Lectures on Economic Inequality

Transcription

1 Lectures on Econoic Inequality Warwick, Suer 208, Slides 4 Debra Ray Inequality and Divergence I. Personal Inequalities, Slides and 2 Inequality and Divergence II. Functional Inequalities, Slides 3 Inequality and Conflict I. Polarization and Fractionalization, Slides 4 Inequality and Conflict II. Soe Epirical Findings Inequality and Conflict III. Towards a Theory of Class Conflict Slides 4. Inequality and Conflict: Polarization and Fractionalization Uneven Growth: Roots Technological change Structural transforation Globalization

2 Slides 4. Inequality and Conflict: Polarization and Fractionalization Uneven Growth: Roots Technological change: (leading to ups in inequality, only slowly eroded) Structural transforation Globalization Slides 4. Inequality and Conflict: Polarization and Fractionalization Uneven Growth: Roots Technological change Structural transforation: (agriculture! industry, anufacturing! services) Globalization

3 Slides 4. Inequality and Conflict: Polarization and Fractionalization Uneven Growth: Roots Technological change Structural transforation Globalization: (sectors with coparative advantage) Slides 4. Inequality and Conflict: Polarization and Fractionalization Uneven Growth: Roots Technological change Structural transforation Globalization Reactions Occupational choice Cross-sector percolation Political econoy Conflict

4 Slides 4. Inequality and Conflict: Polarization and Fractionalization Uneven Growth: Roots Technological change Structural transforation Globalization Reactions Occupational choice: (slow, iprecise, intergenerational) Cross-sector percolation Political econoy Conflict Slides 4. Inequality and Conflict: Polarization and Fractionalization Uneven Growth: Roots Technological change Structural transforation Globalization Reactions Occupational choice Cross-sector percolation: (deand patterns, inflation) Political econoy Conflict

5 Slides 4. Inequality and Conflict: Polarization and Fractionalization Uneven Growth: Roots Technological change Structural transforation Globalization Reactions Occupational choice Cross-sector percolation Political econoy: (lobbying for tax breaks, favored allocations) Conflict Slides 4. Inequality and Conflict: Polarization and Fractionalization Uneven Growth: Roots Technological change Structural transforation Globalization Reactions Occupational choice Cross-sector percolation Political econoy Conflict (this lecture)

6 The Backlash Against Uneven Growth The lives of others on display (on an accelerating treadill) Aspirations and frustrations are socially generated. Unclear if this exposure leads to betterent or to despair. Hirschan s Tunnel

7 Internal Social Conflict 60 Ared Conflict by Type, Extrastate Interstate Internationalized intrastate Intrastate No. of Conflicts Internal Social Conflict 60 Ared Conflict by Type, Extrastate Interstate Internationalized intrastate Intrastate 50 No. of Conflicts WWII! 2000: 240 intrastate ared conflicts: Battle deaths 5 0 (3 8 for interstate) Mass assassination (25 civilians), forced displaceent (60 civilians) In 205: 29 ongoing conflicts. UCDP/PRIO definition: ared conflict, 25+ yearly deaths.

8 Maority of Internal Conflicts are Ethnic , 00 of 700 known ethnic groups participated in rebellion against the state. Fearon 2006 [T]he eclipse of the left-right ideological axis. Brubaker and Laitin (998) In uch of Asia and Africa, it is only odest hyperbole to assert that the Marxian prophecy has had an ethnic fulfillent. Horowitz 985 Ethnicity or Class? One of the great questions of political econoy: It isn t that the Marxian view is entirely irrelevant, but... Econoic siilarity appears to atter as uch or even ore. Conflict is usually over directly contested resources: land, obs, business resources, governent quotas... The iplications of direct contestation: Ethnic arkers. Instruentalis as opposed to priordialis (Huntington, Lewis)

9 Do Ethnic Divisions Matter? Two ways to approach this question. Historical study of conflicts, one by one. Bit of a wood-for-the-trees proble. Horowitz (985) suarizes soe of the coplexity: In dispersed systes, group loyalties are parochial, and ethnic conflict is localized... A centrally focused syste [with few groupings] possesses fewer cleavages than a dispersed syste, but those it possesses run through the whole society and are of greater agnitude. When conflict occurs, the center has little latitude to placate soe groups without antagonizing others. Statistical approach (Collier-Hoeffler, Fearon-Laitin, Miguel-Satyanath-Sergenti) Typical variables for conflict: deonstrations, processions, strikes, riots, casualties and on to civil war. Explanatory variables: Econoic. per-capita incoe, inequality, resource holdings... Geographic. ountains, separation fro capital city... Political. deocracy, prior war... And, of course, Ethnic. But how easured?

10 Inforation on ethnolinguistic diversity fro: World Christian Encyclopedia Encyclopedia Britannica Atlas Narodov Mira CIA FactBook Or religious diversity fro: L Etat des Religions dans le Monde World Christian Encyclopedia The Statesan s Yearbook Fractionalization Fractionalization index widely used: F = Â n ( n ) where n is population share of group. Special case of the Gini coefficient G = M Â Â k= n n k d ik where d ik is a notion of distance across groups.

11 Fractionalization used in any different contexts: growth, governance, public goods provision. But it shows no correlation with conflict. Collier-Hoeffler (2002), Fearon-Laitin (2003), Miguel-Satyanath-Sergenti (2004) Fearon and Laitin (APSR 2003): The estiates for the effect of ethnic and religious fractionalization are substantively and statistically insignificant... The epirical pattern is thus inconsistent with... the coon expectation that ethnic diversity is a aor and direct cause of civil violence. And yet... fractionalization does not see to capture the Horowitz quote. Motivates the use of polarization easures. The Identity-Alienation Fraework Society is divided into groups (econoic, social, religious, spatial...) Identity. There is hoogeneity within each group. Alienation. There is heterogeneity across groups. Esteban and Ray (994) presued that such a situation is conflictual: We begin with the obvious question: why are we interested in polarization? It is our contention that the phenoenon 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...

12 Measuring Polarization Space of densities (cdfs) on incoe, political opinion, etc. Each individual located at incoe x feels Identification with people of siilar incoe (the height of density n(x) at point x.) Alienation fro people with dissiilar incoe (the incoe distance y fro x.) x of y Effective Antagonis of x towards y depends on x s alienation fro y and on x s sense of identification. T (i,a) where i = n(x) and a = x y. View polarization as the su of all such antagoniss Z Z P( f )= T (n(x), x y ) n(x)n(y)dxdy Not very useful as it stands. Axios to narrow down P. Based on special distributions, built fro unifor kernels. Incoe or Wealth

13 Axio. If a distribution is ust a single unifor density, a global copression cannot increase polarization. Incoe or Wealth Axio 2. If a syetric distribution is coposed of three unifor kernels, then a copression of the side kernels cannot reduce polarization. Incoe or Wealth

14 Axio 3. If a syetric distribution is coposed of four unifor kernels, then a syetric slide of the two iddle kernels away fro each other ust increase polarization. Incoe or Wealth Axio 4. [Population Neutrality.] Polarization coparisons are unchanged if both populations are scaled up or down by the sae percentage. Theore. A polarization easure satisfies Axios 4 if and only if it is proportional to Z Z n(x) +a n(y) y x dydx, where a lies between 0.25 and. Copare with the Gini coefficient / fractionalization index: Z Z Gini = n(x)n(y) y x dydx, It s a that akes all the difference.

15 Soe Properties. Not Inequality. See Axio Biodal. Polarization axial for biodal distributions, but defined of course over all distributions. 3. Contextual. Sae oveent can have different iplications. Density Incoe Soe Properties. Not Inequality. See Axio Biodal. Polarization axial for biodal distributions, but defined of course over all distributions. 3. Contextual. Sae oveent can have different iplications. Density Incoe

16 More on a Z Z Pol = n(x) +a n(y) y x dydx, where a lies between 0.25 and. Axio 5. If p > q but p cannot reduce polarization. q is sall and so is r, a sall shift of ass fro r to q r p q 2ε 2ε 2ε 0 a 2a Theore. Under the additional Axio 5, it ust be that a =, so the unique polarization easure that satisfies the five axios is proportional to Z Z n(x) 2 n(y) y x dydx. Easily applicable to ethnolinguistic or religious groupings. Say social groups, n is population proportion in group. If all inter-group distances are binary, then Pol = M M Â Â k= n 2 n k = M Â n 2 ( n ). Copare with F = M Â n ( n ).

17 Polarization and Conflict: Behavior Axioatics suggest (but cannot establish) a link between polarization and conflict. Two approaches: Theoretical. Write down a natural theory which links conflict with these easures. Epirical. Take the easures to the data and see they are related to conflict. We discuss the theory first (based on Esteban and Ray, 20). A Theory that Infors an Epirical Specification groups engaged in conflict. n i : population share of group i, Â i= n i =. Public prize: payoff atrix [ pu i ] scaled by per-capita size p. (religious doinance, political control, hatreds, public goods) Private prize µ per-capita budget, so µ/n i if captured by group i. Oil, diaonds, scarce land

18 Theory, contd. Individual resource contribution r at convex utility cost c(r). (ore generally c(r,y i )). R i is total contributions by group i. Define R = Â i= R i. Probability of success given by p = R R R our easure of overall conflict. Payoffs (per-capita) pu ii + µ/n i (in case i wins the conflict), and pu i (in case wins). Net per-capita payoff to group i is µ Â p pu i + p i c(r i ). n i pub priv cost

19 Contributing to Conflict Assue group leader chooses r i to axiize group per-capita payoff: µ Â p pu i + p i c(r i ). n i Alternative: individuals ax cobination of own and group payoff. Equilibriu: Every group leader unilaterally axiizes group payoffs. Theore. An equilibriu exists. If c 000 (r) 0, it is unique. µ Â p pu i + p i c(r i ). n i

20 ( l) Â p lu i + p i n i where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i. " n i R v ii n iâ n r R 2 v i # = p + µ c0 (r i )

21 where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i. n i R " v ii  # n r R v i = p + µ c0 (r i ) where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i. n i R r i " v ii  n r R v i # = p + µ r ic 0 (r i )

22 where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i. # p i "v ii = p + µ r ic 0 (r i ) where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i. Â p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then Âg i g n i n D i = p + µ r ic 0 (r i )

23 where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i. Â p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then Âg i g n 2 i n D i = p + µ r in i c 0 (r i ) where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i. Â p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then Âg i g n 2 i n D i = R r i n i p + µ R c0 (r i )

24 where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i. Â p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then Âg i g n 2 i n D i = R p + µ p ic 0 (r i ) where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i. Â p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then Âg i g n 2 i n D i = R p + µ p ic 0 (g i R)

25 where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i.  p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then  g i g c 0 (g i R) c 0 n 2 i n D i = (R) R p + µ p ic 0 (R) where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i.  p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then where f(g i,g,r)= g ig c 0 (g i R) c 0. (R) Âf(g i,g,r)n 2 i n D i = R p + µ p ic 0 (R)

26 where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i.  p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then  i  where f(g i,g,r)= g ig c 0 (g i R) c 0. (R) f(g i,g,r)n 2 i n D i =  i R p + µ p ic 0 (R) where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i.  p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then  i where f(g i,g,r)= g ig c 0 (g i R) c 0. (R) Âf(g i,g,r)n 2 i n D i = Rc0 (R) p + µ

27 where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i.  p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then  i Ân 2 i n D i ' Rc0 (R) p + µ Approxiation. where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i.  p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then  i  n 2 i n ld i + i  n 2 i n 6=i n i l ' Rc0 (R) p + µ Opening up D i and defining d i = u ii u i.

28 where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i.  p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then l  i Ân 2 i n d i +( l)â i  n i n ' Rc0 (R) 6=i p + µ Opening up D i and defining d i = u ii u i. where v ii = lu ii +( l)(/n i ) and v i = lu i if 6= i.  p i p D i = p + µ r ic 0 (r i ) where D i = v ii v i. Define g i = p i /n i. Then l  i Ân 2 i n d i +( l)ân i ( i n i ) ' Rc0 (R) p + µ Opening up D i and defining d i = u ii u i.

29 Approxiation Theore Theore 2. R approxiately solves Rc 0 (R) p + µ = lp +( l)f, where l p/(p + µ) is relative publicness of the prize. P is squared polarization:  i  n 2 i n d i F is fractionalization:  i n i ( n i ). Note: Theore is ore coplex with individual contributions. Polarization and Fractionalization With n i = /, P axed at = 2, F increases in : $"!#,"!#+"!#*"!#)" $" %" &" '" (" )" *" +"," $!" $$" $%" $&" $'" $(" $)" $*" $+" $," %!" -./02"34"523.67"

30 How Good is the Approxiation? Holds exactly when there are ust two groups and all goods are public. Holds exactly when all groups the sae size and public goods losses are syetric. Holds alost exactly for contests when conflict is high enough. Can nuerically siulate to see how good the approxiation is. Contests, quadratic costs, large populations, l various:

31 Distances, quadratic costs, large populations, l various: Sall populations, l various:

32 Nonquadratic costs, large populations, l various: Suary Ethnic conflicts are widespread. Yet studies that relate conflict to ethnic divisions (as easured by fractionalization) show little or no correlation. In this lecture we approach the proble fro a conceptual perspective: We axioatize a easure of polarization We argue it is different fro fractionalization We argue that both polarization and fractionalization should enter the conflict equation. We argue that the polarization-conflict nexus is strong when the prize is private, and the fractionalization-conflict nexus is strong when the prize is private. For another parallel exercise with group size, see Suppleent to these slides.