Eq. (5). Inset: Pt(qτ ) computed, at the same t and τ during a quench performed in glycerol. The solid line corresponds to the theoretical equilibrium profile. (b) Asymmetry function of the Pt(qτ ) shown in (a). The straight lines are obtained using Eq. (6).