Keywords: Tax, Internal conflict, Government revenue, Sub-Saharan Africa JEL Codes H2, H56, H11, F5

This article explores the relationship between violent conflicts and tax revenue in Sub-Saharan countries. In a first stage, I estimate the effects of conflicts for 42 countries using panel data analysis. I find that an outbreak of violent conflict leads to an average 1.5 percent loss of tax revenue per capita. The results show that due to the outbreak of violence, government cannot successfully raise revenue, and because the conflict also negatively affects key macroeconomic variables, the tax base shrink and the overall loss is higher. The results also point to an important role of some specificities of Sub-Saharan countries such as ethnic division and natural resource endowment. Drawing on these results, I conduct case study for Central African Republic, Cote d'Ivoire, Congo Republic, Guinea and Guinea Bissau in a second stage using synthetic control method. The results show that the 2002 conflict in Cote d'Ivoire and the 1998 conflict in Guinea-Bissau led to significant drop in tax revenue. The outbreak of conflict did not have significant effects on tax revenue for the remaining three countries.

The author

Alou Adessé Dama PhD candidate, Université Clermont Auvergne, CNRS, CERDI, F-63000 Clermont-Ferrand, France Email address: alou_adesse.dama@etu.uca.fr This work was supported by the LABEX IDGM+ (ANR-10-LABX-14-01) within the program "Investissements d'Avenir" operated by the French National Research Agency (ANR).

Études et Documents are available online at: https://cerdi.uca.fr/etudes-et-documents/ Director of Publication: Grégoire Rota-Graziosi Editor: Catherine Araujo-Bonjean Publisher: Aurélie Goumy ISSN: 2114 -7957

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Études et Documents is a working papers series. Working Papers are not refereed, they constitute research in progress. Responsibility for the contents and opinions expressed in the working papers rests solely with the authors. Comments and suggestions are welcome and should be addressed to the authors.

Introduction

A widely accepted belief is that wars make states stronger through its effects on public expenditure and taxation. Indeed, wars triggered many tax-policy reforms around the world, many of which persisted and remained even after the war. For instance, the share of countries using withholding taxes doubled during World War II, the American civil war saw the United States adopt an income tax (see [START_REF] Besley | Why do developing countries tax so little?[END_REF][START_REF] Hill | The civil war income tax[END_REF][START_REF] Tilly | Warmaking and State Making as Organized Crime[END_REF]. Two important features drives tax policy in time of war: the sheer necessity to finance war and the shared sacrifice or as called by [START_REF] Feldman | War and taxation: When does patriotism overcome the free-rider impulse?[END_REF] "we're in this together" mentality. Studies extending the war-making/ state-making framework to developing countries have resulted in mixed conclusions about whether the process is occurring in similar fashion to that in Europe [START_REF] Taylor | Tilly tally: War-making and state-making in the contemporary third world[END_REF]. Moreover, empirical evidence on this matter for Sub-Saharan Africa is scarce, even though the region has recorded the most conflicts since World War II. This article investigates the impact of conflicts on tax revenue in Sub-Saharan countries. I use data on violent conflicts and non-resource tax revenue for 42 countries for the period 1980 to 2015. Using Ordinary Least Squares (OLS) and entropy balancing, I find a negative and significant effect of violent conflicts on tax revenue. I establish that an outbreak of violent conflicts leads to an average 1.7 percent loss of tax revenue per capita. I furthermore rely on Synthetic Control Method (SCM) and the [START_REF] Pesaran | Estimation and inference in large heterogeneous panels with a multifactor error structure[END_REF] Correlated Common Effect (CCE) estimator to measure the effects of actual conflicts on five countries (Central African Republic, Cote d'Ivoire, Republic of Congo, Guinea and Guinea-Bissau). 1 Our results suggest that conflicts resulted in loss of tax revenue in Cote d'Ivoire and Guinea-Bissau. I also find negative but not robust effects of violent conflicts in Central African Republic and Congo Republic. The results reveal that Sub-Saharan African countries are having what [START_REF] Centeno | Blood and debt: War and taxation in nineteenth-century Latin America[END_REF]Centeno ( , p.1591) called the "wrong kind of war". Due to the outbreak of violence, government cannot successfully raise revenue and because the conflict negatively affects key macroeconomic variables such as the Gross Domestic Product, the tax base shrink, resulting in a higher overall loss of revenue. This loss of tax revenue can be particularly acute in countries where the tax administration was already poorly performing before the violence erupted. Some specificities of these countries such as ethnic division and natural resource endowment also matter in studying how conflict affects tax revenue.

The analysis presented here has three essential contributions. First, it tackles a subject with mixed results and concludes that the war-making/state-making connection does not work in Sub-Saharan Africa, where most conflicts have their root causes in inequalities, ethnic division along with political instabilities. I estimate the average effects of conflicts on tax revenue and focus on the effects of actual wars on specific states. 2 Second it identifies another determinant of tax revenue in developing countries. This is particularly important given the crucial role of domestic revenue mobilization for developing countries to finance their development and reduce poverty.

My research is related to three strands of previous work. First, the is related to the literature on war-making/state-making connection, most associated with Charles Tilly. This literature provides insights on the relationship between conflicts and the states capacity to raise revenue (see for instance [START_REF] Hintze | Military Organization and the Organization of the State[END_REF][START_REF] Peacock | The growth of public expenditure in the United Kingdom[END_REF][START_REF] Tilly | Warmaking and State Making as Organized Crime[END_REF]. This article is also related to the literature on the cost of wars and conflicts. The cost of wars has been studied extensively but mostly on economic growth (see for instance [START_REF] Abadie | The economic costs of conflict: A case study of the Basque Country[END_REF][START_REF] Brück | The economic impact of violent conflict[END_REF][START_REF] Collier | On the economic consequences of civil war[END_REF][START_REF] Costalli | The economic costs of civil war: Synthetic counterfactual evidence and the effects of ethnic fractionalization[END_REF]. Third, the analysis can be linked to the literature on the determinants of the tax revenue in developing countries, in particular research explaining differences in the level of tax revenue (see [START_REF] Burgess | Taxation and development[END_REF] and more recently [START_REF] Besley | Chapter 2 -Taxation and development[END_REF]2014).

The remainder of the paper is organized as follows. Section 2 briefly discusses the literature on taxation and conflicts. Section 3 introduces conflicts in Sub-Saharan Africa and chronicles the origin of the conflict in the five studied countries. Section 4 discusses the empirical strategy and the data. Section 5 presents the results and I conclude in Section 6.

Taxation and conflicts: a review

This section briefly presents some results from the literature on the links between conflicts and taxation and provides some insights on why the relationship may differ by region. For a more discussion on the related literature and the mechanisms by which conflict affects state formation see [START_REF] Rodriguez-Franco | Internal wars, taxation, and state building[END_REF]Taylor and[START_REF] Taylor | Tilly tally: War-making and state-making in the contemporary third world[END_REF].

The literature generally associates wars and conflicts with state formation, in particular its ability to extract/raise revenue. Most studies analysing how war triggered tax reform or shaped the way tax revenue were levied focus on the two world wars and or on the European experiences. [START_REF] Hintze | Military Organization and the Organization of the State[END_REF] as well as [START_REF] Tilly | Warmaking and State Making as Organized Crime[END_REF][START_REF] Tilly | Capital, Coercion and European States[END_REF], highlighted the importance of war in building a state's fiscal capacity. [START_REF] Tilly | Warmaking and State Making as Organized Crime[END_REF], in particular, explains the increase in countries debt and taxes from seventeenth century onward as a function of increasing cost of war making. [START_REF] Besley | Why do developing countries tax so little?[END_REF], showed that the share of countries using withholding taxes doubled during WWII. Peacock and[START_REF] Peacock | The growth of public expenditure in the United Kingdom[END_REF][START_REF] Peacock | Approaches to the analysis of government expenditure growth[END_REF] underlined the role of conflict's crisis, especially those of the two WW in explaining the levy behaviour of authorities. They argued that the increase in taxation caused by wars has a "ratchet effect", so that the postwar levels of taxation do not return to their pre-war levels. [START_REF] Leroy | Sociologie des finances publiques[END_REF] explains that during peace public interventions are restricted by the reluctance to pay tax, while war increases the tolerance to taxation. This characteristic was noticed in the structure of France public finance throughout world war I, especially in the implementation and collection of new taxes (see [START_REF] Cardoni | The 'science'of French public finances in the first World War[END_REF]. [START_REF] Hill | The civil war income tax[END_REF] chronicles the introduction, shaping and evolution of income tax in the United States during the American civil war and said that the country seemed fully prepared to accept this form of taxation as part of the burden made necessary by the war. Of Course, income tax was not the most important element in raising the revenue needed to finance the war effort. But the context of civil war allowed it and other form of direct taxation (interests on bonds for example).

The positive association between war and taxation can be explained through three main mechanisms. The first is the war-making/state making thesis. War is meant to dominate a territory, but since it requires resources, it implies an increase in extraction (mainly taxation). Moreover, the building up of war-making capacity increases the capacity to extract and ultimately leads to an organization with tax-collection agencies, protection services, etc. Second, in an already organized tax system, war periods can be associated to tax reforms because of the sheer necessity and the lower level of resistance from taxpayers. In discussing how war can shape tax system, Hill (1894, p.416) stated: "There were measures which the boldest innovator would hardly have dared propose in time of peace; but under the stress of war they were enacted, sometimes with little opposition and little discussion". War periods can facilitate tax reforms and the introduction of new tax instruments. Some of these measures therefore persist and remain even after the conflict or laid the foundation for sustainable funding of public goods. Finally, War periods can increase taxpayers' willingness to comply with tax obligations. This can be through an increase in patriotism. [START_REF] Feldman | War and taxation: When does patriotism overcome the free-rider impulse?[END_REF] assess the empirical relationship between conflict and tax compliance and show a positive correlation between tax compliance and conflict. They note however that the positive response can be eroded as fatalities grow. This literature shows that wars were proven to be favourable to reforms, contributed to develop some tax systems as well as governments' sources of income.

However, the applicability of this positive relationship beyond Europe remains controversial. Looking at other regions in particular Sub-Saharan, and/or other types of war the effects are not always positive. Latin America, for instance, did not fund its war expenditures by taxes. [START_REF] Jones | War and Public Finance in South America[END_REF][START_REF] Centeno | Blood and debt: War and taxation in nineteenth-century Latin America[END_REF]. Economies nowadays, have more access to borrowing. Consequently, the financing of wars slowly shifted from taxation to debt. Financing war through debt is particularly appealing as the population does not directly bear the cost of war. Moreover, in a context of high poverty and inequality, the government is expected to resort to a debt financing strategy because they are unable to strike a bargain of fiscal sacrifice (see for example [START_REF] Chang | Economic Inequality, War Finance and the Pursuit of Tax Fairness[END_REF]. In a post-conflict situation, tax issues may just receive less attention as the state may choose to focus on reconstruction, humanitarian services or simply be reluctant to impose new tax burdens on already struggling communities [START_REF] Van Den Boogaard | Tax Revenue Mobilization in Conflict-affected Developing Countries[END_REF]. It is also possible that the low priority given to tax issues may simply reflect the structure of contemporary international relations, with significant aid flows from partners in the conflict-affected country.

Scholars of internal wars believe these wars to cause state disintegration (see for instance, [START_REF] Centeno | Blood and debt: War and taxation in nineteenth-century Latin America[END_REF][START_REF] Fearon | Ethnicity, insurgency, and civil war[END_REF]. They usually oppose the effects of war depending on the type. Interstate wars are supposed to have a positive effect on taxation, while intrastate/civil wars have negative effect. Internal conflicts cause deterioration of governance and institutional quality -failure of the tax administration, deregulation of tax procedures, thus leading to inefficiency in the mobilization of tax revenues. This deterioration can be particularly acute in countries where institutional quality was already poor before the violence erupted. Violent conflicts also negatively affect key macroeconomic variables such as the GDP and trade (see for instance [START_REF] Abadie | The economic costs of conflict: A case study of the Basque Country[END_REF][START_REF] Brück | The economic impact of violent conflict[END_REF][START_REF] Glick | Collateral damage: trade disruption and the economic impact of war[END_REF]. These two variables are two main determinants of the tax-to-GDP ratio in developing countries. Most empirical analysis associate them positively to tax revenue. 3 The erosion of the tax base may lead to a decrease in tax revenue. Some specificities of Sub-Saharan countries, such as ethnic fractionalization, natural resources abundance may also alter the positive effects of war on taxation. In a context of natural resource abundance, the "loot seeking'' opportunity can be a motivation for rebellion and violent conflicts (see [START_REF] Collier | Greed and grievance in civil war[END_REF]. Tax revenue may decrease because of the resource abundance as a result of the eviction effects (see [START_REF] James | US state fiscal policy and natural resources[END_REF][START_REF] Jensen | State-building in resource-rich economies[END_REF]. Government will rely on natural resources because they are easier to tax. Weak institutions may also alter the positive effects of war on taxation. In Tilly's framework, the state making effect on war depend on the ability of the state to dominate a territory and be the unique supplier of protection as it 3 GDP has a direct relationship with tax revenue: fiscal instruments diversify with economic development, which can lead to a broadening of the tax base (see [START_REF] Musgrave | Fiscal systems[END_REF]. GDP is strongly correlated with most of the determinants of tax revenue: increase in administrative capacity with economic development, for example. See (Besley andPersson, 2013, 2014, for more discussion). Importation constitutes the tax base for many taxes. In developing countries tax revenue on international trade still represent a significant share of tax revenue. In addition, collecting tax revenue at the import stage is relatively easier and requires less administrative capacity (see [START_REF] Baunsgaard | Tax revenue and (or?) trade liberalization[END_REF] for more discussion). extracts revenue. The evidence in Sub-Saharan African rather points to a different direction as most conflicts lead to more insecurities (remote violence, attacks by bandits, control of some territories by rebel groups). The current insecurity in Mali is an illustration. Although the government, backed by French army (re)gained control over most territories, remotes violence and isolated attacks still occur. Another channel through which the weak institutions may prevent government from raising tax revenue to finance war is the perceived corruption. When populations become increasingly fatigued by and disgruntled with a predator states, they are less willing to share the sacrifice of the conflict by raising revenue for the government. This may even explain their logics behind joining armed groups /Jihadists (see [START_REF] Benjaminsen | Why do pastoralists in Mali join jihadist groups? A political ecological explanation[END_REF]. Ethnic fractionalization also stands as an important trait of Sub-Saharan African countries. It has helped fuel many political instabilities leading to violent conflicts (see examples below). Post-war situation in weak states also gives rises to ethnic based violence (see [START_REF] Cline | Jihadist movements in the Sahel: Rise of the Fulani?[END_REF] for the case of the ethnic violence between Fulani and Dogon in Mali following the outbreak of the conflict).

Three main mechanisms appear as a possible explanation to the negative effects of internal violent conflicts on tax revenue. First, the inability to successfully extract revenue due to the violence, associated to the shrink in the tax base resulting from the decrease in economic variables. Second, the specificities of Sub-Saharan African countries (ethnic division, natural resources abundance, weak institutions) may alter the positive effects of conflicts on taxation. Third, the existence of alternative sources of income such as the increasing access to borrowing and international aid may shift the funding of wars away from taxation.

Conflicts in Sub-Saharan Africa

One striking feature of the African continent is that almost every country has dealt with a conflict since their independence. 4 The number of active conflicts increased substantially in this region during the 1980s and 1990s: looking at the conflicts recorded by UCPD/PRIO 60% of countries analysed in this study were involved at least once in a conflict during the period 1980 to 2015. This number reaches 70% when considering all countries of the African continent. Figure 1 presents the conflict-ridden countries in Africa over the period 1980-2015. The number of years in active conflicts as well as the strength of those conflicts is different from one country to another. Ethiopia, Uganda and Sudan are among the countries that had the most year in active conflicts (see Figure A 1). On average, the strength of conflict increased from the 1960s until the 1990s and decreasing since then [START_REF] Marshall | Conflict Trends in Africa, 1946-2004: A Macro-Comparative Perspective: Report Prepared for Africa Conflict Prevention Poll (ACPP)[END_REF]. Panel A and Panel B in Number of scholars have studied the determinants of conflicts in Africa (see [START_REF] Blattman | Civil war[END_REF] for a complete literature review). Income inequality, natural resource abundance, weak institutions and ethnic division/polarization are among the main and most studied causes. The existence of large resources is associated with a higher probability of conflicts. Primary commodities generate a "loot seeking'' opportunity which can be a motivation for rebellion [START_REF] Collier | Greed and grievance in civil war[END_REF] and reduce the accountability of government to the population [START_REF] Collier | Democracy, development, and conflict[END_REF]. [START_REF] Fearon | Ethnicity, insurgency, and civil war[END_REF] argue that the conflict in poor countries can be seen as an illustration of weak states' limited capacity to control rebellions. [START_REF] Besley | State capacity, conflict, and development[END_REF] links low state capacity and higher probability of civil war to high resources rents. Ethnic division increases the probability of conflicts. [START_REF] Montalvo | Ethnic polarization, potential conflict, and civil wars[END_REF] and later [START_REF] Esteban | Ethnicity and conflict: An empirical study[END_REF] provide empirical evidence of the relationship. The civil wars in the five countries studied are perfect illustrations. Conflicts in the Central African Republic and in Cote d'Ivoire are results of ethnical based political instabilities. Guinea-Bissau and Congo were never able to organize successful transfer of power in a context where income inequalities were growing. The conflict in Guinea stands as the only exception as it was mainly imported and exacerbate by tension between the country and its neighbours, Liberia and Sierra Leone. In the following subsections, I present some backgrounds on the conflicts in these five countries. I complement the description with a detailed chronology of the conflicts in Table A 1.

The Central African Republic (2001)

The Central African Republic experienced its first outbreak of conflict in 2001 after a military faction attempted a coup against President Ange-Félix Patassé. The conflict is the result of years of ethnic division (see to [START_REF] Kłosowicz | Central African Republic: Portrait of A Collapsed State After the Last Rebellion[END_REF]United nations Security Council, 2002 for further details). The country has more than eighty ethnic groups, and not only the largest of them, Gbaja, Banda, Mandija and Sara, compete for power [START_REF] Kłosowicz | Central African Republic: Portrait of A Collapsed State After the Last Rebellion[END_REF]. In 1981, General André Kolinga, a member of the Yakoma tribe, came to power after a coup d'état. The selection of collaborators for state and military offices was based on patronage as well as ethnic and tribal affiliation. The Yakoma tribe, originally from the south of the country, with a population of no more than 5 percent, took over most key positions in the state and army [START_REF] Kłosowicz | Central African Republic: Portrait of A Collapsed State After the Last Rebellion[END_REF]. When Kolinga was replaced by Patassé, from the north of the country, the latter could not trust the army dominated by the Yakoma tribe. He created a well-paid presidential guard as well as a militia both made up of members of the northern tribes. During the attempted coup in 2001, Patassé received help from the Libyans and engaged the notorious bloodthirsty rebels from the Mouvement pour la Libération du Congo (MLC). The latter patrolled the south of the country massacred, raped and robbed the population, resulting in hundreds of deaths in 2001 (see [START_REF] Pettersson | Organized violence, 1989-2018 and peace agreements[END_REF]s UCDP/PRIO dataset) and thousands of displaced [START_REF] Kłosowicz | Central African Republic: Portrait of A Collapsed State After the Last Rebellion[END_REF]. The conflict still continues, alternating calm and turmoil. The highest number of fatalities was recorded in 2013 (see [START_REF] Pettersson | Organized violence, 1989-2018 and peace agreements[END_REF]s UCDP/PRIO dataset).

Cote d'Ivoire (2002)

The conflict in Côte d'Ivoire began in 2002 when soldiers mutinied and took control of the northern part of the country. As in the Central African Republic, the conflict in Côte d'Ivoire is the result of deep-rooted cleavages around ethnicity (for further insights, see [START_REF] Crook | Winning coalitions and ethno-regional politics: the failure of the opposition in the 1990 and 1995 elections in Côte d'Ivoire[END_REF][START_REF] Ogwang | The root causes of the conflict in Ivory Coast. Africa Portal Backgrounder n° 5[END_REF]Reuters, 2007;Turner, 2014a). In the aftermath of independence, the country recorded remarkable growth rates, mainly driven by the export of cocoa and coffee, whose plantations relied on immigrant workers. President Félix Houphouët-Boigny initiated policies favouring immigration from neighbouring countries and improved the rights of immigrant workers. As a result, immigrants and their descendants counted for almost a quarter of the population in 1998 [START_REF] Ogwang | The root causes of the conflict in Ivory Coast. Africa Portal Backgrounder n° 5[END_REF]. In 1990, in the country's first multiparty elections, the two main candidates were Houphouët-Boigny and Laurent Gbagbo. Gbagbo's Front Populaire accused the Parti Democratique and Houphouët-Boigny of promoting the interests of the Baoulé -one of the largest ethnic groups and the tribe of Houphouët-Boigny. From that time on, ethnicity became a major political factor. But it was not until five years later, as the presidential elections approached, that an identity politics would emerge. Houphouët-Boigny won the 1990 elections and died 3 years later. He was succeeded by Henri Konan Bédié, candidate for his own re-election in 1995. Bédié seeing the rise of Alassane Ouattara, from the Rassemblement des Républicains, who drew support from people with northern or Muslim background, will initiate steps to block Ouattara from running for President. On December 8, 1994, a new electoral code, that would require eligible candidates to have both their parents to be Ivoirian nationals in order to run for president, was adopted. In 1995, Bédié also initiated a policy of Ivorian nationalism, called "Ivoirité". The policy was another manoeuvre to make Ouattara candidacy difficult, if not impossible. Bédié was subsequently elected president in 1997, running against Francis Wodié alone, candidate from the Parti Ivoirien des Travailleurs (PIT). The campaign for the 2000 presidential election once again announced an ethnic dimension to political life. The division of the political elite, identity politics, inequalities between north and south, and diversity, not only ethnic but also cultural and religious, led to a coup headed by General Robert GueÏ in December 1999. Once in power, Gueï had a new constitution adopted by referendum in 2000, which emphasized that presidential candidates "must be Ivorian by origin, born to father and mother who are themselves Ivorian by origin; and must have never availed himself of another nationality",5 thus eliminating Ouattara. 6 Gueï lost the presidential elections in 2000 to Gbagbo. The hard-line stance of Gbagbo against northerners prompted disgruntled elements of the army, mainly from the north, to attempt an unsuccessful coup in Abidjan in 2002. Following this failed coup, Gbagbo attempted to demobilize two contingents of the army that were recruited during Gueï's short transition. This led to a mutiny which ended in civil war. More than six hundred casualties were recorded in 2002 (see [START_REF] Pettersson | Organized violence, 1989-2018 and peace agreements[END_REF]s UCDP/PRIO dataset). The conflict lasted until 2004 and another episode erupted in 2011 following the 2010 elections between Gbagbo and Ouattara.

The Republic of Congo (1993)

The 1993 civil war in the Republic of Congo began following the opposition contesting the results of the parliamentary elections. Even though ethnicity was not at the root of the conflict, politicians overtly stimulated ethnic consciousness to mobilize political supporters (For more details, see [START_REF] Clark | Foreign intervention in the civil war of the Congo Republic[END_REF]; United nations Office for the Coordination of Humanitarian Affairs, 2000). After 30 years of one-party political system, the country experimented for the first time a multiparty government in 1991. At the demand of the opposition, President Sassou-Ngesso allowed a sovereign national conference of important political and social figures. A multiparty constitution followed, which was adopted in March 1992. A transitional government was form with the mandate of organizing the elections (parliamentary and presidential). Pascal Lissouba, candidate of the Union Panafricaine pour la Démocratie Sociale (UPADS) is elected president in 1992. UPADS had formed a coalition with the Parti Congolais du Travail (PCT) to gain a majority in parliament. But, a month after his installation as president, the coalition broke down with the withdrawal of the PCT. The PCT joined forces with Bernard Kolélas, who had finished second in the presidential elections and whose party, the Mouvement Congolais pour le développement et la démocratie Intégrale (MCDDI), held the second most seats in the parliament. Lissouba proceeded to dissolve the parliament (against constitutional procedure) and scheduled new parliamentary elections for the following year. After the new elections, UPADS and its minor allies gained a majority. The opposition demanded that many seats be rerun and boycotted the second round of the elections. As the situation became intense, the three main politicians formed private militias to control access to various areas of the capital and the country slipped into civil war. Very quickly the country found itself in a tripartite division along ethno-regional lines. The constituency of Lissouba was made up of the three southern regions of Niari, Bouenza and Lekoumou. Kolélas gained votes in Brazzaville and in the surrounding area of Pool region. Sassou led in four of the northern regions, Likouala, Sangha, Cuvette and Cuvette-Ouest. Clashes between the militias later gave way to mob action by alienated youth. The recorded number of deaths from UCPD/PRIO is 53, but [START_REF] Clark | Foreign intervention in the civil war of the Congo Republic[END_REF] reported two thousand deaths. The war continued and 1997 was one of the most devastating episodes. Another episode happened in 2016.

Guinea (2000)

The 2000 civil war in Guinea is the result of a long-lasting civil war that engulfed Liberia then Sierra Leone (two border countries) in 1990s. It was mainly imported and was exacerbated by tension between Guinean president Lassana Conté and his regional nemesis Charles Taylor, president of Liberia (See [START_REF] Arieff | Still standing neighbourhood wars and political stability in Guinea[END_REF]Turner, 2014c for additional details). Conté Backed rebel movements opposed to Taylor. The support for anti-Taylor rebels played a role in inciting armed attacks on Guinean soil in regions bordering Liberia and Sierra Leone. In September 2000, Guinean dissidents, backed by the Liberian government, militia from ULIMO and rebels from the Revolutionary United Front (RUF) attacked Guinea. Attacks started in the southern part of Guinea (the border areas with Liberia and Sierra Leone) and gradually spread north. More than two hundred deaths were recorded in 2000 (see [START_REF] Pettersson | Organized violence, 1989-2018 and peace agreements[END_REF]s UCDP/PRIO dataset), and a quarter million people were internally displaced. Clashed continued in 2001, the year that marked the end of the conflict. The Guinean conflict is different from most civil wars in Sub-Saharan Africa, as it resulted from neighbouring government retaliation -by financing an insurgency across border. It was also shorter and concerned mostly bordering areas with neighbours Liberia and Sierra Leone.

Guinea-Bissau (1998)

The Guinea-Bissau civil war was triggered by an attempted coup d'état led by General Ansumane Mané against the President Joao Bernardo Vieira. The civil war is a result political instability in a country that failed to organize successful transfer of power since the independence (see Peace Direct, 2015;Turner, 2014b). In 1980, Vieira, then Prime minister, toppled the government of Luis Cabral and remained president since. In January 1998, Viera suspended Mané, an army General and former chief of staff. Mané was accused of negligence in regard to controlling the illegal sale of Guinean arms to the Mouvement des Forces Démocratiques de la Casamance (MFDC), in neighbouring Senegal. Mané, who was very popular among soldiers, was later homearrested. As a reaction, he and a group of allies from the armed forces took over the main military bases and arms depots. That was the beginning of the civil war. Neighbouring Senegal and Guinea intervened as they sent troops in to aid the government. In 1999, Vieira was ousted by Mané and the military junta. Mané briefly headed the junta before National Assembly speaker Malam Bacaï Sanha took power as acting president. In the following presidential elections of 2000, Kumba Iala gained the presidency. Iala rejected a demand from the junta to have a special consultative status. He was overthrown in a coup three years later. Vieira returned from exile and won the 2005 election. He was murdered in 2009 by a group of soldiers. The country has been experiencing a series of political instabilities that still continues.

Methodology and data

Data

Here I present the data and the empirical strategy to measure the causal effects of conflicts on tax revenue. Data on conflicts are from the UCPD/PRIO armed conflict dataset, version 19.1 (see [START_REF] Gleditsch | Armed conflict 1946-2001: A new dataset[END_REF][START_REF] Pettersson | Organized violence, 1989-2018 and peace agreements[END_REF]. The dataset records armed conflicts concerning States and characterized by the use of force between the two parties, and which result in a death toll of at least 25 deaths during a calendar year. Our analysis covers the period 1980-2015. In this timeframe, all the recorded conflicts but four were internal (internal or internationalized internal). The four exceptions were interstate conflicts: Chad and Nigeria in 1983;Burkina Faso and Mali in 1985;Chad and Libya in 1987;and Cameroon and Nigeria in 1996. I use data on non-resource tax revenue from [START_REF] Caldeira | Effort fiscal en Afrique subsaharienne : les résultats d'une nouvelle base de données[END_REF]. The authors provide annual country-level panel data for the period of 1980-2015 for 42 countries of Sub-Saharan Africa. Along with GDP per capita (in 2010 constant US dollar), Trade openness (sum of total import and export as percentage of GDP), the structure of the economy (measured by the added value of agriculture in share of GDP) are the control variables. I collected them from World Bank, World Development Indicators. To explore the role of the specificities of Sub-Saharan African countries, I use ethnic fractionalization, natural resources endowment, the institutional quality. The ethnic fractionalization index is from [START_REF] Alesina | Fractionalization[END_REF]. I use natural resources rent as percentage of GDP from World Bank World Development Indicators to measure countries resource endowment. Institutional quality is measured using the International Country Risk Guide (ICRG) database. Following [START_REF] Frankel | On graduation from fiscal procyclicality[END_REF], I compute an index of institutional quality based on an average of four normalized variables: investment profile, corruption, law and order, and bureaucratic quality. Higher values of the index indicate strong economic and political institutions. I also use alternative source of revenue in developing countries as further controls. I use net development assistance and official aid as a share of GDP and public and publicly guaranteed external debt stocks as share of GDP. The first is obtained from World Bank, World Development Indicators and the second is from World Bank, International Debt Statistics.

For the SCM framework, I use ethnic fractionalization as special predictor to capture the effect of ethnic division.

Table 1 presents the descriptive statistics of the variables included in the analysis. Table B 1 presents the relationships between the variables used in the analysis and statistical significance at the critical level of 5%. Conflicts are negatively associated with most of the variables. The negative association of conflicts and economic growth has been well documented (see e.g., [START_REF] Abadie | The economic costs of conflict: A case study of the Basque Country[END_REF][START_REF] Brück | The economic impact of violent conflict[END_REF]. [START_REF] Glick | Collateral damage: trade disruption and the economic impact of war[END_REF] present evidence of the negative effects of war on international trade. By shrinking economic activities, conflicts contribute to increasing the share of agricultural activities in the economy. Highly divided societies are breeding grounds for conflicts (see e.g., [START_REF] Montalvo | Ethnic polarization, potential conflict, and civil wars[END_REF][START_REF] Esteban | Ethnicity and conflict: An empirical study[END_REF] for discussion on the matter).

Figure 2 and Figure 3 present further stylized facts on the relationship between conflicts and the main predictors. Non-resource tax revenue is higher, on average, in countries that have never faced conflicts (Panels A and B in Figure 2). Countries where conflicts occurred at least once have higher non-resource tax revenue during peace period than during conflicts periods (Panel B in Figure 2). Panel A in Figure 2 shows that the five countries studied have similar tax revenue with countries that I do not study in the SCM framework. Figure 3 presents the predictors variables according to exposure to conflicts. On average, the GDP per capita is lesser during conflict periods than during peace periods and safe countries have the highest level. The added value of agriculture in the share of GDP becomes more important during conflict periods. This is because of the contraction of activities, which in turn, may negatively affects tax collection. Indeed, tax collection is more complicated in the primary sector see [START_REF] Caldeira | Effort fiscal en Afrique subsaharienne : les résultats d'une nouvelle base de données[END_REF].

Additionally, in developing countries, this sector largely evades taxes due to exemptions policies, the means of administration and to the liability of tax thresholds.

Total trade variable has similar trends with GDP per capita. Sources: Tax revenue Dataset for SSA, UCDP/PRIO and authors' own calculations. To manage scales, the GDP per capita was divided by 100.

Figure B 1 presents the evolution of non-resource tax revenue in the five countries studied and compare them to the evolution in safe countries and non-safe countries which do not fit the condition to be treated. Non-tax revenue in Central African Republic is amongst the lowest in the sample and is decreasing over the period. The characteristics of predictors are complicated as well. The lower level of tax revenue is associated to a higher, (almost the highest) level of agriculture added value, lower GDP per capita and international trade. Republic of Congo stands at a direct contrast to Central African Republic. Non-resource tax revenue per thousand inhabitants is high. 7 The country relies a lot on natural resources. International trade is high and mostly about primary resources. Agriculture has a small share of the economy. The GDP per capita is also very high. 8 As public revenue in the country is strongly related to resource tax revenue, it is unsteady and replicates a lot of variations. This may make hard the construction of the counterfactual. Non-resource tax revenue is decreasing in Cote d'Ivoire. Primary activities are an important part of the economic activities. The GDP per capita is above the average level of GDP per capita in conflictridden countries. Non-resource tax revenue in Guinea is low compared to the average level of the sample. Guinea-Bissau presents the same characteristics both in outcomes variables and predictors as the Central African Republic.

Empirical strategy

As a first step to our analysis, I estimate the effects of wars on non-resource tax revenue for an unbalanced panel of 42 countries over the period 1980-2015. I estimate the following equation:

𝑦𝑦 𝑖𝑖,𝑡𝑡 = 𝛽𝛽𝑐𝑐 𝑖𝑖,𝑡𝑡 + 𝛿𝛿𝑦𝑦 𝑡𝑡-1 + 𝛾𝛾𝑥𝑥 𝑖𝑖,𝑡𝑡 + 𝑎𝑎 𝑖𝑖 + 𝜃𝜃 𝑡𝑡 + 𝑢𝑢 𝑖𝑖,𝑡𝑡 , (1)
𝑐𝑐 𝑖𝑖,𝑡𝑡 is a dummy indicator for whether country 𝑖𝑖 experience conflict at time 𝑡𝑡. 𝑢𝑢 𝑖𝑖,𝑡𝑡 represents the error term 𝛼𝛼 𝑖𝑖 and 𝜃𝜃 𝑡𝑡 are respectively country and time fixed effects. The first accounts for unobservable country-specific factors and the second for time specific factors. 𝑦𝑦 𝑖𝑖,𝑡𝑡 and 𝑦𝑦 𝑖𝑖,𝑡𝑡-1 represents the non-resource tax revenue in country 𝑖𝑖 respectively at time 𝑡𝑡 and 𝑡𝑡 -1. Finally, 𝑥𝑥 is a vector of control variables.

At first, I use Ordinary Least Square (OLS) to estimate (1). This provides an average effect of conflict, assuming that the effects are homogeneous over time and across country. To test the sensibility of the OLS estimates from (1), I rely on the entropy balancing method proposed by [START_REF] Hainmueller | Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies[END_REF]. Entropy balancing is a 7 Bear in mind that the population is very low, and the country is very rich in natural resources. 8 We do not address the true distribution of wealth in the country and issues of inequality are beyond the scope of our analysis.

generalization of conventional matching methods that use a re-weighting scheme to incorporate covariate balance into a weight function that is applied to the sample. 9

Since equation ( 1) includes the lagged dependent variable in the right-hand side, the fixed effect estimator is inconsistent because of the correlation between the lagged dependent variable and the error term (see [START_REF] Nickell | Biases in dynamic models with fixed effects[END_REF]. I use the Generalized Methods of Moments (GMM) System estimator, which allows controlling for both unobserved country-specific effects and potential endogeneity of the explanatory variables. Basically, [START_REF] Blundell | Initial conditions and moment restrictions in dynamic panel data models[END_REF] show that this extended GMM estimator is preferable to that of [START_REF] Arellano | Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations[END_REF] when the dependent variable, the independent variables, or both are persistent. I rely on the two-steps system GMM estimator of [START_REF] Blundell | Initial conditions and moment restrictions in dynamic panel data models[END_REF], which is considered to produce more robust estimates toward heteroscedasticity and other disturbances.

I furthermore estimate the average medium-term effect of conflicts episodes using the local projection method from Jordà (2005). Local projection requires estimation of a series of regressions for each horizon h. I apply a more general specification of (1) to our panel data. In the identification strategy, I consider the conflict as an external shock. The equations to be estimated are:

𝑦𝑦 𝑖𝑖,𝑡𝑡+ℎ = 𝛽𝛽 ℎ 𝑐𝑐 𝑖𝑖,𝑡𝑡 + 𝛿𝛿 ℎ 𝑦𝑦 𝑡𝑡+ℎ-1 + 𝛾𝛾𝑥𝑥 𝑖𝑖,𝑡𝑡+ℎ + 𝑎𝑎 𝑖𝑖 + 𝑢𝑢 𝑖𝑖,𝑡𝑡+ℎ , ℎ = 0, 1, … , 10 (2)
After, I turn to exploring the effects of some of the specificities of sub-Saharan countries, with the aim of discovering the main channels through which the negative effects work. I will systematically test how the inclusion of ethnic fractionalization, natural resources abundance, corruption affect the relationship between conflicts and tax revenue. I will also evaluate how access to alternative sources of revenue such as borrowing, or aid affects the relationship. I use entropy balancing as it allows to weight the sample. I also present the results from the GMM-system. 10

The second stage of our analysis is to estimate the effects of actual conflicts on specific countries. Our methodology is inspired by [START_REF] Abadie | Comparative politics and the synthetic control method[END_REF] and [START_REF] Bove | The relationship panel and synthetic control estimators of the effect of civil war[END_REF]. I use SCM to estimate the effect of conflict. Not only does the synthetic control method provide an effective way to define the counterfactual but it provides a way to bridge the quantitative/qualitative divide in comparative politics [START_REF] Abadie | Comparative politics and the synthetic control method[END_REF]. The SCM framework seems particularly suited to the analysis of conflicts in Africa. Given the heterogeneous nature of conflicts in Sub-Saharan Africa, comparative case studies are likely to provide a better understanding of the effects of conflicts. Another reason 9 See [START_REF] Balima | Coups d'état and the cost of debt[END_REF] for an application of this method to estimate the effects of political instability.

10 One potential limitation to these results may be the fact that most of these variables have been used

as determinant of conflicts.

why case study is great is that the intensity of conflict varies, and countries resilience are not the same. The gap between the conflict-ridden country and its artificial counterfactual and the cumulative stream of gaps can identify the yearly effect as well as the cumulative effects of conflicts on subsequent collection of the tax resources over extended periods of time.

I investigate the impact of the conflict for five countries, selected according to the following conditions:

-The treated unit and the control group must not have missing data on the outcome in the 23-year sample period. This is because, I require 13-year pre-conflict to calibrate the synthetic control and 10-year post-war observations to forecast the effect of the civil war. -In case of multiple conflicts, I select the first one in the chronological order.

-Accordingly, the treated country must have experienced its first conflict in 1993 or later, so as the pre-intervention period can be 13 years. In a similar manner, the treated unit must have experienced a conflict at the latest in 2005, to have 10 years of post-conflict window.

The potential donor pool of a treated unit contains countries which did not experience any conflict in that particular 23-year-long time frame. Finally, I construct the donor pool by restricting the size of the potential donor pool to consider only units similar to the treated units (see [START_REF] Abadie | Comparative politics and the synthetic control method[END_REF] for discussion related to the construction of the donor pool). For that matter, I rely on a simple arithmetic approach.

Let us say the potential donor pool of country 𝑖𝑖 is made up of n countries, 𝑐𝑐𝑐𝑐𝑢𝑢𝑐𝑐𝑡𝑡𝑐𝑐𝑦𝑦 1 , 𝑐𝑐𝑐𝑐𝑢𝑢𝑐𝑐𝑡𝑡𝑐𝑐𝑦𝑦 2 , … , 𝑐𝑐𝑐𝑐𝑢𝑢𝑐𝑐𝑡𝑡𝑐𝑐𝑦𝑦 𝑛𝑛 . For each year in the pre-intervention period, I calculate the percentage difference of the dependent variable between country 𝑖𝑖 with respect to each country in the potential donor pool as follows:

𝑝𝑝. 𝑑𝑑𝑖𝑖𝑑𝑑𝑑𝑑 = (𝑦𝑦 𝑖𝑖,𝑡𝑡 -𝑦𝑦 𝑛𝑛,𝑡𝑡 )/𝑦𝑦 𝑖𝑖,𝑡𝑡 I subsequently select countries where the standard deviation of 𝑝𝑝. 𝑑𝑑𝑖𝑖𝑑𝑑𝑑𝑑 is less than or equal to the unit. 11 To evaluate the statistical significance of our estimates, I conducted placebo studies following the paper of [START_REF] Abadie | Synthetic control methods for comparative case studies: Estimating the effect of California's tobacco control program[END_REF], which addressed methodological shortcomings of case study analysis using SCM. I apply the synthetic control method to countries in the donor pool of each treated country. From the placebo test analysis, I calculate the associated p-value of the treated unit post/pre MSPE ratio. It is the proportion of units (placebos and treated) that have a ratio equal or higher than that of the treated unit. 12 The hard-to-overcome difficulty regarding our SCM framework is the presence of missing values in our dataset. The computation of the synthetic version does not allow missing values of the dependent neither for the treated unit nor for the donor pool. This leads to the inability to estimate the effects for Democratic Republic of Congo and Lesotho. Missing values also lead to shortening the countries in the donor pool.

In addition to our SCM framework, I look at individual separate effect using [START_REF] Pesaran | Estimation and inference in large heterogeneous panels with a multifactor error structure[END_REF] Correlated Common Effect (CCE) estimator for the five treated countries. As the sample used is large, T = 36, I can apply the CCE estimator and estimate individual separate effect for the five treated countries (see [START_REF] Pesaran | Estimation and inference in large heterogeneous panels with a multifactor error structure[END_REF].

Empirical results

Average effects of conflicts on tax revenue

I now turn to our benchmark results. Table 2 presents the OLS estimates of the impacts of conflicts on tax revenue. In all specification, conflict is estimated to have a highly significant negative impact on tax revenue. Column 1 does not include any effects. I successively add fixed effects (column 2), and both fixed and time effects (column 3). Columns 4 and 5 include control variables. The coefficient in column 5, which include all the variables and both fixed and time effects, is -13.4. It means that conflicts induce a drop in non-resource tax revenue per capita of about 13 US$, which represents a loss of 4.3%. Estimates using entropy balancing depict smaller loss of revenue (c.f. Table 3). The coefficient in column 5 suggests that conflicts induce a 5.4 loss in non-resource tax revenue, which represents 1.7%. Using the GMM-system estimator, I obtain similar results with a drop of about 1.5% in non-resource tax revenue (c.f. Table 4). The average negative effect of conflicts hovers around 10 US$ per capita in the medium term, representing a loss of 3.2% (c.f. Figure C1).

An insightful result is that the coefficients associated with conflict is higher in column 5 than in column 3 for both Table 2 andTable 3. This suggests that due to the outbreak of violence government cannot successfully raise revenue and because the conflict also negatively affects key macroeconomic variables, the tax base shrink and the overall loss is higher.

12 See the associated R-Package https://cran.r-project.org/web/packages/SCtools/SCtools.pdf.

Exploring the specificities

In this section, I will explore the effects of some of the specificities of Sub-Saharan countries. As discussed earlier, Sub-Saharan African countries present some particularities. It is therefore interesting to investigate how those particularities affect the relationship between conflicts and taxation. In Table 5, I successively include ethnic fractionalization, the endowment in natural resources, and the quality of the institutions. The negative impact of conflict on tax revenue is robust to the inclusion of these additional variables. Moreover, coefficients of the variable of interest in columns 2, and 4 are not only higher than that in column 3 of Table 3, but they are also higher than the coefficient in column 5 of Table 3. The results show that these specificities discussed, ethnic division and resource endowment do matter in studying the impact of conflict on tax revenue. Internal division makes it tougher for government to secure support for the conflict. Resource endowment has an eviction effect on tax revenue as the government rely more on them in financing the conflict, resulting in less tax revenue mobilisation. Results in columns 1 and 2 of Table 6 point to the same direction. A counterintuitive result arises from the inclusion of quality of institutions in Table 5. The absolute value of the magnitude increases. However, it is lower in Table 6.

Table 7 and Table 8 include control for alternative source of funding. Again, the negative impact of conflict on tax revenue is robust. The relationship between the alternative source of funding and the tax revenue is negative. However, the magnitude of the coefficient of the conflict variable becomes smaller when I control for aid and debt. Here I present the effects of conflicts using SCM. For each country, I present the estimated unit weight for donor pool (Table D 1), describing countries used according to SCM algorithm to build the synthetic control of each treated country; the trends in outcome variables of the treated country versus its synthetic control (Figure D 1), measuring the effect of conflict for each year; the gap between the true value of the outcome variable and its synthetic control (Figure 4); the placebo analysis (Figure D 2), where I randomly assign the treatment to countries that did not experience conflicts; and the associated p-value of the treated unit post/pre MSPE ratio (Table D 2).

The estimated effect of conflict on non-resource tax revenue is the difference between non-resource tax and its synthetic version. The divergence between the non-resource tax revenue and its synthetic control after the outbreak of conflict in Cote d'Ivoire and Guinea-Bissau indicates that conflicts have had significant negative impact on non-resource tax revenue. In Cote d'Ivoire, the average yearly estimated gap is 90000 13 (90 US$ per capita). The p-value of the treated unit post/pre MSPE ratio is 0.18, which means that only 18% of the 17 countries (Cote d'Ivoire and its 16 control countries) have a ratio of post/pre MSPE equal of higher than that of Cote d'Ivoire. Two countries have a higher post/pre MSPE ratio than Cote d'Ivoire: Swaziland and Zimbabwe. In The average yearly estimated gap in Guinea-Bissau is 26000 (26 US$). The p-value of the treated unit post/pre MSPE ratio is 0.25, with Guinea-Bissau having the highest post/pre MSPE ratio.

The divergence between the non-resource tax revenue and its synthetic control after the outbreak of conflict in the remaining countries are not statistically significant. The p-value of the treated unit post/pre MSPE ratio is relatively high. The Central African Republic, the Republic of Congo and Guinea-Bissau all experienced an important loss of tax revenue after the outbreak of the violent conflict. However, our estimates are not statistically significant. Guinea stands in the analysis as the only country, where the was no drop in tax revenue after the conflict. The average gap between the nonresource tax revenue and its synthetic control is positive, about 4000 (4 US$ per capita).

Robustness checks

As alternative method, I estimated individual separate effects of conflicts on treated countries using the Pesaran (2006) CCE estimator. Panel A in Table 9 presents the average effects of conflicts across the five treated countries over the period 1980-2015. The coefficient becomes non-significant when I include the control variables. Panel B in Table 9 shows the individual separate effects of conflicts. The results are line with those from the SCM framework. Conflict is estimated to have a highly significant negative impact on tax revenue in Guinea-Bissau. However, in Cote d'Ivoire, the coefficients are not statistically significant. The distribution of estimated coefficients of conflict is presented in Figure 5.

Conclusion

Starting from the reference work of [START_REF] Tilly | Warmaking and State Making as Organized Crime[END_REF], who has stressed the importance of war in building a state's fiscal capacity, this paper estimates the impact of conflicts in Sub-Saharan Africa. The results show that while wars in Western Europe and US were favourable to reforming tax structure and increasing taxes, conflicts, in this case, internal conflicts rather led to a decrease of tax revenue in Sub-Saharan Africa. Internal conflicts not only alter government capacity to collect revenue, but they also reduce economic variables that constitutes the base of many taxes. Specificities such as ethnic division and natural resource endowment associated with the limited capacity to control rebellions hamper the mechanisms through which wars, especially internal wars lead to state building (see [START_REF] Rodriguez-Franco | Internal wars, taxation, and state building[END_REF]. Our results show the importance of stability and peace in developing Sub-Saharan Africa for a steady improvement of domestic revenue mobilization.

Figure B 1. Evolution of non-resource tax revenue

Appendix C: Impact of conflict on tax revenue over 10 years (OLS).

Figure A 2

 2 show the average intensity level of conflict in the 1980s and 2000s.

Figure 1 .

 1 Figure 1. Conflict-ridden countries in Africa, 1980-2015

Figure

  Figure 2. Non-resource tax revenue in safe and conflict-ridden countries (average 1980-2015) Panel A. Treated vs. not treated Panel B. Peace vs. conflict periods

Figure 3 .

 3 Figure 3. Predictors according to exposure to conflict (average 1980-2015)

Figure

  Figure 4. Gap between tax revenue and the synthetic tax revenue

  Figure E 1, I provide additional insight on the post/pre MSPE ratio. I present the gap between the nonresource tax revenue and its synthetic control in Cote d'Ivoire Swaziland and Zimbabwe. The figure shows that the high MSPE in Swaziland and Zimbabwe -which resulted in a higher unit post/pre MSPE ratio than Côte d'Ivoire -can hardly be interpreted as an effect of a treatment in 2002. I then present the trends in outcome variables of the treated country versus its synthetic control (Figure E 2) as well as the yearly gap (Figure E 3) excluding Swaziland and Zimbabwe. The results barely changed.

Figure 5 .

 5 Figure 5. Gap Distribution of individual effects of conflicts for the five treated countries

Figure C1 .

 C1 Figure C1. Impact of conflict on tax revenue over 10 years (OLS).

Table 1 : Descriptive statistics

 1 : Non-resource tax revenue is expressed in 2010 constant US$ per thousand inhabitants. Conflict is a dummy variable that takes 1 if there is a conflict in the country in a given year. GDP per capita is also expressed in constant 2010 US$. Agriculture added value and total trade are in percentage of GDP. Ethnic fractionalization is measured by an index ranging from 0 to 1 see[START_REF] Alesina | Fractionalization[END_REF]. Resource endowment is measure by natural resource rent as percentage of GDP. Net development assistance and official aid as well as Public and publicly guaranteed external debt are expressed as percentage of GDP.

	Variables	Obs.	Mean	Std. Dev.	Min	Max
	Non-resource tax	1435 312546.40 553222.40 1582.75 4000083.00
	Conflict	1512	0.18	0.39	0.	1
	GDP per capita	1474	1892.50	2780.36	131.65	20333.94
	Agriculture added value	1345	27.42	15.70	0.89	72.03
	Total trade	1334	73.97	47.07	6.32	531.74
	Ethnic fractionalization	41	0.65	0.24	0.00	0.93
	Resource endowment	1431	11.61	11.92	0.00	89.17
	ICRG Index	878	0.45	0.11	0.11	0.78
	Net development assistance and official aid	1448	10.79	10.49	-0.25	94.44
	Public and publicly guaranteed external debt 1357	56.66	50.92	0.00	424.98

Note

Table 2 : Impact of conflict on tax revenue (OLS)

 2

	Non-resource tax Per capita (Constant 2010 US$)	(1)	(2)	(3)	(4)	(5)
	Conflicts Dummy	-4.156*	-5.733**	-5.940*	-12.285* -13.411*
		(2.316)	(2.535)	(3.240)	(6.951)	(7.507)
	Non-resource tax Per capita (Constant 2010 US$) (t-1) 1.014*** 0.938***	0.919*** 0.707*** 0.704***
		(0.012)	(0.027)	(0.026)	(0.063)	(0.062)
	GDP per capita (constant 2010 US$)				0.078*** 0.075***
					(0.017)	(0.017)
	Agriculture, value added (% of GDP)				-0.021	0.281
					(0.292)	(0.332)
	Total trade (% of GDP)				-0.270	-0.376
					(0.312)	(0.285)
	Constant	3.948	27.353*** 28.664*** -23.353	-18.151
		(2.729)	(8.527)	(10.363)	(19.615) (14.921)
	Country FE	No	Yes	Yes	Yes	Yes
	Time FE	No	No	Yes	No	Yes
	Observations	1393	1393	1393	1199	1199
	Number of countries		42	42	40	40
	R-squared	0.9819	0.8328	0.8407	0.8659	0.8706
	Adjusted R-squared	0.9819	0.8326	0.8365	0.8654	0.8662

Note: Robust standard errors in parentheses (*** p<0.01, ** p<0.05, * p<0.1). The table reports the OLS estimates of the regression of non-resource tax revenue per capita in constant US$ on the conflict dummy and a set of control variables.

Table 3 : Impact of conflict on tax revenue (entropy balancing)

 3 The table reports the estimates of the second step of the entropy balancing methods. I regress non-resource tax revenue per capita in 2010 constant US$ on the conflict dummy and a set of control variables.

	Non-resource tax Per capita (Constant 2010 US$)	(1)	(2)	(3)	(4)	(5)
	Conflicts Dummy	-2.171* -4.123** -4.918*** -4.184*** -5.350***
		(1.276)	(1.643)	(1.538)	(1.521)	(1.525)
	Non-resource tax Per capita (Constant 2010 US$) (t-1) 1.018*** 0.930*** 0.908*** 0.757*** 0.759***
		(0.012)	(0.032)	(0.033)	(0.055)	(0.055)
	GDP per capita (constant 2010 US$)				0.045**	0.045**
					(0.018)	(0.019)
	Agriculture, value added (% of GDP)				0.041	0.061
					(0.099)	(0.088)
	Total trade (% of GDP)				0.089	0.063
					(0.080)	(0.087)
	Country FE	No	Yes	Yes	Yes	Yes
	Time FE	No	No	Yes	No	Yes
	Observations	1393	1393	1393	1199	1199
	Number of countries	42	42	42	40	40
	R-squared	0.976	0.978	0.979	0.981	0.982
	Adjusted R-squared	0.976	0.977	0.978	0.981	0.981
	Note: Robust standard errors in parentheses (*** p<0.01, ** p<0.05, * p<0.1).

Table 4 : Impact of conflict on tax revenue (GMM-system)

 4 : Robust standard errors in parentheses (*** p<0.01, ** p<0.05, * p<0.1). The table reports the GMM-system estimates of a regression of non-resource tax revenue per capita in 2010 constant US$ on the conflict dummy and a set of control variables. The computed long run estimates and its standard error is displayed in the table.

	Variables

Note

Table 5 : Impact of conflict on tax revenue (entropy balancing) -Controlling for specificities

 5 The table reports the estimates of the second step of the entropy balancing methods. I regress non-resource tax revenue per capita in 2010 constant US$ on the conflict dummy and a set of control variables.

	Non-resource tax Per capita (Constant 2010 US$)	(1)	(2)	(3)	(4)	(5)	(6)
	Conflicts Dummy	-4.489*** -5.670*** -5.287** -6.308*** -6.940*** -8.272***
		(1.576)	(1.584)	(2.085)	(2.004)	(2.538)	(2.557)
	Non-resource tax Per capita (Constant 2010 US$) (t-1) 0.773*** 0.775*** 0.798*** 0.803*** 0.747*** 0.758***
		(0.050)	(0.049)	(0.032)	(0.032)	(0.058)	(0.053)
	GDP per capita (constant 2010 US$)	0.042***	0.042** 0.037*** 0.035*** 0.040*** 0.037***
		(0.016)	(0.017)	(0.008)	(0.008)	(0.012)	(0.012)
	Agriculture, value added (% of GDP)	0.055	0.075	0.076	0.127	0.240	0.339**
		(0.095)	(0.088)	(0.082)	(0.085)	(0.149)	(0.152)
	Total trade (% of GDP)	0.096	0.065	0.072	0.048	0.189	0.151
		(0.081)	(0.087)	(0.132)	(0.131)	(0.136)	(0.139)
	Ethnic Fractionalization	-111.391* -106.942
		(65.970)	(67.528)
	Total natural resources rents (% of GDP)			-0.089	-0.155
				(0.200)	(0.193)
	ICRG index					4.979	-0.930
						(10.691)	(13.125)
	Country FE	Yes	Yes	Yes	Yes	Yes	Yes
	Time FE	No	Yes	No	Yes	No	Yes
	Observations	1,199	1,199	1,199	1,199	771	771
	Number of countries	40	40	40	40	28	28
	R-squared	0.983	0.982	0.986	0.986	0.982	0.984
	Adjusted R-squared	0.982	0.982	0.985	0.985	0.982	0.982
	Note: Robust standard errors in parentheses (*** p<0.01, ** p<0.05, * p<0.1).

Table 6 : Impact of conflict on tax revenue (GMM-system) -Controlling for specificities

 6

	Variables

Note: Robust standard errors in parentheses (*** p<0.01, ** p<0.05, * p<0.1). The table reports the GMM-system estimates of a regression of non-resource tax revenue per capita in 2010 constant US$ on the conflict dummy and a set of control variables. The computed long run estimates and its standard error is displayed in the table.

Table 7 : Impact of conflict on tax revenue (entropy balancing) -Controlling for alternative sources of funding

 7

	Non-resource tax Per capita (Constant 2010 US$)	(1)	(2)	(3)	(4)
	Conflicts Dummy	-1.989	-2.760**	-1.860	-2.669**
		(1.235)	(1.252)	(1.188)	(1.163)
	Non-resource tax Per capita (Constant 2010 US$) (t-1) 0.597*** 0.610*** 0.641*** 0.651***
		(0.088)	(0.084)	(0.087)	(0.084)
	GDP per capita (constant 2010 US$)	0.048*** 0.047*** 0.038*** 0.036***
		(0.015)	(0.016)	(0.011)	(0.011)
	Agriculture, value added (% of GDP)	-0.048	-0.032	-0.059	-0.029
		(0.078)	(0.079)	(0.064)	(0.070)
	Total trade (% of GDP)	0.178**	0.172*	0.161*	0.138
		(0.087)	(0.089)	(0.086)	(0.089)
	Aid	-0.178** -0.202**
		(0.082)	(0.083)
	Public debt			-0.016	-0.018
				(0.016)	(0.026)
	Country FE	No	Yes	Yes	Yes
	Time FE	No	No	Yes	No
	Observations	1,175	1,175	1,099	1,099
	Number of countries	40	40	37	37
	R-squared	0.922	0.926	0.930	0.934
	Adjusted R-squared	0.919	0.920	0.927	0.929
	Note: Robust standard errors in parentheses (*** p<0.01, ** p<0.05, * p<0.1). The table reports the estimates of the second
	step of the entropy balancing methods. I regress non-resource tax revenue per capita in 2010 constant US$ on the conflict dummy
	and a set of control variables.

Table 8 : Impact of conflict on tax revenue (GMM-system) -Controlling for alternative sources of funding

 8

	Variables

Table 9 : Impact of conflict on tax revenue using Pessaran (2006) Panel A. Averages across groups

 9 Note: Robust standard errors in parentheses (*** p<0.01, ** p<0.05, * p<0.1). The table reports the[START_REF] Pesaran | Estimation and inference in large heterogeneous panels with a multifactor error structure[END_REF] CCE coefficients of the regression of non-resource tax revenue per capita in constant US$ on the conflict dummy.

	(1)	(2)

The five countries were selected according to our methodology to have robust synthetic control (see section 4.2).

[START_REF] Taylor | Tilly tally: War-making and state-making in the contemporary third world[END_REF] declares that one striking feature of the debate on war-making/state-making connection is that relatively little attention is focused on the effects of actual wars on specific states.

All the recorded conflicts (from 1980 to 2015) but four were internal (internal or internationalized internal). The four exceptions were interstate conflicts:Chad and Nigeria in 1983; Burkina Faso and Mali in 1985; Chad and Libya in 1987; and Cameroon and Nigeria in 1996.

Article 35 of Loi n°2000-513 du 1er Août 2000 portant constitution de la Côte d'Ivoire. Available at http://www.unesco.org/education/edurights/media/docs/ea778cb20fbdd7a77fe62ae0c85bbd87c0757abd.pdf

Note however that on December 18, 2001, a national reconciliation forum bringing together all political leaders recognized Ouattara's Ivorian nationality.

We alternatively selected 1.5 and 2 as cut-off. We also used a scenario with no restriction, selection all the countries in the potential donor pool. The synthetic control weights did not change except for Cote d'Ivoire.

Acknowledgments

I would like to thank Rabah Arezki, Emilie Caldeira, Luis Corchón, Grégoire Rota-Graziosi for helpful comments in previous versions of the paper. I acknowledge the support received from the Agence Nationale de la Recherche of the French government through the program "Investissements d'avenir" (ANR-10-LABX-14-01). The findings, interpretations, and conclusions expressed in this paper do not necessarily reflect the views of the CERDI.

Appendix

Appendix A: Occurrence and intensity of conflicts in Africa, 1980Africa, -2015.


Nathalie Eisenbaum

Percolation of repulsive particles on graphs

Keywords: Percolation, repulsion, graph, determinantal process, Gaussian process, negative association, Markov chain, stochastic domination. MSC2010 subject classifications : 60A10, 60G10, 60G15, 60G50, 60G55, 60J10, 60K35

What are the percolation properties of a repulsive point process on an infinite connected graph? To treat this question, one starts by clearly state which definition of repulsivity is adopted here. The first issue is then to identify some repulsive point processes. The most known examples of repulsive point process are determinantal point processes. Are they some others? We construct some examples and give a general answer on their percolation properties. In case of determinantal point processes, we establish stochastic domination relations to obtain other sufficient conditions for percolation.

Introduction

Let G be an infinite, connected, locally finite graph with vertex set V and non-oriented edges set E. Given a point process χ on V, we consider the random subgraph of G with vertex set {x ∈ V : χ(x) > 0} and edges set: {[x, y] ∈ E : χ(x) > 0 and χ(y) > 0} and ask whether this random subgraph has an infinite connected component. In short, does this random subgraph percolate? One can also formulate the question as follows: does χ percolate on G ? This question has been first considered for χ Bernoulli point process (i.e. the variables χ(x), x ∈ V, are independent Bernoulli variables). In case all the Bernoulli's have the same parameter p (0 ≤ p ≤ 1), the probability for the Bernoulli point process to percolate, which is an increasing function of p with values in {0, 1}, has a critical value p c (G).

CNRS and Université de Paris, MAP5, France. E-mail: nathalie.eisenbaum@parisdescartes.fr 1 Here we will consider the percolation problem for repulsive point processes. A simple point process χ on V is said to be repulsive if for every B 1 , .., B n mesurable disjoint bounded subsets of V, one has:

IE[χ(B 1 )..χ(B n )] ≤ IE[χ(B 1 )]..IE[χ(B n )].
(1.1)

In the literature (see e.g. [START_REF] Van Lieshout | Spatial point process theory[END_REF]), one finds the following less restrictive definition of repulsivity: Note that for χ Bernoulli point process on V, (1.1) is always satisfied with equality. Also determinantal point processes (DPP in short) are well-known repulsive point processes.

IE[χ(a)
To give other examples we use negatively associated variables.

A sequence of real valued random variables (X n , n ≥ 0) is negatively associated if for every disjoint pair of indexes subsets (I, J) and every increasing fonctionnals F and H from IR I (resp. IR J ) into IR (i.e. they are increasing with respect to each component)

IE[F (X n , n ∈ I)H(X n , n ∈ J)] ≤ IE[F (X n , n ∈ I)]IE[H(X n , n ∈ J)].
With a negatively associated sequence of Bernoulli variables (X a , a ∈ V), one can easily define a simple repulsive point process χ on V, by setting:

χ(f ) = a∈V f (a)X a , (1.3)
for any function f defined on V.

To produce thanks to (1.3), repulsive simple point processes, the first issue is to find such a sequence of negatively associated Bernoulli variables. It can be easily obtained from a sequence of negatively associated variables. One can take advantage of known examples of negatively associated sequences (see e.g. [START_REF] Last | Some remarks on associated random fields, random measures and point processes[END_REF]). In particular one can use negatively associated Gaussian sequences. In section 2, we give various ways to obtain negatively associated Gaussian sequences. Besides, we start section 2 by pointing that determinantal processes are illustrations of (1.3).

One might think that it should be harder for a repulsive simple point process χ on Z d to percolate than for a Bernoulli process with parameters IP [χ(x) = 1], x ∈ V. In section 3, we present a general result for the point processes obtained via (1.3) on Z d , that reinforces this intuition. We also present applications of this result to Gaussian free fields and to determinantal point processes.

In the case of determinantal point processes, we establish stochastic domination relations and use them to obtain other criterions of percolation. They are presented in section 4.

IE[f 1 (M )f 2 (M )] ≤ IE[f 1 (M )]IE[f 2 (M )].
In the special case when S is a locally finite discrete set V and M is a simple point process χ, one has:

The random measure χ is negatively associated iff the sequence (χ(a), a ∈ V) is negatively associated.

In particular, consider any determinantal point process χ on a discrete set V. It has been established by Lyons [START_REF] Lyons | Determinantal probability measures[END_REF] that χ is negatively associated. Hence (χ(a), a ∈ V) is a sequence of negatively associated Bernoulli variables. Moreover χ admits the representation (1.3):

χ(f ) = a∈V f (a)χ(a).

Negatively correlated Gaussian variables

According to Joag-Dev and Proschan [START_REF] Joag-Dev | Negative association of random variables, with applications[END_REF], a centered Gaussian variables sequence (η a , a ∈ V) is negatively associated iff it is negatively correlated (i.e. IE[η a η b ] ≤ 0, for a = b)).

Once found a sequence of centered negatively correlated Gaussian variables (η a , a ∈ V), one easily constructs a sequence of negatively associated Bernoulli variables (Y a , a ∈ V), by, for example, choosing an arbitrary real constant h and setting:

Y a = 1 ηa>h . (2.1)
The problem becomes to find negatively correlated centered Gaussian sequences. The four propositions below present solutions.

Proposition 2.2 For (Y a , a ∈ V) any sequence of pairwise negatively correlated varia- bles, (IE[Y a Y b ] -IE[Y a ]IE[Y b ], (a, b) ∈ V × V)
is the covariance of a negatively correlated centered Gaussian sequence indexed by V.

Proof One has for a

= b: IE[Y a Y b ] -IE[Y a ]IE[Y b ] ≤ 0. Moreover, for every x i , 1 ≤ i ≤ n in IR and every a i , 1 ≤ i ≤ n in V 1≤i,j≤n x i x j (IE[Y a i Y a j ] -IE[Y a i ]IE[Y a j ]) = IE[( n i=1 x i Y a i ) 2 ] -IE[ n i=1 x i Y a i ] 2 ≥ 0. (2.2)
Example 2.2.1 Use the Bernoulli variables corresponding to a DPP on V with kernel (K(a, b), (a, b) ∈ V 2 ), to obtain a negatively correlated centered Gaussian sequence with covariance C given by:

C(a, b) = -(K(a, b)) 2 for a = b and C(a, a) = K(a, a)(1 -K(a, a)).
In case K has only nonnegative entries (K(x, y) ≥ 0, ∀x, y ∈ V), there is another way to obtain a negatively correlated Gaussian sequence. Indeed I -K is positive semidefinite and has nonpositive off diagonal entries.

More generally, one can use any simple point processes satisfying (1.2) to produce repulsive simple point processes (i.e. satisfying (1.1)). To do so, one notes the following immediat proposition.

Proposition 2.3 Let χ be a simple point process on V satisfying (1.2), then (IE[χ(a)χ(b)]-IE[χ(a)]IE[χ(b], (a, b) ∈ V×V)
is the covariance of a negatively correlated centered Gaussian sequence indexed by V. Since χ is negatively associated in the sense of Definition 2.1 (see [START_REF] Lyons | Determinantal probability: basic properties and conjectures[END_REF]), χ satisfies (1.2).

Remark 2.3.2 One could think that anti-ferromagnetic Ising spin systems should correspond to point processes satisfying (1.2). This intuition is false. Consider for example an anti-ferromagnetic Ising spin system with only pair interaction between nearest neighboors on Z 2 . Denote by χ the corresponding point process of sites with positive spin on Z 2 . Split Z 2 into A = {(x, y) ∈ Z 2 : |x + y| is odd} and A c . Thanks to [START_REF] Lebowitz | Griffiths inequalities for anti-ferromagnets[END_REF], one obtains that

IE[χ(a)χ(b)] ≤ IE[χ(a)]IE[χ(b)] if a ∈ A and b ∈ A c and IE[χ(a)χ(b)] ≥ IE[χ(a)]IE[χ(b)] if a, b ∈ A or a, b ∈ A c .
Another way to obtain negatively correlated Gaussian sequences, consists in using Markov processes.

Proposition 2.4 Let P be the transition matrix of a symmetric Markov chain on a discrete space V. Let I be the identity matrix on the discrete space V. Then I -P is the covariance matrix of a negatively correlated centered Gaussian sequence indexed by V.

Indeed (I -P ) is positive semi-definite (see for ex [START_REF] Diaconis | A different construction of Gaussian fields from Markov chains : Dirichlet covariances[END_REF]) and the off diagonal entries of (I -P ) are all nonpositive.

Example 2.4.1 For the simple random walk on Z 2 , the probability to jump to a neighbor is 1/4 :

P (a, b) = 1 4 1 d(a,b)=1
. The centered Gaussian process with covariance (I -P ) is negatively associated.

A Markov process with state space S, is said to be weakly symmetric with respect to a σ-finite measure m on S if its transition semigroup (P t ) satisfies:

S f (x)P t g(x)m(dx) = S g(x)P t f (x)m(dx) for every f , g in L 2 (m).
Proposition 2.5 Denote by L the infinitesimal generator of a Markov process weakly symmetric with respect to m. Let (f n ) n≥0 be a sequence of bounded nonnegative functions with disjoint compact supports, elements of the domain of L. Then there exists a negatively correlated centered process (η n ) n≥0 with a covariance given by:

IE[η n η k ] = - E f n (x) Lf k (x) m(dx) = - E f k (x) Lf n (x) m(dx).
Proof First we remind that (-L) is a positive semi-definite operator on its domain D(L). Hence there exists a centered Gaussian field (η(u), u ∈ D(L)) with covariance

IE[η(u)η(v)] = -< u, Lv >= - E u(x)Lv(x)m(dx) = < (-L) 1/2 u, (-L) 1/2 v > .
For every u and v in D(L):

-< u, Lv >= lim t→0 1 t < u, v -P t v >
(see for ex. Lemma 1.3.4 in [START_REF] Fukushima | Dirichlet forms and symmetric Markov processes[END_REF]). Assume now that u and v are also nonnegative and have disjoint supports. We obtain:

< u, v -P t v >= -< u, P t v >≤ 0
and hence the centered Gaussian process (η(f n ), n ≥ 0) is negatively correlated.

(x) = IR (f (x + y) -f (x) -y 1+y 2 f (x))ν(dy). Fix ε > 0.
Denote by f a a C 2 -function in the domain of L with support equal to (a-ε, a+ε). For any increasing sequence of reals (a n , n ≥ 0) such that d(a i , a i+1 ) = 2ε, the centered Gaussian sequence (η(f an ), n ≥ 0) is negatively correlated with covariance:

IE[η(f a i )η(f a j )] = - IR f a i (x)Lf a j (x)dx.
3 Percolation for repulsive particles on Z d

A criterion for percolation

In the proposition below, we present a criterion for the percolation of repulsive particles on Z d with a configuration satisfying (1.3). Proposition 3.1 For any positive integer d, there exist two real numbers in (0, 1), p dis and p agr such that for every negatively associated sequence of Bernoulli variables (X k , k ∈ Z d ), we have: ). To see that Proposition 3.1 is a consequence of the above criterion, note that thanks to the negative association property, one has, in case (i):

(i) If ∀k, IP [X k = 1] ≤ p dis (d
IP [∀k ∈ A, X k = 1] ≤ k∈A IP [X k = 1] ≤ p dis (d) |A|
and in case (ii):

IP [∀k ∈ A, X k = 0] ≤ k∈A IP [X k = 0] ≤ (1 -p agr (d)) |A| .
Consider a family of repulsive particles on Z d with a spatial configuration χ given by a family of negatively associated Bernoulli variables. Assume that they all have the same parameter p. One might think that the occurrence of a percolation for this population of particles should be harder to happen than if they were all independent with the same marginals. Denote by p site c (Z d ) the critical probability for percolation of a Bernoulli point process with the same probability at each site of Z d . One should legitimately expect that in case χ percolates, one would have: p ≥ p site c (Z d ). Thanks to Proposition 3.1, we know that in case χ percolates, we must have: p ≥ p dis (d). Since any Bernoulli point process is negatively associated, one obtains:

p dis (d) ≤ p site c (Z d ) ≤ p agr (d). (3.1)
According to Molchanov and Stepanov [START_REF] Molchanov | Percolation in random fields[END_REF], one can take: p dis (d) = 1 2d-1 . One also has the following asymptotic [START_REF] Kesten | Asymptotics in high dimensions for percolation[END_REF]: lim d→∞ 2d p site c (Z d ) = 1. Consequently one obtains: lim

d→∞ 2d p dis (d) = 1 and p dis (d) ∼ d→∞ p site c (Z d ), (3.2)
which reinforces the intuition that negative association goes against percolation, at least in high dimension.

For other graphs, this intuition might be false. Here is an example suggested by the referee. Consider the graph with vertex set Z × {0, 1} and the edges set corresponding to * -adjacency. The point process χ is such that the probability to occupy a site is always 1/2, the couples (χ(n, 0), χ(n, 1)) are all independent and: χ((n, 0)) + χ((n, 1)) = 1. This point process is repulsive. Obviously this point process a.s. percolates but the corresponding Bernoulli process a.s. does not percolate.

Determinantal point processes

One should note first that whatever the infinite connected graph G, a DPP is living on, one has the following 0-1 law.

Proposition 3.2 For G any infinite connected, locally finite graph, the probability that a determinantal point process on G contains an infinite connected component is 0 or 1.

Indeed, Lyons [START_REF] Lyons | Determinantal probability measures[END_REF] has shown that a determinantal point process on any infinite discrete set is always tail trivial.

As a direct application of Proposition 3.1, one obtains the following sufficient condition for the occurrence of a percolation for determinantal point processes. A DPP with kernel K is denoted by DPP(K).

Comparing a Gaussian free field with its neighborhood

One can make use of Proposition 3.1 to obtain a result on the so-called Gaussian free fields associated to symmetric transient Markov chain on Z d . To do so, we will establish relations in law between the Gaussian free fields (which are positively correlated), and negatively correlated Gaussian processes (Proposition 3.6). • for any h < h agr , the set {x ∈ Z d : η + (x) ≥ h + y∈Z d P (x, y)η + (y)} has a.s. an infinite connected component.

• for any h > h disc , the set {x ∈ Z d : η + (x) ≥ h + y∈Z d P (x, y)η + (y)} has a.s. only finite connected components.

Note that Theorem 3.4 does not require from the symmetric transient Markov chain to have stationary nor independent increments, nor jumps limited to nearest neighbors. When the considered Markov chain is a random walk (i.e. P (x, y) = p(y -x) for x,y in Z d ), one has the following corollary. • for any h > h c , the set {x ∈ Z d : η + (x) ≥ h + y∈Z d p(y -x)η + (y)} has a.s. only finite connected components.

Moreover the critical level h c satisfies:

p dis (d) ≤ IP [N > h c ] ≤ p agr (d),
where N is a real standard Gaussian variable.

From now on, given a symmetric transition matrix P = (P (x, y)) (x,y)∈Z d ×Z d , we denote by V(x) the set {y ∈ Z d : P (x, y) > 0}.

The above corollary is satisfied is particular by the Gaussian free field η + associated to the simple symmetric random walk on Z d with d ≥ 3, and takes in this case the following form:

There exists a critical real level h c such that: Proposition 3.6 For G infinite connected graph, denote by V its vertex set. Let (X n , n ≥ 0) be a symmetric transient Markov chain on V with transition matrix P = (P (x, y), (x, y) ∈ V 2 ) and Green operator G = (G(x, y), (x, y) ∈ V 2 ). One associates two centered Gaussian processes to X, (η + (x), x ∈ V) and (η -(x), x ∈ V), with respective covariances G and (I -P ). Then we have:

p dis (d) ≤ IP [N > h c ] ≤ p agr (d), and (3.3)
η - (law) = (I -P )η + (3.4) and η + (law)
= Gη -.

The two infinite matrices G and I -P are positive semi-definite. This is the reason why Proposition 3.6 requires a proof. It is is based on the following lemma.

Lemma 3.7 For every nonnegative f on V such that: Gf (a) < ∞, ∀a ∈ V, one has:

(I -P )Gf = f (3.6)
and

G(I -P )f = f (3.7)
Proof of Lemma 3.7 Since G is the Green operator associated to the Markov chain (X n ) n≥0 , for every nonnegative function f on V:

Gf (a) = IE a [ ∞ n=0 f (X n )] = b∈V G(a, b)f (b). Besides: P f (a) = IE a [f (X 1 )]. (I -P )Gf (a) = Gf (a) -P Gf (a) = IE a [ ∞ n=0 f (X n )] -IE a [IE X 1 [ ∞ n=0 f (X n )]] = IE a [ ∞ n=0 f (X n )] -IE a [ ∞ n=1 f (X n )] = IE a [f (X 0 )] = f (a),
which gives (3.6). For (3.7), one writes similarly:

G(I -P )f (a) = Gf (a) -GP f (a) = IE a [ ∞ n=0 f (X n )] -IE a [ ∞ n=0 P f (X n )]] = IE a [ ∞ n=0 f (X n )] -IE a [ ∞ n=0 IE Xn [f (X 1 )]] = IE a [ ∞ n=0 f (X n )] -IE a [ ∞ n=1 f (X n )] = IE a [f (X 0 )] = f (a).
Proof of Proposition 3.6 By definition:

G(x, y) = ∞ n=0 IE x [X n = y] = ∞ n=0 P n (x, y). Set : ϕ = (ϕ x , x ∈ V) = (I -P )η + = ((I -P )η + (k), k ∈ V).
The process ϕ is a centered Gaussian process. We compute the covariation of ϕ.

IE[ϕ(x)ϕ(y)] = IE[(I -P )η + (x)(I -P )η + (y)] = IE[ k∈V(x) (I -P )(x, k)η + (k) q∈V(y) (I -P )(y, q)η + (q)] = k∈V(x) (I -P )(x, k) q∈V(y) (I -P )(y, q)G(q, k) (3.8)
Using (3.6) for the function f = 1 {k} , one obtains: (I -P )G1 {k} (y) = 1 {k} (y), for every y in V, equivalently:

q∈V(y)

(I -P )(y, q)g(q, k) = 1 {k} (y).

(3.9)

Thanks to (3.9), (3.8) leads to

IE[ϕ(x)ϕ(y)] = k∈V(x) (I -P )(x, k)1 {k} (y) = (I -P )(x, y)
One concludes that: (ϕ(x), x ∈ V)

(law)
= (η -(x), x ∈ V). One uses similarly (3.7) to show (3.5).

Proof of Corollary 3.5 When P (x, y) = p(y -x) for x,y in Z d , the two Gaussian centered fields η -and η + associated to X, are stationary. Moreover one has:

y∈V |IE[η -(0)η -(y)]| y∈V(0) P (0, y) ≤ 1.
Hence η -has the property of so-called finite susceptibility. This implies that all the translation invariant events involving η - have probability 0 or 1. Together with Theorem 3.4, a simple monotony argument leads to the conclusion. Remark 3.8 For the special case of the simple symmetric random walk on Z d , one could have taken advantage of a general result of Liggett, Schonmann and Stacey [START_REF] Liggett | Domination by product measures[END_REF] (Theorem 0.0 (i)) on 3-dependent random fields to partially recover (3.3) (i). Indeed, making use of their result, for sufficiently small real h, there exists ρ = ρ(h) > p site c (Z d ), such that:

Bernoulli(ρ) ≺ (1 η -(x)>h , x ∈ Z d ),
where Bernoulli(ρ) denotes a Bernoulli process with parameter ρ. Hence for sufficiently small h, the set {x ∈ Z d : η -(x) ≥ h} has a.s. an infinite connected component. But this argument does not tell us that the percolation critical value of IP [η -(0) > h] should be greater than p site c (Z d ), nor than p dis (d).

We also mention that with the assumptions of Corollary 3.

Stochastic domination for DPP

Stochastic domination relations are a usual tool for percolation results. We establish below some stochastic domination relations involving DPP on discrete sets. Georgii and Yoo [START_REF] Georgii | Conditional intensity and Gibbsianness of determinantal point processes[END_REF] have shown similar relations for determinantal point processes on continuous According to Theorem 5.11 in [START_REF] Lyons | Stationary determinantal processes: phase multiplicity, bernoullicity, entropy and domination[END_REF]: DPP(K f ) ≺ Bernoulli(q) iff q ≥ 1 -GM(1 -f ) and Bernoulli(p) ≺ DPP(K f ) iff p ≤ GM(f ).

One immediately notes that Theorem 5.11 in [START_REF] Lyons | Stationary determinantal processes: phase multiplicity, bernoullicity, entropy and domination[END_REF] is stronger than Theorem 4.1 restricted to this framework. Indeed from Theorem 4.1 one has:

1 1+J f (0) ≤ 1 -K f (0, 0). Since K f (0, 0) = AM(f ) the arithmetic mean of f , one obtains: 1 -K f (0, 0) = AM(1f ) ≤ GM(1 -f ), by Jensen's inequality.

One can take advantage of the above result of [START_REF] Lyons | Stationary determinantal processes: phase multiplicity, bernoullicity, entropy and domination[END_REF] to obtain the following conditions of percolation:

• If GM(f )

  χ(b)] ≤ IE[χ(a)]IE[χ(b)], for any couple (a, b) of distinct points of V (1.2) (sometimes written in term of the pair correlation function IE[χ(a)χ(b)] IE[χ(a)]IE[χ(b)]).

Example 2 . 3 . 1

 231 Let χ be any DPP on R 2 . For any (n, m) in Z 2 , set: A (n,m) = (n, n + 1) × (m, m + 1). Define the simple point process χ on Z 2 by χ((n, m)) = 1 χ(A (n,m) )>0 .

Example 2 . 5 . 1

 251 Consider the generator L of any symmetric Lévy process on IR with no drift, no Gaussian component and Lévy measure ν. For any C 2 -function f in the domain of L: Lf

  ), then a.s. {k ∈ Z d : X k = 1} has no infinite connected component.(ii) If ∀k, IP [X k = 1] ≥ p agr (d), then a.s. {k ∈ Z d : X k = 1} has an infinite connected component.Proposition 3.1 is a consequence of a criterion of Molchanov and Stepanov[START_REF] Molchanov | Percolation in random fields[END_REF] for the occurrence of a percolation transition. We remind it below. It uses the notion of *-adjacent. Two points x and y ofZ d are *-adjacent if sup 1≤i≤d |x i -y i | = 1. A *-connected set is connected w.r.t. *-adjacency.There exist two finite constants c dis d and c agr d depending of the dimension d such that for each {0, 1}-valued random field (X k ) k∈Z d , the following points hold:• If there exists c > 0 such that for every connected subset AIP [∀k ∈ A : X k = 1] ≤ c exp(-c dis d |A|), then a.s. {k ∈ Z d : X k = 1}has no infinite connected component. • If there exists c > 0 such that for every *-connected subset A IP [∀k ∈ A : X k = 0] ≤ c exp(-c agr d |A|), then a.s. {k ∈ Z d : X k = 1} has an infinite connected component. We set p dis (d) = exp(-c dis d ) and p agr (d) = 1 -exp(-c agr d

Proposition 3 . 3

 33 Let (K(x, y), (x, y) ∈ Z d × Z d ) be the kernel of a determinantal point process on Z d . (i) If for every x ∈ Z d , K(x, x) < p dis (d), then a.s. DPP(K) does not percolate on Z d . (ii) If for every x ∈ Z d , K(x, x) > p agr (d), then a.s. DPP(K) percolates on Z d .

Theorem 3 . 4 Fix d ≥ 1 .

 341 Let h agr and h disc be the two finite numbers such that:IP [N > h agr ] = p agr (d) and IP [N > h disc ] = p disc (d),where N is a real standard Gaussian variable. Let (η + (x)) x∈Z d be a centered Gaussian field with covariance the Green function of a transient symmetric Markov chain X on Z d with transition matrix P = (P (x, y)) (x,y)∈Z d ×Z d such that P (x, x) = 0, ∀x ∈ Z d . Then we have:

Corollary 3 . 5

 35 Let (η + (x)) x∈Z d be a Gaussian free field associated to a stationary symmetric transient random walk on Z d . Then there exists a real h c such that |h c | < ∞ and • for any h < h c , the set {x ∈ Z d : η + (x) ≥ h + y∈Z d p(y -x)η + (y)} has a.s. an infinite connected component.

  (i) for any h < h c , the set {x ∈ Z d : η + (x) ≥ h + 1 2d y∈V(x) η + (y)} has a.s. an infinite connected component. (ii) for any h > h c , the set {x ∈ Z d : η + (x) ≥ h + 1 2d y∈V(x) η + (y)} has a.s. only finite connected components. Theorem 3.4 is a direct consequence of Proposition 3.1, Proposition 2.4 and of the following proposition.

Remark 4 .

 4 2 leads to the same kind of results with percolation sufficient conditions lying instead on the spectral radius.In case V = Z d , and there exists a measurable function f fromIR d /Z d into [0, 1] such that: K(a, b) = f (b -a),for a, b ∈ Z d (where f (a) = IR d /Z d f (x)e -2πi<a,x> λ d (dx) for a ∈ Z d with λ d unit Lebesgue measure on IR d /Z d ), one has: J(a, a) = J(0, 0) for every a. Denote this common value by J f (0) and write K f for K. The geometric mean of f is defined by GM(f ) = exp( IR d /Z d log f (x)λ d (dx)).

  > p site c (Z d ) then a.s. DPP(K f ) percolates on Z d .• If GM(1 -f ) > 1 -p site c (Z d ) then a.s. DPP(K f ) does not percolate on Z d .Proof of Theorem 4.1 Notation:K A = (K(a, b), (a, b) ∈ A 2 ) and J[A] = K A (I A -K A ) -1 .Denote by (Y a , a ∈ V) the family of Bernoulli variables corresponding to DPP(K). For any finite subset A = {a 1 , .., a n } of V, the joint law of (Y a 1 , ..., Y an ) is given byIP [Y a 1 = x 1 , .., Y an = x n ] = det(I A -K A ) det(J[A] A 1 ) (4.1)for any x a 1 , .., x an in {0, 1} andA 1 = {a ∈ A : x a = 1}.For any y a 1 , .., y an in {0, 1}, setB 1 = {a ∈ A : x a ∧ y a = 1}. Since: B 1 ⊂ A 1 , one has: det(J[A] A 1 ) ≤ det(J[A] A 1 \B 1 ) det(J[A] B 1 ) ≤ det(J[A] B 1 ) a∈A 1 \B 1 J[A](a, a). (4.2)Multiplying each member of (4.2) by det(I A -K A ), one obtains:IP [Y a 1 = x a 1 , .., Y an = x an ] ≤ IP [Y a 1 = x a 1 ∧ y a 1 , .., Y an = x an ∧ y an ] a∈A 1 \B 1 J[A](a, a)(4.3) For K diagonal matrix indexed by A × A, such that for every a in A: 0 ≤ K(a, a) < 1, denote by ( Ỹa , a ∈ A) the corresponding Bernoulli variables. One has similarly:

  For S locally compact metric space, for any A subset of S, denote by M(A) the set of σ-finite measures on S with support in A. Then a random measure M on S is negatively associated if for every A and B disjoint subsets of S, every nondecreasing real valued function f 1 (resp. f 2 ) on the set of σ-finite measures on S, with support in M(A) (resp. M(B)):

	2 Sequences of negatively associated Bernoulli vari-
	ables
	2.1 Discrete determinantal processes
	Definition 2.1

  5, one can apply a result of Garet (Theorem 1, [3]) to η -to obtain a result of percolation for (|η -(x)|) x∈Z d , which thanks to Lemma 3.7, translates into the same result for (|η + (x) -y∈V(x) p(y -x)η + (y)|) x∈Z d .

sets. In the later the DPP are dominated by Poisson point processes. Surprisingly the discrete case has not been treated already in full generality. The case of stationary DPP and V = Z d has been traited by Lyons and Steif [START_REF] Lyons | Stationary determinantal processes: phase multiplicity, bernoullicity, entropy and domination[END_REF]. We come back to this special case below. For V discrete set, let (K(a, b), (a, b) ∈ V 2 ) be the kernel of a determinantal point process on V. If K has a spectrum included in [0, 1), one sets:

Theorem 4.1 Let K be the kernel of determinantal point process on a discrete set V with a spectrum included in [0, 1), then we have:

The proof of Theorem 4.1 is presented at the end of this section.

Remark 4.2 For K kernel of a DPP on a discrete set V with a spectral radius ρ strictly smaller than 1, we have: 0 ≤ K ≤ ρI. Using the monotony property established by Lyons [START_REF] Lyons | Determinantal probability measures[END_REF], this leads to: DPP(K) ≺ Bernoulli(ρ). But note that the domination relation of Theorem 4.1 is stronger. Indeed the eigenvalues of J are related to the ones of K as follows: λ is an eigenvalue of K iff ( 1 1-λ -1) is an eigenvalue of J. This implies that the spectral radius of J is equal to ( 11-ρ -1). Consequently for every a in V, one has: J(a, a) ≤ 1 1-ρ -1, and hence: Bernoulli( J(a,a) 1+J(a,a) , a ∈ V) ≺ Bernoulli(ρ). Note that in case K = pI with p ∈ [0, 1), one has:

As an immediat application of Theorem 4.1, we give the following sufficient conditions of percolation and absence of percolation on an infinite connected graph G with vertex set V. The critical probability p c (G) is presented in the introduction. We assume that: 0 < p c (G) < 1.

Proposition 4.3 Let DPP(K) be a determinantal process on V such that the spectrum of its kernel K is in [0, 1).

(i) If for every x in V, J(x, x) < 1-pc(G) pc(G) , then a.s. DPP(K) does not percolate on G.

(ii) If for every x in V, J(x, x) < pc(G) 1-pc(G) , then a.s. DPP(I-K) percolates on G.

where Ã1 = {a ∈ A : y a = 1} and B1 = {a ∈ A : x a ∨ y a = 1}. Note that B1 \ Ã1 = A 1 \ B 1 . We choose now : K(a, a) = J[A](a,a) 1+J[A](a,a) , to obtain:

(4.4) Multiplying member by member (4.3) and (4.4), one obtains: , a ∈ V) ∩ A By letting A increase to V, one obtains: DPP(K) ≺ Bernoulli( J(a,a) 1+J(a,a) , a ∈ V).