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Poverty Traps Across Levels of Aggregation:
Poverty-Traps, Coordination Failure, and Optimal Social Policy
Dylan Fitz (Lawrence University) and Shyam Gouri Suresh (Davidson College)
⇤
March 2018
*** Preliminary Draft - Please Do Not Cite ***
Abstract
While there is increasing evidence - in both micro and macro research - that poverty traps impede transitions
out of poverty in certain contexts, less is known about how micro and macro poverty traps interact. We explore
the extent to which layers of poverty traps potentially reinforce each other. For example, if credit market failures
cause micro-level poverty traps, then big-push policies could move households out of poverty. However, if these
households also live within a macro-level poverty trap, then this policy may be ineffective unless matched with a
policy to overcome the macro poverty trap. We explore the conditions under which policy may target one type
of poverty trap and when it is necessary to address multiple layers of poverty traps.
1 Introduction
While recent decades have seen approximately one billion people escape poverty globally (Radelet, 2015), certain
countries, geographic regions, and individuals remain poor year after year and generation after generation. As a
result, future success is uncertain and it may become even more difficult to achieve similar reductions in poverty
in the future. In many cases, persistently poor individuals reside in remote regions where they use low-return
technologies, have limited access to input, output, or labor markets, and where ineffective or corrupt governments
fail to provide essential public goods, property rights, or to overcome coordination failures that could lead to⇤Dylan Fitz, Lawrence University Economics Department, Appleton, WI 54911. Email address: [email protected].
Shyam Gouri Suresh, Davidson College Economics Department, Box 7123, Davidson, NC 28035. Email address:
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more rapid growth and development. As a result, it is important to analyze the conditions under which certain
individuals remain trapped in chronic poverty and the ways in which individual factors, local conditions, and
macro-level government and national factors combine to perpetuate poverty.
The growing poverty trap literature continues to provide essential information about the causes of poverty and
observable poverty trends, but debates exist about the empirical evidence verifying the existence of poverty traps
(Kraay and McKenzie, 2014). Dynamic poverty trap models illustrate how initial conditions impede productivity,
savings, and investment (see, for example, Galor and Zeira [1993], and Bowles et al. [2006]). A wide range of models
provide theoretical justifications for the existence of poverty traps, including ones based on nutrition (Dasgupta
and Ray, 1986), coordination failures (Rosenstein-Rodan, 1943; Murphy et al., 1989), fixed capital investments
(Banerjee and Newman, 1993; Aghion and Bolton, 1997; Carter and Barrett, 2006; Barrett and Carter, 2013), and
lumpy human capital investments (Basu and Van, 1998). Empirical evidence of poverty traps exists in agricultural
areas (Dercon, 1998; Lybbert et al., 2004; Carter and Barrett, 2006), human capital investment (Emerson and
Souza, 2003; Das, 2007), and assets (Zimmerman and Carter, 2003; 1999; 2001; Adato et al. [2006]; Barrett et al.,
2008). Relatedly, a growing body of research finds that small enterprises have large returns to investment (McKenzie
and Woodruff, 2006; de Mel et al., 2008; Fafchamps et al., 2014), small farms have large returns to land (Finan
et al., 2005), and that cash transfers are one of the most effective ways to fight poverty (Haushofer and Shapiro,
2013; Blattman et al., 2014; Blattman and Niehaus, 2014; Banerjee et al., 2015; Blattman et al., 2016; Evans and
Popova, 2017). Similarly, the growing literature on the importance of institutions (Acemoglu et al., 2001; Acemoglu
et al., 2005) and the historical determinants of development (Nunn, 2008; Nunn, 2009) can be interpreted as causing
low-income poverty traps. While poverty traps are challenging to identify empirically (Carter and Barrett, 2006),
this growing literature provides justification for further poverty trap studies.
As the large theoretical and empirical literature on poverty traps indicates, there are a diverse set of causes of
poverty and many different types of poverty traps. Many authors use the term poverty trap to refer to cases in
which multiple equilibria exist, meaning that there are multiple steady states that are separated by a threshold.
In cases where households make it beyond the threshold, they will accumulate assets until they read the non-poor
steady state. In these cases, a short-term transfer can move households beyond the threshold, providing long-run
benefits without requiring further assistance (Rosenstein-Rodan, 1943; Murphy et al., 1989; Sachs, 2006). A recent
survey focused on multiple equilibria poverty traps and found that they “are rare and largely limited to remote or
otherwise disadvantaged areas” (Kraay and McKenzie, 2014).
However, many households remain trapped in poverty even without the existence of a potential high-income steady
state sitting just beyond their reach. Barrett and Carter [2013] clarify this distinction and define single equilibrium
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poverty traps as occurring when there is a single steady state that exists at low income levels. In these contexts,
all households converge on the low-income steady state and short-term transfers will only provide short-term relief
from poverty. Rather than being explained only by capital levels, these types of poverty traps place greater weight
on structural factors that limit opportunities for these households - potentially including bad geography (Jalan and
Ravallion, 2002), disease (Sachs and Malaney, 2002), poor institutions (Acemoglu et al., 2001; Acemoglu et al.,
2005), or other factors that individual households cannot control. While evidence of multiple equilibria is most
common in remote pastoral areas (Lybbert et al., 2004; Barrett et al., 2006), a large number of papers find evidence
of single equilibrium poverty traps (including, for example, Quisumbing and Baulch [2013] and Naschold [2013]).
Given the evidence for both single and multiple equilibria poverty traps, it is important to develop models that can
explain the many causes of poverty and to evaluate policies based on both their benefits and limitations.
In this paper, we develop a model that explores the importance of multiple levels of poverty traps while also
working to endogenously explain the existence of these various poverty traps. First, we focus on fractal poverty
traps, which Barrett and Swallow [2006] define as occurring when “multiple dynamic equilibria exist simultaneously
at multiple (micro, meso, and/or macro) scales of analysis and are self-reinforcing through feedback effects” (p. 3).
They develop an insightful informal model that we expand upon by formalizing each level of aggregation, where
both single and multiple equilibria poverty traps can coexist simultaneously at multiple levels of aggregation. This
model allows us to analyze, for example, why poverty traps often develop in remote regions of poor countries,
where a combination of micro, meso, and macro-level conditions reinforce each other to trap individuals at low
income levels. Second, many structural factors are themselves endogenous to historical and institutional processes.
For example, despite the evidence that institutions and markets differ across different regions and countries, they
develop endogenously and need to be explained themselves. Our model attempts to provide an explanation for the
development of micro-, meso-, and macro-level poverty traps and the ways in which they reinforce or dominate one
another. We will explore the ways in which collective decisions determine structural factors and the ways in which
these structural factors, in turn, explain individual decisions and welfare.
At the micro level, we model individual poverty traps occurring through lumpy production technologies, as individual
farmers can use either a low-return technology or a high-return technology that requires a large fixed cost. For
example, the low-return technology can be considered to be a traditional crop variety or a manual means of
production while the high-return technology can be modern crop varieties (which may require costly learning and
experience), cash crops (such as fruits that require several years to yield), or animal or mechanized production.
While we focus on agriculture, this framework can easily be applied to human capital investments, migration, or
other individual choices and income strategies. We develop a model that uses individual asset and initial capital
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levels to explain the conditions under which certain individuals may be stuck in a poverty trap. These poverty
traps resulting from lumpy investments also require credit market failures and we do not allow for borrowing.
The meso level is described as by Barrett and Swallow [2006] as “communities, groups, networks, and local jurisdic-
tions” and these factors can influence poverty through coordination, cooperation, local public goods, and markets.
Our meso-level poverty trap focuses on the endogenous creation of local markets through traders, who give up
production in order to transport goods from other producers to markets and earn income by charging transport
fees. Individual agents will become traders if it benefits them individually and this can also be considered as an
micro-level poverty trap. However, traders also help integrate producers into markets more efficiently and this can
lead more farmers to invest in higher return crops. As a result, we focus on the growth of traders as being a proxy
for the growth of markets. Multiple equilibria can occur through the failure of any traders to arise (either because
nobody can afford to become a trader or because there is not sufficient demand for trade due to geographic clusters
of subsistence agriculture), the existence of a single trader monopolist that charges high fees, or the existence of a
multiple and competitive traders.
While this current version of our paper focuses on the endogenous selection of individual production technologies
and the entrance of traders, we plan to introduce macro-level poverty traps, which can be driven by coordination
failures, positive technology spillovers, agglomeration effects, conflict, or effective institutions. While any of these
factors can cause multiple equilibria for a given country, we plan to focus on the endogenous transition to democracy
and public goods provision, building on the model of Acemoglu and Robinson [2005]. Consider a country that begins
as a dictatorship, with a ruling elite that chooses little or no taxation and fails to provide public goods, which can
be interpreted as property rights or roads, for example, that can increase the returns to private investments and
encourage growth. If individual farmers and traders can overcome their collective action problems in order to lead
a revolution, then a democracy arises in which the median voter chooses a tax rate that is used to provide roads
which facilitate trade, thus causing more individuals to become traders and increasing the profits of individual
farmers. As a result, multiple equilibria can arise at the macro-level, as poor institutions can persist and, under
certain conditions, good institutions can arise that lead to greater individual micro-level investment and meso-level
market creation.
Our model allows us to determine conditions under which a poverty trap at any level of analysis or a combination
of levels is sufficient or necessary for certain households to be trapped at a low-level equilibrium. We are able
to consider questions about whether the different levels of poverty traps reinforce each other (which indicates
that a policy that only overcomes one problem will be of limited effectiveness) or whether one specific problem
fundamentally explains the others (in which targeting the most fundamental problems will lead to large effects).
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We use our model to analyze the conditions under which certain individuals become trapped in poverty. In particular,
we are interested in individual characteristics (especially asset and initial capital levels), regional characteristics
(including the average levels of assets, the variance of assets, and population density), and (eventually) government
characteristics (taxation, public goods provision, and property rights).
We introduce several exogenous policy changes that are commonly recommended in the poverty trap literature
and evaluate how effective they are at reducing poverty. Presently, these interventions are exogenously included,
however, we plan to endogenize many of these decisions when we formally integrate the macro-level analysis in our
model. First, we consider “big push” policies that provide one-time transfers to poor households and evaluate how
these transfers influence individual farmer incomes, the development of local markets, and aggregate measures of
poverty and incomes. These transfers appear as a one-time increase in farmer capital levels and are based on the
most common definition of poverty traps: the existence of multiple equilibria which provides an opportunity for
one-time policies to transition countries or households beyond a threshold, after which they continue advancing to
the next equilibrium without further support. However, even without multiple equilibria, poverty often occurs not
due to multiple equilibria and low initial income levels, but due to the existence of a single, low, steady state. In
these cases, it is often fixed variables (such as assets, institutions, or geography) that limit growth regardless of
initial capital levels. In fact, these households are even more strongly trapped in poverty - since there is not even
a potential higher equilibrium to reach - but structural policies are required to facilitate their escape. Second, we
build on this concept by analyzing structural changes or transfers, which rather than providing households with
additional capital, increase the productivity of their assets. This can be considered to be an increase in total factor
productivity and may include, for example, better geography, institutions, or other structural factors.
Third, we evaluate the importance of public infrastructure investments, which facilitate the movement of people
and goods since they reduce transportation costs and integrate producers and consumers. We model improvements
in infrastructure as a reduction in the fraction of goods that spoil and are lost en route to markets.
Fourth, we are able to analyze the importance of economic equality and the effectiveness of policies that aim to
ensure more equitable ownership of assets. For example, the creation of more equitable asset levels (a lower variance)
may facilitate the development of markets and trade, thus feeding back into individual farmer investment choices.
In the remainder of the paper, we present our basic model, initial results relating to the conditions under which
poverty traps occur, an analysis of several policy interventions, and our plans for endogenizing the macro-level
political choices.
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2 Historical Examples
Among empirical studies of multiple equilibria individual-level poverty traps, most of the evidence is from remote,
pastoral regions. In many rural areas, farmers engage primarily in livestock production and several studies have
found evidence of poverty traps relating to livestock accumulation, including Lybbert et al. [2004] and Barrett
et al. [2006]. As Kraay and McKenzie [2014] note, “In remote rural areas, isolation reduces the number of available
production technologies, which means the choice between lower-income and higher-income outcomes may be a more
difficult discrete step” (p. 143). However, Kraay and McKenzie [2014] also note that many empirical studies have
failed to find evidence of poverty traps, including Naschold [2013] and Jalan and Ravallion [2004]. In an analysis
of panel data across six countries, McKay and Perge [2013] fail to find evidence of multiple equilibria, despite the
persistence of poverty among many individuals. However, these contrasting findings are consistent with evidence
that geography matters and that geographic capital and assets can influence whether or not poverty traps arise. In
China, Jalan and Ravallion [2002] find evidence of geographic poverty traps, which arise because geographic capital
influences the productivity of household capital, meaning that a household in a well-endowed geographic area can
increase their wealth while “an otherwise identical household living in a poor area sees stagnation or decline” (p.
329). Furthermore, there is evidence that, even if multiple equilibria do not exist, many individuals are trapped
in poverty due to the existence of single but low income steady states (Quisumbing and Baulch, 2013; Naschold,
2013). These can also result from poor geography and remoteness. We are able to integrate this concept into our
model while explaining the conditions under which greater access to markets arises endogenously through either
the choice of some individuals to become traders or through the choice to invest in roads.
Dell [2010] finds that historical institutions (in particular, the mita in Peru) can explain whether or not a specific
region is able to attract public investment in roads and other public goods, which then determines market integration,
economic opportunities, subsistence agriculture, household consumption levels, and health. Our model will help to
explore the conditions under which markets fail to form, public goods are not provided by national governments,
and individuals fail to escape poverty. Furthermore, the transition to greater market-based incentives in China
is an important explanation for the growth and simultaneous reduction of poverty in China, one of the greatest
large-scale transitions out of poverty in human history. Given the importance of markets as a means of unlocking
gains from trade and great individual opportunities, it is important to explain the growth of markets in our model.
The growth of the East Asian Tigers may have succeeded because governments were able to overcome several levels of
poverty traps simultaneously. For example, Rodrik [1995] argues that effective government policies allowed South
Korea and Taiwan to overcome coordination failures at the macro-level by coordinating investments, operating
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state-run enterprises with essential linkages, and subsidizing key private industries. As a result, both countries
experienced surges in investment that drove industrialization across a number of sectors. Also important, however,
was the growth of agricultural productivity and incomes in rural areas. Kay [2002] argues that effective land
reforms in South Korea and Taiwan helped (and even forced) small farmers to adopt high-yield seed varieties and
more intensive production methods. Furthermore, Kay [2002] argues that this agricultural growth helped drive
the successful industrialization, since the state was able to tax away much of the increase in rural incomes and
use this surplus to fund industrial investments. While these policies have important distributional effects worth
questioning, it appears that growth was driven by the ability of both governments to overcome multiple levels of
poverty traps. Agricultural policies caused farmers to adopt higher return production methods despite the fixed costs
(thus overcoming micro-level poverty traps driven by credit market imperfections and lumpy investments) while
industrial policy coordinated investments across a number of sectors (thus overcoming macro-level coordination
failures).
However, the growth of good institutions is not guaranteed to overcome poverty traps or to increase income levels.
Acemoglu et al. [2008] fail to find evidence that democracies lead to greater incomes and instead argue that incomes
and democracy are jointly explained by historical processes and critical junctures. In fact, the above success stories
relied but effective but non-democratic governments in South Korea, Taiwan, and China. When complete, our full
model will help us to explore conditions under which democracies and growth reinforce each other, which one might
arise without the other, and when regions will remain trapped at low income levels with dictatorships.
3 Model
We build a three-level fractal poverty trap model, although the current draft only includes the first two levels. At
the lowest level, individuals face a micro-level poverty trap that can be interpreted as either a low and a high return
technology (such as a subsistence crop and a higher return crop such as fruit or coffee that requires a fixed investment)
or different means of production (such an manual vs. animal or mechanical labor). At the meso (or regional) level,
we focus on access to markets by explaining the endogenous growth of traders, who give up production in order
to focus on transporting goods from other farmers to markets. We allow any individual to become a trader, but
they need to have sufficient capital, for example to afford a pushcart with which they can efficiently transport large
amounts of goods to market. As more efficient transportation options, traders can charge individual farmers fees in
mutually beneficial agreements. In the next version of this paper, we will endogenize institutions, by allowing for
both dictatorships (run by a group of elites) and democracies (in which the median voter decides on the tax rate,
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which is used to provide public goods). Public goods are considered to be transportation infrastructure, which will
then influence the number of transporters and the integration of rural households into markets.
While we focus our analysis on agricultural production and markets, this analysis could easily be extended to other
applications where households face their own constraints (such as lumpy investments in agriculture, human capital,
or migration), regional markets face limitations (such as social networks, poor infrastructure, costly transporta-
tion, or weak markets), and countries suffer from macro-level poverty traps (possibly from bad geography, poor
institutions, lack of property rights, or weak legal systems).
3.1 Micro-Level Model
We base our micro-level model on Ikegami et al. [2016]. Consider a representative individual with a fixed level of
total factor productivity (TFP, ↵) and an initial capital level (k0). Total factor productivity does not change with
time but households invest in capital through time (t). Total factor productivity is a technology multiplier and
measures the potential to earn income on a household’s farm. As such, it could represent household characteristics
(such as ability) or farm characteristics (such as the quality of the land or the amount of rainfall). While TFP
is often assumed to include institutions, we propose to model institutions and access to market separately in our
model.
Given their levels of TFP and capital, individuals choose how to maximize income in period t. Each individual earns
income through agriculture (f (↵, kt)) and chooses between a low return technology and high return technology with
a fixed cost (E), that creates a non-convexity such that:
fL (↵, kt) = ↵k�L
t
fH (↵, kt) = ↵k�H
t � E
where 0 < �L < �H < 1. In agriculture, a high return technology can include high yielding seed varieties, which
require fixed expenditures on seeds, fertilizer, and other inputs, or cash crops such as fruit trees or coffee plants,
which require a large initial expenditure and may take several years to pay dividends.
3.2 Meso-Level Model
In addition to these agricultural options, we endogenously allow for increases in market integration through the
choice of certain individuals to become traders. Barrett and Swallow [2006] describe the meso-level analysis as
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“communities, groups, networks, and local jurisdictions” where “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” (p. 8). In our model, the meso-level analysis
focuses on the endogenous development of greater market access that occurs when individual entrepreneurs choose
to become traders. These individuals give up agricultural production and instead earn money by charging fees to
transport goods. As such, they help to increase access to markets in mutually-beneficial agreements with agricultural
producers.
Initially, all individual agricultural producers described in the micro-level model transport their own goods to
market, possibly on foot or using draft animals. However, this transportation is costly and farmers lose some of
their crop while en route. Assume that only a portion (✓L) of a farmer’s harvest reaches market if they transport
it themselves. Becoming a trader requires sufficient wealth to purchase a pushcart (or car, van, wagon, etc.) and
we model this through a fixed capital threshold (kT = 11) that a farmer must surpass before being able to cash in
their capital for a pushcart. The pushcart can transport the crops of at least eight people (the eight neighbors in
the grid space) and does so while maintaining a greater proportion of each farmer’s harvest (✓H > ✓L).
An individual compares his income as a farmer with his income as a trader and maximizes their profit. In order
to predict one’s potential income as a trader, each farmer evaluates each neighbor to determine if they are already
a trader (and thus would not be a potential customer) and, if not, the maximum fee that each neighbor would be
willing to pay to a trader. With this information gathered from each of the eight neighbors, each potential trader
calculates the fee that would maximize their total revenue if they were to become a trader. If this is greater than
what they would earn as a farmer (and they have sufficient capital), then they decide to become a trader. We assume
that a trader knows the potential fee that each of their eight neighbors would be willing to pay but is only able to
charge a single price for all potential clients, thus acting as a local monopolist that charges the transportation fee
(F ) that maximizes total revenue. They charge their total revenue maximizing fee and their neighbors then decide
whether to continue with subsistence agriculture or to accept the trader’s offer to transport their goods. If multiple
traders develop, then they compete over fees and neighbors choose the lowest fee available.
Given the complex interdependence of traders and farmers, we assume that each trader (or potential trader) assumes
that they will charge the same fee and earn the same profit for all future periods.
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3.3 Macro-Level Model
We are currently adding the macro-level analysis to the paper. Here is a brief and informal description of the macro
model:
The model will include a democratically government that can build per-period public infrastructure using tax
revenue. Public infrastructure will be a public good – i.e., non-rivalrous and non-excludable. Public infrastructure
helps reduce the fixed cost of transport/storage. Taxes are collected as marginal taxes.
At the end of each period, agents will vote for a tax rate (they will be told how much public infrastructure they can
expect the following period for every choice of tax rate). Agents pay taxes right after the votes are counted and
before the next period starts. The taxes collected at the end of a period will be used to finance public infrastructure
in the next period.
The macro poverty trap is similar to the micro and meso traps; the non-convexity generated by this additional
feature can also trap societies into poor outcomes.
Note that both the very poor (i.e., those who do not find it optimal to use the storage/transport technology) and
the very rich (i.e. those for whom a marginal tax rate results in a significant reduction in their level of personal
disposable income compared to their personal gain from public infrastructure) will vote for a low tax or a zero tax
regime. Thus, some level of equality and a moderate level of overall income will be needed for public infrastructure
to become feasible.
3.4 Intertemporal Utility Maximization
With the potential to be either a farmer or a trader, in each period household income is the maximum income
earned from any of their choices:
yt (↵, kt) = max
8>>>>>>>>>>>>>><
>>>>>>>>>>>>>>:
✓LfL (↵, kt) = ✓L (↵kk�L
t )
✓LfH (↵, kt) = ✓L (↵kk�H
t � E)
✓HfL (↵, kt) = ✓H (↵kk�L
t )� F
✓HfH (↵, kt) = ✓H (↵kk�H
t � E)� F
fTrader = (F ) (# of Clients)
Low return independent
High return independent
Low return traded
High return traded
Trader
11
After maximizing income, the household determines optimal levels of consumption (ct) and investment in capital
(it) so as to satisfy the household budget constraint:
ct + it = yt (↵, kt)
Capital growth is modeled as:
kt+1 = it + (1� �) kt
where � is the rate of depreciation. Farmers will accumulate capital until they reach their respective steady state
(which depends on their individual TFP level and their initial capital levels) while traders will maintain capital
levels just above the threshold to become a trader (kT = 11).
Based on these maximum income levels, each individual maximizes their discounted sum of future utility:
max
1X
t=0
�tu (ct)
subject to:
ct + it = yt (↵, kt)
kt+1 = it + (1� �) kt
u (ct) =c1��t � 1
1� �
where � is the CRRA coefficient and � is the discount rate.
3.5 Grid Space and Parameterization
We randomly select a level of TFP (↵) and an initial capital level (k0) for an individual placed in each cell
of a 25 by 25 grid. In the analysis below, we focus specifically on different values of TFP (↵), which include
↵ = {0.985, 1.030, 1.075, 1.120, 1.165}, and our primary analysis involves a uniform distribution over these five
possible values before we adjust the mean and variance of TFP, as described in detail below. We also draw
initial capital levels for each agent based on a uniform distribution k0 ⇠ U [0, 15]. Finally, we also adjust the
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transportation losses to consider an initial poor road access scenario (✓L = 0.55, ✓H = 0.95) and a good/dense road
scenario (✓L = 0.65, ✓H = 1).
Otherwise, the analysis relies on numerical simulation of this multiple asset model based on the following parame-
ters:1
Variable Measure Values
u (ct) CRRA utility u (ct) =c1��t �11��
� CRRA risk aversion parameter 1.5
� Discount rate 0.95
⇢ Rate of time preference
1���
↵ Total factor productivity {0.985, 1.030, 1.075, 1.120, 1.165}
�L Production exponent for low return technology 0.3
�H Production exponent for high return technology 0.45
E Fixed cost of adopting high return agriculture/labor 0.45
k Capital 0.05 to 15
� Depreciation rates 0.08
✓L , ✓H Transportation Losses ✓L = 0.55, ✓H = 0.95 with poor roads
✓L = 0.65, ✓H = 1 with good roads
kT Trader Capital Threshold 11
3.6 Stages of Decision Making
Our agents make decisions asynchronously in three stages.
1. To Farm or Not To Farm. Based on all available information at the start of the round, each agent decides
to be a farmer or a trader. Specifically, each agent looks at each of their eight neighbors and determines what
fee they would be willing to pay a trader, and then compares their expected profit from farming with their
potential profit as a trader. If they decide to be a trader, they post their fees at the end of this stage.
2. Contracts. With all potential traders having posted fees, they go around and write contracts with individual
farmers, where each farmer chooses the lowest possible fee available to them.1This specification is convenient because the limit as � ! 1 is equal to u (c) = ln (c).
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3. Produce and Consume. During the final stage, farmers produce and pay fees to traders, who collect
fees for transporting the goods. In certain cases, an agent may decide to be a trader in Stage 1 only to be
outcompeted by another trader, thus collecting no fees. In these cases, we assume that this particular agent
returns to farming but has to produce and transport their own yields, since it is too late for them to contract
with another trader. At the end of this round, each agent consumes and invests optimally, capital depreciates,
and every agent is relabeled as a farmer or trader.
Following the end of all three stages, the process repeats itself.
4 Policy Interventions
4.1 Road Construction
We consider the impact of a road construction program, which provides an important public good that improves
the ease of transportation. While traders will always be better at transporting goods due their adoption of better
technologies and the resulting economies of scale, improved road networks can improve transportation for both
individual farmers as well as traders. In our model, this occurs through an increase in ✓L and ✓H , with a greater
increase in ✓H helping to encourage more traders. This is predicted to make trade easier and to increase market
integration by making it more profitable to become a trader. With more traders, this also provides benefits to
individual farmers. We first model a scenario in which there are few roads and transportation costly, resulting in
✓L = 0.55 and ✓H = 0.95, and then contrast this with a scenario in which there are dense road networks, resulting
in ✓L = 0.65 and ✓H = 1.
4.2 Total Factor Productivity
While many discussions of poverty traps emphasize one-time transfers that can move households to a higher equi-
librium, many individuals remains trapped in single equilibrium poverty traps, indicating that they are trapped
at poverty but injections of capital would only have short-term benefits. For these types of individuals, structural
changes must occur that increases their productivity, allows them to increase the returns to their labor and capital,
and provides them with new opportunities. In our model, we explore the importance of asset-levels by changing the
mean of the TFP (↵) term, which can be interpreted as policies that increase or decrease the average asset level of
households.
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In our framework, higher asset levels will directly increase individual income levels, since they increase the production
for any level of capital while also allowing more farmers to use the high-return technology. Furthermore, higher
average asset levels can indirectly benefit farmers, since greater assets increase incomes and make it more likely
that neighboring individuals accumulate sufficient capital to become a trader. Once a neighbor becomes a trader,
this provides greater market access, more options, and higher potential incomes for neighbors.
As a result, we test whether or not higher average asset levels influence measures of wealth (including GDP per
capita, the poverty headcount, and the poverty gap) and the growth of markets (the number of traders).
4.3 Equality
It is also possible that regional equality and inequality will influence the meso-level of analysis and that this can,
in turn, influence individual income strategies and investments. While our agents are independent farmers, the
growth of markets might depend on the existence of a critical mass of farmers who are able to pay higher fees to
transport high-return agricultural goods. As a result, more dense networks of wealthier individuals may increase
the profitability of trading, which will influence the growth of markets. Thus, in addition to testing whether average
asset levels impact the number of traders, we also consider whether or not the variance of asset levels impacts the
number of traders. We also consider whether or not the variance of asset levels affects wealth.
5 Results
Holding all of our parameters constant at their starting values and using a uniform distribution of TFP, we run
5,000 simulations of both the “poor roads” and “good roads” and compare the results in Table 1. The results
verify many predicted outcomes: better transportation significantly increases GDP per capita, reduces the poverty
headcount from 29% to 22.2%, and reduces the poverty gap from 6.8% to 3.8%. Interestingly, while better roads do
not significantly increase the share of agents who are farmers, it does increase the share of farmers that use traders
as well as the share of farmers that use the high return technology.
Figure 1 depicts the final activity choices under the poor roads scenario and Figure 2 depicts the good roads scenario.
For any given cell, yellow cells correspond to traders, brown to high-technology farmers that use a trader, green to
low-technlogy farmers that use a trader, light blue to high-technology farmers not using a trader, and dark blue to
low-technology farmers not using a trader.
15
The remaining results are based on simulations that are based on random distributions of TFP. For each simulation,
we draw a random number between 1 and 6 for each of five potential levels of TFP. For each of these five potential
levels of TFP, we then calculate the probability for that level as the random draw divided by the sum of all five
random draws. This provides variance in the mean and standard deviation of TFP across all simulations. We then
run 5,000 simulations of both “poor road” and “good road” scenarios and create a dummy variable equal to 1 if
there are good roads and 0 otherwise.
Figures 3 and 4 depict GDP per capita for different mean TFP levels and various standard deviations of TFP, both
for poor roads (left) and good roads (right). Figure 3 provides evidence that GDP per capita increases both as
mean TFP increases and when roads improve. Figure 4 suggests that the relationship between GDP per capita and
the standard deviation of TFP is less strong, and possibly slightly negative among good road simulations. Figures
5 and 6 provides evidence that both the poverty headcount and the poverty gap decline as both the mean TFP
level increases and when roads improve.
We next use OLS regressions to evaluate the significance of the various predictors of wealth and poverty traps while
controlling for multiple determinants.
Table 2 provides evidence that welfare improves (appearing as an increase in GDP per capita in columns 1-4 and a
decrease in the poverty headcount in columns 5-8) as the average TFP increases, as the standard deviation of TFP
decreases, as more traders appear, and when roads are improved. Respectively, this suggests that welfare improves
when asset levels increase, when equality increases, when access to markets improves, and when infrastructure and
roads improve. While we expect to see many of these results, the fact that the significance of each variable holds
when all the other controls are included (columns 4 and 8) indicates that each factor is important independent of
the others. Thus, while improved asset levels can help households escape poverty at the micro-level and while better
roads can help markets level form (a meso-level factor that we explore next), each factor matters independently
and policies that only address one of these factors may not be sufficient.
Table 3 analyzes the percent of agents who become traders. In our model, this can be an important micro-level
poverty trap since becoming a trader requires a high level of capital but can lead to higher income levels. However, it
can also be considered an important meso-level factor, since traders help increase access to markets for neighboring
farmers. Table 3 indicates that higher average TFP levels and better roads both significantly increase the percent
of traders, but the standard deviation of TFP does not. This suggests that average wealth (resulting from higher
TFP) matters more for the growth of trade than the variance of wealth, which might provide more economies of
scale for traders.
16
Table 4 explores the factors that explain how many farmers are able to overcome individual poverty traps, measured
by the percent of farmers who use the high-return technology. As hypothesized, a greater share of farmers escape
poverty when average TFP levels are higher, when more traders exist, and when roads improve. Each of these
factors increases the returns to farmer investment and make it easier for them to escape poverty by investing in
higher return technologies. While the standard deviation of TFP does not explain the growth of traders, more
farmers use the high return technology when the standard deviation of TFP declines.
6 Conclusions
This develop developed a fractal poverty trap model that allows us to explore various policy interventions at
the individual, local, and national levels. We evaluate the factors explaining the ability of individual farmers to
overcome micro-level poverty traps, the conditions under which traders help create greater access to markets, and
overall welfare levels. In the next stage of our analysis, we plan to endogenously develop institutions, including both
the regime type (democracy or dictatorship) as well as policy (individual tax levels that are used to provide public
goods). This will allow us to answer even more interesting questions, including ones relating to the development
of institutions, the importance of factor endowments and institutions for explaining growth, and the persistence of
poverty traps at multiple levels of aggregation.
Table&1:&Comparing&Good&vs.&Poor&Roads
GDP&Per&CapitaSt.&Dev.&Of&Income
Poverty&Headcount Poverty&Gap
%&Farmers&Using&High&Return&Technology
%&Farmers&Using&Trader %&Traders
Poor&Roads Mean: 1.65 0.74 29.0% 6.8% 60.3% 72.3% 9.8%St.4Dev.: 0.04 0.00 2.4% 0.6% 3.1% 3.2% 0.3%
Good&Roads Mean: 1.93 0.76 22.2% 3.8% 69.9% 75.6% 10.1%St.4Dev.: 0.04 0.02 2.8% 0.5% 2.9% 3.0% 0.5%
Table&2:&&Determinants&of&Welfare
1 2 3 4 5 6 7 8
TFP,mean 0.241*** 0.241*** 0.178*** 0.207*** 40.047*** 40.047*** 40.016*** 40.021***[0.004] [0.004] [0.004] [0.001] [0.001] [0.001] [0.001] [0.001]
TFP,std.,dev 40.043*** 40.037*** 40.040*** 0.045*** 0.042*** 0.043***[0.008] [0.007] [0.002] [0.003] [0.002] [0.001]
%,Traders 11.706*** 6.372*** 45.803*** 44.807***[0.211] [0.046] [0.049] [0.031]
Good,Roads,(=1,if,improved,transportation) 0.222*** 40.041***[0.000] [0.000]
Constant 1.086*** 1.144*** 0.154*** 0.494*** 0.392*** 0.331*** 0.821*** 0.758***[0.012] [0.016] [0.023] [0.005] [0.004] [0.005] [0.005] [0.003]
Observations 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000R4squared 0.285 0.287 0.455 0.976 0.132 0.156 0.651 0.869Standard,errors,in,parentheses
***,p<0.01,,**,p<0.05,,*,p<0.1
GDP&per&capita Poverty&Headcount
Note:,,Each,observation,is,one,of,10,000,simulations,,with,5,000,run,with,poor,roads,and,5,000,run,with,good,roads.,,Controls,include,the,mean,TFP,(alpha),,the,standard,deviation,of,TFP,,the,percent,of,agents,who,are,traders,,and,a,dummy,variable,equal,to,1,if,there,are,good,roads.,,
Table&3:&&Escaping&Meso2Level&Poverty&Traps
1 2 3
TFP'mean 0.005*** 0.005*** 0.005***[0.000] [0.000] [0.000]
TFP'std.'dev 60.000 60.000[0.000] [0.000]
Good'Roads'(=1'if'improved'transportation) 0.003***[0.000]
Constant 0.084*** 0.085*** 0.083***[0.000] [0.001] [0.001]
Observations 10,000 10,000 10,000R6squared 0.105 0.105 0.161Standard'errors'in'parentheses
***'p<0.01,'**'p<0.05,'*'p<0.1
%&of&Agents&who&are&Traders
Note:''Each'observation'is'one'of'10,000'simulations,'with'5,000'run'with'poor'roads'and'5,000'
run'with'good'roads.''Controls'include'the'mean'TFP'(alpha),'the'standard'deviation'of'TFP,'and'a'
dummy'variable'equal'to'1'if'there'are'good'roads.''
Table4:EscapingMicro-LevelPovertyTraps
1 2 3 4
TFPmean 0.097*** 0.097*** 0.064*** 0.071***[0.001] [0.001] [0.001] [0.001]
TFPstd.dev -0.088*** -0.085*** -0.086***[0.003] [0.002] [0.001]
%Traders 6.223*** 4.864***[0.065] [0.039]
GoodRoads(=1ifimprovedtransportation) 0.057***[0.000]
Constant 0.373*** 0.493*** -0.033*** 0.053***[0.004] [0.006] [0.007] [0.004]
Observations 10,000 10,000 10,000 10,000R-squared 0.304 0.354 0.664 0.884Standarderrorsinparentheses
***p<0.01,**p<0.05,*p<0.1
%FarmerswhouseHigh-ReturnTechnology
Note:Eachobservationisoneof10,000simulations,with5,000runwithpoorroadsand5,000runwithgoodroads.ControlsincludethemeanTFP(alpha),thestandarddeviationofTFP,thepercentofagentswhoaretraders,andadummyvariableequalto1iftherearegoodroads.
Figure'1:''Example'Activity'Choices'(with'Poor'Roads)
Figure'2:''Example'Activity'Choices'(with'Good'Roads)
Note:&&Yellow&cells&correspond&to&traders,&brown&to&high6technology&farmers&that&use&a&trader,&green&to&low6technlogy&farmers&that&use&a&trader,&light&blue&to&high6technology&farmers¬&using&a&trader,&and&dark&blue&to&low6technology&farmers¬&using&a&trader.
Note:&&Yellow&cells&correspond&to&traders,&brown&to&high6technology&farmers&that&use&a&trader,&green&to&low6technlogy&farmers&that&use&a&trader,&light&blue&to&high6technology&farmers¬&using&a&trader,&and&dark&blue&to&low6technology&farmers¬&using&a&trader.
Figure'3:'GDP'per'capita'and'TFP'mean
Figure'4:'GDP'per'capita'and'TFP'standard'deviation
Note:&These&figures&plot&GDP&per&capita&and&the&TFP&(alpha)&mean&for&5,000&simulations&with&costly&transportation&(left)&and&5,000&simulations&with&improved&transportation&(right).
Note:&These&figures&plot&GDP&per&capita&and&the&TFP&(alpha)&standard&deviation&for&5,000&simulations&with&costly&transportation&(left)&and&5,000&simulations&with&improved&transportation&(right).
1.4
1.6
1.8
22.
2
2 2.5 3 3.5 4 2 2.5 3 3.5 4
0 1
GDPperCapita Fitted values
MeanofAlphas
Graphs by thetahigh
GDP per capita by Alpha Mean
1.4
1.6
1.8
22.
2
1 1.5 2 1 1.5 2
0 1
GDPperCapita Fitted values
StdofAlphas
Graphs by thetahigh
GDP per capita by Alpha St. Dev.
Figure'5:'Poverty'Headcount'and'TFP'mean
Figure'6:'Poverty'Gap'and'TFP'mean
Note:&These&figures&plot&the&poverty&headcount&and&the&TFP&(alpha)&mean&for&5,000&simulations&with&costly&transportation&(left)&and&5,000&simulations&with&improved&transportation&(right).
Note:&These&figures&plot&the&poverty&gap&and&the&TFP&(alpha)&mean&for&5,000&simulations&with&costly&transportation&(left)&and&5,000&simulations&with&improved&transportation&(right).
.1.2
.3.4
2 2.5 3 3.5 4 2 2.5 3 3.5 4
0 1
povhc Fitted values
MeanofAlphas
Graphs by thetahigh
Poverty Headcount by Alpha Mean
0.0
5.1
2 2.5 3 3.5 4 2 2.5 3 3.5 4
0 1
povgap Fitted values
MeanofAlphas
Graphs by thetahigh
Poverty Gap by Alpha Mean
24
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