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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

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Poverty Traps

Xavier Sala-i-Martin

Columbia University

Poverty Traps: Theory

  • Start with Fundamental Equation of “Solow-Swan”:

    • Δk=sf(k) - (δ+n) k


    • 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






Poverty Traps: Theory

  • Demographic trap (impoverished families choose to have lots of children)

Demographic Trap







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

Problem 5: Poor Countries did not grow less than others

Problem 5 (cont): Poor Countries did not grow less than others

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

Source: Easterly 2005

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%)

Source: Easterly 2005

Problem 8: And take offs are not related to Aid

Problem 9: Accelerations are more likely to occur poorest countries

  • Haussman, Pritchett and Rodrik (2004)

  • Theory suggest that accelerations should be less likely to occur among poorest countries.

Problem 10: Quah (1996): Seems Evidence in favor of Traps

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


  • Not very robust (Kremer, Onatski and Stock show that it depends on one or two data points)

Additional Problems

  • There is capital in the developing world but it is not invested in the developing world

  • Correlation between Aid and Growth is zero (more on this later).

  • Is it Poverty Traps or Corruption?

    • Countries with low scores on “corruption” tend to grow 1.3% less than other countries (Easterly 2006)

    • Multiple regression: holding constant “corruption”, the “level of poverty” does not matter (Easterly 2006)

Final Note

  • If it is “corruption” but we increase aid (we double in the next five years, and double it again five years later) because we think “poverty traps”, could we possibly induce more corruption?

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