Poverty Traps

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Poverty Traps Xavier Sala-i-Martin Columbia University Poverty Traps: Theory Start with Fundamental Equation of “Solow-Swan”: Δ k=sf(k) - ( δ +n) k or Δ k/k=sf(k)/k - ( δ +n)

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Poverty Traps

Xavier Sala-i-Martin

Columbia University

Poverty Traps: Theory
• Δk=sf(k) - (δ+n) k

or

• Δk/k=sf(k)/k - (δ+n)
• If s and n are constant, and f(.) is neoclassical (concave with inada conditions), then UNIQUE AND STABLE STEADY STATE
• Poverty Trap Theory: instead of unique and stable steady state, THREE STEADY STATES and Lower and Upper steady states stable and middle one unstable
Poverty Traps: Theory
• Savings trap (savings rate is close to zero for poor countries for subsistence reasons and then shuts up as income increases)
• Nonconvexity in the production function (there are increasing returns for some range of k)
Savings and Non-Convexities Traps

Stable

Stable

δ+n

Unstable

s(k)f(k)/k

Poverty Traps: Theory
• Demographic trap (impoverished families choose to have lots of children)
Demographic Trap

Stable

Unstable

s(k)f(k)/k

Stable

δ+n

k

Poverty Traps: Implications
• The main implication is that a country that is “stuck” in a poverty trap (the low income steady state) that receives aid in the form of capital that is less than the distance between its initial position and the next steady state, it converge back to the low steady state.
• Hence, the fact that aid has not worked in the past does not prove that it is ineffective.
• In fact, the poverty trap implies that the total amount of aid must be increased enough to put countries over the unstable steady state
• IMPORTANT NOTE: this is different from having two savings lines (if we have two savings lines with two steady states, then NO amount of aid will work!)
Problem 1: Savings Trap
• Need to have THREE steady states:
• For savings line to cross three times the depreciation line, you need the savings rate have to behave in “s” shape:
• First low and constant (the savings line declines so it crosses de depreciation line from above and describes a stable steady state)
• Then s should be raising for intermediate levels of k (so that the product s(k)*f(k)/k is upward sloping)
• Then it should stay constant at a higher level (so that s(k)*f(k)/k becomes downward sloping again
• In sum, it is NOT enough to argue that “poor people save less”.
• There is NO evidence that saving rates accelerate sufficiently rapidly to justify the savings poverty trap (Kraay and Raddatz (2005))
Problem 2: Savings Trap
• If there is technological progress, the savings trap automatically disappears!
Problem 3: Demographic Trap
• If there is technological progress, the savings trap automatically disappears!
Problem 3: Fertility Behavior
• True that fertility declines as income increases... but population growth is the sum of fertility, minus mortality, plus net migration
• Mortality also declines with capital (and income)
• And net migration increases with capital
• Hence, need to argue that fertility declines MORE THAN OFFSET mortality declines, migration reversals and the diminishing returns to capital so that the savings and depreciation lines cross three times
• This is empirically unlikely
Problem 4: Non-Convexities Trap
• Normally, non-convexities can be easily convexified (for example, by using an average of the two technologies)
• Thus, not only you need to argue that non-convexities exist, but need to argue that non-convexities cannot be “convexified” by averaging production from below the convex and above area
• This is a lot harder

Sachs shows that poor countries have grown less after 1975.

But how do we explain positive growth (1.9% per year) between

1950 and 1970?

Problem 6: Conditional Convergence
• Holding constant institutional variables, the partial correlation between initial income and growth is negative
• Again: To have poverty traps, we should have multiple steady states with same savings and depreciation lines (not that there are multiple savings lines).
• If there are multiple savings lines, there is no reason to have increased aid
Problem 7: Little Evidence of “Take Offs”
• Define take off as a period of large sustained growth (more than 1.5%) following a long period of zero growth (defined as -0.5% to +0.5%)
• Haussman, Pritchett and Rodrik (2004)
• Theory suggest that accelerations should be less likely to occur among poorest countries.
Forecasting the future of the WDI (by country)
• Quah’s Methology: Based on historical experience
• pp=probability of poor in 1960 staying poor in 2000
• pr=probability of poor becoming rich
• rp=probability of rich becoming poor
• rr=probability of rich staying rich
Forecasting the future of the WDI (by country)
• Npoor(2040)=Npoor(2000)*pp+ Nrich(2000)*rp
• Nrich(2040)=Npoor(2000)*pr+ Nrich(2000)*rr
• Repeat the procedure infinite many times to get the ergodic (steady-state) distribution
• Conclusion: depends on Venezuela and Trinidad-Tobago
Problem
• Not very robust (Kremer, Onatski and Stock show that it depends on one or two data points)