By Matija Kovacic and Claudio Zoli. Fondazione Eni Enrico Mattei (FEEM) Venice, October 2014

Transcription

1 Ethnic Distribution, Effective Power and Conflict By Matija Kovacic and Claudio Zoli Department of Economics, Ca Foscari University of Venice Department of Economics, University of Verona Fondazione Eni Enrico Mattei (FEEM) Venice, October 2014

2 Introduction Introduction Conflict as Economic Problem: Political Instability, Poor Quality of Institutions, Bad Economic Policies, Disappointing Economic Performance (Alesina et al, 2003 (JEG); Easterly and Levine, 1997 (QJE); Mauro, 1995 (QJE); La Porta et al, 1999) Ethnic Diversity/Conflict Nexus: Ethnic Dimension of Conflict, Three Main Approaches + Climate Change Approach? From Distributional Point of View: Ethnic Fractionalization (Alesina et al, 2003, JEG; Easterly and Levine, 1997, QJE) Ethnic Polarization (Montalvo and Reynal-Querol, 2005, AER) Ethnic Dominance (Collier and Hoeffler, 2004, OEP; Schneider and Wiesehomeier, 2008, JPR)

3 Introduction Problem Still no broad consensus is reached on which distributional aspect of ethnic diversity is associated with conflict, ceteris paribus (Collier and Hoeffler, 2004; Fearon and Laitin, 2003; (APSR); Fearon, Kasara and Laitin, 2007, (APSR); Hegre and Sambanis, 2006, (JCR); Sambanis, 2004, (JCR); Montalvo and Reynal-Querol, 2005, (AER); Cederman and Girardin, 2007, (APSR); Cederman, Min and Wimmer, 2009, (ASR)) Why should some aspects of diversity be related to instability? Recent contributions: Esteban and Ray, 2011 (AER), Esteban, Mayoral and Ray, 2012 (AER) Possible Explanation: The relevance of each distributional aspect depends on the features of the population distribution across ethnic groups Possible Solution: A measure that weights different distributional aspects according to specific features of ethnic distribution

4 The Aim of This Paper The Aim of This Paper Question: Are distributional aspects of ethnic diversity important (if yes, which one?) or conflict is driven exclusively by other forces? Starting Point: Esteban and Ray s (1994) [ER] approach to social antagonism and conflict: Alternative Definition of Groups Power, Groups may form coalitions Finish Line: Parametric Class of Indices of Conflict Potential (general in nature), Role of groups Power and Between-Groups Interaction in the determination of Conflict Potential, Empirical Investigation of the relationship between the derived indices and the onset of (ethnic) conflict

5 Starting Point Starting Point: ER (1994) Social Antagonism n 2 number of groups Let π i > 0 be group i s population share; i π i = 1; Π = (π 1, π 2,, π n ) ER conceptualize social antagonism (that arise from income polarization) as: ER(Π) = K i π i π j T (π i, D ij ) j i where groups and between-groups distances, D ij, are defined in terms of income y i > 0, i Function T (π i, D ij ) measures the Effective Antagonism felt by i towards j and is defined as: T (π i, D ij ) = π α ER i y i y j ; α ER (0, 16]

6 Starting Point Antagonism derives from alienation which is given by y i y j, and it becomes effective once it is translated into voicing or protest How efficient groups are to do this is captured by π α ER i where α ER is the polarization sensitivity parameter If we assume D ij = 1 if i j and D ij = 0 if i = j, then: ER αer (Π) = K i π 1+α ER i (1 π i ) which is a discrete version of ER(Π) Total social antagonism (or conflict potential) is given as a product of two components: Power component, π α ER i, Interaction component, π i (1 π i )

7 Starting Point Using ethnic (or religious) instead of income attributes to define groups, and imposing α = 1, ER αer (Π) reduces to the RQ index of Discrete Ethnic (Religious) Polarization (Montalvo and Reynal-Querol, 2002, 2005): RQ(Π) = K i π 2 i (1 π i ) For K = 4, the index ranges between 0 and 1 Power associated to each group is given by π i for all i Groups power does not depend on n and Π i In terms of probability, the RQ index can be interpreted as the probability that out of three randomly selected individuals, two of them belong to the same group RQ attains its maximum at symmetric bimodal distribution

8 Starting Point For α = 0, K = 1 and ethnicity (religion or language) as a criteria to define groups, ER αer (Π) reduces to the Gini s Heterogeneity Index (Gini, 1912) or Ethnic (Religious, Ethno-Linguistic) Fractionalization Index: F (Π) = i π i (1 π i ) The Power of each group is constant and normalized to 1, hence, independent of π i and n The index is defined as the probability that two randomly selected individuals belong to different ethnic groups F (Π) assumes an increasing relationship between fractionalization/fragmentation and conflict vulnerability

9 Basic Specification : Basic Specification Starting from ER, we define a function Φ that combines the group s effective power with the alienation felt towards others: P (Π) = i π i π j Φ(π i, Π, ˆD ij ) j i In order to define ˆD ij, we use discrete metric: { Dˆ 0 if i = j, ij = 1 if i j Assume Φ(Π, π i, 0) = 0 and let φ(π i, Π) := Φ(Π, π i, 1) with φ not necessarily continuous in π i The P index becomes: P (Π) = K i φ(π i, Π) π i (1 π i )

10 Axiomatic Derivation of the Effective Power Function Axiomatic Derivation of the Effective Power Function Group i s Effective Power is defined as: φ n (π i, Π) : [0, 1] n R + Axiom 1: Normalization φ n (π i, Π) = 1, i = 1,, n i Axiom 2: Monotonicity φ n (π i, Π) φ n (π j, Π) if π i π j, i, j; i j

11 Effective Power Function - Case 1: Two Groups Case 1 Two Groups Given Π = (π, 1 π), π > 0, we define the Relative Effective Power between groups r(ρ) as: φ 2 (π) π φ 2 = r(ρ) where ρ = (1 π) 1 π is the groups Relative Population Size Axiom 3: Two Groups Relative Power Homogeneity (2GRPH) Given Π and Π, let π, π < 1/2 ρ, ρ < 1 Then, if r(ρ), r(ρ ) 0: r(λρ) r(ρ) = r(λρ ) r(ρ ) = r(λ); ρ, ρ < 1, λ > 0 st λρ, λρ < 1

12 Effective Power Function - Case 1: Two Groups Lemma 1 Given n = 2, the Effective Power of a group with population share π satisfies Normalization, Monotonicity and 2GRPH, iff: where φ 2 (π) = φ 2 α(π) for α R +, π α φ 2 α := π α for α 0, and + (1 π) α 1 if π > 1/2, φ 2 := 1/2 if π = 1/2, 0 if π < 1/2 Analogies with Contest Function (Tullock, 1967, 1980; Skaperdas, 1996, ET)

13 Effective Power Function - Case 1: Two Groups Figure 1: Effective Power Function as a function of α; n = Α Α = 6 Α = 2 Α = 1 Α = α measures the elasticity of the relative effective power wrt relative population size

14 Effective Power Function - Case 2: Arbitrary Number of Groups Case 2 Any arbitrary Number of Groups Two Crucial Assumptions: A1 Groups are allowed to form coalitions with other groups A2 We consider only bipartitions of the populations Important: we do not assume any endogenous mechanism of coalition formation - symmetric distribution Let C i be the set of all coalitions c, st i c Since we consider only bipartitions, the effective power of a coalition c C i is (Lemma 1): φ 2 (c) = φ 2 ( j c π j )

15 Effective Power Function - Case 2: Arbitrary Number of Groups The marginal contribution of group i to the worth of a coalition c is (Shapley, 1953): m i (c) = φ 2 ( j c π j ) φ 2 ( j c π j π i ) The sum of marginal contributions over all coalitions group i can theoretically belong to is: M i = c C i m i (c) The effective power of any group i is a function of M i, such that the following two axioms are satisfied:

16 Effective Power Function - Case 2: Arbitrary Number of Groups Axiom 4: The Relative Effective Power between any i and j For any i, j N, i j and n 2; g : R + R + such that for φ n > 0 we have: φ n (π i, Π) φ n (π j, Π) = g(m i) g(m j ) Axiom 5: n Groups Relative Power Homogeneity (ngrph) Given Π and Π with the same n, n 2, if φ n (π j, Π) > 0 then: M i M j = M i M j φn (π i, Π) φ n (π j, Π) = φn (π i, Π ) φ n (π j, Π )

17 Effective Power Function - Case 2: Arbitrary Number of Groups Theorem 1 The Effective Power of group i satisfies Axioms 1-5 if and only if: φ n (π i, Π) = M α i j M α j, i, j N; i j; α R + where Mi α is obtained making use of φ 2 α(c) Group i s effective power is defined as the relative sum of marginal contributions Finally, the P index of conflict potential is: P n α (Π) = K i M α i j M α j π i (1 π i ); α R +

18 Different α : Different α Case 1: α = 0 When α = 0, the effective power of each group is constant and equal to 1/n The P Index of Potential Conflict becomes: P0 n (Π) = 4 1 π i (1 π i ) = 4 1 n n F (Π) When all groups have the same size: i P0 n (Π) = 4 1 n 1 n n Not exactly the Fractionalization Index, but scaled by 4/n For a given n - same ranking order as F (Π)

19 Different α Case 2: α = 1 When α = 1, the Effective Power of groups equals their respective population shares Hence, the P index reduces to the RQ index of discrete ethnic polarization: P n 1 (Π) = 4 n πi 2 (1 π i ) i=1 Hence, for the cases of α = 0 and α = 1, the groups Effective Power depends, respectively, only on n and π i and not on Π i For any α 0 and α 1, φ(π i, Π) is a function of both π i and Π i, for all i N

20 Different α Case 3A: α Effective Power of groups converges to their respective Relative Penrose-Banzhaf Index of voting power (β) in a simple majority game (L Penrose, 1946; JF Banzhaf, 1956) 4π (1 π ) if π > 1/2, P (Π) n = 1 θ n (1 P0 n(π)) if π = 1/2, where 4 i β iπ i (1 π i ) if π < 1/2 θ n = n 2 n 1 + n 2 and π indicating the relative size of the largest group Value function (Lemma 1), however, different from Penrose-Banzhaf algorithm - parity condition

21 Different α Case 3B: α ; n = 3 4π (1 π ) if π > 1/2, P (Π) 3 2 = P 0 3(Π) if π = 1/2, P0 3(Π) if π < 1/2 With n > 3 and π < 1/2, the PB Voting Power is not equal to 1/n: Π = (034, 031, 02, 015) 1/3, 1/3, 1/3, 0 Π = (045, 025, 02, 01) 1/2, 1/6, 1/6, 1/6 Π = (025, 025, 025, 025) 1/4, 1/4, 1/4, 1/4

22 Example: 3 Groups, Different α Example: Three Groups We consider the case of 3 groups because: With n = 2 all the indices are the same, RQ index is insensitive to population transfers when π i = 1/3 for some i, With π i fixed for some i, the indices can be expressed as a function of the relative size of only one group ( i π = 1) Relative size of one group is fixed to 1/3: We want to compare alternative population distributions with the uniform distribution Figure 2: P Index for α = 0, α = 1, and the extreme element α

23 Example: 3 Groups, Different α Figure 2: P Index for α = 0 (green), α = 1 (red) and α (blue) 100 Α Α = Α Α =

24 Figure 3: P index for α = 0 (green), α = 1 (red) and α > 1 (blue)

25 Ethnic Diversity and Conflict: An Empirical Investigation Ethnic Diversity and Conflict: An Empirical Investigation Sources of Data: Ethnic Power Relations Data Set - EPR (Cederman, Min and Wimmer, 2009) Estimation Method: Logistic Regression, Rare Event Logistic Regression, Random Effect Logistic Regression Dependent Variables: Ethnic conflict Onset ( 25 battle-death [BD]), Low and Intermediate Intensity Ethnic conflict Onset (25 BD < 1000) Explanatory Variables: Fearon and Laitin (2003); Hegre and Sambanis (2006); Cederman, Min and Wimmer (2009, 2010) Robustness Checks: Time and Regional Controls, Dummy Variables for Dominance, Ethnic Exclusion and Political Competition Variables

26 Features of ED do matter if properly combined into one single measure Among all diversity indices, only the P n is significantly different from 0 Moreover, the goodness of fit increases with α: the highest value is obtained for α Dominance Dummy Variables lose significance when included with P n in the regression If P n increases from the average to the maximum value, the probability of conflict increases by 8131% compared to 3942% for the RQ index; 1SD P n + 52% and RQ + 23% The results are robust to the inclusion of political exclusion and competition variables, regional and time controls as well as different estimation techniques Analogous results for the Low and Intermediate Intensity Ethnic Conflicts Ethnic Distribution, Effective Power and Conflict Ethnic Diversity and Conflict: An Empirical Investigation Results

27 Ethnic Diversity and Conflict: An Empirical Investigation Regression Results: Ethnic Conflict Onset - Baseline Model EW Onset Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 Gdp/L -0128*** -0129*** -0132*** -0121*** -0125*** -0128*** -0132*** -0135*** Population 0389*** 0389*** 0389*** 0363*** 0375*** 0383*** 0390*** 0405*** Democracy Anocracy 0569** 0571** 0560** 0541** 0552** 0562** 0561** 0580** Oil/L Mountains 0186** 0186** 0192** 0202** 0189** 0187** 0192** 0225** Instability NC State New State 2167*** 2165*** 2194*** 2211*** 2180*** 2171*** 2194*** 2254*** RQ 1335** P(α = 2) 1560** P(α ) 1750*** 1766** 4218*** FRAC Constant *** *** *** *** *** *** *** *** Time Controls Yes Yes Yes Yes Yes Yes Yes Yes Reg Dummies Yes Yes Yes Yes Yes Yes Yes Yes N Observations N Countries Pseudo R Wald Chi *** *** *** *** *** *** *** *** Bic Aic

28 Figure 4: P versus RQ - number of conflict onsets P Index with PB Power, Averaged by Country Discrete Polarization Index (RQ), Averaged by Country

29 Figure 5: Pseudo R 2 as a function of α Pseudo R Squared Value of the Coefficient Alpha

30 Ethnic Conflict Onset - Exclusion and Competition EW Onset Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Gdp/L -0142*** -0142*** -0142*** -0142*** -0141*** -0140*** -0141*** Population 0359*** 0363*** 0379*** 0354*** 0361*** 0369*** 0394*** Excl Pop 0341*** 0326*** 0312*** 0362*** 0355*** 0354*** 0364*** Center Segm 0118*** 0116*** 0113*** 0114** 0138*** 0158*** 0177*** Imperial Past Democracy Anocracy Oil/L 0017** 0017** 0016** 0017** 0018** 0019** 0020** Mountains ** Instability NC State New State 2331*** 2324*** 2323*** 2354*** 2325*** 2312*** 2315*** EEurope*Y 0100*** 0100*** 0102*** 0098*** 0099*** 0100*** 0102*** RQ P(α = 2) P(α ) 1465** 2253*** FRAC Time Controls Yes Yes Yes Yes Yes Yes Yes Reg Dummies Yes Yes Yes Yes Yes Yes Yes Reg Time Trend Yes Yes Yes Yes Yes Yes Yes N Observations Pseudo R Wald Chi *** *** *** *** *** *** *** Bic Aic

31 Ethnic Conflict Onset - Dominance Dummies Logit EW Onset Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 Gdp/L -0150*** -0145*** -0142*** -0145*** -0143*** -0144*** -0144*** -0142*** Population 0453*** 0429*** 0416*** 0402*** 0433*** 0412*** 0409*** 0364*** Democracy Anocracy 0635*** 0605** 0588** 0566** 0642*** 0615** 0605** 0572** Oil/L 0016** 0015** ** 0017** 0016** 0016** Mountains 0170** 0164** 0178** ** 0182** 0193** 0196** Instability NC State New State 2160*** 2150*** 2178*** 2175*** 2180*** 2161*** 2190*** 2203*** CH (45-90%) 0614** *** SW (60-90%) ** RQ ** P(α ) 1428** 1717*** FRAC 1742** 2219*** Constant *** *** *** *** *** *** *** *** Time Controls Yes Yes Yes Yes Yes Yes Yes Yes Reg Dummies Yes Yes Yes Yes Yes Yes Yes Yes N Observations N Countries Pseudo R Wald Chi *** *** *** *** *** *** *** *** Bic Aic

32 Open Research Questions: Climate change and conflict? Climate Change and Conflict Nexus - as in the case of ethnic diversity NO consensus on empirical findings (Raleigh and Urdal, 2007; Theisen, 2008; Theisen, 2013; Buhaug and Theisen, 2012) One possible reason: Focus on groups and Across groups dynamics, rather than pure aggregates It is not the overall level of resource scarcity and/or natural disasters that matters - relative rather than aggregate impact + (interest) groups power (direct link to institutions and governance) (only in part in Butler and Gates, no empirics) A distributional approach to conflict (Kovacic, 2014): Ethnic, Political and Resource Distribution Groups Power versus Across-Groups Interaction