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A poverty trap is a self-perpetuating condition whereby an economy, caught in a vicious circle, suffers from persistent underdevelopment. Although it is often modelled as a low-level equilibrium in a static model of coordination failures, we discuss the concept in a dynamic setting. This is because, in a static setting, we would be unable to distinguish poverty traps from (possibly temporary) bad market outcomes, such as recessions and financial crises, that are also often modelled as low-level equilibriums in a static model of coordination failures.

On the Mechanics of Poverty Traps

Imagine that the state of the economy in period t is represented by a single variable, xt, where a higher x means that the economy is more developed, and that the equilibrium path follows a deterministic one-dimensional difference equation, xt+1 = F(xt). Once the initial condition, x0, is given, this law of motion can be applied iteratively to obtain the entire trajectory of the economy.

In Fig. 1a, F(x), stays above the 45° line everywhere, hence the economy grows forever (as in the endogenous growth models). In Fig. 1b, for any x0, the economy converges to x* (as in the Solow growth model). In either case there is no poverty trap, since the long-run performance of the economy is independent of the initial condition, no matter how underdeveloped the economy is initially. (Confusion sometime occurs because a few authors use the term ‘trap’ to describe the situation depicted in Fig. 1b, in the sense that growth is not sustainable. However, this should more appropriately be called ‘the limit to growth’. This limit is not caused by the initial poverty of the economy.)

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Poverty Traps, Fig. 1

In Fig. 2a and b, on the other hand, the long-run performance depends on the initial condition. When the economy starts above xc, it will stay above xc and may either grow forever or reach a higher stationary state. However, if it starts below xc, it will be trapped forever below xc. In this sense, both figures exhibit a poverty trap in its strong form. In Fig. 2a, the economy caught in the trap will converge to the low-level stationary state. In Fig. 2b, it will fluctuate below xc. In both cases, the economy will remain poor only because it is poor. Thus, the poverty becomes its own cause. It is this self-perpetuating nature that sets ‘the poverty trap’ apart from ‘the limit to growth’.

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Poverty Traps, Fig. 2

Both Fig. 2a and b project the very stark view that the economy can never escape from the poverty trap. This should not be taken too literally. The essential message of poverty traps is that poverty tends to persist, and that it is difficult, but not necessarily impossible, for the economy to escape from it. Poverty traps in their weak form are depicted in Fig. 3a and b. In Fig. 3a, the economy has to experience stagnation for long time as it travels through the ‘narrow corridor’ between F(·) and the 45° line, before eventually succeeding in taking off. In Fig. 3b, the economy may or may not manage to escape the trap after experiencing (possibly many) periods of volatility. For all practical purposes, the situations depicted in Fig. 2a and b and Fig. 3a and b are difficult to separate, but the message is the same: the self-perpetuating nature of poverty.

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Poverty Traps, Fig. 3

The above analysis can be extended in many directions. First, one could add stochastic shocks to the system, as xt+1 = F(xt, ξt+1). Such shocks perturb the map, which may switch the graph back and forth between Figs. 2a (or 2b) and Figs. 3a (or 3b). This can be viewed as a jump in the state variable in the case of the additive shocks, xt+1 = F(xt) + ξt+1. (For example, natural disasters, plagues and wars could cause the capital–labour ratio to jump up and down.) In the presence of such stochastic shocks, the economy may occasionally and recurrently escape or fall into the trap. Hence, the analysis has to be described in terms of the stochastic kernel; see Azariadis and Stachurski (2005) for a detailed discussion of stochastic poverty trap models.

Second, the above analysis assumes that xt+1 is uniquely determined as a function of xt. If the underlying economic models permit multiple equilibria, as often is the case with models of external economies and strategic complementarity, then F(·) becomes a correspondence, and the (deterministic) equilibrium path follows the difference inclusion, xt+1 ∈ F(xt). See Matsuyama (1997) for some examples. Figure 4 depicts one possibility, suggesting that the economy is stuck in a low-level stationary state, in part due to coordination failures. In this case, the economy could escape the poverty trap if it succeeded in coordinating on a higher equilibrium, as indicated by the dotted arrow. (If such coordination takes place through a realization of some coordination devices, ‘sunspots’, it can be viewed as a model of endogenous stochastic shocks.)

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Poverty Traps, Fig. 4

Third, the underlying economic model may imply that the law of motion be described in a multi-dimensional system. For example, the state space may be two-dimensional, (x; q), where x is the state (or backward-looking) variable, such as the capital stock, and q is the co-state (or forward-looking) variable, such as the asset price or consumption, and the law of motion is given by a two-dimensional difference equation, (xt+1, qt+1)= F(xt, qt). In this case, for a given initial condition, x0, the equilibrium condition may not uniquely pin down the initial value, q0. That is, there may be multiple equilibrium paths, with self-fulfilling expectations, which suggests another way in which the economy may escape from the poverty trap; see Matsuyama (1991). Or the dimensionality of the state space may be equal to the number of industries in a multi-industry model, or to the number of countries in a multi-country world economy model. In such a high-dimensional system, one could encounter a much richer set of dynamics, where the long-run behaviour can depend on the initial condition in a much more complex manner.

Some Models of Poverty Trap

Many (dynamic) models of poverty traps have been proposed in the literature. The common feature of these models is the presence of some external economies or strategic complementarities that give rise to the circular causation. Here is a highly selective list.

Learning-by-Doing Externalities

The infant industry argument for protection (see Corden 1977, for a synopsis) is a classic example. When firms are inexperienced and unproductive, they cannot offer wages high enough to attract workers from other sectors, and hence are not able to accumulate experience. Temporary protection has been suggested as a way to break the vicious circle. Helping some industries accumulate experience to escape from a poverty trap, however, may end up pushing the economy into another poverty trap, as it could prevent other (new and possibly more promising) industries from growing. If the scope of productivity improvement in any industry is limited, then the only way of avoiding poverty traps and achieving sustainable growth is to keep the delicate balance so that production will shift constantly from one industry to another, as existing industries become mature and new industries are born; see Stokey (1988); Brezis et al. (1993); Matsuyama (2002).

Search Externalities

The difficulty of finding business partners can discourage many from entering an industry, which in turn makes it even harder for others to find business partners. See Diamond (1982).

Human Capital Externalities

Following the Lucas (1988) model of endogenous growth based on human capital accumulation, Azariadis and Drazen (1990) showed how it could lead to the existence of poverty traps, when human capital is subject to threshold externalities.

Market Size and Division of Labour

Adam Smith argued that ‘the division of labour is limited by the extent of the market’. Young (1928) argued that the extent of the market is also limited by the division of labour. That is, economic growth can be achieved by means of greater specialization, which was formalized by Romer (1987) and others. Building on this body of work, Ciccone and Matsuyama (1996) showed how the economy can be caught in a poverty trap. The basic mechanism is that advanced technologies require the use of highly specialized equipment and producer services. In the underdeveloped economy, the limited availability of specialized inputs forces downstream industries to rely on less advanced technologies, which do not require the use of specialized inputs. This in turn leads to a small market size for specialized firms in upstream industries. Hence, the economy is caught in the vicious circle of limited market size and limited division of labour.

Financial Developments

In countries with limited opportunities to diversify risk, entrepreneurs are discouraged from making productive but risky investments. This in turn leads to a limited set of traded financial assets, which reduces the opportunity to diversify risk. See Saint-Paul (1992) and Acemoglu and Zilibotti (1997).

Low Wealth/Low Investment

When external finance is more costly than internal finance, a decline in borrower net worth leads to a higher investment distortion. In Bernanke and Gertler (1989), this leads to a decline in the investment, which in turn leads to a decline in the net worth of the next generation of entrepreneurs, hence generating persistence in the aggregate investment dynamics. In Matsuyama (2004), the same mechanism could make some (but not all) countries in the world caught in the vicious circle of low net worth–low investment. Matsuyama (2007) showed how the trap can sometimes take the form of greater volatility (as shown in Fig. 2b). In a set-up that allows for wealth distribution to evolve over time, Banerjee and Newman (1993) suggested that greater initial wealth inequality, to the extent that it increases the number of entrepreneurs rich enough to finance their investments, can lead to a higher aggregate investment, which in turn could help the poor in the long run, thereby breaking the vicious circle.

Demographic Trap

Nelson (1956) is among the first to argue that underdeveloped countries are caught in the vicious circle of high population growth and low per capita income. Becker et al. (1990) showed how the economy may be caught in the vicious circle of high fertility–low human capital. Basu (1999) and Doepke and Zilibotti (2005) discussed child labour traps. In Matsuyama (2000), inter-generational persistence of a high labour force participation rate by the elderly could lead to a poverty trap.

Contagious Social Norms

Tirole (1996) showed how corruption or other unethical behaviour can be contagious and persistent. He considered the setting where, in the presence of imperfect information, the reputation of a member of the group (say, a firm in the industry) depends not only on his own past behaviour, but also on the past behaviour of other group members. Then, when the group has the reputation of being dishonest, it would be difficult for the member to establish a reputation for honesty. This induces him to behave dishonestly, thereby contributing to the bad reputation of the group.

Modelling Inertia

Underdevelopment is often modelled as a Pareto-dominated equilibrium in a static game of strategic complementarities. Murphy et al. (1989) is the best-known example. By adding some inertia, which restricts the ability of the players to switch their strategies, one can convert virtually any static game of strategic complementarities into a dynamic model of poverty traps, where both the initial condition and expectations can play a role in determining the long-run performance of the economy. See the techniques developed by Matsuyama (1991) and Matsui and Matsuyama (1995).

Some Cautionary Remarks on Interpretations

The poverty trap is often interpreted as an explanation for cross-country income difference. As such, it is frequently viewed as an alternative to the models that attribute cross-country income difference to the cross-country difference in, say, TFP and/or investment distortions. This is a misinterpretation. First, the message of poverty trap models is the self-perpetuating nature of poverty. It suggests that the long-run performance of an economy could be much better if its initial condition were better. It does not mean that the cross-country difference in the long-run performance is due mostly to the difference in their initial conditions. Second, the notion of poverty trap does not contradict the observation that low income is often associated with low TFP and/or high investment distortions. Indeed, many poverty trap models attempt to explain the two-way causality between low-income and low TFP and/or high investment distortions. By endogenizing TFP and/or investment distortions, these poverty trap models go one step further than the models that treat these variables as exogenously given.

Many calls for foreign assistance for underdeveloped countries can be understood using the notion of poverty trap; see, for example, Sachs et al. (2004). Indeed, the poverty trap is often viewed as a powerful case for policy activism. However, one should be careful when using any particular model of the poverty trap to make policy proposals. It is important to keep in mind that each model of the poverty trap is designed to highlight one particular feedback mechanism behind the vicious circle. To this end, other sources of the poverty trap are deliberately assumed away. In reality, of course, many sources of the poverty trap are likely to coexist. If there is one important lesson from the literature reviewed above, it should be that there are hundreds of traps that the economy can fall into, and any policy intervention that attempts to pull the economy out of one trap may end up pushing it into another. As we know, any attempt to solve a problem can often become a source of another, even bigger problem. For more on this issue, see Matsuyama (1996), which discusses economic development as ‘complex’ coordination problems.

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