Conflict and Distribution

Transcription

1 Conflict and Distribution Lecture I at Boston University, April 5, 2011 Debraj Ray, New York University

2 Internal Conflict is Endemic : battle deaths in 25 interstate wars approx. 3.33m 127 civil wars in 73 states (25 ongoing in 1999). (over 1/3 of all countries) 16m+ dead as a direct result Does not count displacement and disease. Does not count ongoing ethnic violence, such as Hindu-Muslim violence in India. Economic costs: 8% of world GDP (Hess (2003))

3 Battle Lines are Predominantly Ethnic In much of Asia and Africa, it is only modest hyperbole to assert that the Marxian prophecy has had an ethnic fulfillment. Horowitz (1985) Brubaker and Laitin (1998) on eclipse of the left-right ideological axis Fearon (2006), , approx. 700 ethnic groups known, over 100 of which participated in rebellions against the state.

4 Palestinian conflict Patani conflict in Southern Thailand Ethnic Pashtun/Taliban in Pakistan Sunni insurgency in Iraq Ethnic wars in Burma Civil war in Cote d Ivoire Darfur (Fur-Arab) The Kurdish conflict Uganda (LRA) Chechnya (Chechen Muslims vs the state) Sri Lanka: Tamil-Sinhala Bosnian war (ethnic Serbs and Croats against Bosnian Muslims) French wars of religion Hindu-Muslim violence

5 Primordial or Instrumental? Ancient hatreds, reinforced by myth/legend/discourse: Samuel Huntington s Clash of Civilizations (1993, 1996). Similar position adopted by many other social scientists (e.g., orientalists such as Bernard Lewis). Cultural fundamentalism close to primordialism Instrumentalism Revolution versus exclusion Ethnicity broadly construed a marker for carving a larger share

6 Do Ethnic Divisions Matter? Two ways to approach this question. Historical study of conflicts, one by one. e.g., Horowitz (1985). Statistical approach (Collier-Hoeffler, Fearon-Laitin, Miguel-Satyanath-Sergenti, Montalvo- Reynal)

7 Typical variables for conflict: civil war onset or incidence Explanatory variables: Economic. per-capita income, inequality, resource holdings... Geographic. mountains, separation from capital city... Political. democracy, prior war... And, of course, ethnic divisions. But how measured?

8 Information on ethnolinguistic diversity from: World Christian Encyclopedia Encyclopedia Britannica Atlas Narodov Mira CIA FactBook Ethnologue Or religious diversity from: L Etat des Religions dans le Monde World Christian Encyclopedia The Statesman s Yearbook

9 Fractionalization Fractionalization index widely used: F = m n j (1 n j ) j=1 where n j is population share of group j. Special case of the Gini coefficient G = m M n j n k δ ik j=1 k=1 where δ ik is a notion of distance across groups. Has been used in many different contexts (growth, governance, public goods provision).

10 But the correlation with conflict isn t strong. See Collier and Hoeffler (2002), Fearon and Laitin (2003), Miguel-Satyanath-Sergenti (2004). Fearon and Laitin (APSR 2003) The estimates for the effect of ethnic and religious fractionalization are substantively and statistically insignificant... The empirical pattern is thus inconsistent with... the common expectation that ethnic diversity is a major and direct cause of civil violence.

11 And yet... fractionalization does not seem to capture the Horowitz quote: In dispersed systems, group loyalties are parochial, and ethnic conflict is localized... A centrally focused system [with few groupings] possesses fewer cleavages than a dispersed system, but those it possesses run through the whole society and are of greater magnitude. When conflict occurs, the center has little latitude to placate some groups without antagonizing others. Motivates the use of polarization measures. More generally, need to ground the empirical exercises more firmly in theory.

12 The Identity-Alienation Framework Society is divided into groups (economic, social, religious, spatial...) Identity. There is homogeneity within each group. Alienation. There is heterogeneity across groups. In our 1994 Econometrica paper, we presumed that such a situation is conflictual: We begin with the obvious question: why are we interested in polarization? It is our contention that the phenomenon of polarization is closely linked to the generation of tensions, to the possibilities of articulated rebellion and revolt, and to the existence of social unrest in general...

13 Measuring Polarization (adapted from Duclos, Esteban and Ray (2003)) Space of densities (cdfs) on income, political opinion, etc. Each individual located at income x feels Identification with people of similar income (the height of density n(x) at point x.) Alienation from people with dissimilar income (the income distance y x of y from x.) Effective Antagonism of x towards y depends on x s alienation from y and on x s sense of identification. where i = n(x) and a = x y. T (i, a)

14 View polarization as the sum of all such antagonisms P (f) = T (n(x), x y ) n(x)n(y)dxdy Not very useful as it stands. Axioms to narrow down P. Based on special distributions, built from uniform kernels. Income or Wealth

15 Axiom 1. If a distribution is just a single uniform density, a global compression cannot increase polarization. Income or Wealth

16 Axiom 1. If a distribution is just a single uniform density, a global compression cannot increase polarization. Income or Wealth

17 Axiom 2. If a symmetric distribution is composed of three uniform kernels, then a compression of the side kernels cannot reduce polarization. Income or Wealth

18 Axiom 2. If a symmetric distribution is composed of three uniform kernels, then a compression of the side kernels cannot reduce polarization. Income or Wealth

19 Axiom 3. If a symmetric distribution is composed of four uniform kernels, then a symmetric slide of the two middle kernels away from each other must increase polarization. Income or Wealth

20 Axiom 3. If a symmetric distribution is composed of four uniform kernels, then a symmetric slide of the two middle kernels away from each other must increase polarization. Income or Wealth

21 Axiom 4. [Population Neutrality.] Polarization comparisons are unchanged if both populations are scaled up or down by the same percentage. Theorem 1. A polarization measure satisfies Axioms 1 4 if and only if it is proportional to n(x) 1+α n(y) y x dydx, where α lies between 0.25 and 1. Compare with the Gini coefficient / fractionalization index: Gini = n(x)n(y) y x dydx, It s α that makes all the difference.

22 Some Properties 1. Not Inequality. See Axiom Bimodal. Polarization maximal for bimodal distributions, but defined of course over all distributions.

23 3. Global. The local merger of two groups has effects that depend on the shape of the distribution elsewhere. Density Income

24 3. Global. The local merger of two groups has effects that depend on the shape of the distribution elsewhere. Density Income

25 3. Global. The local merger of two groups has effects that depend on the shape of the distribution elsewhere. Density Income

26 3. Global. The local merger of two groups has effects that depend on the shape of the distribution elsewhere. Density Income

27 3. Nonlinear. Same direction of population or income movements may cause polarization to go down or up, depending on context. Density Income

28 3. Nonlinear. Same direction of population or income movements may cause polarization to go down or up, depending on context. Density Income

29 3. Nonlinear. Same direction of population or income movement may cause polarization to go down or up, depending on context. Density Income

30 More on α Pol = n(x) 1+α n(y) y x dydx, where α lies between 0.25 and 1. Axiom 5. If p > q but p q is small and so is r, a small shift of mass from r to q cannot reduce polarization. r p q 2ε 2ε 2ε 0 a 2a

31 More on α Pol = n(x) 1+α n(y) y x dydx, where α lies between 0.25 and 1. Axiom 5. If p > q but p q is small and so is r, a small shift of mass from r to q cannot reduce polarization. r p q 2ε 2ε 2ε 0 a 2a

32 Theorem 2. Under the additional Axiom 5, it must be that α = 1, so the unique polarization measure that satisfies the five axioms is proportional to n(x) 2 n(y) y x dydx. Easily applicable to ethnolinguistic or religious groupings. Say m social groups, n j is population proportion in group j. If all inter-group distances are binary, then Pol = M M n 2 jn k = j=1 k=1 M n 2 j (1 n j ). j=1

33 Polarization and Conflict: Behavior Axiomatics suggest (but cannot establish) a link between polarization and conflict. Two approaches: Theoretical. Write down a natural theory which links conflict with these measures. Empirical. Take the measures to the data and see they are related to conflict. I discuss the theory first (based on Esteban and Ray (2010)).

34 A Simple Model of Conflict m groups; N i in group i, m i=1 N i = N. They fight over a budget ; per capita value normalized to 1. A fraction λ of this budget is available to produce society-wide public goods. The winning group gets to choose the goods. u ij = public goods payoff to a member of group i if a single unit per-capita of the optimal mix for group j is produced. The remainder 1 λ is privately divided, again among the winning group.

35 Conflict Resources Individual resource contribution r at utility cost c(r): smooth, thrice differentiable, with c (r) > 0, c (r) > 0, c (r) 0. Example: c(r) = r θ /θ, with θ 2. R i is total contributions by group i. Define R = m R i. i=1 Probability of success given by p j = R j R R is our measure of overall conflict.

36 Payoffs Per-capita payoff to group i is λu ii + (1 λ)(n/n i ) = λu ii + (1 λ)/n i (in case i wins the conflict), and λu ij (in case some other group j wins). So net expected payoff to an individual k in group i is π i (k) = m j=1 p jλu ij + p i (1 λ) n i c (r i (k)).

37 How do Individuals Make Contributions? One extreme: individuals maximize own payoff. Another extreme: there is full intra-group cohesion and individual contributions maximize group payoffs. Intermediate situations: define person k s extended utility by U i (k) (1 α)π i (k) + α l i π i (l), where α lies between 0 and 1. Interpretations for α: group cohesion. (i) intragroup concern or altruism (ii)

38 Equilibrium A collection {r i (k)} of individual contributions where for every group i and member k, r i (k) maximizes (1 α)π i (k) + α l i π i (l) which is the same as maximizing [(1 α) + αn i ] p i 1 λ n i + λ m p j u ij c(r i (k)) j=1 given the contributions of everyone else. Theorem 3. An equilibrium always exists. If c (r) 0, it is unique.

39 Approximation Theorem For each i let γ i p i /n i : correction factors. Theorem 4. In equilibrium, neglect the joint impact of the deviation of correction factors from unity. Then the per-capita cost of conflict is approximately ˆρ, where ˆρc ( ˆρ) = ω 1 + ω 2 G + α[λp + (1 λ)f ], where ω 1 (1 λ)(1 α)(m 1)/N and ω 2 λ(1 α)/n and G is the Gini (using public goods losses δ ij u ii u ij ) F is fractionalization P is the Esteban-Ray (quadratic) polarization index.

40 Remarks ˆρc ( ˆρ) = (1 λ)(1 α) N + λ(1 α)g N + α[λp + (1 λ)f ], If all goods private and no group cohesion, then λ = α = 0 and there is only private conflict, goes to 0 as N. Only get action for large N if there is group cohesion: α > 0. In that case, polarization has more effect for public goods, fractionalization more for private goods.

41 Some Intuition Look at two groups i and j, and consider any member of i. Conflict the loss ij if j wins, times probability of win p j. Impact of individual contribution is roughly of the order of N 1. Combining, individual s contribution related to n j ij /N. So total contributions from group i proportional to n i n j ij /N after normalizing by population. Now unpack ij. E.g., when α = λ = 1: ij = N i d ij.

42 How Good is the Approximation? Holds exactly when there are just two groups and all goods are public. Holds exactly when all groups the same size and public goods losses are symmetric. Holds almost exactly for contests when conflict is high enough. is. Can numerically simulate to see how good the approximation

43 (a) α = 0.5, θ = 2, λ = 0, Corr = 0.99 (b) α = 0.5, θ = 2, λ = 0.2, Corr = 0.99 (c) α = 0.5, θ = 2, λ = 0.8, Corr = 0.97 (d) α = 0.5, θ = 2, λ = 1, Corr = 0.88

44 (a) α = 0.5, θ = 2, λ = 0, Corr = 0.99 (b) α = 0.5, θ = 2, λ = 0.2, Corr = 0.99 (c) α = 0.5, θ = 2, λ = 0.8, Corr = 0.98 (d) α = 0.5, θ = 2, λ = 1, Corr = 0.97

45 (a) α = 0.5, θ = 2, λ = 0.2, Corr = 0.99 (b) α = 1, θ = 2, λ = 0.2, Corr = 0.99 (c) α = 0.5, θ = 2, λ = 0.8, Corr = 0.97 (d) α = 1, θ = 2, λ = 0.8, Corr = 0.96

46 (a) α = 0.5, θ = 2, λ = 0.5, Corr = 0.99 (b) α = 0.5, θ = 3, λ = 0.5, Corr = 0.99 (c) α = 0.5, θ = 4, λ = 0.5, Corr = 0.99 (d) α = 0.5, θ = 10, λ = 0.5, Corr = 0.99

47 Empirical Investigation 131 countries over (pooled cross-section as in all studies). Conflict data on incidence and onset from PRIO. prio25: battle-related deaths in the year. priocw: prio25 + total exceeding 1000 battle-related deaths. prio1000: 1,000+ battle-related deaths in the year. Two non-binary indicators also used. Incidence x : x satisfied in current five-year period for some year. Onsetn x : x satisfied in current period, but not in n years before.

48 Groups Fearon database: culturally distinct groups in 160 countries. Potential endogeneity in any such procedure. Ethnologue: information on linguistic groups. Ethnologue lists 6,912 living languages + group sizes. Arguably exogenous, but the pathways one step removed...

49 Preferences and Distances Ideally want preferences over group-specific public goods. But very hard, and necessarily plagued by endogeneity. We use linguistic distances on language trees. E.g., all Indo-European languages in common subtree. Spanish and Basque diverge at the first branch; Spanish and Catalan share first 7 nodes. Max: 15 steps of branching. Similarity s ij = common branches maximal branches down that subtree. Distance κ ij = 1 s δ ij, for some δ (0, 1]. Baseline δ = 0.05 but results robust to different values.

50 Additional Variables and Controls Among the controls: Population GDP per capita Dependence on oil Mountainous terrain Democracy Also: Estimates of group concern from World Values Survey Indices of publicness and privateness of the prize

51 We estimate the equation ρc (ρ) it = X 1i β 1 + X 2it β 2 + ε it X 1i distributional indices X 2i controls (including lagged conflict variable) With binary outcomes, interpret as latent variable model: P (priox it = 1 Z it ) = P (ρc (ρ) > W Z it ) = H(Z it β W ) where Z it = (X 1i, X 2it ) Baseline: uses max likelihood logit (results identical for probit). p-values use standard errors robust to within-country correlation and heteroskedasticity

52 Baseline with different measures of incidence; Fe, δ = 0.05 Variable priocw prio25 prio1000 prio-int isc P 6.39 (0.004) F 1.14 (0.051) G/N (0.196) gdp (0.057) pop 0.16 (0.172) lag (0.029) (0.031) (0.001) 0.09 (0.375) (0.001) 0.88 (0.154) (0.065) (0.406) (0.033) (0.035) (0.001) 0.06 (0.491) (0.001) (0.546) (0.615) Contr yes yes yes yes yes Pse-R Meth Logit Logit Logit O. Logit OLS Obs

53 Variations with Fe, δ = 0.5; and data from Ethnologue Variable prio25 priocw prio1000 prio25 priocw prio1000 P 7.37 F 0.75 (0.108) G/N (0.050) gdp pop 0.10 (0.303) lag (0.001) 0.88 (0.135) (0.160) (0.021) 0.17 (0.125) (0.009) 0.83 (0.190) (0.127) (0.499) (0.002) 0.65 (0.115) (0.087) (0.108) (0.007) 0.79 (0.129) (0.384) (0.020) 0.24 (0.018) (0.028) 0.47 (0.377) (0.205) (0.185) 2.79 Contr yes yes yes yes yes yes Pseu-R Source Fe0.5 Fe0.5 Fe0.5 Eth0.05 Eth0.05 Eth0.05 Obs

54 Variations with conflict onset data Var onset2 onset5 onset8 onset2 onset5 onset8 P 5.60 (0.033) F 0.64 (0.313) G/N (0.086) gdp (0.001) pop 0.09 (0.417) 4.93 (0.040) 0.82 (0.221) (0.098) (0.003) 0.10 (0.378) 5.20 (0.030) 0.78 (0.255) (0.096) (0.001) 0.07 (0.530) 4.00 (0.145) 0.62 (0.348) (0.176) (0.001) 0.09 (0.413) 3.84 (0.145) 0.74 (0.282) (0.259) (0.003) 0.10 (0.329) 3.67 (0.169) 0.72 (0.305) (0.256) (0.001) 0.08 (0.452) Contr yes yes yes yes yes yes Pse-R Source Fe0.05 Fe0.05 Fe0.05 Fe0.5 Fe0.5 Fe0.5 Obs

55 Variations with regional effects and time trends Variable [1] [2] [3] [4] [5] [6] P 6.43 (0.006) F 1.59 (0.018) G/N (0.186) gdp (0.002) pop 0.12 (0.377) lag (0.006) 2.31 (0.011) (0.026) (0.012) 0.01 (0.926) (0.005) 1.15 (0.099) (0.293) (0.228) 0.14 (0.458) (0.018) 1.14 (0.064) (0.204) (0.074) 0.19 (0.124) (0.007) 1.17 (0.049) (0.206) (0.045) 0.16 (0.146) (0.006) 1.44 (0.021) (0.154) (0.009) 0.11 (0.391) 3.76 Contr yes yes yes yes yes yes Pse-R Meth Logit Logit Logit Logit Logit Logit Reg/T RegDum Africa Asia L.Am. T T*Reg Obs

56 Variations with other estimation methods Var [1] [2] [3] [4] [5] [6] P 7.46 (0.008) F 1.22 (0.060) G/N (0.251) gdp (0.01) pop 0.22 (0.129) lag (0.004) 1.14 (0.032) (0.179) (0.013) 0.16 (0.178) (0.039) 0.08 (0.047) (0.495) (0.006) 0.02 (0.033) (0.083) 0.06 (0.358) 0.00 (1.000) (0.635) 0.02 (0.003) (0.001) 1.70 (0.018) (0.106) (0.021) 0.14 (0.402) (0.005) 2.16 (0.007) (0.324) (0.002) 0.24 (0.180) Contr yes yes yes GDP instr yes yes Pse-R Meth RE PA RC 2SLS Logit O. Logit Obs

57 Heterogeneity in λ and α across countries. alph constructed from WVS. lam = public*gdp public*gdp + oil/pop. Variable prio25 priocw prio1000 prio-int P *lam*alph (0.005) F *(1-lam)*alph 5.27 G/N*10 6 *lam*(1-alph) 5.99 (0.92) gdp pop 0.80 (0.580) lag (0.055) (0.743) (0.854) 0.25 (0.107) (0.428) (0.948) (0.636) 0.10 (0.530) (0.004) (0.486) (0.009) 0.02 (0.880) 1.38 Contr Yes Yes Yes Yes Pseu-R Method Logit Logit Logit Logit Obs

58 Distances: linguistic vs binary Variable [1] [2] [3] [4] P 4.49 (0.069) F 0.48 (0.443) G/N (0.614) R 6.83 (0.004) gdp (0.006) pop 0.28 (0.006) lag (0.309) (0.284) 4.83 (0.062) (0.009) 0.22 (0.043) (0.113) 0.32 (0.741) (0.800) (0.071) 0.27 (0.007) (0.001) 1.09 (0.055) (0.283) (0.116) (0.058) 0.23 (0.018) 3.74 Pseu-R Method Logit Logit Logit Logit Source F E(δ = 0.05) F E(δ = 0.05) ET H(δ = 0.05) ET H(δ = 0.05) Obs

59 Summary Conflicts of inclusion and exclusion just as important as class conflict, maybe more. Often made salient by the use of ethnicity or religion. Do societies with ethnic divisions experience more conflict? We develop two theories of conflict and distribution: axiomatic, behavioral Both point the finger at polarization as determinant of conflict. Theory appears to find strong support in the data.