Political Violence and the Geographic Concentration of Countries Jordan Adamson * Original Draft: Sep 15, 2015 This Draft: December 22, 2016

Abstract How does the number of countries within a geographic area affect political violence? I exploit variation in the colonial borders of African countries to create a measure of “geopolitical concentration” by calculating a Herfindahl-Hirschman Index of country surface areas within a given geographic area. I find that violence is higher when there are many countries in an area. I also find a non-linear relationship, that violence decreases at a decreasing rate over geopolitical concentration. Furthermore, there is a larger proportion of internal violence in more concentrated regions and geopolitical monopolies actually increase violence in larger geographic regions.

Keywords: conflict, geopolitical concentration, spatial HHI, political violence JEL Classification: C23, D7, H11, P48, R12 *I

am grateful to Patrick Warren for ongoing discussion and advice. I would also like to thank William Dougan, Robert

Fleck, Andrew Hanssen, Robert Tollison, Daniel Wood and also the Clemson Workshop in Public Economics for comments and suggestions. Thanks to Leah Kitashima, Tim Bacon, Jacob Burgdorf, Cesar Castellon, Ben Schwall and Alex Fiore for ongoing discussions.

If these States should either be wholly disunited, or only united in partial confederacies, the subdivisions into which they might be thrown would have frequent and violent contests with each other. - Alexander Hamilton 1787

1

Introduction

Reducing violence is a basic justification for the state and a central argument for the territorial unification of countries.1 Many political philosophers, from Hamilton and Montesquieu to the ancient Greek and Romans, have considered the number states in a geographic region to be an important factor for peace. In recent years, there has also been much policy debate surrounding Joe Biden’s discussion of splitting Iraq.2 To investigate, I compile a spatiotemporal dataset and create a novel measure of geopolitical concentration that measures the size distribution of countries in a geographic area. I find the relationship between geopolitical concentration and violence is non-linear: the reduction in violence is large when there are many countries, but then flattens out. Violence may even increase near monopolization due to an increase in internal violence.

There is a strong reason to posit that having fewer countries in a geographic area would reduce violence. Hobbes’ (1651) argued that “during the time men live without a common Power to keep them all in awe, 1 This

has been a particularly important idea in European political history. The Schuman Declaration (1950) was a

precursor to the EU. It declares that “A united Europe was not achieved and we had war”. The declaration designed unification so that “The solidarity in production thus established will make it plain that any war between France and Germany becomes not merely unthinkable, but materially impossible”. The 1814 Congress of Vienna had the object to resize the main powers to remain at peace. 2 See

the article at http://www.nytimes.com/2006/05/01/opinion/01biden.html

1

they are in that condition which is called Warre”. Many theories build on this logic (McGuire and Olson 1996, Konrad and Skaperdas 2012, Powell 2013). The closest model comes from Hirshleifer (1995) who predicts that more resources will be allocated towards fighting with a greater number of players.3

But geopolitical monopolization could also increase violence. Competition between a greater number of alternative governments could lead to more constraints on predatory policy. Having more political units in an area could lead to more political innovation on issues directly or indirectly affecting violence. Concentrating political resources could also cause people to fight for control. Generally, Economists stress the benefits to competition in markets, and some of that logic may also extend to politics (Stigler 1972). Gary Becker (1988) said it best when he said “competition among nations tends to produce a race to the top” 4

The question is difficult to address empirically. First, it is difficult to collect the requisite data on violence and political territories. Second, it is difficult to integrate and measure the data in a way that answers the questions. Third, there are identification problems, as one cannot run experiments on borders. Observational data also has problems. One problem is that boundaries could change in response to violence. Another problem is that a confounding factor could determine both state size and violence. For example, a time series of growing state size and a decline in violence might only show that technology changed both the incentives of civilians to fight each other and also for autonomy.5 Fourth, there are many types of political contestants that are excluded when only looking across countries or within countries. For example, it’s important to consider when one country finances an internal rebellion inside the borders of 3 Some

scholars argue for a more ambiguous relationship (Tullock 2006, Snidal 1985).

4 http://www.hoover.org/research/euroskeptic-speaks-out 5 This

is as concern for cases from early agricultural empires to 17th century Europe.

2

a rival. My setting and approach addresses each of these issues.

There are two spatial data sets that allow me to look at violent outcomes in Africa. These data sets span 1989-2015 and record the different types of actors. There is also a data set on African borders that provides a good argument for causality, as these borders were determined by the colonial powers of Europe in the scramble for Africa and have not much changed since (Michalopoulos and Papaioannou 2016, African Union Border Programme 2014).6 This means that most African borders are not the consequence of the recent violence. Furthermore, it is unlikely that some third factor determined the previous colonial borders and is determining the current violence. This helps to eliminate the major identification concerns present in most studies of this nature.

I create a measure of the spatial concentration of political power called “Geopolitical Concentration”. It calculates the HHI of the size distribution of country surface areas within a geographic window.7 This new measurement, based on Geographic-Information-Systems technology, allows me to tie the African borders and violence together in way that answers the big question.

I find that the effect of geo-political monopolization on violence is non-linear: violence decreases with geo-political concentration but at a diminishing rate. To help explore this first finding, I perform a variety 6 African

Union Border Programme 2014 quotes the 1906 British Prime Minister, Lord Salisbury, as stating “We [the

British and the French] have been engaged in drawing lines upon maps were no white man’s foot ever trod: we have been giving away mountains and rivers and lakes to each other, only hindered by the small impediments that we never knew exactly where the mountains and rivers and lakes were”. See Figure 7 in the Appendix for data from de-colonization in the 1960s 7 This

helps address problems with traditional data. For example, using countries as both the unit of observation and

the explanatory variable. This data structure is also used by political economy scholars (Buhaug and Rød 2006, Besley and Reynal-Querol 2014, Abramson 2016a, Alesina, Michalopoulos, and Papaioannou 2016, Adamson 2016).

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of procedures. When I look at different geographic scales, I find that the relationship in larger geographic windows looks more like a “reverse J”. This means that monopolies look worse when extending over a larger geographic area. I also disaggregate violence into cateogries based on the different types of contestants. The results show that the share of “government vs rebel-or-civilian” violence is increasing with concentration. This suggests that although monopolization discourages external conflict, complete monopolization is a source of internal conflict.

2

Background and Contribution

2.1

Political Economy

There are many theories relating geopolitical concentration to violence. However, mapping these theories to data is difficult.8 Many theories abstract away from geography - i.e. spatial location is not a factor.9 Most theories do not consider the multiple types of violence also at play.10

Economic models generally predict that greater hegemony reduces violence. McGuire and Olson (1996) argue that the hegemon will “treat those subject to its power as well as it treats itself”. Alesina and Spolaore (2003[P.95]) argues “larger countries can provide better and cheaper security for their citizens”. Similarly Konrad and Skaperdas (2012) argue that “in contrast to ordinary economic markets, the more competition there is in the market for protection, the worse it is”. When modeling the gov8 For

one, the terms “anarchy” and “power” are often inconsistent across authors or not present at all (Snidal 1985,

Donnelly 2015). Höhn (2011)provides a large encyclopedia of the different measures of power. 9 Alesina

and Spolaore (2005) is an exception that explicitly considers geography

10 Political

scientists have long looked at civil conflicts. There is also a burgeoning economic literature on violence and

contestants within a government (Acemoglu, Robinson, and Santos 2013, North, Wallis, and Weingast 2009). Another international-relations literature focuses on the violence between governments.

4

ernments choice to monopolize violence, Powell (2013) assumes that there is “an increase in economic activity resulting from the monopolization of violence and the higher level of security that comes with it.”

Some authors suggest a more ambiguous relationship between political hegemony and violence.11 Snidal 1985 argues that “the common presumption of recent analyses that hegemony is widely beneficial rests on such special assumptions that it should be rejected”. It is not clear that violence will decrease if an area transitions from multi-polar to bi-polar to mono-polar worlds. Grossman (2002) argues that the benefits to a state system versus anarchy depends “on the effectiveness of the technology of predation”. Tullock (1974, 2006) occupies a middle ground when he questions the regularity and importance of the “balance of power”.

There are some reasons why having alternative governments could help reduce violence.12 . I classify these reasons into 2 main categories: constraints and innovation. The constraints idea is that more competition could cause the the government to provide better services (Tiebout 1956, Fleck and Hanssen2013). Better policing or foreign policy, for example. One could also adapt the models of Grossman (1996 2002) to show that more symmetric contestants decreases predation. The innovation idea is that better ideas emerge when there is a greater variance in policy. A political version of the discovery process from Hayek (1948) could suggest a direct effect. More political units encourages the discovery of new arrangements and adaptation to circumstance. Montesquieu (1748) argues that “Should a popular insurrection happen in one of the confederate states, the others are able to quell it. Should abuses creep into 11 Wittman 12 Many

(1991) argues generally that “At some point, dis-economies of scale arise.”

of these ideas have ancient roots. This is illustrated by Juvenal’s question “quis custodiet ipsos custodes?” (“Who

will guard the guardians?” Hurwicz 2007) and the warning from Tacitus (98) “All this in their ignorance they called civilization, when it was but a part of their servitude”

5

one part, they are reformed by those that remain sound.” Alternatively, the “Hume-North hypothesis” suggests an indirect effect. Political innovation on factors like tax and regulatory policy could improve economic growth (Bernholz and Vaubel 2005). This could raise the opportunity cost of violence.13

Theoretical exploration has also highlighted the issues in claiming a causal relationship. In many cases, if not most cases, the state’s size and boundaries are not something we can take as exogenous (Carneiro 1970, Friedman 1977, Grossman and Kim 1996, Alesina and Spolaore 2003, Turchin 2013, Thayer 2015, Boix 2015, and Abramson 2016).14

2.2

Political Violence

There is an interdisciplinary literature explaining political violence. There is a historical literature that argues about the importance of state-size and political control in reducing violence. This literature shapes our understanding of the role of government but has to rely on historical data. I contribute by providing an argument for causality. There is also a literature on violence in modern Africa with sub-literatures on borders and territories. I contribute by bridging both literatures. To the literature on violence in modern Africa, I add a measure of the size distribution of countries, something that economists, historians, and political theorists argue is important. To the historical literature, I add new evidence that considers both local and national actors and explores the location of violence as well as the level.

We live in what is probably the most peaceful time to exist in hundreds, perhaps thousands of years (Pinker 2012). However, the cause is not well understood (N. P. Gleditsch et al. 2013). Some scholars 13 Chu

(2010) also discusses this.

14 These

authors consider the size of the state as an outcome variable. Alesina and Spolaore (2005) and Koyama et al (W.P.

2015) explicitly argue causality in the reverse direction.

6

attribute this decline to the rise of a large and powerful state that constrains man’s violent nature (Gat 2006, Pinker 2012, Morris 2014).15 The main evidence is the historical association of smaller and weaker states with more violence.

There are many issues in both establishing and explaining this historical decline in violence. Scholars debate the historical data on political hegemony, violence, and human nature (Fry 2015).16 There are many issues in comparing a small number of political groups in different time periods. Furthermore, ancient and medieval data often have correlations that don’t address causality.17

The empirical results on the effects of state-building in modern Africa are mixed (Bandyopadhyay and 15 Pinker

(2012) shows that state versus non-state societies while Morris (2014) shows the rates of violence were lower

around the golden age of the ancient Roman Empire than in the following and previous periods. He does note the issue that the process of enlargement expansion for Rome was very violent. 16 There

is a dispute on the empirical record for pre-historic rates of violence. Fry (2015) Chapter 7 points out flaws

in Pinker (2012) research, including the omission of major environmental events, sample selection in grave-site studies, and fossil interpretation. Tullock (1974) argues “Hobbes’ ‘war of all against all’ was not part of human history”. Power assymetry often increases predatory violence, as Gat (2006[P. 134]) argues “Killing in nature is normally done against the defenseless, when the odds are heavily tilted”. In our very early history the most common type of conflict is an asymmetric assault (Fry 2015, P. 320). 17 It’s

true that the Roman Dictatorship was more peaceful than the Roman Republic and that the Roman Dictatorship was

on average larger. However, the size of Rome is not random and so a causal argument would need to address endogenous empire size in addition to controlling for other factors. It’s also difficult to establish a causal relationship in 17th century Europe. One major factor is that is that military technology determined the size of the European states Boix (2015) North (1982) and this technology could also directly affect the opportunity cost of fighting rather than producing. In medieval Europe North (1982 P 209) argues that “military technology which altered the survival size of states led to ... economic expansion.” Also in medieval Europe “the period of the commercial revolution, an era during which there was a sharp increase in the number of independent states, coincided with the decline in the military dominance”. In pre-modern Europe, Abramson (2016) finds evidence that variation in patterns of economic development and urban growth caused fragmented political authority in some places and the construction of geographically large territorial states in others.

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Green 2013, Englebert and Tull 2008).18 Activities like “border-expansion” and “state-building” often appear like a predatory process at the micro level.19 Labelling an issue as state-failure calls for a solution that could actually hurt instead of help. Political power in Africa is not a panacea.

The literature on African violence has highlighted many factors.20 Political borders and territories play an important role in violence in modern Africa (Toft 2014).21 Tiebout-competition is also a noted factor (Barros and Serafim 2016).

There are different types of conflict and they should not be analyzed independantly. Theoretically, the onset of one type of conflict can directly affect the onset of another other. For example, a civil war could weaken the country to external attackers or external conflict could unite a body politic. Furthermore, external actors do finance internal conflicts next door. Cunningham and Lemke (2013) performs a novel empirical study that combines the different types of political violence. He argues that “The norm of 18 Bandyopadhyay

and Green (2013) find no empirical relationship between nation-building and civil war. Likewise,

Englebert and Tull (2008) note that the empirical results on state-building are “paltry’, and argues that “the centralizing desire to reconstruct the formal sovereign state may neglect or even undermine the local institutional initiatives’. 19 Furthermore,

It is not clear that empirical results found in international relations give the right counterfactual. For

example, we know that neightbours are more likely to fight, but does that imply there shouldn’t be any neighbors? 20 Particularly

in Africa, national borders are often analyzed in terms of ethnic division (Michalopoulos and Papaioannou

2016,Alesina, Michalopoulos, and Papaioannou 2016). Population densities and clusters are also a major determinant in the level of conflict in Africa (Raleigh and Hegre 2009), and geopolitical concentration is related to the degree to which population clusters and countries boundaries align. State-capacity and the location of violence in Africa today is correlated with historical conflict (Dincecco 2014, Besley and Reynal-Querol 2014). Kornprobst (2002) emphasized regional integrity norms when noting that West Africa had more border disputes but managed them all peacefully, in contrast to the horn of Africa which had fewer but violent disputes from the 1950s - 1990s. 21 Toft (2014) summarizes “this corpus of research clearly demonstrate that armed disputes over territory are a major source

of the global distribution of violence and destruction”. Across a number of civil-war data sets, Quinn (2015) finds a positive correlation between contested geographic areas and civilian killings by governmental forces.

8

studying these phenomena separately has limited scholars’ understanding of violent conflicts”.22 Buhaug and Rød (2006) pioneer a spatially disaggregated approach and discover that territorial conflict is more likely to occur near the borders, but conflict over state governance does not.

3

Data

3.1

Unit of Analysis

My study uses data on Africa between 1989 and 2015. My unit of analysis is a geo-cell with 2 spatial dimensions (x, y) and time (t). The idea of observing violence at the grid level was developed in political science but is being adopted by economists (Iyigun, Nunn, and Qian 2015, Adamson 2016). I create the geo-cells by geographically dividing Africa into a grid of equal-area rectangles for every year.23 I use a 1000x1000 grid with each cell having dimensions 7101meters x8876meters, i.e. the white dot in Figure 2. I drop all geo-cells that are water, which leaves 476743 geo-cells for each year. This lattice structure does aggregate some of the data but enables me to use the statistical tools developed in the econometric literature.

The differences across geo-cells are important. In appendix section 6.1 I explore the differences in 22 A

battle is often a mix between pure types. There is a concern that one could define “type” to get a desired result. It

would be misleading if the same actors were fighting but one classifies them differently based on if there is a border drawn or not. 23 To perform the geographic calculations, I must project the three dimensional earth-ellipsoid onto a two dimensional grid.

I use the Mollweide projection because this is commonly used for equal-area grids (Snyder 1987). Equal area projections directly control for any bias that comes from the variables being a function of the geo-cell area. This is important because the Y-variable is a count (which are theorized to be a spatial point process and thus a function of area) and the main X-variable is designed to measure the geo-political concentration (in an area). I have aggregated data from smaller geographic cells and data sampled from continuous space to discrete cells.

9

violence that come from spatial or temporal variation. Violence is notoriously difficult thing to predict, but even more so at a particular location in a particular time. However, the variation across space has far greater explanatory power compared to variation across time. Many of the nonparametric specifications and robustness checks use data that are averaged over time.

3.2

Political Violence

I define violence as the number of deaths resulting from an armed conflict resulting in death where at least one group is a political organization. This is measured by two different institutes: the Armed Conflict Location and Event Data (ACLED, Raleigh, Linke, et al. 2010) and the Uppsala Conflict Data Program (UCDP, Sundberg and Melander 2013). Table 1: Violence Defined Source

Years

Violence

ACLED

1997-2014

“Activity that occurs within the context of a civil war, and violent activity that occurs outside of civil wars, particularly violence against civilians, militia interactions, communal conflict and rioting”

UCDP

1989-2015

“Contested incompatibility that concerns government and/or territory, where the use of armed force between two parties, of which at least one is the government of a state, results in at least 25 battle-related deaths”

The baseline analysis does not disaggregate violence into different classifications or typologies (i.e. Civil War vs. Interstate War). I later examine the different types of violence. See section 4.5 for further discussion.

3.3

Geopolitical Concentration

Political boundary data comes from Weidmann and K. Gleditsch (2010). Figure 1 shows political boundaries in Africa (2015) with fatalities (over all years) plotted as points. Areas with darker color represent 10

a higher intensity.24 Figure 1: Political Geography of Armed Conflict

I calculate a Herfindahl-Hirschman Index over the country shares of land within a window around each geo-cell. An area is geo-politically monopolized if HHI = 1. Each cell has a geographic area/window with diameter w, a total land surface area s(w), and a land surface area for each country in that window si (w). For each cell I calculate an HHI value based on the larger surrounding window;

 HHI(w) = ∑ i

24 Each

si (w) s(w)

2

overlapping point is semi-transparent and has a size that represents the number of deaths.

11

(1)

Figure 2: HHI Calculation Consider one specific example of the calculation. For one geo-cell, drawn as the white dot in Figure 2, I construct a 50x50 window around it (the grey square shown in Figure 2 and in Figure 1). Then I calculate the surface areas of the countries in that area, which are Nigeria (.1), Cameroon (.48), and Chad (.42) in order from left to right. Then I calculate the HHI value of those land shares, which is 0.4 in this instance.

Geopolitical concentration, as measured by HHI, is intended to measure competition between countries. It is a continuous measure which takes into account the size of each country. This measure emphasizes the territorial aspect of the state.25 . A value of 0 indicates an area has infinitely many small countries and a value of 1 indicates a single large one.

There are two issues to address when choosing geo-cell size: the issues of aggregation and the issue of what HHI really captures.26 Coarse geographic grids have many of the same binning/aggregation problems inherent in cross-country regression. Such aggregated units of observation throw away much information, give imprecise results, and have potential robustness issues.27 However, fine geo-cells have an HHI value that only indicates if the cell is on the border or not.28 25 Abramson

(2016 ) defines of the state as “organizations that maintain a quasi-monopoly of violence over a fixed terri-

tory.” Webers’ (1919) definition of the state is the “monopoly of the legitimate use of physical force within a given territory”. 26 The 27 If

issue of what HHI means is analogous to choosing the “extent of the market” in anti-trust regulation.

one moves the grid 1% up and 1% left a measure could be quite different

28 Too

fine observations also makes everything looks like noise. As an extreme example, we could compare a 1meter2 x

1minute geo-cells.

12

My solution is to separate the issues of aggregation and measurement meaning, performing robustness on both dimensions. I isolate the issues by making HHI a function of the window size w for any given grid granularity. I chose a very fine grid, with geo-cells approximately the size of a small US county. This size errs on being “too small” in order to minimize the aggregation issue, while remaining computable. I then correct for spatial autocorrelation in the appendix.29 I also look at different window sizes, which changes what HHI captures. The smaller window sizes are thus more similiar to the measures used in the Tiebout tax-competition literature (Costa-Font, De-Albuquerque, and Doucouliagos 2015) and political science literature (Buhaug and Rød 2006). Examining different windows for HHI serves as both a robustness check and as a way to distinguish between theories.

How does the HHI measure compare with other calculations of political boundaries? Distance to border and National Contiguity are similiar measures and more common. Contiguity (measuring direct contact) is similiar to case of HHI with very small window sizes (w → 0). The same is not true for distance to border and larger window sizes. HHI not only considers the effect of having a second country close by, but also a third and a fourth etc. Moreover, the distance to border measure masks “relevant market” issue because the relevant market is always the closest national boundary. When compared, HHI and BorderDistance have a positive (correlation of 0.7 as shown in Figure 11). The importance of this correlation will be talked about more in section 4.6. However, much violence is away from the borders, as shown in Figure 1, and this suggests that BorderDistance is not driving the results for HHI.

To illustrate the HHI calculation, Figure 3 shows the calculation for window sizes of 50x50 and 80x80, 29 I

also reshape the data as a point process on a continuous geographic space as analyzed in Appendix Figure 10.

13

with the area of the window (km2 ) marked below the title. This Figure shows what “geo-political concentration” is and what it means to look at different geographic scopes. As a preview to the results, Table 9 and Figure 5 show the results are robust to many window sizes. For the baseline HHI calculation, I choose a window size of 50x50 (≈ 160, 000 km2 or the size of Washington State) and later use different window sizes as robustness. Figure 3: Geo-Political Concentration (HHI) (b) Window Size 80x80

(a) Window Size 50x50

2e+06

0.6

0.4

−2e+06

−2e+06

0.4

0.8

−4e+06

0.2

−2e+06

0e+00

2e+06

4e+06

6e+06

−2e+06

Longitude

3.4

0e+00

2e+06

4e+06

6e+06

Longitude

Control Variables

Population at the geo-cell level is documented every 5 years: 1990, 1995, 2000, (CIESIN 2005) and 2000, 2005, 2010, 2015 (WorldPop n.d.). I linearly interpolate over each geo-cell to create a yearly population variable (Pop). Distance from any country’s capital (CAPdist) is calculated based on data on capitals from Weidmann and K. Gleditsch (2010). The amount of economic activity is approximated with night time lights (Lights) which comes from NASA from 1992 until 2003. The number of diamond 14

HHI

HHI

Latitude

0e+00

0.8

0.6

1.0

0e+00

2e+06

1.0

−4e+06

Latitude

4e+06

km²=403375

4e+06

km²=157568

mines (Diamond) and the number of oil and gas fields (Petro) within a geo-cell are also included as controls (Gilmore et al. 2005 Lujala, Ketil Rod, and Thieme 2007) 30 Terrain ruggedness (T RI) is calculated from elevation data (FAO/IIASA/ISRIC/ISSCAS/JRC 2012) and distance to coast (COAST dist) is calculated from data on country borders. The ethnic boundaries from the Murdock Map (Murdock, Blier, and Nunn 1959) is used in calculating an HHI(ethnic) score.31 Finally, precipitation (Precip) from Hijmans et al. (2005) is included as a control.

The control variables can be classified into 2 categories: Geographic and Political. Geographic controls are Diamond, Petro, Precip, COAST dist, T RI. Political-Economic controls are POP, Lights, CAPdist. Ethnic has an isolated discussion in section 4.7. The geographic variables are most likely to satisfy exogeneity conditions. Although violence can’t determine the amount of diamonds or oil in the ground it can possibly adversely affect the search for mines in that area. Political-economic controls are also less likely to satisfy exogeneity conditions. Population and Lights can be affected by violence (i.e. flight of capital and labor). The capital locations are not frequently altered, but can be moved (even if only temporarily) in times of crisis. I address this issue by looking at results with and without these controls. If the qualitative results are similiar in both cases, then there is not much concern. For the main analysis Geographic and political controls are denoted as G&P in the table columns or notes for which they are used.

Country-level variables are not included because country fixed effects are used in some specifications. This specification compares geo-cells within the same country, so country level variables are unlikely to 30 I

measure the number of petro-fields in a geo-cell rather than the proximity to any petro-field.

31 This

dataset is measured with error and are not likely to be randomly assigned. Both the locations of groups and their

relevance could be considered outcome variables. I recognize this issue, and qualify the results the coefficient estimates for HHI(ethnic) with caution.

15

explain these results. Likewise, Africa-wide variables that change over time are not included. Country and time fixed effects are denoted as C&T in the table columns or notes for which they are used.

4

Empirical Analysis

4.1

Econometric Specification

My main relationship under consideration is between violence and geo-political concentrations. This is formalized in equation 2. Recall that the unit of observation is a geocell with location x, y in period t.

#Deathsx,y,t = f (HHIx,y,t )

(2)

However, to help address external validity, I use the two data sets discussed in Section 3.2. I also use a logarithmic transformation, with the interpretation of partial elasticity, in order to compare the results from each data set. Appendix section 6.4 explores negative-binomial and non-logarithmic variants of the bivariate relationship.

I first examine the bivariate data with a statistical loess model l(, θ ), with tuning parameter θ .32 Denote ε as random error. This relationship is shown in equation 3. The non-parametric models are computationally complex, so the data are averaged over time and the standard errors are generated via bootstrapping.

log( #Deathsx,y + 1) = l( HHIx,y , θ ) + εx,y 32 The

(3)

loess prediction is an interpolation over a set predictions from locally weighted OLS regressions. My specification

is with tricubic weights and a linear X variable with span paremeter 1/2.

16

I also estimate another non-parametric version of equation 2 but with the violence data in its natural form - i.e. a spatial point process without any transformation to the data. The results of this alternative model are shown in Appendix Section 6.3. The results of the spatial point process model are qualitatively similiar and suggest that my shaping of the data is not driving the results.

After looking at the geocell data under the most flexible model in equation 3, it appears that a parametric model with a quadratic relationship is a reasonable simplification of the relationship in both data sets. In Appendix Table 8 I also use a linear-linear model and a negative-binomial model, and the qualitative predictions remain similiar.

33

I fit the bivariate regression in equation 4 with standard errors corrected

for heteroskedasticity and autocorrelation over time (i.e. clustered on geocell). I overlay the predictions of equations 4 and 3 for comparison in Figure 4. I correct for spatially autocorrelated error terms in the appendix with data collapsed over time.

2 log(#Deathsx,y,t + 1) = HHIx,y,t βhhi + HHIx,y,t βhhi2 + εx,y,t

(4)

I then add in 2 sets of control variables as well as time and country fixed effects in a multivariate OLS regression. The variables were discussed in Section 4.3, and I label them GEO, POL, C, or T .

2 βhhi2 log(#Deathsx,y,t + 1) = HHIx,y,t βhhi + HHIx,y,t

+ γgeo GEOx,y,t + γ pop Popx,y,t + γ pol POLx,y,t + γcCx,y,t + γt Tx,y,t + εx,y,t 33 As

(5)

will be discussed shortly, the basic relationship is quadratic. The quadratic HHI terms under quadratic OLS and

the negative binomial regressions also predict that violence is minimized before 1 and at a slightly lower HHI that the logquadratic model.

17

There is little reason to think the geographic variables could be endogeneous. That is not necessarily true for POL, C, or T . However, the sins of omission seem larger than the sins of inclusion for population or country level factors. Time fixed effects also remain because it seems more natural to compare geocell’s within in the same time period. For this reason, my preferred specification includes geographic controls and population, as shown in equation 6.

2 log(#Deathsx,y,t + 1) = HHIx,y,t βhhi + HHIx,y,t βhhi2

+ γgeo GEOx,y,t + γ pop Popx,y,t + γcCx,y,t + γt Tx,y,t + εx,y,t

(6)

I then perform robustness tests on my results. I discuss what results change and don’t change based on my choice of geographic scale (w). The appendix also contains some more complicated variants of the above the models, and uses data collapsed over time. In appendix section 4.7, I explore the interaction of country and ethnic borders in detail. I first create a measurement of the degree of mismatch between country-ethnic boundaries that can be decomposed into a simple function of 2 HHI scores and then look at how the degree of mismatch correlates with violence. I also disaggregate onset and intensity, consider violence as extremum, and account for spatial auto correlation in the Y variables. I also fit a non-parametric version of 6 in Appendix section 6.4 equation 7.

4.2

Bivariate Relationship

Figure 4 shows the basic bivariate relationship between violence and geo-political concentration. Each data set is fit with a parametric OLS model (no fill) and a non-parametric LOESS model (solid fill).34 34 The

LOESS envelope is the result of a bootstrap with 200 runs from the data after it was collapsed and averaged over

time. Each bootrstrap run had 476743 samples of the collapsed data which contained 476743 observations. The quadratic estimation did not average the data over time.

18

The loess predictions show a darker central line that represents the predicted relationship and envelopes that represent a 95% confidence interval. For both data sets, the data show an initial downward trend that plateaus. The estimates relationship suggests that the costs of geo-political monopolization might eventually outweigh the benefits at a monopoly value. Non-parametric analysis shows that larger window sizes reinforce the idea of a “U” shape, as seen in Section 4.4. Furthermore, a predicted minimum of violence before complete monopolization is not an artifact of functional form.35

0.010

Figure 4: Violence vs HHI: Bivariate Model

0.000

0.002

log( #Deaths +1) 0.004 0.006 0.008

ACLED UCDP 95% C.I. Quadratic 95% C.I. LOESS

0.2

4.3

0.4

0.6 HHI

0.8

1.0

Multivariate Relationship

Tables 2 and 3 show the summary statistics for the control variables and their correlation with HHI (HHIcorr). The control variables are not strongly correlated with HHI, indicating that the controls are 35 First,

assuming a quadratic form does not imply a maximum or minimum of violence with HHI ∈ [0, 1]. Second,

the result is not driven by outliers since violence is declining less, and possibly U-curved, where more of the data are ( HHI ∈ [.4, 1] ). Third, the non-parametric results here might suggest seperate regimes, but specific thresholds/regimes depends on the window size parameter (as seen in Figure 5) and probably also depend on the time and place of study.

19

balanced over HHI. However, since these other variables are plausibly an outcome of violence and other variables, the uncontrolled relationship is informative.36 The summary statistics are for data that have been averaged over time. Table 2: Summary Statistics: Political Controls CAPdist min 0.589 mean 374.817 max 1, 057.278 HHIcorr -0.058

Ethnic

Lights

POP

0.039 0.335 1 0.149

0 0.254 255 0.051

0 0.002 4.941 0.001

Table 3: Summary Statistics: Geographic Controls

min mean max HHIcorr

Diamond

Petro

Precip

COASTdist

TRI

0 0.001 10 -0.004

0 0.030 2 0.085

0 56.162 375.880 -0.142

0 667.663 1, 816.133 -0.039

0 111.862 3, 105.097 0.015

Table 4 reports the quadratic estimates using different sets of controls. The parametric fit is shown in columns 1 and 2. The row ArgMin shows the predicted value of HHI that minimizes violence. Both coefficient magnitudes for geo-political concentration are reduced when including fixed effects and controlling for other factors. The interior argMin is still found. 36 This

is even true for the geographic variables, as perceptions and information about natural geographic features are not

random.

20

Table 4: Geo-Political Concentration and Violence 1 2 ACLED UCDP −0.0388 (0.0036) HHIˆ2 0.0246 (0.0024) Controls N Interactions N F.E. N ArgMin 0.79 # Obs 8581374 HHI

−0.0459 (0.0029) 0.0296 (0.0019) N N N 0.77 12395318

3 4 ACLED UCDP

5 6 ACLED UCDP

7 8 ACLED UCDP

−0.0102 (0.0026) 0.0058 (0.0018) G N C&T 0.88 8581374

−0.0124 (0.0035) 0.0071 (0.0023) G&P N C&T 0.88 3337201

−0.0062 (0.0037) 0.0091 (0.0024) G&P Y C&T

−0.0153 (0.002) 0.0095 (0.0014) G N C&T 0.8 11918575

−0.0227 (0.0031) 0.0136 (0.0021) G&P N C&T 0.83 5720916

−0.0089 (0.003) 0.0134 (0.0021) G&P Y C&T

3337201 5720916

Notes: The Y variable is log(Fatalities+1) in every column. Columns 1 and 2 is the bivariate OLS specification. All other columns control for population, specified geographic (G) or political (P) controls, and include Country (C) and Time (T) fixed effects. Columns 7 and 8 include interaction terms of HHI and geo controls. Heteroskedastic-Consistent Clustered (on Spatial ID) standard errors reported.

4.4

Window Extent

As discussed in Section 3.3, the window size (w) is important in the construction of the HHI measure. I . Figure 5 is a variant of Figure 4 that looks at HHI(w) for w = (40, 50, 60, 80). There are two main findings. One is that the finding of diminishing marginal returns to concentration, for HHI ∈ [0, .8] is robust. The other finding is that complete monopolization is much more violent under larger window sizes. While the “violence uptick” is not found with smaller windows, the “U” shape becomes more pronounced with larger window sizes. The same result is found in appendix Table 9, a variant of Table 4, which includes control variables. The red line represents data from ACLED, blue from UCDP.

Different geographic windows show that the elasticity of violence with respect to HHI is a function of time. Time and space are inextricably linked, and the distance a person can travell is a function of time. Thus smaller geographic windows measure the immediate ability to flee and larger windows better measure long-run process. 21

Figure 5: Violence vs. HHI: by Window Size (w)

log(#Deaths+1) 0.00

0.00

log(#Deaths+1)

0.01

50

0.01

40

HHI 0.2

1.0

HHI 0.2

log(#Deaths+1) 0.00

0.00

log(#Deaths+1)

0.01

80

0.01

60

1.0

HHI 0.2

1.0

HHI 0.2

1.0

This result is suggestive of one mechanism through which political competition mitigates violence. The mechanisms are not mutually exclusive, and many are consistent with violence decreasing at a diminishing rate. But the innovation based argument is more in line the with long run results. Recall that the innovation based argument is that more political units in an area leads to more political innovation on issues directly or indirectly affecting violence. This innovation argument is stronger in the long run. Recall that the constraints based argument is that a greater number of alternative governments leads to more constraints on predatory policy. This constraints argument should be evident in the short run. If political innovation is mechanism we see more of in the long-run large-window regressions, then long-run political innovation appears to be the stronger effect in deterring violence.

4.5

Dis-aggregating Violence by Type

One natural explanation for finding a non-linear relationship is that it aggregates two distinct relationships. Fewer larger territories within a given geographic region could reduce the number of external 22

contestants but also increases the number of internal contestants. I classify conflicts into three types: (1) Government versus Government (2) Government versus Rebels-or-Civilians (3) Rebel/Civilian versus Rebel/Civilian. It appears that the geographic concentration of political power either encourages predatory behavior from a government or encourages militant groups to capture the government. This change in the type of violence over HHI helps explain the aggregate non-linear trend.

Figure 6 displays the non-parametric bivariate relationship between each type of violence and HHI. This was estimated with loess on data averaged over time. There is a clear difference in the relationship based on different types of violence. Appendix Table 10 displays the regressions for each of type, and also shows there is a substitution away from violence between Governments for HHI closer to 1. Figure 6: Fatalities vs. HHI by type

0.4

HHI

1.0

log( #Deaths +1)

ACLED UCDP

0.00

log( #Deaths +1)

ACLED UCDP

0.00

0.000

log( #Deaths +1)

ACLED UCDP

Reb/Civ−Reb/Civ

0.01

Gov−Reb/Civ

0.01

0.001

Gov−Gov

0.4

HHI

1.0

0.4

HHI

1.0

Table 5 shows how the share of violence of type Gov vs Reb/Civ changes with HHI. The ratio of (Gov vs Rebel/Civilian) to (Rebel/Civilian vs Rebel/Civilian) violence is increasing with HHI. This is a substitution towards violence between Gov and Rebels/Civilians. This finding is roughly consistent with 23

Montesquieu’s (1748) idea that “If a republic be small, it is destroyed by a foreign force; if it be large, it is ruined by an internal imperfection.” I call this Montesquieu’s tradeoff. Table 5: Government vs. Rebel/Civilians share of Violence ACLED

UCDP

HHI 0.00028 (0.00006) Controls G F.E. C&T

0.00029 (0.00003) G C&T

Notes: The Y variable is Gov−Reb/Civ and the X variable is HHI. Heteroskedastic-Consistent Clustered (on AllTypes Spatial ID) standard errors reported. Also included are Population, Geographic controls (G), Country (C) and Time (T) fixed effects.

4.6

Distance to Border

I also look at the distance from a geo-cell to the nearest border (BorderDistance). I do this because BorderDistance is a similiar measure to HHI and the difference between the measures is informative to the underlying mechanism. Distance to border could be important for many reasons, one being the ability to flee. While HHI has some of that too, it also affects political innovation. It is also informative to know if the results for HHI are just a results of it’s correlation with BorderDistance. I find that HHI is statistically important and qualitatively similiar results when controlling for BorderDistance in Table 11.37 Distance to border could measure factors other than the ability to flee, further suggesting it is not the main benefit from larger HHI. On the other hand, the independent significance of HHI further enforces the idea that political innovation is a major factor.

4.7

Ethnic Territories

I also explore the role of “Ethnic Concentration” using the same HHI calculations but for Ethnic boundaries. Table 12 reports the results of controlling for HHI(ethnic). A quadratic shape for HHI is still 37 The

baseline controls, CAPdist, Lights, POP, Diamond, Petro, Precip, COAST dist, T RI, are also included.

24

found with coefficient magnitude similiar to those found in 4.3. The negative coefficient on HHI(ethnic) means that areas with fewer ethnic groups have less violence. Table 6: aHHI Regressions ACLED UCDP −0.037 (0.0037) HHIˆ2 0.0241 (0.0024) HHI(ethnic) −0.0061 0.0002 F.E. ArgMin 0.766 HHI

−0.0434 (0.0029) 0.0282 (0.0019) −0.0043 0.0002 0.769

ACLED UCDP −0.0104 (0.0026) 0.006 (0.0018) −0.0022 0.0003 C 0.865

−0.0143 (0.002) 0.0089 (0.0013) −0.0014 0.0002 C 0.805

Notes: Dependant variable is log( # Fatalities +1). Heteroskedastic-Consistent (type 3) robust t values reported. Data collapsed and averaged over time. Population and Geographic controls are included in all regressions. Regressions with FE=’C’ include country fixed effects.

Perhaps the relationship with Ethnicity is also more complex. Table 12 in appendix section 6.8 include models with a quadratic HHI(ethnic) term and an interaction term for HHI × HHI(ethnic) which was estimated to be positive. As with country areas, a quadratic relationship better approximates the relationship between HHI(ethnic) and violence. The result is that at near-monopoly values for HHI, the marginal effect of geo-political concentration is to cause even more violence when there are fewer ethnic territories in that area. At far-from-monopoly values, the pacifying effects of geo-political concentration are smaller.

5

Conclusion

By looking at borders in modern Africa, I am able to identify the causal effect of geographic concentration of countries on political violence. Many scholars have thought about this question, but it has remained unanswered by the modern literature on violence and the state. I find that there is a reduction in violence for non-monopolized regions. However, the benefits to geo-political concentration plateau 25

and eventually slightly reverse. This aggregate trend is partly a result of that fact that the geographic concentration of countries affects internal and external violence differently (Montesquieu’s tradeoff). Furthermore, the available data also suggest that the benefits could stem from long-run innovation, but more work is needed here.

I have not claimed that the optimal extent of government is at the point which minimizes violence. At the relevant margin, there is likely a trade-off between the benefits of reduced violence and other goods. Although violence is costly, some of the greatest periods of intellectual productivity in western history (Ancient Greece, Enlightenment Europe) also seem to correlate with lower geo-political concentration and more violence.

I evaluate the promise of reduced violence with a territorial unification of political units. As military governor in Nigeria, Chukwuemeka Odumegwu Ojukwu, once argued “Europe found peace through Balkanization, why not Africa through Balkanization?” (Spears 2007). The Hobbesian logic, that more countries leads to more violence, is mostly right, but not always. One cannot ignore the heterogeneous responses from different actors and the benefits from alternative governments broadly defined.

26

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6

Appendix Figure 7: Time Maps of African Borders

1964

1970

1976

1982

1988

1994

2000

2006

2012

6.1

Source of Violence

Is the violence coming from differences across space or differences across time? To find out, I estimate three models for each data-set. I first regress violence on geo-cell and year fixed effects and calculate the R2 . This gives a sense of how much violence can be explained by differences across years and differences across geo-cells. I then seperately regress violence on geocell fixed effects and year fixed effects and report those R2 . I see that the R2 for geo-cell fixed effects orders of magnitude larger than the R2 for yearly fixed effects. This means that the vast majority of the differences in violence over space 33

and time is due to spatial variation rather than temporal variation.38 Table 7: Variance Partitioning ACLED UCDP Time + Space 0.21283 0.15354 Time 0.00022 0.00016 Space 0.21261 0.15338 Notes: The Y variable is log(Fatalities+1) in each column. The rows indicate which set of fixed effects where used as explanatory variables. Each table entry represents the R2 for that model.

6.2

Bi-Variate Data

Figure 8 is a scatter plot of HHI and the level of violence (in log terms). On the top axis is a histogram of HHI and on the right axis is a histogram of violence. Since there are many geo-cells, the (X,Y) data are binned into 50x50 bins. The points in each plot below is a count of the number of observations in each bin. The histograms above and to the right of the plot showing the distribution of the raw data. This is the baseline data used in the regressions but note that larger geo-cells have a different distribution with a mean and median HHI closer to 0. The histograms at the top of Figure 8 show that no observations have HHI < .2, many observations have HHI > .4, and many - but less than half - have HHI close to 1. The histograms on the side of Figure 8 show that there are many non-violent geo-cells.39 The violence data do not resemble a nice distribution (i.e. gaussian or poisson). This data is not averaged over time. 38 One

caveat is that the quantitative results about the R2 for time fixed effects depend on how small the time intervals. For

example, monthly fixed effects would change the R2 for the Time and Time+Space fixed-effects models. 39 This

is explored in the robustness section and appendix.

34

Figure 8: Geo-Political Concentration vs. Violence (a) ACLED

6.3

(b) UCDP

Robustness: Unit of Observation Transformation

One potential issue is the size of the geo-cells. As the cell size approaches 0, the geographic space is transformed into a 2D continuum. I can analyze this case by considering the data as a point process on a random field. This is a natural formulation as the original data on violence comes as a list of points. The intensity of the violent point is dependant on the amount of political competion. This relationship is calculated using the “rho hat” function (Baddeley et al. 2012), and is plotted in the figure below. One rough intuition is to take the set of violent points that correspond to an HHI value and then compare the number of those points against their spatial dispersion.40 The non-parametric continuous-space analog 40 The

ρ function compares how the spatial intensity of HHI compares to the spatial density of HHI. Denote yi as the

locations of violence and xi as the HHI scores evaluated at yi. Density references the probability of (xi = x) at yi. Intensity references the expected number of (xi = x) at yi. For each value of HHI, x in [0, 1], construct ρ = gf ; g =the spatial density of xi = x evaluated at yi, and f =the spatial intensity of xi = x evaluated at yi. If the density of HHI is high, then the intensity should also be high. However, if the intensity of xi is low, then this comes from a negative correlation with intensity of violence. Another way to think about this is to fix the number of points in a region for each x. Then look at whether there are many sub-locations with almost no points or a single sub-location with many points. The single sub-location with many points indicates that there is much violence at the only place where HHI = x.

35

displays results consistent with the baseline.

5e−09

Figure 9: Point Process Violence vs. Raster HHI

0e+00

1e−09

2e−09 3e−09 Violence Intensity

4e−09

ACLED UCDP

0.2

6.4

0.4

HHI 0.6

0.8

1.0

Robustness: Functional Form Transformation

I look at 3 different bivariate functional form models: linear-linear OLS, log-linear OLS, negative binomial GLM. I then predict violence over HHI ∈ [.25, 1] and record the argMins in Table 8. The use of the logarithmic transformation allows us to compare partial elasticities across data-sets, but is not changing the qualitative results. The data used here was not averaged over time. Table 8: ArgMins and Functional Form

ACLED UCDP

OLS: Log-Quad

OLS: Lin-Quad

NegBin: Lin-Quad

0.78 0.78

0.74 0.76

0.73 0.78

36

I also fit the generalized additive model in equation 7. This helps verify the conditional relationship of violence with HHI and violence is also non-linear. Denote s as smoothing spline.41 The data used here is averaged over time.

ln(#Deaths + 1) = s(HHI) + s(Lights) + s(POP) (7) + s(Diamond) + s(Precip) + s(COAST dist) + s(T RI)

0.006 0.004 0.000

0.002

log(#Deaths + 1)

0.008

0.010

Figure 10: GAM predictions of conditional relationship

0.2

0.4

0.6

0.8

HHI

41 Petroleum

data was dropped due in this specification due to spline estimation issues

37

1.0

6.5

Robustness: Window Sizes Table 9: Geo-Political Concentration and Violence by Window Extent

HHI(40) HHI(40)ˆ2 Geo-Cell Area [milesˆ2] ArgMin HHI(50) HHI(50)ˆ2 Geo-Cell Area [milesˆ2] ArgMin HHI(60) HHI(60)ˆ2 Geo-Cell Area [milesˆ2] ArgMin HHI(80) HHI(80)ˆ2 Geo-Cell Area [milesˆ2] ArgMin # obs Controls F.E.

ACLED Estimate Std. Error

UCDP Estimate Std. Error

−0.0142 0.008 38936 0.887 −0.0124 0.0071 60837 0.88 −0.0114 0.0066 87606 0.861 −0.008 0.0048 155744 0.835 3337201 G&P C&T

−0.022 0.0129 38936 0.85 −0.0227 0.0136 60837 0.832 −0.0212 0.0129 87606 0.824 −0.0145 0.0087 155744 0.832 5720916 G&P C&T

(0.0044) (0.0029)

(0.0035) (0.0023)

(0.0029) (0.002)

(0.0024) (0.0017)

(0.0038) (0.0025)

(0.0031) (0.0021)

(0.0025) (0.0017)

(0.0021) (0.0015)

Notes: The Y variable is ln(Fatalities+1). Heteroskedastic-Consistent Clustered (on Spatial ID) standard errors reported. Also included are Geographic (G) and political (P) controls and Country (C) and Time (T) fixed effects.

6.6

Robustness: Disaggregated Types

Table 10 displays the regressions for each of type. Each Y variable corresponds to the log number of fatalities for a certain type of conflict. The quadratic relationship is not strongly found for Gov vs. Gov types of violence.42 However, the other types both have a significantly positive coefficient for HHI 2 . 42 A

similar relationship is also found when using the Correlated of War data-set which only looks at inter-state violence.

38

Table 10: Geo-Political Concentration and Violence by Typology Gov-Gov Gov-Gov Gov-Reb/Civ −0.00012 −0.00001 (0.00003) (0.00001)

HHI HHIˆ2

N 8581374 11918575 ArgMin 1 1 Controls G G F.E. C&T C&T

−0.00542 (0.00176) 0.00293 (0.00119) 8581374 0.926 G C&T

Gov-Reb/Civ Reb/Civ-Reb/Civ Reb/Civ-Reb/Civ −0.00982 (0.00144) 0.00638 (0.00098) 11918575 0.769 G C&T

−0.00508 (0.0018) 0.00289 (0.00121) 8581374 0.879 G C&T

−0.00605 (0.00121) 0.00345 (0.0008) 11918575 0.876 G C&T

Notes: The dependant variable is log(Fatalities +1) for each Type of conflict. The types of contestant are denoted in the columns; Government (Gov) and Rebel or Civilian (Reb/Civ). ACLED data used in Columns 1,2,3 and UCDP in 4,5,6. Heteroskedastic-Consistent Clustered (on Spatial ID) standard errors reported. Also included are Population, Geographic controls (G), Country (C) and Time (T) fixed effects.

Distance to Border Figure 11: HHI and BorderDistance Correlation correlation = 0.7

0e+00

1e+05

2e+05

3e+05

data averaged over time

Border Distance

6.7

0.2

0.4

0.6 HHI

39

0.8

1.0

Table 11: Geo-Political Concentration and Border Distance

HHI HHIˆ2

ACLED UCDP

ACLED.1 UCDP.1

−0.0297 (0.0035) 0.0183 (0.0023)

−0.0317 (0.0036) 0.0203 (0.0024) −0.0181 0.0031 0.779

−0.0373 (0.0027) 0.0236 (0.0018)

Bdist ArgMin 0.814

0.79

−0.0402 (0.0028) 0.0267 (0.0019) −0.0269 0.0024 0.753

Notes: The Y variable is log(Fatalities+1) in every column. All columns control for CAPdist, Lights, POP, Diamond, Petro, Precip, COASTdist, TRI. Columns 3 and 4 also include Bdist, which is the distance to border in megameters (1E7m). Heteroskedastic-Consistent Clustered (on Spatial ID) standard errors reported.

6.8

Robustness: a Micro-Founded Measure of Mismatch for Regression Analysis

I want to consider “What is the effect on violence of countries areas being different from ethnic areas?” I will briefly lay out the alternative HHI measure (aHHI) which measures the dissimilarity between two different sets of shares, with the idea that there is the distribution of territorial shares we observe and a counter factual distribution which matches ethnic boundaries. To empirically analyze this question, I decomposed aHHI, which is unobserved, into 2 HHI scores that are ubserved and a third uncertain term.

Denote s j as country j share of land in a geo-cell and scj as the counter factual share under other circumstances. The measure aHHI is the distance between distributions

aHHI =

r

∑(s j − scj )2

(8)

j

This measure comes from exploiting some of the similarities between HHI measure in economics, the Variance measure in statistics (HHI is closely related to variance of the market shares), and the Distance measure in mathematics ( HHI is closely related to the euclidean distance between locations). Further40

more, the same mathematics are applicable to other economic questions, such as “under what conditions HHI is a good measure of competition?”

43

If each alternative share is 0 (as in the limiting case of an infinite number of infinitesimally small countries), then aHHI 2 = HHI. However, in the more realistic case when every country has a unique alternative share then the distribution is not just shifted but also changes shape. Considering scj as ethnic boundaries, aHHI = 0 if country boundaries and ethnic boundaries perfectly align and aHHI gets larger the greater the mismatch. If “alternative equilibrium” would instead mean that every person (rather than every ethnic territory) would there own country, then distance between equilibrium and HHI are essentially the same measure. To be clear

√ HHI is equivalent to the special case of aHHI(scj = 0).

The distance between equilibrium measure can be decomposed (shown in equations below) into two separate HHI measures which allow for isolated comparative statics. These are the calculations behind Table 12, but “dissimilarity of share distribution” is a measure that can be applied elsewhere.

44

For

land areas, s j is country j share of land in that geo-cell and scj is the share of ethnic boundaries and N is the number of actors who can grab land. I drop summation subscripts; ∑ = ∑Nj and remember the accounting identity ∑ s j = 1 so that s¯j = 1/N, where. I set out to show that the distance from competitive equilibrium aHHI can be measured in terms of two HHI scores. The first lemma shows that by adding a 43 It’s known that concentration and competition are not the same thing (Stigler 1972).

The difference between the observed

and competitive distributions of shares (aHHI) is a measure of how non-competitive the situation is. The aHHI measure ends up nesting the HHI as an extreme case, and indicates that changes in HHI in general do not net out the bias of HHI. My work does not provide a comprehensive and micro-founded proof of exactly when HHI is a good or bad measure, but follows the intuition that HHI is a better measure when the competitive situation is more like perfect competition. 44 A

natural application of aHHI is comparing “competitive” and “non-competitive” equilibria, in which case aHHI is the

distance from competitive equilibrium.

41

0, the variance of the shares is a function of HHI. The second lemma also adds a 0, and is used only a technical necessity to transform an interaction term into functions of HHI. The ρ parameter is the degree to which the s j and scj align.

Lemma 1

1 (s j − s¯j )2 N∑ 1 1 2 = s2j + ∑ s¯j 2 − ∑ s j s¯j ∑ N N N 1 1 = HHI − 2 N r N r 1 1 HHI − = N N

σ 2j =

σj

(9) (10) (11) (12)

Lemma 2

∑ s j scj

=

∑(s j − s¯j )(scj − s¯cj ) + ∑ s j s¯cj + ∑ scj s¯j + ∑ s¯j s¯cj

=

∑(s j − s¯j )(scj − s¯cj ) + N ∑ s j + N ∑ scj − N

=

∑(s j − s¯j )(scj − s¯cj ) + N

1

1

1

1

(14) (15)



= = = = = =

 1 1 c c ¯ N (s j − s¯j )(s j − s j ) + ∑ N N   1 N COV (s j , scj ) + N 1 Nρσ j σ cj + N ! r r ! r r 1 1 1 1 1 Nρ HHI − HHI c − + N N N N N r r 1 1 1 HHI c − + ρ HHI − N N N r HHI HHI c 1 1 ρ (HHI)(HHI c ) − − + 2+ N N N N

(13)

42

(16) (17) (18) (19) (20) (21)

Proof

aHHI 2 =

∑(s j − scj )2 = ∑ s2j + ∑ sc2j − 2 ∑ s j scj r

= HHI + HHI c − 2ρ

(HHI)(HHI c ) −

(22)

HHI HHI c 1 2 − + 2− N N N N

(23)

This term can then be simplified into a regression framework using an asymptotic approximation. Taking the limit as N → ∞ yields

aHHI 2 → HHI + HHI c − 2ρ

p (HHI)(HHI c )

(24)

Although HHI was the focus of the main analysis, the empirical results explicitly considering HHI(ethnic) are shown in Table 12. Using the theory above, “dissimilarity of shares” can be expressed in terms of two HHI scores: one for country land-shares and one for ethnic-land shares. Table 12: aHHI Regressions ACLED UCDP −0.0341 (0.0036) HHIˆ2 0.0203 (0.0024) HHI(ethnic) −0.0266 0.0015 HHI(ethnic)ˆ2 0.0139 0.001 HHI x HHI(ethnic) 0.0101 0.0011 F.E. ArgMin 0.78 ArgMin (Ethnic) 0.6 HHI

−0.0411 (0.0029) 0.0238 (0.0018) −0.0245 0.0012 0.0104 0.0007 0.0139 0.0008 0.76 0.57

ACLED UCDP −0.0106 (0.0026) 0.0051 (0.0018) −0.0066 0.0017 0.0009 0.0011 0.0046 0.0011 C 0.88 0.77

−0.0145 (0.002) 0.008 (0.0013) −0.0052 0.0012 0.0004 0.0008 0.0044 0.0008 C 0.82 0.67

Notes: Dependant variable is log( # Fatalities +1). Heteroskedastic-Consistent (type 3) robust t values reported. Data collapsed and averaged over time. Population and Geographic controls are included in all regressions. Regressions with FE=’C’ include country fixed effects.

43

6.9

Robustness: Dis-aggregating Onset and Intensity

One might also think that geo-political concentration has on the extensive and intensive (Onset and Intensity) margins of conflict. For example, suppose monopolized areas don’t often have violence, but when it occurs it erupts in full chaos. Furthermore, the presence of many zero’s can be indicative of censoring, either theoretical (i.e. many corner solutions of non-violence) or empirical (i.e. systematically not recording violence). This can lead to inconsistent estimates.45 Furthermore, the UCDP data are empirically left censored at 25 deaths. Table 13 report the coefficient estimates for Tobit models type 1 and 2. The Y variable does not have a logarithmic transformation, so cross data-set comparisons no longer compare partial elasticities. However, the predicted ArgMins are qualitatively similiar to the baseline. The different effects of geo-political concentration on the intensive and extensive margins are not driving the qualitative results in the baseline model.

45 The

intuitive reason being that that the conditional expectation function, of the OLS model, is not generally independent

of the covariates. For example, let us observe y, x from a Tobit type2 process. Let y˜ = xβ + ε be the relationship for violence (truncated) and y∗ = xγ + ν for whether we observe violence at all. First note that

E(y) ˜ = E(y|y∗ ˜ > 0)P(y∗ > 0) + E(0|y∗ ≤ 0)P(y∗ ≤ 0) = E(xβ |y∗ > 0)P(y∗ > 0) + E(ε|y∗ > 0)P(y∗ > 0) = xβ P(xγ + ν > 0) + E(ε|xγ + ν > 0)P(xγ + ν > 0)

There are 3 sources of bias for an ols estimator: non-random selection (ε|xγ + ν > 0), any differences between (γ, β ) that leave γ unestimated, and the nonlinear probability function P(). The OLS estimator B = (x0 x)−1 x0 (y − e) has expecations that do not correspond to any theoretical variable. Note

    E x0 (y˜ − e) = x0 xβ P(xγ + ν > 0) + E x0 ε|xγ + ν > 0 P(xγ + ν > 0)

44

Table 13: Political Competition and the Margins of Violence

HHI HHIˆ2 ArgMin

I ACLED

I UCDP

-49.60 31.20 0.79

-2, 475 1, 640.90 0.78

II:S II:O II:S II:O ACLED ACLED UCDP UCDP -2.70 1.70

-4.40 2.90 0.71

18.90 -369.70 -9.10 247.50 0.76

Notes: The dependant variable is Fatalities. Geographic and Population controls included. Only coefficients for HHI and HHI reported for Tobit type I and II models. Header ‘:S’ denotes the selection model for Ever Fatalities and ‘:O’ denotes the outcomes model for # Fatalities. ArgMins based on a loess on the predicted fatalities evaluated at the data.

6.10

Robustness: Violence as Extremum

Some readers may be concerned that violence is a rare and extreme event for the same reasons in section 6.9. I address this by using the Generalized Extreme Value (GEV) distribution to fit the extensive margins of conflict. The GEV distribution is used to fit binary data for rare-events that might not look like an “S”. 46

A special case of the GEVit is the Gumbit with a shape parameter of 0. Table 14 compares the Logit,

Gumbit, and GEVit models.47 Although the point estimates are not the same, Logit, Gumbit, and GEVit models give quadratic coefficients. It seems unlikely that this is driving the qualitative results found in the baseline. 46 Formally,

the model is P(#Deaths > 0) = P(Xβ + ε > 0) = P(ε > −Xβ ) = 1 − F(−Xβ ) where F(−Xβ ) =

exp −1[1 + τ(−Xβ )/σ ]−1/τ . The marginal effect is f (−Xβ ) βhhi + βhhi2 HHI . 47 I

estimate the shape parameter of the GEVit by optimizing a concentrated likelihood function with respect to that pa-

rameter. For any fixed shape parameter, I optimize the likelihood of a binary GEV distribution. I then optimize over the shape paremeter.

45

Table 14: Violence as a Rare Event

HHI HHIˆ2 ArgMin

Logit Logit

Gumbit Gumbit

GEVit GEVit

-7.40 -11.98 4.79 7.73 0.83 0.84

-1.30 0.82 0.85

-0.51 0.31 0.86

-2.39 1.52 0.84

-1.11 0.70 0.85

Notes: The Y variable is I(# Fatalities> 0). Also included are Population and Geographic controls. ACLED data shown in columns 1,3,5. UCDP data shown in columns 2,4,6. The estiamted shape parameters for GEVit are 0.41 for ACLED and 0.416 for UCDP. ArgMins based on a loess on the predicted fatalities evaluated at the data.

6.11

Robustness: Spatial Auto Correlation

One might be concerned that the results are being driven because the violence for each cell in a neighborhood is all jointly determined. I address this concern by testing a SAR model. The SAR model includes spatial lags (i.e. each Yi is a function of all the other Y j in the neighborhood). This is analogous to a “peer effects” model. The two-stage generalized method of moments (GMM) uses the spatially-lagged X variables as an instrument, but it is questionable as if the instrument satisfies a number of requisite assumptions for valid inference. For this same reason, Maximum Likelihood was used, but this added computational complexity. The table below reports the coefficients for the spatial lags with population geographic controls and country fixed effects. Table 15: Spatial AutoCorrelation of Violence ACLED HHI HHI2 mfx direct -0.008 mfx indirect -0.002 mfx total -0.010 direct t-val -3.329

0.005 0.001 0.006 2.753

UCDP HHI HHI2 -0.011 -0.003 -0.014 -5.673

0.007 0.002 0.009 5.099

Notes: Y variable is log(Fatalities+1). The first row represents the direct effect of HHI, the second row the indirect (or displacement) effect, and the third row the combined effect. The last row repors the standard error for the indirect effect based on Monte Carlo Maximum Likelihood methods. Also by MCML the spatial lags and standard errors of (ρ, SEρ ) are (1.9500e-01, 3.3238e-07) for ACLED and (2.5400e-01, 3.7298e-07) for UCDP respectively.

Heteroskedastic-Consistent (HC type 3) and cluster (on spatial ID) corrected standard errors were used 46

throughout the paper. However, one might be concerned about spatially auto-correlated standard errors. If violence is miscoded into one cell away from another, this would causes spatial autocorrelation. If the cell size was “too small” to be considered independant, then this would cause spatial autocorrlation. A maximum likelihood estimation of the Spatially Auto-correlated errors (SAC) is available, but this method requires functional form assumption. I report the HC3 and SAC t values in the table 16 below for each data set under an OLS specification that has Population and Geographic controls as well as country fixed effects.48 . One non-trivial step in the estimation process is to choose how to weight the neighbours. I try 2 methods called SAC(8) and SAC(vario). SAC(8) uses equal weights on the 8 nearest neighbours. SAC(vario) first runs the OLS model, calculates the spatial correlation of the residuals as a function of distance in what’s called a variogram analysis, and finally constructs the spatial weights based on the variogram. It appears that spatial auto-correlation is not a major concern, as the t values for SAC and HC3 models are close and large enough to reject conventional significance tests. Table 16: Standard Error Correction

HHI HHIˆ2

48 The

ACLED Est.

HC3

SAC(8)

SAC(vario)

UCDP Est.

HC3

SAC(8)

SAC(vario)

-0.011 0.006

-4.096 3.490

-3.606 3.054

-4.089 3.407

-0.014 0.009

-7.351 6.746

-6.227 5.659

-7.618 6.880

spatial weights matrix becomes computationally prohibitive to work with under any model (GMM of MCML). The

reported results use a spatial weights matrix which has positive weight for the nearest neighbour. However, a larger weights matrix was estimated based on fitting a variogram to the residuals from an OLS regression and the standard errors were qualitatively similar

47