THE ORIGINS OF INEQUALITY: Insiders, Outsiders, Elites, and - - PDF document

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THE ORIGINS OF INEQUALITY: Insiders, Outsiders, Elites, and Commoners Gregory K. Dow (gdow@sfu.ca) Clyde G. Reed (reed@sfu.ca) Department of Economics Simon Fraser University November 2009

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INTRODUCTION We explore the prehistoric origins of economic inequality. Hereditary inequality is unknown among mobile hunter- gatherers (although some differences in work tasks and food consumption based on age and sex do exist). Sedentary foraging societies are a mixed bag. Some are largely egalitarian, but others have hereditary inequality, both across and within communities. Agriculture is not a necessary condition for inequality, but it often does lead to more pronounced stratification, which is usually based on elite control over land. For evidence, see Kelly (1995), Johnson and Earle (2000), and many others.

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Our model focuses on food. Inequality means differences across groups and individuals in food consumption. More generally: quantity, quality, variety, reliability. More generally still: the material standard of living. We do not address political power or social status, but in early societies these dimensions of inequality were clearly correlated with economic inequality. The key exogenous variable: Productivity of labor in food acquisition (determined by nature and technology). The key endogenous variables: Population, property rights, and inequality.

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Our Story in Brief Rising productivity increases regional population density in the long run for Malthusian reasons. The highest local population densities are at the best sites in a region. When the population at a site becomes large enough, the insiders can prevent further entry by outsiders. This leads to insider-outsider inequality across sites (which occurs first at the best sites and then spreads). Further productivity growth eventually makes it profitable for insiders to hire outsiders as food producers. This leads to elite-commoner inequality within sites (which occurs first at the best sites and then spreads). Over time, inequality of both types increases.

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We argue that these predictions are consistent with data from archaeology and anthropology. At the most general level, our theory is consistent with two stylized facts about early societies: (a) Productivity is correlated with population density, both over time and cross-sectionally. (b) Population density is correlated with inequality, both

• ver time and cross-sectionally.

We also argue that our theory is consistent with specific cases: the Channel Islands, the northwest coast of North America, southwest Asia, and Polynesia.

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Outline Introduction The Theoretical Model (part one) The Theoretical Model (part two) Summary of Empirical Implications Four Cases from Archaeology and Anthropology Conclusion

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THE THEORETICAL MODEL (part one) A Production Site With An Exogenous Outside Option At a production site, food output is θsf(L) where θ > 0 reflects regional natural resources/technology; s > 0 reflects the quality of the individual site; and L ≥ 0 is labor time used for food production. The input of land is normalized at unity. A1 The function f is twice continuously differentiable with f(0) = 0; f′(L) > 0 for all L > 0; f′′(L) < 0 for all L > 0; f′(0) = ∞; and f′(∞) = 0. Individual agents are negligible relative to total labor at the site (L). Each agent is endowed with one unit of time. These endowments are used for food production, exclusion

• f outsiders, or some combination of the two (no leisure).

The outside option of an individual agent is w > 0, which is the food available by migration to another site. There is an infinitely elastic supply of outsiders who will enter the site if they are not excluded and can obtain more than w by doing so.

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Insiders who cooperate to prevent land appropriation by

• utsiders are called an elite.

An elite of size e allocates its time between food labor (ef) and guard labor (eg) subject to ef ≥ 0, eg ≥ 0, and ef + eg = e. A2 Given elite food labor ef ≥ 0, the minimum guard labor needed to exclude outsiders is eg = g(ef), where g(0) ≡ eg

0 ∈ (0, ∞). There is some ef 0 ∈ (0, ∞) such that g(ef)

= 0 for all ef ≥ ef

• 0. The function g is twice

continuously differentiable on ef ∈ [0, ef

0) with g′(ef) <

0 and g′′(ef) > 0. See Figure 1. Now consider any time allocation (ef, eg) ∈ E. Available food is shared equally among the members of the elite. Each member receives (1) y(ef, eg) = [max c ≥ 0 θsf(ef + c) - wc]/(ef + eg) where c is the number of commoners admitted to the site. Each member of the elite enjoys the surplus (2) v(ef, eg) = y(ef, eg) - w

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An elite forms at a production site if and only if v(ef, eg) ≥ 0 for some (ef, eg) ∈ E. In this case we say the site is closed. Otherwise it is open. If the elite at a closed site chooses c > 0, we say that the site is stratified. We denote the total population at a site (elite and commoners together) by n = e + c. A3 When a site is closed, the time allocation (ef, eg) maximizes v(ef, eg) subject to (ef, eg) ∈ E. The commoner population is determined as in (1). When a site is open, there is no elite and the commoner population satisfies θsf(c)/c = w. At open sites, no set of agents can gain by excluding others. There is entry into the site if food per capita is above w and exit if food per capita is below w.

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Proposition 1 (existence and uniqueness). Define z = θs/w > 0. For a closed site there is a unique elite and commoner time allocation ef(z) ∈ [0, ef

0], eg(z) = g[ef(z)], and c(z)

≥ 0. Time allocation at a closed site depends only on the ratio of productivity (θs) to the outside option (w) at that site.

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Proposition 2 (open sites). There is an A > 0 such that the site is open for z ∈ (0, A) and closed for z ∈ [A, ∞). For an open site there is a unique c(z) ≡ n(z) > 0 that is continuous and increasing on (0, A). We have c(z) → 0 as z → 0 and define c(0) ≡ 0. We also have c(z) → c-(A) as z → A from below, where c-(A) uniquely satisfies Af[c-(A)]/c-(A) ≡ 1. Proposition 2 shows that for low values of z ≡ θs/w, the site is in the commons. As site quality rises, population rises. The site becomes closed at z = A.

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Proposition 3 (closed and unstratified sites). The functions ef(z), eg(z), e(z), c(z), and n(z) are continuous on (A, ∞). These functions are right continuous at z = A. There is a B > A such that the site is closed and unstratified for z ∈ [A, B], and stratified for z ∈ (B, ∞). Thus c(z) = 0 on [A, B] and c(z) > 0 on (B, ∞). There is some constant ef

A > 0 such that ef(z) = ef A on

[A, B]. Let η ≡ ef

0f′(ef 0)/f(ef 0) be the output elasticity at ef 0,

where η ∈ (0, 1). (a) If 1 + g′(ef

0) ≤ η then ef A = ef 0 and c-(A) = e(A) so that

n(z) is continuous at the boundary z = A (see Figure 2a). (b) If η < 1 + g′(ef

0) then ef A < ef 0 and c-(A) > e(A) so that

n(z) drops discontinuously at the boundary z = A (see Figure 2b). For intermediate values of z ∈ [A, B] a site is closed but not yet stratified. A commoner class arises for B < z.

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Proposition 4 (closed and stratified sites). (a) If 1 + g′(ef

0) ≤ 0 then ef(z) = ef 0 for all z ∈ [B, ∞).

(b) If 0 < 1 + g′(ef

0) < η there are C, D with B < C < D ≤

∞ such that ef(z) = ef

0 for z ∈ [B, C] and ef(z) is

decreasing on [C, D]. If g′(0) ≤ -1 then D = ∞. If -1 < g′(0) then D < ∞ and ef(z) = 0 for all z ∈ [D, ∞). (c) If 1 + g′(ef

0) = η then C = B with ef(C) = ef

• 0. All other

results are as in (b). (d) If η < 1 + g′(ef

0) then C = B with ef(C) = ef A < ef

• 0. All
• ther results are as in (b).

(e) In (b), (c), and (d), eg(z) is increasing on [C, D] and e(z) is decreasing on [C, D]. In all cases, c(z) and n(z) are increasing on [B, ∞). In (a), the site never moves away from the corner solution (ef

0, 0) for any value of z because the cost of guard labor (in

foregone food output) is always too large. In the other cases, as z increases the elite begins to contract for C < z. This is accompanied by a gradual decline in elite food labor and a rise in guard labor. Total population rises due to a more than compensating increase in commoners. Eventually the elite may specialize in guard labor and rely entirely on food produced by commoners.

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THE THEORETICAL MODEL (part two) Regional Inequality With An Endogenous Outside Option This section studies inequality in a region with a continuum

• f production sites.

Site quality is s ∈ [0,1] where the number of sites of quality s is given by the density function q(s) > 0. Mobility is costless within the region, but agents cannot leave the region (deserts, mountains, ocean). The outside option (w) at one site depends on the food that can be obtained from migration to another site.

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Terminology Food per capita for the elite (y) is called luxury. Food per capita for commoners (w) is called the wage. The surplus v = y - w is called inequality. In practice, a variety of economic institutions could be used by elites to extract surplus from commoners. We assume that the elite owns land and pays commoners a wage, but the same economic outcomes could be obtained in other ways. Our central result is that increased region-wide productivity leads to more inequality at every closed site. Productivity growth also leads to more closed sites and more stratified sites.

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Population Time is discrete. In period t, the total adult population for the region is Nt. Each individual adult in period t has children who survive to become adults in period t+1. The number of such children is equal to the parent's food income multiplied by a constant γ > 0 (all adults identical). Children of richer parents are more likely to survive to adulthood, children are a normal good, or both. The aggregate number of new adults in any period t+1 is γYt where Yt is regional food output in period t. A constant fraction δ > 0 of the adult population dies in each period after their children are born. Thus Nt+1 = (1-δ)Nt + γYt. In a long run equilibrium Y/N = δ/γ ≡ β (Malthusian).

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The long run equilibrium condition can be written as (3) ∫0

1 θsf[ef(xs) + c(xs)]q(s)ds = β ∫0 1 n(xs)q(s)ds

where x ≡ θ/w ∈ (0, ∞) Earlier, the population at a site with z = θs/w was denoted by n(z). Here x ≡ θ/w is the region-wide ratio of productivity to the wage, so z = xs. The population density at a typical site of quality s is n(xs).

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Property Rights Two break points in the distribution of site qualities: (4) a(x) ≡ A/x and b(x) ≡ B/x From Propositions 2 and 3, a site is open if s ∈ [0, a(x)); closed but unstratified if s ∈ [a(x), b(x)]; and both closed and stratified if s ∈ (b(x), 1]. Proposition 5 (existence). For each θ > 0 there is at least one w > 0 satisfying (3). There are no solutions to (3) such that w > β. For θ ≤ βA, w = β satisfies (3). For θ > βA, any solution to (3) has w < β. We would like to use equation (3) to obtain a relationship between the exogenous productivity θ and the endogenous wage level w.

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In practice, it is easier to treat θ and w as functions of x. Condition (3) gives (6) θ = ϕθ(x) ≡ βN(x)/Y(x) and w = ϕw(x) ≡ βN(x)/xY(x) where N(x) ≡ ∫0

1 n(xs)q(s)ds

and Y(x) ≡ ∫0

1 sf[ef(xs) + c(xs)]q(s)ds.

As shown in Figure 3, a ray from the origin in (θ, w) space has slope 1/x, so each ray is associated with a unique point [ϕθ(x), ϕw(x)] from (6). This point must satisfy condition (3) and no other point on the same ray can do so.

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Proposition 6 (inequality). Consider any two equilibria (θ1, w1) and (θ2, w2) and any site quality s such that the site is closed in both equilibria. Denote the corresponding levels of luxury and inequality at the site by (y1, v1) and (y2, v2). If θ1 < θ2 and x1 < x2 then y1 < y2 and v1 < v2. Thus higher productivity yields more luxury and greater inequality whenever θ and x move in the same direction, regardless of whether w rises or falls.

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Suppose for each productivity level θ > 0, the equilibrium with the highest wage w is selected. Under this equilibrium selection rule, the requirements of Proposition 6 are satisfied (see Figure 4). Proposition 7 (equilibrium selection). Let W(θ) ≡ {max ϕw(x) such that ϕθ(x) = θ}. (a) W(θ) is well-defined for all θ > 0. (b) If w is determined according to W(θ) then θ1 < θ2 implies x1 < x2. Corollary If w is determined according to W(θ) then increasing productivity implies increasing luxury and increasing inequality at every closed site. The selection rule in Proposition 7 implies that backward- bending segments of the equilibrium locus [ϕθ(x), ϕw(x)] can be ignored (see Figure 4).

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Property Rights Implications Rising productivity causes the site qualities a(x) and b(x) to fall in (4). Thus the best sites are closed first. Over time the set of open sites [0, a(x)] contracts and the set of closed sites [a(x), 1] expands. Eventually, the best sites become stratified and the set of stratified sites (b(x), 1] likewise expands. As θ → ∞, we have x → ∞, which gives b(x) → 0. Thus at high productivity levels, almost all of the sites in the region become closed and stratified.

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Notes 1. Under the condition in Proposition 3(a), regional population N(x) is an increasing function of x and therefore of productivity. However, if the condition in Proposition 3(b) applies, closure of new sites could cause regional population to fall as productivity rises. At sufficiently high productivity levels, this property rights effect is dominated by the rising demand for commoner labor at stratified sites, so population must increase with productivity. 2. It is difficult to sign the relationship between the productivity parameter θ and the wage w. When the first sites are closed, this relationship is negative, but at higher productivity levels it could go the other way. However, commoners are never better off than they were when all sites were open.

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SUMMARY OF EMPIRICAL IMPLICATIONS 1. At least initially, enclosure of previously open sites and contraction of the commons increases absolute poverty (since regional food per capita is a constant). 2. I/O inequality emerges before E/C inequality. In each case, inequality starts at the best sites before spreading to less attractive sites. 3. The elite at each stratified site typically shrinks, while the commoner class expands. Eventually the elite may specialize in guarding land.

• 4. Under reasonable assumptions, higher productivity

implies greater inequality (both between insiders and

• utsiders, and also between elites and commoners).

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Methodological Comments 1. Our theory is abstract and general. We think it is the simplest story that fits the broad sweep of the data. 2. Other relevant factors could include risk, warfare, trade, food storage, public works, land improvements, resource depletion, and craft specialization. 3. However, these factors are not logically necessary (we can explain a lot without them). 4. History may be over-determined. We derive sufficient conditions for inequality but there may be other sets of sufficient conditions.

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FOUR CASES FROM ARCHAEOLOGY AND ANTHROPOLOGY The Channel Islands (off the coast of southern California). Hunter-gatherers heavily dependent on marine resources. Slow productivity and population growth before 1500 BP. Good evidence of insider/outsider inequality after 1500 BP (skeletal remains show superior nutrition at the best sites). This occurred around the time of a negative climate shock that induced migration from poor sites to better ones. Despite the negative climate shock, population continued to grow for the region as a whole after 1500 BP, probably due to technological improvements (bow and arrow, fishing, plank canoes, etc).

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Our interpretation: the net effect of climate and technology was continued productivity growth and regional population

• growth. Our theory predicts emergence of insider-outsider

inequality at the best sites. The climate shock hit inferior sites disproportionately and motivated migration to superior sites. This reinforced the pure productivity effect from technology. After 650 BP, good evidence of elite/commoner inequality (differences in burial practices). By European contact in 1542 AD, the society was ranked, with hereditary chiefs who often married into chiefly families on the mainland.

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The Northwest Coast of North America. The earliest record of human habitation in the region dates to around 12,000 BP. Evidence of improving technology, particularly between 4500 and 3000 BP: net weights, toggling harpoons, fish weirs, storage boxes, and improved canoes. Stable territorial groups and differences in grave goods by 4000 BP.

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Population levels were higher during 3800-1500 BP than in earlier periods. Large permanent extended households by 3500-3000 BP. Peak population levels reached during 200-1770 AD. Good evidence of inequality in the latter period: markedly different house sizes and major differences in the richness

• f burial mounds.

At European contact (1770s) these were ranked societies with elites, commoners, and slaves. Consistent with prediction that technical progress should lead to rising population and growing inequality.

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Southwest Asia. The early Natufian period (15,000 - 13,000 BP) followed the last ice age. Warm climate with plentiful rainfall. Population growth occurred during this period. It was accompanied by a transition from mobile to largely sedentary hunting and gathering. Differences in burial practices in this period. Inequality? Differences in burial practices disappear at the time of a large negative climate shock (the Younger Dryas: 13,000 - 11,600 BP). They do not reappear until more than 2000 years later, after agriculture has been established.

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There is evidence of insider-outsider inequality during the climate reversal (13,000-11,600 BP). Skeletal remains show superior nutrition at the best sites. A puzzle: bad climate lowered productivity and regional population dropped. Why inequality across sites? The negative shock (aridity) hit inferior sites hardest and motivated migration to superior sites. This increased local population density to the point at which it was feasible and profitable to exclude outsiders. After 11,600 BP the climate recovered, agriculture spread, and differential burial practices are found occasionally. Clear stratification only emerges thousands of years later.

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Polynesia. An enormous region in the Pacific Ocean bounded roughly by the Hawaiian Islands, Easter Island, and New Zealand. Islands differ widely in size, climate, topography, soil fertility, and ecosystems. All Polynesian societies are descended from a common ancestral culture based on domesticated plants and animals, hunting, foraging, and fishing. Migration and colonization over thousands of years had generated a diverse assortment of social structures by the time of European contact. In cross section, there are strong correlations among (a) richness of natural endowment; (b) population density per unit of arable land; and (c) degree of inequality.

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The most highly stratified island chains are Hawaii, Tonga, the Society Islands, and Samoa. Of ten island chains for which data are available, these are also the four with the highest population densities per unit

• f arable land.

The islands with the best endowments of natural resources and thus the highest productivity of food labor are Hawaii, the Society Islands, and Samoa (no data for Tonga). Hawaii stands out as having the best resource endowment. It is also the case with the most extreme stratification. Time series data for Hawaii works as we would expect (but have to incorporate disequilibrium population dynamics).

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CONCLUSION The theory does well. In some cases we have to account for complicating factors such as climate shocks that hit inferior sites more strongly,

• r a founding population initially below the steady state.

We can extend the theory to deal with kinship, downward mobility, and slavery. Better tests require better data. We need good nutrition data from skeletal remains. In particular, we need data on the variance in nutrition both within and across communities for a given region. We want to know how these variances evolved over time for a given region. We want to know whether increases in variance were associated with improved natural resources, technical progress, and/or higher regional population density.