Topic 5 Poverty Traps PDF

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Topic 5: Poverty Traps

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Essential readings: • Ray, D. (1998). Chapter 8 in: Development economics. Princeton University Press. (Section 8.4) • Ghatak, M. (2005). Theories of poverty traps and anti-poverty policies. The World Bank Economic Review, 29(supplement), S77-S105.

1. Nutritional poverty traps • “There will be a poverty trap whenever the scope for growing income or wealth at the very fast rate is limited for those who have too little to invest, but expands dramatically for those who can invest a bit more.” (Banerjee and Duflo, 2011, p.11)1 • Nutritional poverty traps are explained using an S-shaped (work capacity) curve. • Consider a simple relationship between income today and income tomorrow: •

y t = f (yt−1) . •

-

Income today: income that an individual has today, out of which he/she has to consume and save. Income tomorrow: savings today are invested, which then give the income for tomorrow. Standard assumption: this relationship is concave. To get the steady-state (SS): 45° line: income today  income tomorrow. Relate it to Solow’s model: in SR, it matters what the starting point is; in LR, we have conditional convergence.

- With a concave relationship between income today and income tomorrow, there is no poverty trap. Income tomorrow 45° line

Income today

Banerjee, A. V. and Duflo, E. (2011). Poor economics: A radical rethinking of the way to fight global poverty. New York: Public Affairs. 1

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- However the relationship is not always concave. - Poverty trap zone: ‣ Income in the future is lower than the income today. ‣ This happens when the curve is below the 45° line.

Income tomorrow 45° line

poverty trap zone outside the poverty trap

Income today

- One explanation for these poverty traps is nutrition-based. ‣ The income is so low that it cannot even cover the basic needs. ‣ Due to low levels of nutrition, the poor do not have the capacity to work. ‣ This leads to double feedback loop: low income ⟹  cannot buy more food ⟹  poor

nutrition  ⟹ cannot work  ⟹ income falls  ⟹ … • Defining the capacity curve:

- Consider a poor worker eats in the morning, works all day, gets a wage in the evening, this income is then used to eat again tomorrow, and so on.

- Let y be income, we have the following two implicit relationships: (i) How much more production can you be if you have bit more to eat:

y t = waget × productivityt = f (nutritiont ) (ii) How much more do you eat when you have more income: nutrition  t = g (yt − 1)

- Putting the two together gives us the capacity curve as: y t = f [g (yt − 1)] 2

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- Poverty will exist only if the capacity curve intersects the 45° line from below: 

∂yt >1 ∂yt − 1

∂f ∂g ∂yt = ∂yt − 1 ∂g ∂yt − 1  ∂f g ∂g yt − 1 f = × × ∂g f ∂yt − 1 g yt − 1 ∂f g is the nutrition-productivity elasticity, ∂g f ∂g yt − 1 where  is the income-nutrition elasticity, and ∂yt − 1 g f where  : at 45° line f = yt − 1 . yt − 1 where 

- Condition for the poverty trap to exist: 

∂g yt − 1 ∂f g × >1 ∂g f ∂yt − 1 g

2. Different views of poverty • Ghatak’s paper generalises the poverty trap models. • He gives different conditions under which poverty traps can arise. • Specifically focus on two different views of poverty and thus two different reasons for poverty traps: (i) Friction driven poverty traps

- Nutritional poverty traps is a special case of this. - ‘poor but rational’: poor are just like non-poor in terms of their potential, but they face tighter constraints.

- They face external frictions, e.g. credit market imperfections, non-convex technologies, etc., that prevent them from making the most of their endowments.

- This gives us friction based poverty traps. - In this view, poverty is not the only inequitable and inefficient. - If policy removes the external frictions, then poverty traps will cease to exist. (ii) Scarcity driven poverty traps

-

These are also often refereed to in the literature as the behavioural poverty traps. ‘poor but behavioural’ There are no external frictions. Poor face tighter constraints, this leads them to make choices, which are very different from the non-poor.

- Choices, made under scarcity, reinforce poverty — giving us scarcity driven poverty traps. - Policy focus here will have to be either on redistribution or behaviour change. - This view is often used to blame the poor for their poverty. 3

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3. Benchmark model: No poverty trap • Let  ¯k be the initial levels of endowments of capital stock (can be initial levels of wealth), which are given exogenously: Production function faced by individual: A  f (k) • Profits from the production:  = max A f (k) − rk Π k

In perfectly competitive markets with no capital market imperfections, individuals can borrow/lend in the market, so production is nor constrained by initial capital endowments. • Income for individual:

y =

Π+ r ¯ k (lender) { Π− r ¯ k (borrower)

where r is the market return from capital (rental rate). • Each period people save at a constant rate s. • Individuals’ preferences over consumption (c) and bequest (b) are given as: U(c, b) = log c + β log b where β > 0 , b > 0 and utility is maximised subject to constraint c + b ⩽ y. • Bequest at time t is capital endowment for time  t + 1, which gives:

bt = kt + 1 (amount"not"consumed"this"period = capital"in"next"period) 

• Assume capital depreciates fully at the end of each period. • So with perfect capital markets we have:

k t + 1 = s(Π+ rk t) which is shown as the red line in the Figure 1. • In this case, we have convergence, i.e. no poverty trap. - Initial endowments and all other parameters do not matter in the LR.

- Everyone has a potential of their capital (hence income) increasing over time, till SS. Figure 1: Convergence in the Solow Model (Source: Ghatak, 2015). kt + 1 kt + 1 = kt SS

•

0

k 0 k 1NC

k C1 k*

k t + 1 = s( Π + r k t) k t + 1 = s A f (k t )

kt

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4. Model with frictions • Let say that capital markets are not perfect. For simplicity, assume there are no capital markets. • Now the income of the individual is constraint by their endowments, i.e. the capital they have, which gives us: y = A f (k t ) • The capital accumulation equation now is:

k t + 1 = s A f (kt ) which is shown as the blue curve in Figure 2. • We still get convergence, i.e. no poverty trap, it is just that it is now slower. • Capital market imperfections by themselves are not sufficient to generate poverty traps. • Along with capital market imperfections, say we now have non-convexities in the production technologies. • The production function now is:

y = A f (k) for k > k

and

y = w for k < k

w  < A f (k)

such that

where w  is the returns from subsistence activity. • This gives us now Figure 2, which has non-convergence, i.e. poverty traps. • We have a friction based poverty trap. Figure 2: Non-convergence in the Solow Model (Source: Ghatak, 2015). kt + 1

kt + 1 = kt SS

•

k t + 1 = s( Π + r k t) k t + 1 = s A f (k t )

sw 0

k* L

k

k* H

kt

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5. Model with non-homothetic preference • Consider two goods, x and y. • Homothetic preferences: given fixed prices, as income increases, individuals consume x and y in the same proportion. • Non-homothetic preferences: given fixed prices, as income increases, individuals consume different proportions of x and y. • For scarcity driven poverty traps, we assume that poor have different preferences compared to nonpoor, i.e. we have non-homothetic preference. • This means we can get the poverty traps from income effect only, i.e. do not need external frictions. • Start with the benchmark model: - Production function faced by individual: A  f (k) - Profits from production: Π= max A f (k) − rk k

- We have no capital market imperfections. - Income for individual: y =

Π+ r ¯ k (lender) { Π− r ¯ k (borrower)

• Individuals now have preferences over three goods: consumption (c), bequest (b) and luxury good (z). • Individuals utility function is now given as:  (c, b, z ) = log c + β log(b + B) + γ log(z + Z ) U where B  > 0 , Z > 0 , β ∈ [0, 1] , γ ∈ [0, 1] and MU   (b) when b = 0 is higher than MU (z ) when z = 0. • At low levels of income, all income is spent on consumption. For moderate levels of income, it is split between consumption and bequest. At high levels of income, it is split between consumption, bequest and luxury goods. • As the income increases, the proportion of the three goods consumed changes, share of c decreases and share of z increases. Hence, we have non-homothetic preferences. • As before we still have k t + 1 = bt . • Individual’s problem is: U  (ct , bt , z t ) = log ct + β log(bt + B) + γ log(z t + Z )

± rk t • subject to constraint c t + bt + z t = Π

and k t + 1 = bt.

• Solution to this problem gives us two different thresholds for k: k and k such that k > k . There are corresponding thresholds for income y. • Implication of this preference structure is: k t + 1 = 0 for k t < k . β

k t + 1 =

1+β( β

rk t + Π ) − constant

1+β+γ(

for"k ⩽ k t ⩽ k

rk t + Π ) − constant for"kt ⩾ k 6

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Figure 3: Income effects and poverty traps (Source: Ghatak, 2015). kt + 1 SS

•

0

k

k

k*

kt

• Poverty traps can exist without any external frictions, via strong income effects in the behaviour of individuals. • What we have discussed is one example of scarcity driven poverty trap, where income effects come from non-homothetic preferences are used. • There are other possibilities as well: - Scarce recourse can be attention span or cognitive ability of limited time.

- Effect can work through human capital rather than physical capital.

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