Understanding Poverty Traps: Implications and Solutions
Poverty traps theory, as proposed by Xavier Sala-i-Martin, explores the dynamics that keep countries in a cycle of poverty. It identifies three main traps: savings trap, non-convexity in production, and demographic trap. The theory suggests that to break out of poverty traps, countries may need increased aid to push them beyond unstable steady states toward higher income levels. Overcoming these traps requires a nuanced understanding of saving behaviors, production functions, and demographic factors.
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Poverty Traps Xavier Sala-i-Martin Columbia University 2002??
Poverty Traps: Theory Start with Fundamental Equation of Solow-Swan : k=sf(k) - ( +n) k or k/k=sf(k)/k - ( +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 1. Savings trap (savings rate is close to zero for poor countries for subsistence reasons and then shuts up as income increases) 2. Nonconvexity in the production function (there are increasing returns for some range of k)
Savings and Non-Convexities Traps Stable Stable +n Unstable s(k)f(k)/k
Poverty Traps: Theory 3. Demographic trap (impoverished families choose to have lots of children)
Demographic Trap Stable Unstable s(k)f(k)/k Stable +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
Problem 5: Poor Countries did not grow less than others
Problem 5 (cont): Poor Countries did not grow less than others Per Capita Growth 1950-2001 1950-1970 1975-2001 1.60% 1.90% Poorest Fifth in 1950 0.80% Other Countries Source: Easterly 2005 1.70% 2.50% 1.10% 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%)
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
Problem 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?
