Marion Richard Oliver

Vanden Eynde
email: o.vandeneynde@psemail.eu

Marion Richard
email: marionajrichard@gmail.com

Oliver Vanden

Eynde ||

Cooperation between National Armies: Evidence from the Sahel borders

Keywords: Counterinsurgency, Civil Conflict Counterinsurgency, Civil Conflict JEL Classification: D72, D74, L23

The effectiveness of security operations often depends on cooperation between different national armies. Such cooperation can be particularly important when international borders are porous. In this project, we investigate how the creation of an international armed force that could operate across international borders (the G5-Sahel Joint Force) affected conflict dynamics in the Sahel region. Relying on a regression discontinuity design, we find that the G5 mission lowered the intensity of conflict locally in its zone of operation. Further analysis of geographical conflict propagation patterns indicates that the G5-Sahel force facilitated security operations in border areas.

Introduction

Security operations are often constrained by international borders. Different countries may not share the same interests in conflicts, and armed groups can use neighbouring territories as a safe haven. Such safe havens have emerged along the border between Afghanistan and Pakistan, or the one between Venezuela and Colombia. However, even if the interests of neighbouring countries are broadly aligned, armed groups could exploit frictions in information-sharing between neighbours, legal constraints on armed forces crossing borders, or a failure to internalize the displacement of conflict across borders. A context that illustrates these frictions clearly is the ongoing Jihadist conflict in the Sahel. This conflict spans several West-African nations, which are each involved militarily in a fight against these groups. The conflict is particularly intense around the region's porous borders.

Our paper investigates if improved cooperation between national armies in the Sahel region makes security operations more effective. We focus in particular on the creation of a multi-national military force that could cross international borders, the so-called "G5 Sahel" mission. This mission started operating in 2017 and focused in particular on the 3-frontier region of Mali, Niger, and Burkina Faso. A priori, the effect of this mission on conflict dynamics is unclear. On the one hand, the mission solved legal constraints on operations in border areas, it may have increased troop levels and improved communication between national armies. In addition, it could have led to an internalisation of the externalities that characterize security provision in border areas. On the other hand, the joint mission might have introduced new coordination frictions between the army units from different countries.

Relying on data from the Armed Conflict Location and Event Database (ACLED), we assess the effect of the introduction of the G5 mission on the basis of two empirical exercises. First, we exploit the limitation of the zone of operation of the G5 mission to a 50 kilometer bandwidth around the concerned borders. Using a regression disconti-1 nuity around the zone of operation, we show that conflict is less intense where the G5 mission is active. This result does not seem to be driven by geographical displacement.

We observe less violence initiated by Jihadist groups, and less violence initiated by security forces against ethnic militia. As the mandate of the G5 mission was restricted to combating Jihadist groups, these results suggest that the G5 mission operated in line with its objectives and achieved a degree of effectiveness in the outcomes we measure.

Heterogeneity analysis reveals that violence drops more strongly in the operating zone of the G5 Sahel force when the terrain favours the mobility of armed groups, i.e. when ruggeness is higher and the border does not overlap with a major river.

To shed more light on the underlying mechanism, we conduct a second exercise in which we try to assess more directly if the G5 mission facilitated security operations in border areas. We focus on major French attacks on jihadist groups. We expect these attacks to trigger the movement of jihadist groups and new security operations. In the aftermath of these trigger attacks, we do see less security operations in border areas when the G5 mission is not active. However, when the G5 mission is active, this effect disappears. These findings offer additional support for the idea that the G5 force facilitated security operations in border areas.

Our paper adds to a small literature in economics and political science that studies the effect of borders on conflict outcomes with granular conflict data. [START_REF] Martínez | Transnational insurgents: Evidence from colombia's farc at the border with chávez's venezuela[END_REF] shows that the presidency of Hugo Chavez in Venezuela increased the presence of FARC rebels in Colombian municipalities along the border. Studying the geography of conflict, [START_REF] Mueller | Ethnic violence across space[END_REF] argue that raising physical barriers at ethnic frontiers could reduce conflict. [START_REF] Blair | The fortification dilemma: Border control and rebel violence *[END_REF] provides evidence from Iraq showing how border protections reduce the victimization of civilians by rebel fighters. However, this paper does not look at how borders affect the propagation of groups whose objectives are not limited to one country. In addition, the role of a cross-national force is particularly interesting as a policy intervention, as the construction of fences is practically not feasible in many settings, and may hamper with economic activity in border areas.

To our knowledge, our paper is the first to measure the effect of military cooperation between national armies on the conflict dynamics in border areas. We add to the large literature on the empirical study of conflict using econometric methods. This literature has studied the effects of economic shocks on conflict extensively (e.g. [START_REF] Miguel | Economic shocks and civil conflict: An instrumental variables approach[END_REF][START_REF] Ferrara | Conflict, climate, and cells: A disaggregated analysis[END_REF][START_REF] Dube | Commodity price shocks and civil conflict: Evidence from colombia[END_REF][START_REF] Berman | This mine is mine! how minerals fuel conflicts in africa[END_REF][START_REF] Eynde | Targets of violence: Evidence from india's naxalite conflict[END_REF]. The role of religious and ethnic diversity (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], as well as the role of political institutions as drivers of civil conflict [START_REF] Besley | Pillars of Prosperity: The Political Economics of Development Clusters[END_REF] have also been studied at length. 1 In parallel, there is increasing evidence on how development interventions affect conflict [START_REF] Berman | Do working men rebel? insurgency and unemployment in afghanistan, iraq, and the philippines[END_REF][START_REF] Crost | Aid under fire: Development projects and civil conflict[END_REF][START_REF] Fetzer | Can workfare programs moderate conflict? evidence from india[END_REF]). Finally, and closest to the current project, a very recent literature evaluates the effect of military interventions. For example, [START_REF] Dell | Nation building through foreign intervention: Evidence from discontinuities in military strategies[END_REF] find that aerial bombing campaigns by the US in Vietnam increased the support for communist insurgents. There is not much work studying in the organizational aspects of war and military planning. 2 Fetzer et al. (2021) study changes in military cooperation in the context of the security transition from NATO to the Afghan National Army in Afghanistan. This paper finds that the security transition improved security in a first stage, but worsened outcomes when NATO troops were withdrawn physically. The authors argue that these patterns are consistent with the Taliban lying low strategically to facilitate of the withdrawal. Of course, this setting is distinct from the one of cooperation between neighbouring countries which we focus on in the current paper. Given the importance of international cooperation for the effective provision of security, the questions addressed by our paper are particularly relevant -for the Sahel region and beyond.

As far as work on the Sahel region is concerned, our paper is also one of the first quantitative empirical studies of conflict in the region. Focusing on the seasonal migration of herders (transumant pastoralists), [START_REF] Mcguirk | Transhumant pastoralism, climate change, and conflict in africa[END_REF] find that rainfall deficiency has exacerbated the conflict between pastoralists and agriculturalists. While these authors do not explicitly restrict their analysis the Sahel region, the processes they study are particularly important in the region we study. In Mali, [START_REF] Richard | An indirect cost of conflict : Insecurity as a barrier to seasonal migration in mali[END_REF] finds that the insecurity induced by the conflict hampers seasonal migration and, hence, reduces lean season consumption in village usually relying on this type of migration and an income source. [START_REF] Calvo | Fear not for man? armed conflict and social capital in mali[END_REF] study the effect of conflict in Mali on social capital. They find that conflict exposure increases engagement political associations, which could deepen the conflict to the extent that these organizations act as interest groups for particular ethnic groups. [START_REF] Premand | Cash and conflict large-scale experimental evidence from niger[END_REF] study a large-scale conditional cash transfer scheme in Niger, and find that this programme increased conflict intensity.

These recent contributions all shed light on important aspects of the conflict. However, our paper is the first to focus on the security operations in this conflict.

Background

The Sahel region has been plagued by conflict in recent years, with armed groups operating across borders and increasing violence since the 2012 Tuareg-led rebellion in Mali.

This rebellion was followed by the proliferation of armed groups, including ethnic militias and jihadist groups. The concentration of violent events has been particularly high in the border areas, spreading from Mali to neighboring countries.

To address this instability, several international peacekeeping and counter-terrorism missions have been launched in the region. In January 2013, the French launched Operation Serval to regain control of the north of Mali, which was followed by the Barkhane operation, which has maintained a lasting presence in the country until its complete withdraw in May 2022. In April 2013, the United Nations deployed the Multidimensional Integrated Stabilization Mission in Mali (MINUSMA).

In February 2014, the G5-Sahel was created to facilitate military cooperation between Mali, Burkina Faso, Niger, Mauritania, and Chad. The G5-Sahel Joint Force was established by a UN resolution in June 2017,3 and its command became active in September of that year. While the G5S initiative was strongly supported by France, analysts underline that the initiative came largely from the participating countries themselves [START_REF] Touchard | Quels défis pour la Force[END_REF]. Morevoer, the G5S force was operationally independent from the French military mission.

The G5-Sahel force had a mandate focused on combating jihadist groups and trafficking gangs. It gave national armies the possibility to operate outside of the national territory, within pre-defined operation zones. In those zones, the force was also tasked with supported development interventions [START_REF] Touchard | Quels défis pour la Force[END_REF]. The activities of the G5 Sahel force were temporarily disrupted in June 2018, when a major suicide attack hit the G5 Sahel Joint Force headquarters. The resulting damage led to a suspension of activities until January 2019.

The Joint Force of the G5 Sahel was composed of 5,400 men across eight battalions.

The battalions were distributed around three operations areas, with a Malian and a Mauritanian battalion operating jointly in the Western operation zone at the border between Mali and Mauritania, four battalions with troops from Mali, Burkina Faso, Niger and Chad based in the Central Zone, at the border between Mali, Niger and Burkina Faso (the 3-frontier area), and a Nigerian and Chadian battalion based in the Eastern operation zone at the border between Chad and Niger. In G5 Sahel internal unclassified documents we have access to, 14 operations were reported in the Central Zone between 2017 and 2020, while only five and four operations were conducted respectively in the Western and Eastern operation zone during the same period. For each of the three zones, the G5S had a dedicated command. In theory, battalions also included a number of police and judiciary personnel to widen the capacities of the force [START_REF] Touchard | Quels défis pour la Force[END_REF]. More generally, the G5S mission also facilitated communication between army units along the border. For example, reports mention the creation of a phone book covering the border zones with mobile numbers of officers along the border, which improves the reactivity of forces in these areas [START_REF] Boeke | Boeke, sergei; chauzal,grégory[END_REF].

The operating zones for the G5-Sahel mission were initially defined as buffers of 50 km around the international borders the borders, but in January 2020, an announcement was made to extend the operating zone to 100 km. 4 As the implementation of this extension is unclear, 5 the focus in our empirical analysis remains on the 50km buffer zone in the time period between September 2017 and January 2020.

We do not have access to the exact geographical locations for all G5-Sahel operations operations. However, in figure A 1 we map all the events reported in the ACLED data that mention the G5-Sahel force explicitly or that involve G5-Sahel members operating outside of their national territories. The spatial distribution of these events is consistent with a focus of the G5 Sahel joint force on the 3-frontier region between Mali, Niger and Burkina Faso, and with a restriction of operations within the 50 km buffer zone around these borders. For most of our empirical analysis, we will hence focus on this Central zone.

From 2020 onward, two military coups in Mali generated tensions with the international community. The country finally left the G5-Sahel in May 2022, leading to the de facto end of the organization. Nevertheless, the G5-Sahel Joint Force was an essential part of international efforts to restore stability to the region for more than 5 years. Our paper attempts to assess its effect on conflict dynamics.

Theoretical Framework

The provision of security in border areas entails specific challenges. Armed groups may be more mobile than security forces, who are not allowed to cross borders. Anticipating the possibility of armed groups to flee to safe havens, security forces may decide not to intervene in border zones. 6 In addition, investments in security in border areas may have externalities for neighbouring countries which are not taken into account when countries decide on how much investments to make in border zones. For all these reasons, security provision might be under-optimal in border areas.

The G5-Sahel mission could have increased or decreased conflict intensity, depending on the mechanism of influence. First of all, counter-terrorism forces could be a deterrent or neutralize armed groups, leading to a reduction in observed violence. However, counter-terrorism operations are also likely to result in greater fatalities among armed group members, and they could lead to violent escalation. Similarly, counter-terrorism forces could be an additional risk factor for civilians. These may become collateral victims, or could suffer from retaliation of armed groups against suspected collaborators. Moreover, organizational frictions between national armies could reduce the effectiveness of the joint force. Descriptive accounts point at severe coordination problems in terms of equipment and command structures [START_REF] Touchard | Quels défis pour la Force[END_REF].

In thinking about the impacts of the G5 mission, the effects could be direct, involving the operations of G5-Sahel units, but also indirect when they involve other units whose behaviour changes in response to the presence of the G5-Sahel mission. For example, the improved communication between border forces that the G5S mission facilitated is likely to affect all units.

Our empirical approach will not enable a fine distinction between all mechanisms. However, the sign of the net effects we estimate, in combination with a detailed analysis of different types of violence, will help us to narrow down the mechanisms underlying our findings. In addition, heterogeneous effects can shed some further light on the causal channels. If the G5 mission improves military coordination in border areas where militants are more mobile, we could expect the impacts to be most pronounced where it is also easier for armed groups to move without being detected or interrupted -for example in rugged areas.

Data

Our main source of violence data is ACLED (Armed Conflict Location Event Data).

ACLED is a database that tracks and records information on armed conflicts and political violence around the world. The data is sourced from a variety of sources, including traditional media, social networks, NGOs, international organizations, and local partners. For each violent event, the ACLED data records the number of fatalities that occurred. The events are also geo-coded, meaning that their location is identified and mapped. The locality of the events is coded at different levels of precision. This coding precision will be important for our study, as our regression discontinuity approach will exploit fine geographical variation. In addition to its localisation, each ACLED event is dated precisely. Further sub-categories are created based on the actors involved in each event. These sub-categories help to differentiate between different types of violence, such as conflicts between state and non-state actors or violence between different nonstate actors. Overall, the ACLED data provides a comprehensive and detailed record of violent events and their associated actors, fatalities, and locations. While the reported fatalities are likely to be biased as underscored by the ACLED data description as "prone to manipulation by armed groups, and occasionally the media", this noisy measure may still contain some information about conflict intensity, and has been shown to correlate strongly with climatic shocks (e.g. [START_REF] Ferrara | Conflict, climate, and cells: A disaggregated analysis[END_REF], population displacement (e.g. [START_REF] Tai | Violence and internal displacement: Insights from nationwide mobile phone data[END_REF]. and child health (e.g. [START_REF] Tapsoba | The cost of fear : Impact of violence risk on child health during conflict[END_REF]. As a robustness check, we also use a transformation of the fatality variables recording whether any fatality is reported.

We map the ACLED data and use information on the operation zones of the G5-Sahel mission that we obtained from official documents. To this mapped violence data, we add granular data on nightlight emissions and geographical features such as road access, urbanization, ruggedness and closeness to rivers. These additional variables will be used to support the validity of our empirical approach.

Figure A 1 shows the trends in violence, based on the ACLED data, in the "central operation zone", i.e. the three border area of Burkina Faso, Mali, and Niger. Violence is clearly trending upwards from early 2017 onwards. This increase is particularly pronounced in areas very close (within 15 km) to the international borders, while the broader operation zone of the G5 mission follows a trend that is similar to the one observed for the areas outside of the G5 operation zone. While this graph illustrates the overall conflict dynamics and is important for the context of our study, we do not think it allows us to identify the effect of the G5-Sahel mission. The low levels of violence before the launch of the G5-Sahel force in September 2017 make the setting ill-suited for a difference-in-difference approach. Moreover, the G5-mission was created in anticipation of the conflict becoming more gradually intense in the border areas, and the strategies of various actors may have contributed to this intensification. Hence, estimating the effect of cooperation between national armies necessitates a more granular approach. We develop such empirical strategies in the next section.

Empirical strategy

We will study the effect of the G5 Sahel mission through the lens of two empirical exercises. First, we will use a regression discontinuity design to assess whether violence levels are different in the operation zones of the G5-mission. We are interested in comparing areas where national armies cooperate to areas that are under the sole responsibility of national army units. The precise definition of the operation zone of the G5 mission offers a plausibly exogenous assignment to these two security environments. In particular, we leverage the spatial discontinuity created by the limitation of the G5-Sahel operation zone within 50 km of G5-Sahel countries' borders:

y i = α + βBorder i + δ (Distance i -z 0 ) + δ ′ Border i • (Distance i -z 0 ) + δ b + η c + ϵ i (1)
In this specification, the outcome y i is our measure of conflict at the grid-cell i level. z 0 refers to the limit of the buffer zone, at 50 km. Distance i measures the distance to the 50km buffer limit. We could expect this running variable to correlate with conflict outcomes -for example, conflict could be systematically more intense when we are closer to the international border. In our empirical approach, we want to control for such impacts, and evaluate instead whether the operation zone of the G5 creates a discontinuous change in conflict outcomes. The discontinuity is be captured in the equation by Border i , which indicates whether grid-cell is less than 50km from the border. We also include border segment fixed effects δ b and country fixed effects η c . We allow for a data-driven choice of two bandwiths for optimal mean squared error (MSE) point estimation with Calonico-Cattaneo-Titiunik procedure [START_REF] Calonico | Robust nonparametric confidence intervals for regression-discontinuity designs[END_REF]. As the RD approach relies on a fine coding of conflict events, we use granular gridcells (0.025 by 0.025 degrees), and we focus on ACLED events with the highest precision level for our main results. We show findings for alternative coding as robustness checks. To support the validity of the RD approach, we will show continuity of geographical characteristics and pre-G5 levels of violence around the border of the operation zone.

To shed further light on the mechanisms underlying the RD results, we will rely on a second empirical exercise. Here, we study how the response of violence to trigger events differs in border areas and depending on whether the G5 mission is active or not.

As trigger events, we focus on major French operations against Jihadist groups, which we identify as operations that claim at least 5 fatalities. These events are followed by a marked intensification of conflict, as shown in figure A 6 in the online appendix. In a triple difference approach, we will compare the response to trigger events between border and non-border areas, and when the G5-Sahel mission is active versus not active.

We structure the data in 0.1 by 0.1 degree grid-cells. We restrict ourselves to trigger operations that are less than 250km from the three-border area. Then, we construct a window of 8 weeks, and a geographical circle of 100km, around each trigger operation.

When gridcells are part of multiple event windows, we keep only the first window for that gridcell. 7 In total, our sample has 48 trigger operations, and 20 of these take place when the G5-Sahel mission is not active.

The resulting estimating equation is:

y i,p,t = ζBorder i * Post t,p + χBorder i * Post t,p * G5 t + η i + γ p,t + ϵ i,p,t (2)
In this equation, y i,p,t is a measure of conflict at time t in gridcell i for a window around operation p. t is measured in two-week periods. The outcome Border i indicates whether grid-cell is less than 50km from the international border, so within the operation zone of the G5-Sahel force. Post t,p is one in the time periods after the trigger operation. G5 t is an indicator for when the G5 Force is active. 8 We also include operation by time fixed effects (γ p,t ), as well as gridcell level fixed effects (η i ). We cluster standard errors at the gridcell-level. While our main interest is in the triple difference specification above, we will also show results where we estimate time-to-operation effects in event study graphs. The graphical patterns show a gradual increase in conflict as one moves closer to the international border. This effect can be due to the strategic importance of the border for the security forces, as well as the net benefits of operating in these areas from the perspective of armed groups. However, the RD results show a discontinuous jump in this pattern within the operation zone of the G5. The graphical patterns also suggest that the results are not driven by symmetrical displacement, where the reduction within the operation zone is offset by increased violence just outside the operation zone. Of course, it is impossible to rule out more gradual displacement. However, interpretationally, this would still provide evidence of the local effectiveness of the G5-Sahel mission. As we set out in the theoretical framework, it is far from obvious ex ante that the mission should have reduced violence -even locally. Panel A in Table 1 shows RD estimates for different estimation approaches and outcomes. We see that the general pattern of lower fatalities in the G5 operation zone holds across estimation methods and outcomes. The magnitude of the effect is large: crossing into the operation zone of the G5 mission reduces the number of fatalities in a given gridcell by 0.04, whereas the mean number of fatalities per gridcell is around 0.03. The reduction in violence is observed for security operations, attacks by armed groups, and violence against civilians. The effects are a bit more marked for the number fatalities than for event counts, but they go in the same direction.

Results

RD results

To shed more light on the mechanisms underlying the observed reduction in violence, the subsequent panels in Table 1 show RD results for a finer classification of violent events based on the actors involved. Panel B focuses on violence involving islamist groups. Interestingly, security operation against islamist groups do not decrease significantly in the operation zone of the G5 region. However, there are less attacks by armed jihadist groups and less attacks against civilians. Strikingly, there is a more pronounced reduction in security force violence against ethnic militia groups, while these ethnic militias do not reduce their violence significantly. As the official mandate of the G5-Sahel force is focused on combating Jihadist groups, these findings suggest the G5-Sahel mission reduces violence initiated by the actor it is supposed to target. In this sense, the mission appears to be effective.

Table 2 presents important validity checks for the RD approach. It confirms the absence of discontinuities in pre-G5 conflict measures as well as geographical characteristics. Hence, we are confident that the regression discontinuity estimates are picking up the causal effect of grid-cells belonging to the operation zone of the G5 mission.

Heterogeneity analysis

Table 3 show heterogeneous results by characteristics of the border. The reduction in violence is most pronounced in areas that are more rugged and areas that are further away from rivers. Rugged terrain makes it easier for armed groups to move without Notes : Discontinuity estimated at 50 km. Data-driven choice of two bandwidths for MSE-optimal point estimation. Local polynomial of order 1. Additional country and border controls. All conflict events occurring within 250km of each considered G5-Sahel borders are included for the period between September 2017 to January 2020. Include events coded with geo-precision level 1 only. Cells that intersect with the limit of the 50km buffer of intervention are dropped from the sample. Robust Calonico-Cattaneo-Titiunik standard errors in parentheses-*** p<0.01, ** p<0.05, * p<0.1.

detection and hampers their pursuit or interception by security forces. In contrast, rivers create physical barriers that facilitate detection and interception. Hence, these patterns consistent with the hypothesis that the G5 is most effective where borders are most porous. 9 Figure A 5 in appendix illustrates the definition of border segments characteristics used for this heterogeneity analysis. The patterns are a bit harder to interpret for the distance to MINUSMA forces. The reduction in violence is larger in the vicinity of MINUSMA forces, which could capture complementarities between the G5 Sahel mission and MINUSMA. However, the difference in the magnitude of coefficients is small compared to the differences we see for ruggedness or overlap with rivers.

Table A1 in appendix further shows heterogeneity by border and country member, suggesting the G5 is most effective at the border between Mali and Burkina Faso.

Robustness of the RD results

In the appendix, we present RD plots for a wider range of outcomes in figures A 3 and A 4. 10 Table A5 offers a detailed comparison of alternative 9 Modern RD methods are not set up to estimate heterogeneous effects, so we do not formally test the difference between coefficients. Another caveat to this interpretation is that that some of difference between these regions already appears in the mean of the dependent variable.

10 One issue highlighted by the graphs in figure A 3 is the small number of security operations against Islamist groups in the optimal RD bandwidth. Figure A 4 shows this number increases when including less precisely coded events.Table A5 provides results for coarser geographical precision levels.

coding approaches for the main violence outcomes. It includes results where the fatality numbers are subject to an inverse hyperbolic sine transformation. It also considers measures that include violence events that are coded less precisely (level 2 in ACLED).

Including these less precisely coded violence events tends to makes the RD estimates less precise too. However, the broad patterns we found in our main results are generally robust to these alternative measurement approaches. Table A2 replicates the main RD results over the Western and Easter operations zones and finds no discontinuity in any outcome, which is consistent with the lower treatment intensity in these areas.

Table A3 further shows that the results are also robust to dropping cells crossed by the 50km buffer line, top-coding the 1% top fatalities and transforming the fatalities variable to a dummy indicating any fatality. Table reproduces the RDD results with manually set banwdith and a standard linear estimation of the G5 area effect while controlling for several transformation of the distance to the border and flexible controls for longitude and latitude, with stable coefficients across specifications.

Response to trigger events

We now turn to our second empirical exercise, which compares responses of violence events to trigger operations. Figure 3 shows the differential violence in border areas when the G5 mission is active, split up in 2-week time periods around each trigger event. Panel A shows that relatively more violence events occur in border areas (so, within the G5-Sahel operation zone) when the G5-Sahel force is active.

The split-up by type of violence in Panels B to D suggests that it is mostly the violence initiated by security forces that is driving this intensification. Focusing on panel B alone, this intensification is visible relatively soon after the trigger event. Table 4 confirms these patterns. Interestingly, it also shows that when the G5 mission is not active, there are less security operations following a trigger event in border areas.11 This finding supports the hypothesis that security forces are hampered in their operations when the G5-Sahel mission is not active. However, this relative reduction in the intensity of operations is entirely off-set when the G5 mission is active. This result suggests that the G5-Sahel mission did achieve its goal of facilitating operations in border areas. This pattern is mirrored by violence against civilians. Additional analysis in table A6 suggests that this effect is mostly coming from violence by security forces against the civilian population.12

Robustness of the trigger event analysis

In the appendix, we test the sensitivity of the results to an alternative criterion for the trigger event, where we focus on operations in which at least 10 (instead of 5) people died (Table A7). These results are noisier, as the more selective criterion reduces the sample, but the pattern on military operations is the same and significant (at 10%) for the event measures. In Table A8, we present results for an alternative coding of the G5 operation period, treating the entire period from September 2017 onwards as "active". In this coding, we ignore the incapacitation of the G5 mission after the 2018 suicide attack. Compared to table 4, we find similar patterns for military operations -they are lower in border areas before the G5 is active, and increase afterwards. 13 While the reductions in violence by armed groups are not immediately observable, the response estimates are not set up to capture the longerterm dynamic impacts of security operations in border areas. For such global effects, we think our earlier RD results are more insightful.

Conclusion

This paper examines how the establishment of an international armed force capable of crossing borders, known as the G5-Sahel, influenced the intensity and spatial distribution of conflict in the region's porous border areas. Our analysis indicates that the G5 mission reduced the intensity of conflict, at least locally, within its operation zone. By studying how the spatial distribution of violence responds to trigger events, we also find that the mission facilitated security operations in border areas. In this sense, our results offer a coherent narrative, whereby improved cooperation between national armies contributes to a reduction in equilibrium levels of violence. It should be kept in mind that the armies that are part of the G5-Sahel mission are regularly accused of human rights abuses, and we see that fatal violence against civilians mirrors their activities in our data.

Hence, the welfare implications of our findings are far from clear in the context we study.

In addition, the local effects that we estimate do not allow us to evaluate whether the G5 mission has helped to reduce levels of conflict at the aggregate level. The geographical spread of jihadist groups and the ongoing security challenges in the Sahel region put the local improvements we document in sharp perspective. In spite of these limitations, we think it is important to document that establishing zones in which national armies share security responsibilities can change conflict dynamics. These findings are particularly relevant for the many border regions in which armed groups exploit coordination frictions between national security forces. Notes : Discontinuity estimated at 50 km. Data-driven choice of two bandwidths for MSE-optimal point estimation. Local polynomial of order 1. Additional country and border controls. All conflict events occurring within 250km of each considered G5-Sahel borders are included for the period between September 2017 to January 2020. Include events coded with geo-precision level 1 only. Cells that intersect with the limit of the 50km buffer of intervention are dropped from the sample. Robust Calonico-Cattaneo-Titiunik standard errors in parentheses-*** p<0.01, ** p<0.05, * p<0.1. Notes : Discontinuity estimated at 50 km. Data-driven choice of two bandwidths for MSE-optimal point estimation. Local polynomial of order 1. Additional country and border controls. All conflict events occurring within 250km of each considered G5-Sahel borders are included for the period between September 2017 to January 2020. Include events coded with geo-precision level 1 only. Empty cells means the discontinuity could not be estimated due to lack of variability in the dependent variable. Robust Calonico-Cattaneo-Titiunik standard errors in parentheses-*** p<0.01, ** p<0.05, * p<0.1. Notes : Discontinuity estimated at 50 km. Data-driven choice of two bandwidths for MSE-optimal point estimation. Local polynomial of order 1. Additional country and border controls. All conflict events occurring within 250km of each considered G5-Sahel borders are included for the period between September 2017 to January 2020. Include events coded with geo-precision level 1 only. Cells that intersect with the limit of the 50km buffer of intervention are dropped from the sample. Robust Calonico-Cattaneo-Titiunik standard errors in parentheses-*** p<0.01, ** p<0.05, * p<0.1. Notes : Manual choice of bandwidths. Additional country controls, no border segment controls. All conflict events occurring within 250km of each considered G5-Sahel borders are included for the period between September 2017 to January 2020. Include events coded with geo-precision level 1 only. Only estimate of coefficient of interest "Cell within G5 operation zone" reported. Control variables include distance to the G5 central border, latitude, longitude, and squared and cubic transformations of latitude and longitude. Distance to the border and its transformation and are allowed a different slope within and outside of the operation zone while the effect of latitude and longitude is assumed to be the same within and outside of the G5 area to avoid overfitting. Robust standard errors in parentheses-*** p<0.01, ** p<0.05, * p<0.1. Notes : Discontinuity estimated at 50 km. Data-driven choice of two bandwidths for MSE-optimal point estimation. Local polynomial of order 1. Additional country and border controls. All conflict events occurring within 250km of each considered G5-Sahel borders are included for the period between September 2017 to January 2020. Military operations involving islamist groups record fatalities from islamist groups only, whereas attacks by armed group and attacks on civilians involving islamist goups record fatalities caused by islamist groups. Idem for communal militia and unidentified armed groups. Empty cells means the discontinuity could not be estimated due to lack of variability in the dependent variable. Robust Calonico-Cattaneo-Titiunik standard errors in parentheses-*** p<0.01, ** p<0.05, * p<0.1. Notes: Segments overlapping with rivers are defined as those segments within five km of a river over 40% of their total length. Segments "close" to MINSUMA are segments for which the minimum distance between a MINUSMA base and the segment is lower than the median distance. Segments in "high rugged" areas are segments for which the average ruggedness of cells crossed by the segments is above the median ruggedness of cells crossed by the other segments.

Figure 1 :

 1 Figure 1: Foreign Military Operations in Sahel regions

  Figure 2 compares fatalities in gridcells within the G5-Sahel central operation zone to those in gridcells just outside the operation zone during the period of activity of the G5 mission within 50km of international borders. The local linear regressions in Panel A and B shows a clear discontinuity in the number of total conflict fatalities and civilians fatalities caused by Islamist groups at the border of the operation. There are less fatalities where the G5 mission is active, especially for events involving Islamist groups whose containment was the objective of the G5 mission. The discontinuity appears stronger with the data-driven optimal bandwidth (Calonico-Cattaneo-Titiunik procedure to minimise bias and variance of the RD estimator) which mostly excludes cells closer to the international border.

Figure A 2

 2 Figure A 2 in Appendix shows the comparison for the total number of fatalitiesduring the G5 mission period and before September 2017, when the G5 mission was not active. There is no discontinuity in the pre-treatment period, which supports the validity of the RD approach.

Figure 2 :

 2 Figure 2: Regression Discontinuity for G5 central operation zone

Figure 3 :

 3 Figure 3: Reaction to trigger events -border areas under G5

Figure A 2 :

 2 Figure A 2: Regression Discontinuity for G5 operation zone

Figure A 3 :

 3 Figure A 3: RDD plots with optimal buffer for sub-groups, geo-precision level 1

Figure

  Figure A 5: Border segments characteristics

Figure A 6 :

 6 Figure A 6: Reaction to trigger events -time patterns (no differences)

Table 1 :

 1 Discontinuity in conflict intensity for G5 Sahel Central operation zone by actors 2017-2020. Discontinuity estimated at 50 km. Data-driven choice of two bandwidths for MSE-optimal point estimation. Local polynomial of order 1. Additional country and border controls. All conflict events occurring within 250km of borders between Burkina Faso, Mali and Niger are included for the period between January 2011 and September 2017. Include events coded with geo-precision level 1 only. Empty cells means the discontinuity could not be estimated due to lack of variability in the dependent variable. Military operations involving islamist groups record fatalities from islamist groups only, whereas attacks by armed group and attacks on civilians involving islamist goups record fatalities caused by islamist groups. Idem for communal militia and unidentified armed groups. Robust Calonico-Cattaneo-Titiunik standard errors in parentheses-*** p<0.01, ** p<0.05, * p<0.1.

		All events	Military operations	Attacks by armed groups	Attacks on Civilians
		Fatalities (count)	Events	Fatalities (count)	Events	Fatalities (count)	Events	Fatalities (count) Events
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Panel A: All events
	Robust	-0.0449***	-0.0108	-0.0050**	-0.0022***	-0.0359**	-0.0073	-0.0319***	-0.0033
		(0.0165)	(0.0073)	(0.0025)	(0.0007)	(0.0151)	(0.0069)	(0.0113)	(0.0051)
	Mean DV	0.027	0.011	0.003	0.001	0.024	0.010	0.016	0.007
	Standard Deviation	1.115	0.220	0.211	0.033	1.073	0.198	0.646	0.123
	Observations within buffer	3726	5881	7285	4865	3609	6378	3285	7668
	Observations untreated	38392	25505	27652	42229	32315	22713	34083	22389
	Bandwidth untreated (km)	71.101	46.514	50.720	78.387	59.485	41.264	62.884	40.734
	Bandwidth treated (km)	6.499	10.214	12.582	8.413	6.280	11.000	5.684	13.220
	Panel B: Events involving Islamist groups
	Robust	-0.0244**	-0.0094***	-0.0015	-0.0008	-0.0244**	-0.0094***	-0.0132***	-0.0041*
		(0.0115)	(0.0035)	(0.0017)	(0.0005)	(0.0115)	(0.0035)	(0.0047)	(0.0021)
	Mean DV	0.015	0.006	0.000	0.000	0.015	0.006	0.005	0.003
	Standard Deviation	0.875	0.123	0.067	0.011	0.875	0.123	0.273	0.076
	Observations within buffer	6957	5243	8599	6298	6957	5243	4079	8771
	Observations untreated	37374	39015	30246	28692	37374	39015	25485	45587
	Bandwidth untreated (km)	69.241	72.389	55.643	52.692	69.241	72.389	46.456	84.874
	Bandwidth treated (km)	12.079	9.105	14.864	10.868	12.079	9.105	7.090	15.092
	Panel C: Events involving Communal militia
	Robust	-0.0084	0.0019	-0.0025	-0.0017***	-0.0084	0.0019	-0.0081	0.0035
		(0.0085)	(0.0033)	(0.0018)	(0.0006)	(0.0085)	(0.0033)	(0.0076)	(0.0029)
	Mean DV	0.008	0.002	0.002	0.001	0.008	0.002	0.006	0.001
	Standard Deviation	0.573	0.058	0.195	0.028	0.573	0.058	0.516	0.042
	Observations within buffer	3270	11604	6942	4750	3270	11604	3114	12034
	Observations untreated	39963	24751	29184	34175	39963	24751	35309	20710
	Bandwidth untreated (km)	74.163	45.224	53.602	63.075	74.163	45.224	65.131	37.586
	Bandwidth treated (km)	5.664	19.825	12.034	8.208	5.664	19.825	5.421	20.548
	Panel D: Events involving civilians
	Robust	-0.0319***	-0.0033	-0.0020*	-0.0011***	-0.0249**	-0.0004	-0.0319***	-0.0033
		(0.0113)	(0.0051)	(0.0012)	(0.0004)	(0.0104)	(0.0046)	(0.0113)	(0.0051)
	Mean DV	0.016	0.007	0.002	0.000	0.013	0.006	0.016	0.007
	Standard Deviation	0.646	0.123	0.191	0.024	0.600	0.112	0.646	0.123
	Observations within buffer	3285	7668	7553	5101	3190	9994	3285	7668
	Observations untreated	34083	22389	16038	33412	27594	21360	34083	22389
	Bandwidth untreated (km)	62.884	40.734	28.872	61.633	50.602	38.746	62.884	40.734
	Bandwidth treated (km)	5.684	13.220	13.036	8.807	5.544	17.149	5.684	13.220
	Notes :

Table 2 :

 2 Continuity in conflict intensity and geographical variables for G5 Sahel Central operation zone before G5 Sahel first operation. Discontinuity estimated at 50 km. Data-driven choice of two bandwidths for MSE-optimal point estimation. Local polynomial of order 1. Additional country and border controls. All conflict events occurring within 250km of borders between Burkina Faso, Mali and Niger are included for the period between January 2011 and September 2017. Include events coded with geo-precision level 1 only. Robust Calonico-Cattaneo-Titiunik standard errors in parentheses-*** p<0.01, ** p<0.05, * p<0.1.

		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
		Conflict variables			Geographical variables
		before Sept 2017
	Variables:	Events Fatalities(#) GHS pop Nightlight 2017 Nightlight 2014 NDVI	Road	Rivers	Cities Ruggedness
	Conventional	0.0005	-0.0004	-0.3384	-0.0034	-0.0024	0.2634 -0.3823 0.2758	0.1124	0.0909
		(0.0021)	(0.0020)	(4.1348)	(0.0027)	(0.0029)	(0.2451) (0.4188) (0.6033) (0.6682)	(0.4954)
	Bias-corrected	0.0007	-0.0006	-2.2285	-0.0044*	-0.0032	0.2521 -0.6176 0.2674 -0.0362	0.0989
		(0.0021)	(0.0020)	(4.1348)	(0.0027)	(0.0029)	(0.2451) (0.4188) (0.6033) (0.6682)	(0.4954)
	Robust	0.0007	-0.0006	-2.2285	-0.0044	-0.0032	0.2521 -0.6176 0.2674 -0.0362	0.0989
		(0.0024)	(0.0028)	(4.7529)	(0.0032)	(0.0035)	(0.2928) (0.4756) (0.7200) (0.7954)	(0.5605)
	Mean DV	0.004	0.010	36.676	0.195	0.009	131.669 21.677	36.819 116.643	13.787
	Standard Deviation	0.357	0.920	214.323	0.262	0.260	16.791	36.265	33.116 101.818	20.645
	Observations within buffer	5369	4476	7415	10155	6911	6319	8565	11255	12201	6700
	Observations untreated	14332	6874	14654	11793	11971	15691	9974	17162	18665	8946
	Bandwidth untreated (km) 25.662	12.131	26.330	21.065	21.399	28.188	17.742	30.911	33.761	15.923
	Bandwidth treated (km)	9.389	7.804	12.804	17.466	11.981	10.904	14.798	19.211	20.821	11.560
	Notes :

Table 3 :

 3 Discontinuity in conflict intensity for central G5-Sahel operation zones 2017-2020, heterogeneity by border segment characteristics.

		Low rugged	High rugged	Close river	Far river	Close MINUSMA	Far MINUSMA
		Fatalities Events Fatalities	Events	Fatalities Events Fatalities Events Fatalities Events Fatalities Events
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
	Conventional	-0.0106	-0.0024 -0.0733*** -0.0211*** -0.0133* -0.0143 -0.0559*** -0.0049 -0.0776** -0.0203* -0.0275* -0.0078
		(0.0136) (0.0097) (0.0245)	(0.0070)	(0.0078) (0.0096) (0.0205) (0.0082) (0.0324)	(0.0108)	(0.0143) (0.0077)
	Bias-corrected	-0.0165	0.0002 -0.0688*** -0.0229*** -0.0139* -0.0155 -0.0572*** -0.0048 -0.0698** -0.0218** -0.0317** -0.0095
		(0.0136) (0.0097) (0.0245)	(0.0070)	(0.0078) (0.0096) (0.0205) (0.0082) (0.0324)	(0.0108)	(0.0143) (0.0077)
	Robust	-0.0165	0.0002	-0.0688** -0.0229*** -0.0139* -0.0155 -0.0572** -0.0048 -0.0698** -0.0218* -0.0317* -0.0095
		(0.0155) (0.0111) (0.0271)	(0.0084)	(0.0082) (0.0102) (0.0225) (0.0096) (0.0338)	(0.0122)	(0.0163) (0.0088)
	Mean DV	0.019	0.007	0.035	0.015	0.009	0.005	0.037	0.014	0.034	0.011	0.024	0.011
	Standard Deviation	1.199	0.195	1.029	0.241	0.836	0.185	1.228	0.235	1.454	0.266	0.869	0.189
	Observations within buffer	1762	3897	2649	2484	897	1751	2715	4121	1575	2652	2293	3407
	Observations untreated	13548	12904	18614	16068	8351	9764	24504	12972	15627	14709	20820	14782
	Bandwidth untreated (km)	50.896	48.364	67.359	57.882	49.290	57.831	65.951	33.791	78.887	74.118	60.958	42.814
	Bandwidth treated (km)	6.443	13.852	8.814	8.347	5.222	10.297	6.685	10.149	7.560	12.593	6.250	9.322

Table 4 :

 4 Reaction to trigger events

		All events		Military operations	Attacks by armed groups	Attacks on Civilians
		Fatalities (count) Events Fatalities (count) Events Fatalities (count) Events Fatalities (count) Events
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Border x Post	-0.50	-0.16*	-0.52*	-0.13**	0.02	-0.03	-0.70**	-0.06
		(0.50)	(0.09)	(0.30)	(0.06)	(0.41)	(0.06)	(0.30)	(0.06)
	Border x Post x G5	1.40**	0.17*	1.46***	0.19***	-0.07	-0.01	1.41***	0.03
		(0.67)	(0.10)	(0.47)	(0.07)	(0.49)	(0.07)	(0.50)	(0.07)
	Mean DV	0.797	0.199	0.370	0.062	0.427	0.138	0.412	0.108
	Standard Deviation	5.260	0.638	3.846	0.412	2.901	0.423	2.814	0.368
	Observations	2538	2538	2538	2538	2538	2538	2538	2538
	Clusters	282	282	282	282	282	282	282	282

Notes: Observations at the grid-cell level, binned in two-week periods, in two-month windows around major French operations

(2010- 2020)

. Results are based on estimating equation (

2

). Standard errors are clustered at the grid-cell level and presented in parentheses; stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

Table A1 :

 A1 Discontinuity in conflict intensity for central G5-Sahel operation zones 2017-2020, by country/border.

		Mali		Burkina Faso	Niger	MLI-BFA	MLI-NER	NER-BFA
		Fatalities Events Fatalities Events	Fatalities	Events	Fatalities Events Fatalities Events Fatalities Events
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
	Conventional	-0.0399* -0.0088 -0.0842** -0.0246** -0.0042*** -0.0052*** -0.0813* -0.0124 -0.0198*** -0.0056	-0.0073	-0.0064
		(0.0213) (0.0109) (0.0369)	(0.0114)	(0.0016)	(0.0017)	(0.0460) (0.0119) (0.0066) (0.0053) (0.0104) (0.0077)
	Bias-corrected	-0.0499** -0.0081 -0.0802** -0.0271** -0.0042*** -0.0054*** -0.1031** -0.0169 -0.0150** -0.0063	-0.0029	-0.0066
		(0.0213) (0.0109) (0.0369)	(0.0114)	(0.0016)	(0.0017)	(0.0460) (0.0119) (0.0066) (0.0053) (0.0104) (0.0077)
	Robust	-0.0499** -0.0081 -0.0802** -0.0271*	-0.0042*	-0.0054** -0.1031* -0.0169 -0.0150** -0.0063	-0.0029	-0.0066
		(0.0246) (0.0125) (0.0382)	(0.0139)	(0.0021)	(0.0022)	(0.0613) (0.0141) (0.0074) (0.0065) (0.0109) (0.0083)
	Mean DV	0.026	0.011	0.045	0.020	0.013	0.004	0.033	0.014	0.021	0.008	0.028	0.012
	Standard Deviation	0.999	0.243	1.213	0.270	1.197	0.085	1.081	0.253	1.077	0.199	1.205	0.198
	Observations within buffer	1592	4393	1736	1489	950	1475	2852	3114	7180	3559	3871	3364
	Observations untreated	16791	14490	8179	7730	11640	9115	35848	27757	30602	38130	6194	14467
	Bandwidth untreated (km)	72.991	63.214	52.278	49.213	73.416	57.273	130.390 102.342	126.416	154.848	49.630	115.350
	Bandwidth treated (km)	6.800	18.233	9.986	8.625	5.728	8.952	10.506	11.491	31.853	15.773	30.229	26.307

Table A2 :

 A2 Discontinuity in conflict intensity for all G5-Sahel operation zones 2017-2020, all regions.

		All events		Military operations	Attacks by armed groups	Attacks on Civilians
		Fatalities (count) Events Fatalities (count)	Events	Fatalities (count) Events Fatalities (count) Events
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Panel A: Central Zone (Mali-Niger-Burkina Faso three borders regions)
	Robust	-0.0452***	-0.0092	-0.0045*	-0.0022***	-0.0356**	-0.0056	-0.0321***	-0.0024
		(0.0161)	(0.0067)	(0.0024)	(0.0007)	(0.0143)	(0.0063)	(0.0114)	(0.0047)
	Mean DV	0.026	0.010	0.003	0.001	0.022	0.009	0.015	0.007
	Standard Deviation	1.071	0.200	0.211	0.032	1.030	0.178	0.640	0.119
	Observations within buffer	3641	5821	7214	4863	3570	6358	3201	7491
	Observations untreated	34378	21575	29292	44030	29242	19120	29838	18975
	Bandwidth untreated (km)	63.484	39.229	53.794	81.883	53.718	34.596	54.787	34.321
	Bandwidth treated (km)	6.347	10.099	12.443	8.409	6.189	10.973	5.569	12.931
	Panel B: Eastern Zone (Niger-Chad border)
	Robust	-0.0138	-0.0003	-0.0018	-0.0003	-0.0108	-0.0005	-0.0035	0.0011
		(0.0148)	(0.0045)	(0.0016)	(0.0002)	(0.0120)	(0.0043)	(0.0044)	(0.0045)
	Mean DV	0.004	0.002	0.001	0.000	0.003	0.002	0.002	0.002
	Standard Deviation	0.332	0.098	0.142	0.015	0.256	0.085	0.137	0.080
	Observations within buffer	3904	8375	3587	3587	3935	8259	3927	8598
	Observations untreated	13977	24559	9555	8462	18746	22374	9858	17576
	Bandwidth untreated (km)	45.304	78.924	30.996	27.498	60.539	72.039	32.022	56.787
	Bandwidth treated (km)	12.819	27.554	11.753	11.753	12.904	27.168	12.884	28.231
	Panel C: Western Zone (Mali-Mauritania border)
	Robust		-0.0002			-0.0003		-0.0002
			(0.0003)			(0.0003)		(0.0002)
	Mean DV		0.002			0.001		0.001
	Standard Deviation		0.058			0.055		0.038
	Observations within buffer		2750			2750		2589
	Observations untreated		11367			13264		14096
	Bandwidth untreated (km)		20.655			24.049		25.824
	Bandwidth treated (km)		4.771			4.771		4.521

Table A3 :

 A3 Discontinuity in conflict intensity for central G5-Sahel operation zones 2017-2020, Robustness checks.

		All events	Military operations	Attacks by armed groups	Attacks on Civilians
	Fatalities (count)	Events	Fatalities (count)	Events	Fatalities (count)	Events	Fatalities (count)	Events
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Panel A: Splitted cells dropped
	Robust	-0.0525**	-0.0284***	-0.0023	-0.0031***	-0.0449**	-0.0232***	-0.0231	-0.0144***
		(0.0237)	(0.0090)	(0.0048)	(0.0009)	(0.0224)	(0.0082)	(0.0148)	(0.0047)
	Mean DV	0.028	0.011	0.003	0.001	0.024	0.010	0.016	0.007
	Standard Deviation	1.122	0.220	0.213	0.033	1.080	0.198	0.648	0.123
	Observations within buffer	1930	3069	2646	4005	1833	3280	1463	4178
	Observations untreated	42957	38014	41047	49234	37312	32178	34938	33698
	Bandwidth untreated (km)	81.727	72.396	78.116	93.936	70.949	61.274	66.506	64.139
	Bandwidth treated (km)	4.944	6.966	6.113	8.479	4.765	7.291	4.218	8.756
	Panel B: Top-coded fatalities (0.01)
	Robust	-0.0394***	-0.0110	-0.0054**	-0.0022***	-0.0315**	-0.0074	-0.0320***	-0.0034
		(0.0144)	(0.0073)	(0.0025)	(0.0007)	(0.0130)	(0.0069)	(0.0117)	(0.0051)
	Mean DV	0.024	0.011	0.003	0.001	0.020	0.010	0.014	0.007
	Standard Deviation	0.748	0.220	0.203	0.033	0.687	0.198	0.474	0.123
	Observations within buffer	5131	5878	7379	4865	5089	6358	4621	7606
	Observations untreated	35693	25267	27394	43013	29074	22521	33368	21791
	Bandwidth untreated (km)	65.999	46.142	50.227	80.011	53.424	40.894	61.575	39.637
	Bandwidth treated (km)	8.874	10.204	12.752	8.414	8.789	10.976	7.997	13.119
	Panel C: Any fatality
	Robust	-0.0049**	-0.0110	-0.0010***	-0.0022***	-0.0042*	-0.0074	-0.0042**	-0.0034
		(0.0023)	(0.0073)	(0.0004)	(0.0007)	(0.0023)	(0.0069)	(0.0020)	(0.0051)
	Mean DV	0.004	0.011	0.000	0.001	0.003	0.010	0.003	0.007
	Standard Deviation	0.060	0.220	0.020	0.033	0.058	0.198	0.051	0.123
	Observations within buffer	5586	5878	6355	4865	5613	6358	5166	7606
	Observations untreated	34557	25267	41484	43013	31794	22521	32913	21791
	Bandwidth untreated (km)	63.862	46.142	77.063	80.011	58.605	40.894	60.730	39.637
	Bandwidth treated (km)	9.714	10.204	10.965	8.414	9.737	10.976	8.955	13.119

Table A4 :

 A4 Discontinuity in conflict intensity for central G5-Sahel operation zones 2017-2020, OLS estimations with flexible controls for coordinates.

		All events		Military operations	Attacks by armed groups	Attacks on Civilians
		Fatalities (count) Events Fatalities (count) Events Fatalities (count) Events Fatalities (count) Events
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Panel A: 15-100 km buffer
	Linear distance ctrl	-0.0297**	-0.0053	0.0023	-0.0005	-0.0297**	-0.0049	-0.0162*	-0.0010
		(0.0137)	(0.0043)	(0.0034)	(0.0006)	(0.0128)	(0.0039)	(0.0090)	(0.0023)
	Linear lat. lon. ctrl	-0.1247*	-0.0105	-0.0170	-0.0055*	-0.1078	-0.0035	-0.0616	-0.0029
		(0.0740)	(0.0233)	(0.0182)	(0.0030)	(0.0691)	(0.0211)	(0.0486)	(0.0127)
	Linear dist. lat. lon. ctrl	-0.0301**	-0.0055	0.0022	-0.0005	-0.0301**	-0.0051	-0.0165*	-0.0011
		(0.0137)	(0.0043)	(0.0034)	(0.0006)	(0.0128)	(0.0039)	(0.0090)	(0.0023)
	Linear dist. sq lat. lon. ctrl	-0.0295**	-0.0053	0.0023	-0.0005	-0.0296**	-0.0049	-0.0161*	-0.0010
		(0.0137)	(0.0043)	(0.0034)	(0.0006)	(0.0128)	(0.0039)	(0.0090)	(0.0023)
	Linear dist. lat. lon. & flex. lat. lon. ctrl	-0.0296**	-0.0053	0.0023	-0.0005	-0.0297**	-0.0049	-0.0162*	-0.0010
		(0.0137)	(0.0043)	(0.0034)	(0.0006)	(0.0128)	(0.0039)	(0.0090)	(0.0023)
	Linear, sq and cubic distance ctrl & flex. lat. lon. ctrl	-0.0278	-0.0081	-0.0077	-0.0018	-0.0134	-0.0052	-0.0176	0.0000
	Mean DV	(0.0274)	(0.0086)	(0.0068)	(0.0011)	(0.0256)	(0.0078)	(0.0180)	(0.0047)
	Standard Deviation
	Observations within buffer	74332	74332	74332	74332	74332	74332	74332	74332
	Panel B: 50 km buffer
	Linear distance ctrl	-0.0266**	-0.0034	-0.0002	-0.0006	-0.0241**	-0.0027	-0.0227***	-0.0006
		(0.0129)	(0.0037)	(0.0035)	(0.0005)	(0.0119)	(0.0034)	(0.0082)	(0.0021)
	Linear lat. lon. ctrl	-0.1259*	-0.0049	-0.0258	-0.0062**	-0.1010	0.0019	-0.0738*	-0.0011
		(0.0683)	(0.0198)	(0.0186)	(0.0029)	(0.0631)	(0.0178)	(0.0436)	(0.0110)
	Linear dist. lat. lon. ctrl	-0.0274**	-0.0036	-0.0003	-0.0006	-0.0247**	-0.0029	-0.0232***	-0.0007
		(0.0129)	(0.0037)	(0.0035)	(0.0005)	(0.0119)	(0.0034)	(0.0082)	(0.0021)
	Linear dist. sq lat. lon. ctrl	-0.0265**	-0.0033	-0.0002	-0.0005	-0.0240**	-0.0026	-0.0226***	-0.0005
		(0.0129)	(0.0037)	(0.0035)	(0.0005)	(0.0119)	(0.0034)	(0.0082)	(0.0021)
	Linear dist. lat. lon. & flex. lat. lon. ctrl	-0.0268**	-0.0034	-0.0002	-0.0006	-0.0242**	-0.0027	-0.0229***	-0.0006
		(0.0129)	(0.0037)	(0.0035)	(0.0005)	(0.0119)	(0.0034)	(0.0082)	(0.0021)
	Linear, sq and cubic distance ctrl & flex. lat. lon. ctrl	-0.0240	-0.0061	-0.0047	-0.0016	-0.0139	-0.0038	-0.0120	-0.0001
	Mean DV	(0.0258)	(0.0075)	(0.0070)	(0.0011)	(0.0239)	(0.0067)	(0.0165)	(0.0041)
	Standard Deviation
	Observations within buffer	84395	84395	84395	84395	84395	84395	84395	84395

Table A5 :

 A5 Discontinuity in conflict intensity for G5 Sahel Central operation zone 2017-2020 , robustness checks.

				Military operations					Attacks by armed groups					Attacks on Civilians
			Geo1			Geo2			Geo1			Geo2			Geo1			Geo2
		Events	Fatalities(#) Fatalities(IHS)	Events	Fatalities(#) Fatalities(IHS)	Events	Fatalities(#) Fatalities(IHS) Events Fatalities(#) Fatalities(IHS) Events Fatalities(#) Fatalities(IHS) Events Fatalities(#) Fatalities(IHS)
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)	(17)	(18)
	Panel 0: All Events
	Conventional	-0.0020***	-0.0046**	-0.0018***	-0.0032**	-0.0280**	-0.0056***	-0.0054	-0.0349***	-0.0085**	-0.0013	-0.0194	-0.0025	-0.0019	-0.0299***	-0.0087***	0.0005	-0.0499***	-0.0081*
		(0.0006)	(0.0021)	(0.0007)	(0.0015)	(0.0119)	(0.0014)	(0.0055)	(0.0135)	(0.0034)	(0.0090)	(0.0174)	(0.0050)	(0.0041)	(0.0099)	(0.0030)	(0.0066)	(0.0180)	(0.0043)
	Bias-corrected	-0.0022***	-0.0045**	-0.0021***	-0.0036**	-0.0355***	-0.0064***	-0.0056	-0.0356***	-0.0092***	-0.0015	-0.0187	-0.0023	-0.0024	-0.0321***	-0.0095***	-0.0002	-0.0530***	-0.0085**
		(0.0006)	(0.0021)	(0.0007)	(0.0015)	(0.0119)	(0.0014)	(0.0055)	(0.0135)	(0.0034)	(0.0090)	(0.0174)	(0.0050)	(0.0041)	(0.0099)	(0.0030)	(0.0066)	(0.0180)	(0.0043)
	Robust	-0.0022***	-0.0045*	-0.0021**	-0.0036**	-0.0355**	-0.0064***	-0.0056	-0.0356**	-0.0092**	-0.0015	-0.0187	-0.0023	-0.0024	-0.0321***	-0.0095***	-0.0002	-0.0530***	-0.0085*
		(0.0007)	(0.0024)	(0.0008)	(0.0018)	(0.0151)	(0.0018)	(0.0063)	(0.0143)	(0.0040)	(0.0104)	(0.0192)	(0.0058)	(0.0047)	(0.0114)	(0.0036)	(0.0075)	(0.0206)	(0.0051)
	Observations within buffer	4863	7214	5751	5789	5058	4798	6358	3570	5053	6298	4142	6011	7491	3201	4391	7558	3829	5759
	Observations untreated	44030	29292	39076	33127	27298	42675	19120	29242	24499	14974	19095	17148	18975	29838	27214	15163	32646	24930
	Bandwidth untreated (km)	81.883	53.794	72.495	61.152	50.043	79.308	34.596	53.718	44.758	26.884	34.538	30.886	34.321	54.787	49.873	27.252	60.108	45.535
	Bandwidth treated (km)	8.409	12.443	9.997	10.051	8.738	8.282	10.973	6.189	8.726	10.868	7.238	10.403	12.931	5.569	7.665	13.044	6.734	10.013
	Panel A: Events involving Islamist groups
	Conventional	-0.0006	-0.0012	-0.0006	-0.0013	-0.0129	-0.0023**	-0.0083***	-0.0238**	-0.0077***	-0.0048	-0.0222*	-0.0040	-0.0035*	-0.0120***	-0.0058***	-0.0022	-0.0153*	-0.0035
		(0.0004)	(0.0012)	(0.0005)	(0.0010)	(0.0084)	(0.0010)	(0.0029)	(0.0104)	(0.0016)	(0.0063)	(0.0126)	(0.0035)	(0.0019)	(0.0040)	(0.0013)	(0.0035)	(0.0088)	(0.0025)
	Bias-corrected	-0.0008*	-0.0014	-0.0007	-0.0015	-0.0162*	-0.0026***	-0.0086***	-0.0233**	-0.0082***	-0.0047	-0.0199	-0.0041	-0.0039** -0.0127***	-0.0062***	-0.0024	-0.0165*	-0.0037
		(0.0004)	(0.0012)	(0.0005)	(0.0010)	(0.0084)	(0.0010)	(0.0029)	(0.0104)	(0.0016)	(0.0063)	(0.0126)	(0.0035)	(0.0019)	(0.0040)	(0.0013)	(0.0035)	(0.0088)	(0.0025)
	Robust	-0.0008	-0.0014	-0.0007	-0.0015	-0.0162	-0.0026**	-0.0086**	-0.0233**	-0.0082***	-0.0047	-0.0199	-0.0041	-0.0039*	-0.0127***	-0.0062***	-0.0024	-0.0165*	-0.0037
		(0.0005)	(0.0016)	(0.0006)	(0.0013)	(0.0107)	(0.0013)	(0.0034)	(0.0110)	(0.0019)	(0.0074)	(0.0139)	(0.0041)	(0.0022)	(0.0045)	(0.0015)	(0.0041)	(0.0100)	(0.0030)
	Observations within buffer	5862	8375	7966	8043	6400	5318	5216	6358	4362	6216	5476	6227	8805	4082	4305	10042	4433	7214
	Observations untreated	29991	31396	33112	39346	26259	36853	31051	33063	31190	18758	24261	23732	31039	22979	34691	22650	33467	35520
	Bandwidth untreated (km)	55.143	57.782	61.133	72.892	48.054	68.135	57.037	61.027	57.349	33.943	44.218	43.266	57.018	41.878	64.116	41.144	61.729	65.589
	Bandwidth treated (km)	10.167	14.412	13.678	13.835	11.047	9.272	9.051	10.971	7.606	10.709	9.587	10.729	15.159	7.100	7.507	17.238	7.726	12.443
	Panel B: Events involving Communal militia
	Conventional	-0.0015***	-0.0024*	-0.0013**	-0.0022***	-0.0145*	-0.0029***	0.0018	-0.0071	-0.0007	0.0031	-0.0126	0.0012	0.0028	-0.0073	-0.0007	0.0042	-0.0096	0.0008
		(0.0005)	(0.0014)	(0.0005)	(0.0007)	(0.0080)	(0.0009)	(0.0028)	(0.0078)	(0.0022)	(0.0033)	(0.0091)	(0.0027)	(0.0024)	(0.0068)	(0.0021)	(0.0028)	(0.0079)	(0.0023)
	Bias-corrected	-0.0017***	-0.0023*	-0.0016***	-0.0023***	-0.0191**	-0.0034***	0.0025	-0.0087	-0.0005	0.0036	-0.0134	0.0012	0.0036	-0.0086	-0.0010	0.0047	-0.0105	0.0007
		(0.0005)	(0.0014)	(0.0005)	(0.0007)	(0.0080)	(0.0009)	(0.0028)	(0.0078)	(0.0022)	(0.0033)	(0.0091)	(0.0027)	(0.0024)	(0.0068)	(0.0021)	(0.0028)	(0.0079)	(0.0023)
	Robust	-0.0017***	-0.0023	-0.0016**	-0.0023***	-0.0191*	-0.0034***	0.0025	-0.0087	-0.0005	0.0036	-0.0134	0.0012	0.0036	-0.0086	-0.0010	0.0047	-0.0105	0.0007
		(0.0006)	(0.0018)	(0.0006)	(0.0008)	(0.0109)	(0.0012)	(0.0034)	(0.0088)	(0.0026)	(0.0039)	(0.0100)	(0.0031)	(0.0029)	(0.0078)	(0.0024)	(0.0034)	(0.0088)	(0.0026)
	Observations within buffer	4755	6890	5476	5091	5229	5338	10870	3309	9967	10823	3303	8302	11883	3130	6965	10822	3246	6980
	Observations untreated	34435	30027	38051	28846	28834	46875	20431	34722	27457	14629	25405	14983	19491	32549	23613	13150	24587	15319
	Bandwidth untreated (km)	63.599	55.228	70.365	53.008	52.982	87.325	37.051	64.177	50.360	26.269	46.299	26.905	35.277	59.875	43.029	23.576	44.910	27.519
	Bandwidth treated (km)	8.221	11.943	9.588	8.793	9.080	9.306	18.590	5.764	17.098	18.525	5.735	14.268	20.289	5.447	12.098	18.521	5.619	12.137
	Panel C: Events involving civilians
	Conventional	-0.0010***	-0.0023	-0.0007**	-0.0017***	-0.0133*	-0.0026***	0.0005	-0.0215**	-0.0065**	0.0032	-0.0226	-0.0035	-0.0019	-0.0299***	-0.0087***	0.0005	-0.0499***	-0.0081*
		(0.0003)	(0.0022)	(0.0004)	(0.0005)	(0.0080)	(0.0008)	(0.0037)	(0.0092)	(0.0029)	(0.0059)	(0.0151)	(0.0041)	(0.0041)	(0.0099)	(0.0030)	(0.0066)	(0.0180)	(0.0043)
	Bias-corrected	-0.0011***	-0.0023	-0.0010***	-0.0018***	-0.0179**	-0.0031***	0.0005	-0.0232**	-0.0072**	0.0033	-0.0243	-0.0037	-0.0024	-0.0321***	-0.0095***	-0.0002	-0.0530***	-0.0085**
		(0.0003)	(0.0022)	(0.0004)	(0.0005)	(0.0080)	(0.0008)	(0.0037)	(0.0092)	(0.0029)	(0.0059)	(0.0151)	(0.0041)	(0.0041)	(0.0099)	(0.0030)	(0.0066)	(0.0180)	(0.0043)
	Robust	-0.0011***	-0.0023	-0.0010**	-0.0018***	-0.0179	-0.0031***	0.0005	-0.0232**	-0.0072**	0.0033	-0.0243	-0.0037	-0.0024	-0.0321***	-0.0095***	-0.0002	-0.0530***	-0.0085*
		(0.0004)	(0.0015)	(0.0004)	(0.0007)	(0.0109)	(0.0011)	(0.0043)	(0.0102)	(0.0033)	(0.0068)	(0.0165)	(0.0047)	(0.0047)	(0.0114)	(0.0036)	(0.0075)	(0.0206)	(0.0051)
	Observations within buffer	5133	7755	5965	5004	5258	5342	9893	3114	4497	9816	3758	6347	7491	3201	4391	7558	3829	5759
	Observations untreated	35314	15956	25090	30217	28488	48181	17759	24679	23498	14268	20983	19806	18975	29838	27214	15163	32646	24930
	Bandwidth untreated (km)	65.140	28.706	45.821	55.599	52.221	89.869	32.063	45.074	42.811	25.545	38.073	35.807	34.321	54.787	49.873	27.252	60.108	45.535
	Bandwidth treated (km)	8.884	13.360	10.330	8.659	9.149	9.323	16.967	5.422	7.829	16.837	6.566	10.943	12.931	5.569	7.665	13.044	6.734	10.013

Table A6 :

 A6 Reaction to trigger events -by Actor Observations at the grid-cell level, binned in two-week periods, in two-month windows around major French operations (2010-2021). Results are based on the estimating equation presented above. Standard errors are clustered at the grid-cell level and presented in parentheses; stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

		All events		Military operations	Attacks by armed groups	Attacks on Civilians
		Fatalities (count) Events Fatalities (count) Events Fatalities (count) Events Fatalities (count) Events
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Panel A: Events involving Islamist groups
	Border x Post	-0.09	-0.04	-0.10	-0.06	-0.16	-0.04	-0.17	-0.00
		(0.19)	(0.05)	(0.19)	(0.05)	(0.19)	(0.05)	(0.16)	(0.04)
	Border x Post x G5	0.46	0.01	0.44	0.09*	0.02	0.01	0.20	-0.04
		(0.28)	(0.06)	(0.28)	(0.05)	(0.25)	(0.06)	(0.20)	(0.04)
	Panel B: Events involving Communal militia
	Border x Post	-0.39	0.01	-0.20	-0.05	0.18	0.01	-0.10	0.00
		(0.48)	(0.04)	(0.16)	(0.04)	(0.36)	(0.04)	(0.10)	(0.03)
	Border x Post x G5	1.10*	-0.03	0.86**	0.08*	-0.09	-0.03	0.18	-0.02
		(0.62)	(0.05)	(0.35)	(0.04)	(0.43)	(0.05)	(0.24)	(0.04)
	Panel C: Events involving Security Forces and civilians
	Border x Post							-0.06	-0.43*
								(0.04)	(0.24)
	Border x Post x G5							0.09*	1.03**
								(0.05)	(0.40)
	Observations	2538	2538	2538	2538	2538	2538	2538	2538
	Clusters	282	282	282	282	282	282	282	282
	Notes:

Table A7 :

 A7 Reaction to trigger events -alternative criterion Observations at the grid-cell level, binned in two-week periods, in two-month windows around major French operations (2010-2020) claiming at least 10 lives. Results are based on estimating equation (2). Standard errors are clustered at the grid-cell level and presented in parentheses; stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

		All events		Military operations	Attacks by armed groups	Attacks on Civilians
		Fatalities (count) Events Fatalities (count) Events Fatalities (count) Events Fatalities (count) Events
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Border x Post	0.22	-0.12	-0.54	-0.24*	0.77	0.12	-0.05	0.02
		(1.12)	(0.17)	(0.48)	(0.13)	(1.02)	(0.12)	(0.34)	(0.08)
	Border x Post x G5	-0.21	0.05	0.68	0.23*	-0.89	-0.18	0.11	-0.11
		(1.20)	(0.18)	(0.57)	(0.13)	(1.06)	(0.13)	(0.48)	(0.09)
	Mean DV	0.839	0.215	0.358	0.065	0.480	0.151	0.379	0.114
	Standard Deviation	5.530	0.677	3.958	0.435	3.110	0.445	2.551	0.377
	Observations	2169	2169	2169	2169	2169	2169	2169	2169
	Clusters	241	241	241	241	241	241	241	241
	Notes:

Table A8 :

 A8 Reaction to trigger events -alternative "G5 treatment period" Observations at the grid-cell level, binned in two-week periods, in two-month windows around major French operations (2010-2020) claiming at least 10 lives. Results are based on estimating equation (2). Standard errors are clustered at the grid-cell level and presented in parentheses; stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

		All events		Military operations	Attacks by armed groups	Attacks on Civilians
		Fatalities (count) Events Fatalities (count) Events Fatalities (count) Events Fatalities (count) Events
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Border x Post	0.73	-0.09	-0.70	-0.34*	1.43	0.25	0.34**	0.10
		(1.68)	(0.27)	(0.77)	(0.20)	(1.53)	(0.17)	(0.16)	(0.10)
	Border x Post x G5 (post Sep 2017)	-0.32	0.05	1.24	0.36*	-1.56	-0.31*	-0.12	-0.15
		(1.71)	(0.28)	(0.82)	(0.20)	(1.54)	(0.18)	(0.35)	(0.10)
	Mean DV	0.797	0.199	0.370	0.062	0.427	0.138	0.412	0.108
	Standard Deviation	5.260	0.638	3.846	0.412	2.901	0.423	2.814	0.368
	Observations	2538	2538	2538	2538	2538	2538	2538	2538
	Clusters	282	282	282	282	282	282	282	282
	Notes:

A number of recent papers have highlighted how specific sub-national institutions can spur or mitigate conflict (e.g. Shapiro and Eynde

[START_REF] Blair | The fortification dilemma: Border control and rebel violence *[END_REF][START_REF] Fetzer | Does democracy moderate resource-induced conflicts ? Review of Economics and Statistics[END_REF], or how institutional arrangements arise in war settings (de la Sierra, 2020;[START_REF] Dincecco | Pre-colonial warfare and long-run development in india[END_REF].2 Exceptions are[START_REF] Ager | Killer incentives: Rivalry, performance and risk-taking among german fighter pilots, 1939-45[END_REF], who study the role of incentives for fighter pilots in the German air force during World War II, and[START_REF] Acemoglu | The perils of high-powered incentives: Evidence from colombia's false positives[END_REF] who study the incentive for Colombian soldiers to target civilians and claim them as rebel fatalities. However, the focus of our paper is not on individual incentives, but on military cooperation.

UN Resolution 2364[START_REF] Martínez | Transnational insurgents: Evidence from colombia's farc at the border with chávez's venezuela[END_REF].

G5 Sahel, 26 January 2020, https://www.g5sahel.org/les-chefs-d-etat-major-des-pays-du-g

5-sahel-rendent-plus-operationnelle-la-force-conjointe.5 We observe not a single trans-border operation outside of the 50km buffer in the ACLED data. As late as December 2021, the French UN delegation website described the G5 mission as being active in a 50km zone (https://onu.delegfrance.org/france-s-action-in-the-sahel.)

Theoretically, the possibility of displacement could also lead to a number of security operations in border zones that is above its optimal level, as neighbouring countries compete to try to push groups across the border. However, this mechanism seems most plausible when investments in security and displacement are long-lived, which is not the case in the context of the Sahel.

This approach prevents us from using already treated gridcells as a control in future comparisons. As has been highlighted by the recent literature on difference-in-difference methods, such comparisons could introduce negative weights in the estimated treatment effect (de Chaisemartin and D'Haultfoeuille, 2022).

As we are interested in immediate response patterns, we will consider the period in which the G5-Sahel mission was incapacitated by a suicide attack on its headquarters as a period in which the G5 is not active, between June 2018 and January 2019.

Figure A 7 presents event studies around trigger events, comparing border and non-border areas, and showing these patterns separately for periods in which the G5-Sahel mission is active or not. Panel C shows the relative reduction in security operations in border areas after trigger events, and Panel D shows how this pattern reverses when the G5-Sahel mission is active.

In this table, military operations against Islamist groups and communal militia respond in a similar way, which may appear at odds with the results of the RD analysis, where security force attacks against militia groups declined more than against Islamist groups. It should be kept in mind that the trigger events always involve Islamist groups, so that the nature of security force operations against communal militias may be different in trigger analysis. Indeed, it is impossible to disentangle the ethnic and religious dimensions of the conflict fully. In addition, it is also worth keeping in mind that there are limitations to the coding of actors (a substantial share of events involves unknown actors).

In contrast to the main results, the coefficient on attacks against civilians is significantly positive before the G5 is active in the alternative coding. Low levels of violence before September 2017 hamper the comparability of violence patterns between the pre-and post-periods, so we do not want to emphasize this result. However, it is possible that the nature of violence against civilians changes over time. Before 2017, they could have suffered from poor security in border areas, whereas the intensification of the conflict might have them more vulnerable during military operations.

* This research was supported by ANR grant COOPCONFLICT and EUR grant ANR-17-EURE-0001.

Any errors remain our own. We are grateful to seminar participants at PSE, the Stockholm School of Economics (SITE), IRSEM, CERDI, and TSE, and the University of Lausanne, for their insightful comments on this project.

Appendix to Cooperation between National Armies

For Online Publication Notes: Observations at the grid-cell level, binned in six months periods (2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020)(2021)(2022). The sample comprises the central Zone (Mali-Niger-Burkina Faso three borders regions). Included events coded with geo-precision level 1 only.


Eduardo Maristany De Las Casas

Naoya Takahashi
email: naoya.takahashi@u-bordeaux.fr

TINS Spotlight

Keywords: Anterolateral motor cortex, projection neurons, motor planning, voluntary movement, retrograde monosynaptic tracing

published or not. The documents may come

MAIN

The anterior lateral motor area (ALM) is part of the frontal motor cortex, involved in the planning, initiation, and execution of skilled motor tasks, particularly those requiring precise control and coordination [START_REF] Inagaki | Neural Algorithms and Circuits for Motor Planning[END_REF]. Dysfunction or inactivation of ALM can lead to impairments in motor control, resulting in difficulties with targeted movements. ALM sends its output to various cortical and subcortical brain regions. Recent studies demonstrated that within ALM, different subpopulations of neurons projecting to specific downstream targets have distinct roles in preparation and execution of voluntary movements. For instance, studies in mice showed that ALM neurons projecting to the thalamus maintain motor planning-related activity during memory epochs, while those projecting to the medulla contribute significantly to the execution of planned movements [START_REF] Economo | Distinct descending motor cortex pathways and their roles in movement[END_REF][START_REF] Inagaki | A midbrain-thalamus-cortex circuit reorganizes cortical dynamics to initiate movement[END_REF]. The ALM receives input from a brain-wide network including multiple cortical and subcortical regions. Recent studies emphasize the importance of long-range inputs, such as thalamocortical inputs, in shaping and coordinating the characteristic activity patterns of ALM neurons during movement planning and execution [START_REF] Inagaki | A midbrain-thalamus-cortex circuit reorganizes cortical dynamics to initiate movement[END_REF][START_REF] Guo | Maintenance of persistent activity in a frontal thalamocortical loop[END_REF][START_REF] Yang | Thalamus-driven functional populations in frontal cortex support decision-making[END_REF]. However, systematic investigation of the specific sources of input to each neuronal subpopulation within ALM was largely lacking. Delineating ALM's upstream input circuitry is essential to understand the diverse functions of ALM in voluntary movements.

To provide a comprehensive picture of input sources to the ALM, in a recent publication, Xu et al. mapped in mice the brain-wide synaptic connections to diverse neuronal subpopulations in the ALM [START_REF] Xu | Whole brain inputs to major descending pathways of the anterior lateral motor cortex[END_REF]. ALM subpopulations were classified based on their subcortical downstream targets: thalamus, SC, pons, and medulla. To probe the upstream circuitry of these subpopulations, the authors employed a sophisticated viral strategy, combining rabies virus with retrograde virus carrying Cre recombinase (Figure 1a). By selectively injecting retrograde Cre virus into each of the downstream subcortical target regions of ALM and performing rabies tracing on the resulting Cre-expressing ALM subpopulations, the authors were able to map the presynaptic input neurons of each projection-specific ALM subpopulation. The comprehensive analysis of the whole-brain input map for each subpopulation revealed that, overall, the ALM subpopulations were targeted by neurons from the same subset of brain regions, primarily in the ipsilateral hemisphere. However, the study brought to light compelling quantitative differences in input weight from upstream cortical and thalamic subregions between the different subpopulations (Figure 1b). Of notable interest were the differences observed between thalamus-projecting ALM neurons and medulla-projecting neurons, discussed in some more detail below. These neurons differ in their gene-expression patterns and perform different roles in motor planning and execution [START_REF] Economo | Distinct descending motor cortex pathways and their roles in movement[END_REF][START_REF] Inagaki | A midbrain-thalamus-cortex circuit reorganizes cortical dynamics to initiate movement[END_REF].

Thalamus-projecting ALM neurons: Xu et al. found that thalamus-projecting ALM neurons received less input from motor thalamic areas compared to other subpopulations [START_REF] Xu | Whole brain inputs to major descending pathways of the anterior lateral motor cortex[END_REF]. This observation may appear surprising given the growing consensus on the causal involvement of the cortico-thalamo-cortical loop in motor planning activity in ALM [START_REF] Economo | Distinct descending motor cortex pathways and their roles in movement[END_REF][START_REF] Guo | Maintenance of persistent activity in a frontal thalamocortical loop[END_REF]. However, this discrepancy might be due, in part, to the distinction between the cell types projecting to the thalamus. In their assay, Xu et al. did not distinguish between pyramidal-tract (PT) neurons in layer 5 and cortico-thalamic (CT) neurons in layer 6, both of which project to the motor thalamus. Previous studies demonstrated that in ALM, PT neurons, but not CT neurons, receive input from the thalamus [START_REF] Guo | Anterolateral Motor Cortex Connects with a Medial Subdivision of Ventromedial Thalamus through Cell Type-Specific Circuits, Forming an Excitatory Thalamo-Cortico-Thalamic Loop via Layer 1 Apical Tuft Dendrites of Layer 5B Pyramidal Tract Type Neurons[END_REF]. Nevertheless, Xu et al. found that among the subnuclei in the motor thalamus, thalamus-projecting neurons preferentially receive input from the ventrolateral and ventromedial nuclei [START_REF] Xu | Whole brain inputs to major descending pathways of the anterior lateral motor cortex[END_REF]. These nuclei act as pivotal relay stations for the cerebellar-thalamo-cortical and basal ganglia-thalamo-cortical pathways, which have been suggested to shape motor preparatory activity in ALM [START_REF] Li | Cortico-cerebellar interactions during goaldirected behavior[END_REF][START_REF] Wang | A cortico-basal ganglia-thalamo-cortical channel underlying short-term memory[END_REF], especially for thalamus-projecting PT neurons [START_REF] Economo | Distinct descending motor cortex pathways and their roles in movement[END_REF].

Notably, the results reported by Xu et al. suggested that ALM receives direct long-range input from the substantia nigra pars reticulata, cerebellum, and superior colliculus [START_REF] Xu | Whole brain inputs to major descending pathways of the anterior lateral motor cortex[END_REF]. The presence of these inputs seems to be at odd with prior anatomical analyses, which, to our knowledge, did not report similar pathways, calling for further work to clarify these discrepancies.

According to Xu et al.'s analysis, the presynaptic neurons in these three areas, labeled through rabies tracing, constituted a very small fraction (<1% of total input neurons), and exclusively connected to thalamus-projecting ALM neurons. As noted by the authors, the presence of these connections requires further validation through functional studies, such as combining patchclamp recordings with optogenetics. If confirmed, these connections could potentially support direct communication from distributed subcortical regions to ALM, which may play a crucial role in modulating the planning and timing of movements.

Medulla-projecting ALM neurons: These neurons are crucial in initiating planned motor movement [START_REF] Economo | Distinct descending motor cortex pathways and their roles in movement[END_REF][START_REF] Inagaki | A midbrain-thalamus-cortex circuit reorganizes cortical dynamics to initiate movement[END_REF]. Recent research has revealed that the midbrain-thalamo-cortical pathway activates these neurons, facilitating the transition in ALM from preparatory activity to execution mode, ultimately triggering planned movements [START_REF] Inagaki | A midbrain-thalamus-cortex circuit reorganizes cortical dynamics to initiate movement[END_REF]. In support of this notion, Xu et al. found that, compared to the other ALM neuron subpopulations, medulla-projecting neurons receive more input from the parafascicular nucleus (PF) [START_REF] Xu | Whole brain inputs to major descending pathways of the anterior lateral motor cortex[END_REF], which in turn receives strong innervation from midbrain structures, such as the pedunculopontine nucleus and midbrain reticular nucleus [START_REF] Inagaki | A midbrain-thalamus-cortex circuit reorganizes cortical dynamics to initiate movement[END_REF]. The preferential connections with PF could shape the ALM output to the medulla, facilitating the release of prepared movements. In the context of motor disorders, it is interesting to note that PF degenerates early in Parkinson's disease [START_REF] Henderson | Degeneration of the centre median-parafascicular complex in Parkinson's disease[END_REF], a neurodegenerative disorder that leads to difficulties in initiating movement. Therefore, the PF-ALM-medulla pathway represents a potential target for addressing such motor disorders.

In conclusion, the work of Xu et al. reveals a complex wiring diagram of inputs that drive each ALM subcircuit, which may support distinct roles in movement preparation and execution.

These insights contribute to our understanding of the neural circuits involved in voluntary movements and may have implications for potential therapeutic interventions targeting motor disorders in the future. providing inputs to ALM starter cells (green/magenta) projecting to the thalamus. Adapted from [START_REF] Xu | Whole brain inputs to major descending pathways of the anterior lateral motor cortex[END_REF]. (B) Proportion of inputs across brain regions to ALM neurons projecting to different downstream targets: thalamus, superior colliculus (SC), pons, and medulla [START_REF] Xu | Whole brain inputs to major descending pathways of the anterior lateral motor cortex[END_REF].

FIGURESFigure 1 |

 1 FIGURES

ACKNOWLEDGMENTS

We thank D. Jaeger (Emory University, Atlanta) and N. Yamawaki (Aarhus University, Aarhus) for comments and discussions on the manuscript. N.T. was supported by the CNRS, the University of Bordeaux (Initiative of Excellence), the Region Nouvelle-Aquitaine, the ATIP-Avenir program, and the Brain Science Foundation. E.M.C. was supported by the NIH BRAIN Initiative RO1 grant (1RO1NS111470), HORIZON.1.1 -European Research Council (ERC) program (Grant agreement ID: 101055340), and Einstein Foundation Berlin Grant (EVF-2017-363).

AUTHOR CONTRIBUTIONS

E.M.C. and N.T. wrote the manuscript.

DECLARATION OF INTERESTS

The authors declare no competing interests.