Spatial Rice WD

Fractal Poverty Traps

Christopher B. Barrett Department of Applied Economics and Management 315 Warren Hall, Cornell University, Ithaca, NY 14853-7801 USA [email protected] Telephone: 607-255-4489 Fax: 607-255-9984

Brent M. Swallow World Agroforestry Centre P.O. Box 30677, Nairobi, Kenya [email protected] Telephone : +254-20-524000 Fax : +254-20-524001

March 2005 revision Comments greatly appreciated

© Copyright 2005 by Christopher B. Barrett and Brent Swallow. All rights reserved. Readers may make verbatim copies of this document for non- commercial purposes by any means, provided that this copyright notice appears on all such copies. Fractal Poverty Traps

Abstract: This paper offers an informal theory of a special sort of poverty trap, one in which

multiple dynamic equilibria exist simultaneously at multiple (micro, meso and/or

macro) scales of analysis and are self-reinforcing through feedback effects. Small

adjustments at any one of these levels are unlikely to move the system away from its

dominant, stable dynamic equilibrium. Governments, markets and communities s are

simultaneously weak in places characterized by fractal poverty traps. No unit operates

at a high-level equilibrium in such a system. All seem simultaneously trapped in low-

level equilibria. The fractal poverty traps formulation suggests four interrelated

strategic emphases for poverty reduction strategies.

Keywords: poverty traps, thresholds, Africa, chronic poverty, economic growth, Millenium

Development Goals

1 Acknowledgements

We thank Larry Blume, Doug Brown, Michael Carter, Alain de Janvry, Andrew Mude, Ben

Okumu, Frank Place, two anonymous reviewers and participants at the January 2003

ICRISAT/DFID conference on “Rural Livelihoods and Poverty Reduction Policies” for helpful discussions. This work was made possible in part by grants from the United States Agency for

International Development, through the BASIS CRSP, grant number LAG-A-00-96-90016-00, and the Strategies and Analyses for Growth and Access (SAGA) cooperative agreement, number

HFM-A-00-01-00132-00. All views, interpretations, recommendations, and conclusions expressed in this paper are those of the authors and not necessarily those of the supporting or cooperating organizations.

2 1. INTRODUCTION At least one-fifth of the world’s population suffers extreme poverty, living on less than $1/day. In Sub-Saharan Africa alone, the share of total population living in extreme poverty has remained stuck at between 45 and 50 percent for the past fifteen years, with population growth raising the total number of extreme poor in Africa to more than 290 million people.1 Although extreme poverty is most widespread in Africa as a share of population, it has likewise stabilized as a share of population in Latin America, while Asia’s vastly larger population translates into nearly three times as many people in extreme poverty on that continent. Increasing the incomes of the more than 1.2 billion people living in extreme poverty by just $1/day per person would require an extra $450 billion per year extra for these poor people, not counting associated income gains to others. Such a staggering figure is beyond any feasible overseas development assistance flows. Achieving the global poverty reduction objectives enshrined in the Millennium Development Goals will require a strategic focus on how to propel self-reinforcing growth among the poor.

In this paper we therefore focus on two key aspects of the poverty reduction challenge: the dynamics of growth among the poor and self-reinforcing patterns of chronic or persistent poverty.2 We know that much poverty is transitory.3 People commonly suffer – or even, less commonly, choose – short-term income losses that push them below an inherently arbitrary poverty line for a relatively brief period of time. Then they recover without explicit external assistance. While even transitory poverty is undesirable, it typically causes less concern among policymakers and scholars than does chronic poverty. While people in transitory poverty are able to rebound relatively quickly from adverse shocks, those in chronic poverty remain poor for much more extended periods.4

3 Figure 1 captures the crucial distinction between persistent and transitory poverty through a simple comparison of poverty dynamics in the United States with that in three rural African sites in which we have worked for several years: northern

Kenya and central and south-central Madagascar.5 The leftmost point on each series reflects the headcount poverty measure at one point in time, as measured against the poverty line noted in parentheses, measured in real 2002 US dollars/day per person.

Subsequent points depict the percentage of the population that was poor in both the initial period and the subsequent survey period(s). If all poverty were persistent, the lines would all be horizontal, as those who were poor in the initial survey period would always remain poor. If all poverty were transitory, the lines would collapse to the x axis rapidly.

[Figure 1 about here]

The results presented for the United States show a surprisingly high level of poverty in the United States: a headcount measure of poverty of 22.3 percent in 1993 measured against a poverty line equivalent to $15.05 per person per day for a family of four. Most of this poverty was transitory, however. Less than 25% of the households who were poor in 1993 were still poor after one year and only 5.3 percent were still poor after two years. Median time in poverty was only 4.5 months (Naifeh 1998).

By contrast, most poverty in these African cases appears distressingly persistent. In the site with the lowest rates of ultra-poverty (Vakinankaratra, the prime central highlands agricultural region in Madagascar’s wealthiest province), 60 percent of those who were ultra-poor in one year remained ultra-poor five years later. In

Madagascar’s poorest province (Fianarantsoa), more than 80 percent of the ultra-poor were still ultra-poor after five years. And among agro-pastoralists in semi-arid

4 north central Kenya, more than 90 percent of the initially ultra-poor remained so after

18 months.

These crude comparisons underscore an important qualitative point: it is not just the magnitude of poverty but, perhaps even more importantly, the nature and duration of poverty that differentiates much of the developing world from the wealthy countries.

Where anti-poverty policy in the wealthy countries largely revolves around the provision of safety nets to cushion people against short-term shocks and to help them

“get back on their feet again” quickly, in the developing countries the task is far more challenging. The persistent poverty of developing countries is of grave concern not only because of the severe material deprivation it represents, but equally because of the feelings of hopelessness that such dim prospects can induce.

Such observations give salience to the concept of poverty traps into which people may fall and have difficulty escaping. The idea of a poverty trap differs in an important way from standard economic models of growth. In particular, the notion of a poverty trap depends fundamentally on the existence of multiple dynamic equilibria, as we explain in detail in the next section. The contribution we offer, in section 3, is to articulate an informal theory of a special sort of poverty trap, one in which multiple dynamic equilibria exist simultaneously at multiple (micro, meso and/or macro) scales of analysis and are self-reinforcing through feedback effects. We label this phenomenon a fractal poverty trap, drawing on the fractal geometric concept of self-similarity with independence of scale.6 A fractal pattern repeats itself at all scales of aggregation, with each scale reinforcing the pattern at other scales. As we argue in section 4, mounting empirical evidence suggests the existence of poverty traps exhibiting such a fractal pattern, although there has been no rigorous test of the

5 hypothesis to date. In Section 5 we discuss some of the implications of fractal poverty traps for policy and research.

2. POVERTY TRAPS

The essential logic of standard economic growth models is reflected in Figure 2.

The horizontal axis depicts some measure of household well-being (e.g., income, expenditure, asset holdings, anthropometric status, etc.) in an initial time period, t. The vertical axis depicts the same measure at a future period, t+1. The diagonal line from the origin reflects points where well-being is the same in both periods, i.e., points of dynamic equilibrium. Curve 1 depicts a growth function, wherein households that start from a level of well-being below the poverty line steadily, but perhaps quite slowly,

grow towards the dynamic equilibrium welfare level, WH, as reflected by the arrows on the growth path. When the curve lies above the diagonal line, future well-being exceeds current, i.e., there is growth. When the curve lies below the diagonal line, there is decline.

Standard economic growth models can thus be fully consistent with the observation of persistent poverty, which will occur either if growth converges to a very

low welfare level, i.e., below the poverty line (WPL), or if it simply takes more time to exit poverty than has elapsed since the household was first observed. Moreover, growth may be conditioned by a variety of factors. For simplicity of exposition, assume there are two distinct groups within an economy, each following a different growth trajectory,

one of which (path 1 in Figure 2) leads out of poverty, to a dynamic equilibrium at WH, while the other (path 2) does not, stabilizing at a sub-poverty line dynamic equilibrium,

7 WL. In principle, it might therefore seem that one

6 doesn’t need any new theoretical apparatus to understand the extraordinary persistence of poverty in places such as rural Africa.

Yet a mass of empirical evidence against the hypothesis of unconditional convergence has recently motivated considerable research on economic growth processes, at both macro and micro levels.8 Moreover, the recent UN Millennium Task

Force recommendations rest on a fundamentally different conceptualization of why persistent poverty exists: multiple dynamic equilibria that create a tipping point between decline and growth, as reflected in the UN Millennium Project final report (2005, p.39):

“The key to overcoming the poverty trap is to raise the economy’s capital stock – in infrastructure, human capital, and public administration – to the point where the downward spiral ends and self-sustaining economic growth takes over. This requires a

‘big push’ of basic investment ….”

Standard economic models of growth implicitly assume a single dynamic equilibrium, and hence the (perhaps conditional) convergence of all growth paths towards a single level of welfare.9 But if multiple dynamic equilibria exist, then the picture is somewhat different. As reflected in Figure 3, the growth function then

becomes S-shaped, with stable dynamic equilibria at high and low levels of welfare (WH

10 and WL, respectively). The existence of multiple equilibria implies at least one

unstable dynamic equilibrium, a critical threshold, depicted by WC in Figure 3. While

one naturally returns to stable equilibria (WH and WL) after small shocks, one naturally moves away from an unstable equilibrium after a shock. Thus the direction of change in well-being shifts – or “bifurcates” in the more formal jargon – from growth to decline at the unstable equilibrium.

7 Notice how this poverty trap framework departs from the standard economic theory of convergence towards a unique dynamic equilibrium: households can move toward either of two (or more) stable dynamic equilibria, with the resources at their disposal affecting the one towards which they naturally gravitate. Meagre initial endowments can trap households in a low-level equilibrium. Small transfers then cause only modest, short-lived gains because the local dynamics of growth pull recipients back to toward the low-level equilibrium before long. With a significant, positive shock, however, they may be able to escape the basin of attraction of the low-level equilibrium and move onto a positive growth trajectory towards a higher stable dynamic equilibrium welfare level. Depending on where the poverty line is set, such a positive shock may move the household out of poverty. This helps explain the emphasis on large scale transfers in the UN Millennium Project final report. Conversely, non-poor households that suffer a significant adverse shock can be knocked far enough below the high-level equilibrium that they cross the critical threshold and experience further decline, collapsing towards the low-level equilibrium. Hence the growing emphasis on safety nets as a central plank of poverty reduction strategies.

The key to systems characterized by multiple dynamic equilibria is the existence

of critical thresholds such as WC – in other words, points of “take off” – at which the pull of one equilibrium gives way to the attraction of another.11 The evolution of well- being over time then depends on where one sits relative to the critical threshold(s) at which the growth function bifurcates. People, communities, nations or multinational regions have a difficult time rising beyond such thresholds without assistance, and can unexpectedly slip beneath them and have difficulty recovering.12 Although we do not claim that poverty traps – much less fractal poverty

8 traps – explain all persistent poverty, the concept has begun to attract considerable attention and to underpin, albeit subtly, much contemporary debate on development policy.

3. AN INFORMAL THEORY OF FRACTAL POVERTY TRAPS What might bring about the S-shaped dynamics characteristic of poverty traps? The explanation we offer here is that there exists of a range of distinct strategies,13 defined as a set of activities undertaken by (individual or collective) decision-makers using available assets to shape current and future standards of living.14 Choices among strategies depend on the opportunities available to and the constraints faced by decision-makers and the relative returns to each strategy.15 Each strategy maps a stock of assets into flows of welfare based on underlying production and exchange mechanisms – production technologies, organizational forms, market and nonmarket resource allocation arrangements – and exogenous determinants of production and exchange (e.g., rainfall and other biophysical phenomena, local institutional history, exogenous market prices), as well as the risks associated with prices, yields, and assets.

Strategy choice reveals agents’ preferences among the feasible options they face. The set of feasible strategies depends on the stock of assets one controls: financial, human, natural, physical and social capital. Some strategies are effectively open to any decision-maker. At the scales of households or individuals, for example, exclusive reliance on selling unskilled labor is almost universally feasible. Entry barriers commonly restrict access to other strategies that offer expected returns superior to those generated by such universally accessible strategies. Among desirable strategies, the higher the entry barrier, the higher the expected returns to the activity

9 for those who can surmount the barrier, else the strategy would never be optimal and thus never be chosen.

When there exist multiple strategies in dynamic equilibrium, poverty traps may arise. Let us tie this back directly to the preceding discussion. One can imagine a multiple equilibrial system with two (or more) convergent growth paths of the sort shown in Figure 2 partially superimposed over one another. For example, consider the two convergent growth paths depicted in thick, dashed lines in Figure 3. Each individual growth path has a unique, stable dynamic equilibrium. But at the critical threshold, one should switch from one growth path to the other. The outer envelope of the two separate functions then approximates the overall growth trajectory of the system, reflected in the S-shaped, solid curve. Each strategy is associated with a distinct stable dynamic equilibrium.

When one chooses a strategy, one implicitly selects the equilibrium towards which one naturally moves over time, given the state of the system. For example,

Lybbert et al. (2004) demonstrate that southern Ethiopian pastoralists face two strategies – migratory or sedentarized pastoralism – reflecting two different dynamic wealth equilibria. The dynamic wealth equilibrium associated with migration is relatively high, while that associated with sedentarization is low. Pastoralists prefer not to sedentarize, but if they start off with too small a herd or lose too many animals to drought, disease or (human or wildlife) predators, the superior strategy of transhumant grazing is not accessible to them, for reasons Lybbert et al. (2004) explain. Poorer pastoralists therefore adopt a sedentarization strategy and predictably settle into a low- level wealth equilibrium.

The key to understanding the genesis of poverty traps therefore lies in understanding the nature of transitions – or, more importantly, the absence of

10 transitions – between strategies. Why do some pastoralists remain mobile while others do not? Why do some farmers adopt improved production technologies or enter high value-added marketing channels while others do not? What are the barriers that effectively preclude adoption of superior strategies?

Carter and Barrett (2005) argue that (formal or informal) financial market failures are essential to the possibility of a poverty trap. If those with low asset stocks could borrow freely, they would do so in order to cross the critical thresholds, adopt superior strategies and thereby follow the growth trajectory to a stable dynamic equilibrium beyond the poverty line. This financing constraint often exists at multiple scales, from individuals and households unable to access credit because of insufficient collateral, to local governments unable to borrow on capital markets due to limited tax collection capacity, to national governments rationed out of global financial markets because of political risk or debt overhang. Where such constraints exist at multiple levels, they become interdependent. Hence the fractal nature of poverty traps.

A fractal poverty trap is then a special case of a poverty trap. Fractal poverty traps involve multiple dynamic equilibria that exist simultaneously at multiple (micro, meso, and/or macro) scales of analysis such that they are self-reinforcing through feedback effects. The low-level equilibrium prevailing at one scale makes a higher-level equilibrium inaccessible at the next lower scale, and vice versa. For example, a government lacking capacity to collect significant tax revenues from a poor population finds itself unable to afford expensive investments (e.g., in physical or institutional infrastructure) necessary to induce firms to invest in fixed capital formation and new job creation. Given firms’ lack of incentive to expand, most production occurs in very small units that are unable to finance the acquisition of cutting-edge technologies. The resulting low-level of productivity barely covers

11 proprietors’ consumption needs, leaving little to save. The banking system thus lacks adequate time deposits to provide adequate investible funds for lending to businesses for expansion and the state has only a modest tax base on which to draw to pay for public goods and services.

Low farm-level productivity often likewise originates from a fractal poverty trap. Small farmers’ reticence to adopt improved production technologies sometimes has community-scale origins in coordination failures due to social cleavages that result, for example, in failures to coordinate weed, water or pest control. Of course, the higher-order coordination failure itself results from the lack of individual incentive to adopt improved management or production practices, following the familiar logic of the Prisoner’s Dilemma.

These are inherently systems characterized by multiple equilibria at multiple scales, i.e., fractal poverty traps. Higher-level equilibria exist, as manifest by the fact that other economies, firms and farms use high-yielding crop varieties or organize into large units enjoying significant economies of scale and easy access to capital markets.

But the set of incentives and constraints faced by decision-makers at multiple levels lead them to choose lower-level equilibrium strategies.

Through any of several such mechanisms, constraints that lead to a low-level equilibrium strategy choice at one level of aggregation have spillover effects on both larger and smaller units, creating a self-reinforcing feedback loop. Small adjustments at any one level are unlikely to move the system away from its dominant stable dynamic equilibrium. Governments, markets, communities and households are thus simultaneously weak in places characterized by fractal poverty traps. No unit operates at a high-level equilibrium in such a system. All seem simultaneously trapped in low- level equilibria.

12 In such systems, past disadvantage and adverse shocks can persist, even after the original source(s) of shock or disadvantage (e.g., ethnic or racial discrimination, political patronage) have passed. Conversely, positive asset shocks due to transfers, windfall gains or transitory policy interventions that increase the returns or reduce entry costs to higher return strategies can have permanent effects. Even temporary interventions such as initial (but short-lived) subsidies to new technology adoption, finite-lived support for the creation of new organizations or educational loans, asset redistribution through mechanisms such as land reform, or safety nets to prevent asset decumulation in response to income shocks can have disproportionately large impacts in such situations. The challenge of reducing chronic poverty associated with poverty traps revolves around finding ways to remove or transcend the thresholds and financial constraints that limit accumulation and access to remunerative strategies. The challenge posed by fractal poverty traps is that interventions need to be simultaneously applied at all scales where low-productivity strategies reinforce one another.

4. ARE THERE REALLY FRACTAL POVERTY TRAPS?

With available literature and empirical evidence, we can offer empirical evidence consistent with the hypothesis of fractal poverty traps, but cannot offer a formal test of the hypothesis. This section therefore illustrates the potential applicability of the fractal poverty traps concept to macro, meso, and micro scales of analysis.

Formal hypothesis testing is left to future research.

Under the fractal poverty traps hypothesis, variation in outcomes and poverty dynamics within units at collective scales – from household up through multinational region – result primarily from differences in (i) initial asset holdings, which may be

13 the product of past shocks, (ii) available production technologies, market prices and participation costs, and environmental conditions (e.g., rainfall) that affect returns to a strategy across different units, (iii) sunk costs to technology acquisition, market participation and institution building (e.g., financing costs), and (iv) internal and external social factors – e.g., likelihood of coordination, cooperation and conflict – that affect the organization of production and exchange.

Meanwhile, variation in outcomes between collective units commonly arise from organizational and institutional characteristics that create inter-scale linkages. For example, communities in which households cooperate actively in the resolution of coordination and externality problems tend to suffer less poverty and enjoy greater economic mobility than communities plagued by collective action problems. Nations within recurrent civil strife suffer higher poverty and lower growth than nations that maintain internal peace. Regions in which firms work out effective vertical contracting arrangements tend to enjoy stronger employment growth and technological change than those in which volatile spot markets mediate most transactions (Porter 1990, Fujitsa et al .1999). Districts with good information and marketing linkages to metropolitan centers commonly acquire new production and processing technologies sooner and grow faster than regions with poorer physical and social connections to other units.

(a) Macro scale To some extent, development studies originated and continued as an area of research because of the fractal nature of poverty traps at macro scale. Whole regions of the globe – Sub-Saharan Africa, South

Asia, Southeast Asia, Latin America and the Caribbean, North Africa, Central Asia, and

Central and Eastern Europe – have been mired in widespread, acute poverty for prolonged periods of time. The empirical

14 economic growth literature often captures macro scale poverty traps through the use of crude regional dummy variables, wherein a dummy variable for “Africa”, “Latin

America” or other such broad populations is included and commonly found to be associated with statistically significantly negative effects on economic performance

(Barro and Sala-i-Martin 1995, Collier and Gunning 1999).

A variety of explanations exist for broad geographic clustering of poverty in the world at the scale of nation states and groups of countries, most of which turn largely on exogenous conditions. Many of the classical development theories fit the fractal poverty traps model very well, as they arise from positive technological spillovers due to internal or external economies of scale (Young 1928, Rosenstein-Rodan 1943, Nurkse

1953, Myrdal 1957). They recognized the existence of positive pecuniary externalities associated with industrialization such that one industry's growth depended on the existence of a market for its products, a market most likely to develop in cities among the labor force of other industries. This creates fundamental interdependence among industries due to inherent coordination problems. Failure to coordinate, these authors cautioned, would lead economies into a "low-level equilibrium trap." Even Hirschman’s

(1958) focus on backward (and to a lesser extent, forward) linkages between industries, although cast in contrast to Nurkse (1953) as an argument for “unbalanced” growth, likewise rested on the idea that investments in sectors with the strongest linkages would endogenously generate broad-based growth. These "high development" theories emphasized strategic complementarity among sectors due to coordination effects and inherent nonconvexities due to positive externalities and increasing returns to scale technologies.16

15 Some more contemporary explanations of macro scale poverty traps turn on the biophysical characteristics of regions, especially how humidity and temperature affect micro-level agriculture and health and how distance to ocean ports and the mass of global economic activity affect commerce at the individual firm level (Sachs and

Warner 1995, 1997, Gallup and Sachs 1998, Bloom and Sachs 1998). Other explanations turn on history-dependent social phenomena, whether the ethnic divisions that permeate countries and regions (Easterly and Levine 1997, Collier and Gunning

1999), histories of political violence (Barro 1991, Easterly and Levine 1997, Collier and

Gunning 1999), the complex effects of subjugation by different colonial powers on internal and external organization (Acemoglu et al. 2001, 2002), the historical accidents of urbanization (Fujita et al. 1999), or wealthy country policies that distort global market prices.

Each of these explanations fits the fractal poverty traps framework. All involve exogenous factors that affect asset accumulation and the development strategies chosen by governments. Some explanations turn on lower returns to specific strategies (e.g., agriculture or manual labor in hot and diseased settings), while others add to nations’ or regions’ fixed costs of accessing state-of-the-art technologies or high value-added markets, with the same end effect.

(b) Meso scale

At meso scales of analysis – communities, groups, networks, and local jurisdictions – coordination, cooperation and conflict are especially important determinants of asset accumulation, transformation of assets into goods and services, and distribution of those goods and services among units within the aggregate. Thus the institutional arrangements that shape interactions among units and between scales

16 weigh especially heavily in establishing the equilibrium into which a regional or local economy settles.

In game theoretic terms, a coordination problem exists when the returns to an activity increase as others undertake the same activity, with multiple equilibria emerging naturally. A low-level equilibrium might involve, for example, disrespect for individual property rights, which may be individually optimal behavior conditional on everyone else not honoring property rights, but collectively irrational in that everyone could be made better off if property rights were made secure and honored costlessly by all parties. Similarly, cooperative equilibria lead to high-level economic equilibria, while noncooperative equilibria tend to lead to lower-level economic equilibria.

The theory of fractal poverty traps fits many of these meso-scale patterns.

Groups that can cooperate and coordinate effectively are better able to produce public goods (e.g., roads, water management infrastructure, schools, health clinics) and services (e.g., security, reliable communications, sanitation) that crowd in private investment at more micro levels, leading to higher tax revenues and ultimately higher level economic equilibria. High rates of public investment typically accompany high private investment, in cycles of mutual causation.

A growing body of research suggests that poverty is particularly prevalent and persistent in “less favored lands” that are far removed from market and political centers, experience persistent conflicts, and attract low levels of government investment and services. The core of this argument is that these areas have been less favored by both nature, in the form of lower and more erratic rainfall and poorer soils, and people, through infrastructural and institutional deficiencies and high levels of market volatility and political disturbance. Poor communications and transport

17 infrastructure so inflate costs of market participation that households rationally opt out of commercial agriculture and settle for low-return semi-subsistence production with few improved, purchased inputs (Omamo 1998a, 1998b). National policies routinely impose costs on poorer regions for the benefit of other, richer regions, such as quarantine-based methods of animal disease control in Kenya (Barrett et al. 2003), taxation and general public services provision (Bates 1983), and agricultural pricing and distribution policies (Lipton 1977). Weak markets and low access to public services induce farmers to resist market participation and uptake of modern technologies, which in turn reduces commercial and government incentives to intervene in these regions (Fafchamps and Moser 2003, Minten and Barrett 2005). Ravallion

(2002) and Jalan and Ravallion (2002) find evidence of geographic poverty traps associated with spillover effects of the level and composition of local economic activity. The income growth of rural Chinese households is affected by that of their neighbours, with significant cross-sectoral spillovers from farm to nonfarm activities.

Smith et al. (2001) find that inter-district differences in agroecological conditions, physical and social service endowments and recent experience of health (especially

HIV-AIDS) shocks explain many of the differences in livelihood strategies and welfare trajectories of people in rural Uganda.

A smaller number of studies have focused on the magnitude and determinants of differences in poverty between communities within particular geographic areas.

Krishna (2002) has studied differences in welfare between villages in the Indian state of Rajastan and found internal social cohesion and the strength of linkages to external sources of power and finance to be the most important determinants of village development performance. Dercon (2004) used panel household data from Ethiopia to assess the determinants of inter-village differences in the dynamics of poverty,

18 finding inter-village differences to be related to initial differences in key assets: size of land holdings, educational achievement, and road infrastructure. In an analysis of household data from 808 non-pastoralist communities in Kenya that were surveyed in

1994 and again in 1997, Christiaensen and Subbarao (2001) found income diversification, market access, adult literacy, and access to electricity reduced vulnerability, while the incidence of malaria increased vulnerability.

Some ethnic minorities, such as the African American population in the United

States or indigenous upland ethnic groups in southeast Asia, experience significantly higher levels of poverty than the general population due to systematic biases in the provision of public services, lower access to labor markets, and/or insecure property rights. Such market failures and social rigidities may induce adaptations of local organizations that help in some respects, but create other problems (Hoff et al. 1993).

For example, social networks that provide mutual insurance in the absence of effective financial markets can create obstacles to adoption of new technologies (Hogset 2002,

Moser and Barrett 2002), expansion of small businesses (Fafchamps and Minten 2002,

Platteau 2000), and financing of capital accumulation (Mogues and Carter forthcoming). Social networks and group identity have multiple effects, some of which foster asset accumulation and welfare improvements, others of which retard economic advance in poor communities, leading to precisely the sort of multiple equilibria that underpin poverty traps (Durlauf 2001, Barrett 2005b,c).

The accumulation of physical assets can occur in any of four ways. First, individuals and households in an area may mobilize resources, through voluntary contributions or taxes, to obtain additional assets for use by a public agency. Consider, for example, a group that raises funds for the construction of a clinic in the

19 local area. In that case, resources move from the micro to the meso-scale. Second, a public agency can accumulate assets by reinvesting profits obtained from selling their services. For example, a clinic may levy a surcharge on its services to build up an investment account for expansion. Third, a public agency may be allocated funds from a local government that taxes local citizens or economic activity. In such cases, resources are mobilized from within the meso-scale. Fourth, a public agency or organization may implement programmes on behalf of, or with support from more aggregate scales of government or from external sources such as development agencies or non- governmental organizations, establishing a macro-to-meso link. Regardless of the accumulation mechanism, however, non-linearities in coordination, transaction or agency costs may generate thresholds in asset accumulation. Shifting from one strategy to another may be associated with a shift in the mechanisms of asset accumulation.

Besides mobilizing investment in physical assets, meso-scale groups may also augment private returns by regulating the use of collective natural resources, such as forests, rangelands and waterways. The theories of open access and common property, which date back to Gordon (1954), stress the importance of meso-scale coordination of micro-scale decision making in order for resource use to be efficient. Both theoretical and empirical studies of natural resource management from around the developing world stress tradeoffs between the effectiveness of governance structures that make and enforce rules and the associated transaction costs (Ostrom 1990, Baland and Platteau

1996). One example of a threshold effect would arise from the sunk transaction costs of hiring forest guards to enforce rules on extraction of products from a community forestry. Communities that can afford the sunk

20 investment in hiring and equipping guards can achieve a higher-level equilibrium than can otherwise identical communities that are unable to make such investments. At meso-scales, it is clear that asset thresholds have inter-related economic, collective action and political dimensions. Many public goods and services exhibit increasing returns to scale and scope at subnational level.17 Equally, the demand for public services depends upon the structure and efficiency of markets for substitute services. For example, the lack of private insurance or credit markets increases people’s willingness to participate in collective risk pooling and the potential benefits of public sector options for credit or risk buffering.

The political dimension of asset accumulation thresholds refers to the governance of meso-scale government agencies and organizations. Since the 1980s there has been a strong trend toward decentralized provision of public services and devolved authority for natural resource management. Governments in countries such as

Mali, Bolivia, Uganda and the Philippines now have fairly autonomous local governments that exercise significant responsibility for providing services to local residents. To date, however, there is mixed evidence regarding the ability of decentralized government agencies to mobilize local resources and create conditions that crowd in private investigate. Bardhan (2002) argues that the relative performance of centralized versus decentralized administrative arrangements ultimately depends upon the extent to which they are captured by elites.

Meso-scale phenomena are not restricted to institutions of collective action. Of particular importance, markets are socially constructed institutions. Once one gets to aggregate scales of communities and regions, the terms on which individuals can buy or sell goods and services – terms that are effectively exogenous at the individual or household scale – begin to turn in part on how communities of households organize

21 themselves. Producer organizations such as cooperatives and periodic markets organized by local jurisdictions, as well as local contracting conventions, physical security and road and marketing infrastructure all have pronounced effects on market conditions. The east and southeast Asian experience underscores the importance of agricultural producer organizations to facilitate bulk purchases of inputs and sales of outputs, access to extension services, and political voice. Some organizations have been set up by government, some by private firms and some have emerged spontaneously within communities. We understand relatively little about how efficacy varies with group origins, but we do know that some marketing organizations can prove extremely effective in achieving economies of scale or scope, in securing access to higher-return markets, and in stabilizing input and output prices faced by even small producers

(World Bank 2003).

(c) Micro scale The essence of micro scale poverty traps is that households and individuals remain in chronic poverty because they are unable to self-finance investments needed to generate high returns because of the lumpy nature of or the risk inherent to those investments and because they are unable to obtain external finance because of weak credit and insurance markets. This manifests itself in discrete strategies exhibiting markedly different welfare distributions, where the ex ante poor choose strategies offering less attractive stochastic returns than the ex ante rich choose, simply because the more attractive strategies lie beyond their means (Dercon and

Krishnan 1996, Bardhan et al. 2000, Ellis 2000, Barrett et al. 2005). A growing mass of empirical evidence underscores the importance of initial asset holdings in determining households’ income growth and the likelihood of exit from poverty (Dercon 1998,

Elbers et al. 2002, Adato et al. 2004, Barrett et al. 2004, Lybbert et al. 2004). When

22 these patterns are interrelated with meso- and/or macro-scale poverty traps, one finds a fractal poverty trap.

Simply put, initial conditions matter. Those with few or no assets are far less likely to acquire scarce skills or capital necessary to enter into remunerative activities that lead to higher income and consumption. Moreover, households caught on the wrong end of such traps often end up in a pattern of persistent poverty and steady degradation of the natural resource base on which they depend, with potentially adverse spillover effects on neighbours who rely on the same resources (Shepherd and Soule

1998, Coomes and Burt 1997, Coomes et al. 2000, Barrett et al., 2002b).

The most extreme cases of micro scale poverty traps involve essentially irreversible human capital accumulation failures due to childhood undernutrition, illness and lack of education. Perhaps the most compelling models of poverty traps emerge at this micro scale, where undernutrition and morbidity early in life can lead to permanent reductions in physical stature and health status associated with sharply increased risk of involuntary employment and lower incomes in adulthood (Dasgupta 1997, Strauss and

Thomas 1998), and where household-scale financial constraints can cause underinvestment in the education of children, propagating poverty across generations

(Loury 1981). Of course, poor health and education then weakens labor productivity and the ability of firms and communities to take advantage of human capital spillovers that affect aggregate productivity and consumption growth (Ravallion 2002).

5. FINDING PATHWAYS OUT OF PERSISTENT POVERTY So what are the key implications of fractal poverty traps for policy and research? Does the fractal poverty traps concept provide any insights into pathways

23 out of poverty for the 1.2 billion people presently suffering extreme poverty? In this section we discuss four interrelated strategic emphases that emerge directly from the fractal poverty traps formulation.

First, it is possible that significant but short-lived transfers to individuals, households, communities, and nations caught in low-level equilibria can enable them to cross crucial thresholds presently inaccessible to them and thereby make it feasible for them to switch to positive growth trajectories that can carry them out of persistent poverty. This is the essence of the strategy advanced in the UN Millennium Project final report. Threshold effects and poverty traps imply a potentially large role for transitory policy interventions to enable people to overcome constraints that keep them from reaching the nearest relevant threshold and subsequently embarking on an endogenous growth path to a higher equilibrium. In much of Asia, short-term state investment in rural roads, electrification, water, marketing systems for improved seeds and inorganic fertilizers, institutions supporting small industry and services, etc. ignited private investment. The possibility of “crowding in” investments reflects the possibility of higher level equilibrium.

Note that these policies do not have to be fiscally sustainable in the long-run since the crucial positive effects come in the short-term. Such interventions nonetheless need explicit sunset provisions so that they do not become permanent drains on scarce fiscal resources. Moreover, it may be important to coordinate interventions at multiple scales. If fractal poverty traps exist, then investments at any one scale are shaped not only by the direct returns associated with asset accumulation or productivity growth at that scale, but also by indirect effects resulting from how investment at one scale affects patterns at other scales..

24 Second, public agencies need to assess the possibilities for eliminating or moving thresholds through interventions at aggregate scales that make previously inaccessible strategies feasible at more disaggregated scales. Examples include public investments in water supplies that reduce illness, time spent drawing water, and variability in crop yields; microfinance institutions that increase access to credit and insurance; producer groups that reduce unit costs for purchased inputs and increase unit revenues for product sales; and transport infrastructure improvements to reduce costs of market participation.

Third, there is a critical need for effective safety nets set above critical thresholds so as to prevent people from falling unexpectedly into chronic poverty.

Safety nets that can prevent the non-poor from falling into poverty in response to uninsured shocks should be included in poverty reduction strategies. Strategies that seek to enhance economic growth without providing safety nets are rather like draining the bathtub with the spigot still on. As soon as some leave the basin of poverty, others enter, maintaining the overall level of poverty at great private and social cost. Especially where adverse asset shocks due to manmade or natural disasters are commonplace, safety nets to insure consumption and reduce asset decumulation can be valuable instruments for ensuring subsequent recovery with minimal need for further assistance.

This can induce poor people to choose asset portfolios and activity patterns with greater expected returns and greater risks, endogenously stimulating income growth that in turn generates resources to support the safety net. Perhaps the most essential safety nets are those that protect human health and education, keeping children adequately nourished and in school regardless of what is happening to their family’s income and those that ensure that adult workers

25 enjoy sufficient, balanced nutrient intake to maintain physical productivity during temporary downturns.

Finally, fractal poverty traps carry important implications for decentralization.

Following the principle of subsidiarity, it typically makes sense to devolve authority over a resource or public service to the lowest possible scale within which the associated externalities can be fully internalized and at which provision of the good or service can be done efficiently (i.e., realizing available economies of scale or scope).

The scale-sensitivity dimension of the subsidiarity principle is too often lost in contemporary discussions of public services provision, resource conservation design, and related arenas in which the principle of subsidiarity is commonly invoked. The default position appears to have become decentralization, although this may not always be appropriate. Applied researchers and policymakers need to identify the scale(s) at which (i) market and coordination failures are most limiting and it appears feasible and cost-effective to provide temporary assistance to surmount thresholds, (ii) spillover effects that will shift thresholds at lower scales, indirectly igniting accumulation and opening up pathways out of poverty for some presently trapped. Toward that end, prioritization exercises must take place at multiple scales and there must be serious attempts to integrate these, not just cursory exercises as has too often been the case in recent PRSP processes (Swallow 2005).

Because many key factors behind persistent poverty – for example, water and health care availability, soil fertility degradation – result from processes involving policies at multiple scales of government and linkages among those scales, some poverty traps originate at multiple scales simultaneously. For example, soil fertility degradation – one of the most pressing problems confronting much of rural east Africa – has its origins in individual and household scale phenomena associated with

26 meager land holdings and liquidity constraints to the purchase of mineral fertilizer or livestock, in community scale phenomena associated with tenurial regimes that limit investment incentives and impede effective organization of producer marketing groups to improve smallholders’ terms of trade, in regional scale thresholds associated with transport infrastructure and fertilizer distribution, and in national and multinational scale traps related to fertilizer production capacity and agricultural and natural resources management research. Overcoming soil fertility problems – or other limiting factors with multi-scalar etiology – requires some combination of public action (e.g., a revolving fund for fertilizer), collective action (e.g., multi-purpose commodity clubs that can tax on delivery), and private action (e.g., investment in fertilizers or integrated crop-livestock systems). This necessarily requires multi-scalar approaches to develop, adapt and apply improved transition strategies so as to facilitate asset accumulation and productivity growth among the chronically poor and thereby enable them to escape the fractal poverty traps that appear to ensnare so many today. The concept of fractal poverty traps implies a need (i) to broaden poverty analysis beyond the familiar micro- macro dichotomy prevalent in economics so as to take intermediate scales of aggregation seriously, (ii) to address appropriate roles for subnational scale institutions in poverty reduction strategies,18 and (iii) to consider how investments at any particular scale are shaped not only by the direct returns associated with asset accumulation or productivity growth at that scale, but also by prospective indirect effects resulting from how investment at one scale might affect thresholds, and patterns of asset accumulation or productivity growth at other scales.

27 5. NOTES

1 This and other poverty statistics in this paragraph come from the World Bank’s Global

Poverty Monitoring system on the web at http://www.worldbank.org/research/povmonitor/.

2 In the interests of brevity, we rely on the standard income and expenditure poverty conceptualization. But our theory of fractal poverty traps links this orthodox view with broader concepts of vulnerability and voicelessness, especially as all three are linked through asset holdings and production and exchange mechanisms.

3 Baulch and Hoddinott (2000) and the various studies cited there offer detailed discussions of alternative concepts, operational definitions of “chronic” and “transitory” poverty, and a host of empirical studies of these phenomena.

4 For example, the special issue of World Development edited by Hulme and Shepherd (2003).

5 The household survey data underpinning the three African sites are described in detail in

Barrett et al. (2004). We emphasize the crudeness of these illustrative comparisons. The welfare measures and poverty lines are not perfectly comparable between the rural African and U.S. sites and the former are only locally (not nationally) representative samples. We use this graphic only to make a basic qualitative point and recommend against making any specific, quantitative inferences among these imperfectly comparable series.

6 See Mandelbrot (1977, 1983) for the seminal contributions to fractal geometry.

7 Carter and Barrett (2005) discuss analogies between such heterogeneous micro-level growth processes and analogous concepts of “conditional” and “club” convergence in the macroeconomic growth literature.

8 Easterly (2001) offers an especially accessible, even entertaining review of the evolution and empirical testing of macroeconomic theories of growth. After beginning this paper, we discovered that he too uses the term “fractal poverty traps,” although purely descriptively.

Barro and Sala-i-Martin (1995) and Durlauf and Quah (2000) offer a more formal review of theories of and empirical evidence on economic growth. Recent micro-growth studies of note include Baulch and Hoddinott (2000), Carter and May (2001), Elbers, Gunning and Kinsey

28 (2002), Jalan and Ravallion (2002, 2004), Lokshin and Ravallion (2002), Ravallion (2002),

Adato et al. (2004), Barrett et al. (2004), Dercon (2004) and Lybbert et al. (2004).

9 If there exists exogenous technical change, convergence is toward a common rate of growth.

10 There may be more than two such equilibria; we simplify for expositional purposes.

11 Such points necessarily reflect locally increasing returns to scale, although this can occur even with strictly convex production technologies. See Barrett (2005a) or Carter and Barrett

(2005) for more on these and related points on the microeconomics of growth in multiple equilibrial systems.

12 The fall is necessarily unexpected, for if one could anticipate a shock severe enough to push one past such a threshold, one would avert it if at all possible.

13 At the micro scale of individuals and households, the literature often refers to livelihood strategies reflecting the activities households undertake (Scoones 1998, Ellis 2000, Hulme and Shepherd 2003). However, at more aggregate scales, collective choice is reflected in development strategies that nest within them individual and household scale livelihood strategies. We therefore use the more general, scale-independent concept of strategies.

14 Formally, a single, variable returns to scale technology could generate such effects. But, as

Carter and Barrett (2005) argue, such cases are far less likely than distinct choices among production technologies, livelihoods, etc.

15 These returns may be multidimensional, reflecting income, risk, prestige, and other distinct factors of intrinsic value to individual decision-makers.

16 For a modern, formal development of the classical models, see Murphy et al. (1989).

17 Economies of scope relate to the variety of goods and services provided, while economies of scale relate to the volume of any single good or service provided. In both cases, per unit costs decrease over some range of output.

18 A focus on the distinct roles of meso-scale institutions distinguishes this paper from much of the U.S. based literature on fiscal federalism as well as the more recent literature on decentralized governance in transition and developing countries. The fiscal federalism

29 literature concentrates on efficient production and allocation of public services to households and firms with different preferences (see Oates (1999) for an excellent recent review). By contrast, the newer literature on decentralized governance in developing countries focuses on issues such as accountability, regional disparities, leakage, and capture by elites (e.g., Bardhan

2002).

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38 Figure 1: Comparative Poverty Dynamics 70 Ngambo, Northern Kenya 2000-2 ($0.25) 60

50 Fianarantsoa, Southern Madagascar 1997-2002 ($0.25) 40

20 Vakinankaratra, Central Madagascar 1997-2002 ($0.25) 10 United States 1993-94 ($15.05) 0 1 2 3 4 5 0 Continuous years in poverty Sources: USA: Naifeh (1998), others BASIS CRSP project. Poverty line levels are all in inflation-adjusted 2002 US dollars.

39 Figure 2: Welfare Dynamics Under The Convergence Hypothesis

Well-being t+1

Well-being t

WH WL WPL H

WPL WL 40 Figure 3: Welfare Dynamics Under the Poverty Traps Hypothesis

Well-being t+1

WL WPL WC WH

Well-being t 41