Development Economics

Debraj Ray, Fall 2010

Convergence vs Divergence

Multiple Equilibria

History Dependence

Political Economy, including Conflict

Credit Constraints

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Convergence and Divergence

Textbook development woes:

Low K per person,

Undernutrition,

Low education,

Limited sanitation, safe water and housing,

High population growth rates,

High infant mortality rates, etc.

Some are defining characteristics of underdevelopment.

Others one step removed: often serve as “explanations”.

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Enormous empirical literature spawned on these “explanations”.

E.g., regress g on “exogenous” factors: s or n, initial y or h.

Mostly after some notion of convergence (Solow, turnpike).

Basic idea: the “Law” of Diminishing Returns.

Poorer countries grow faster, catch up, converge.

Need to control for other stuff: s, n, “politics”, “corruption”,religion, . . .

So, to be fair, “unconditional convergence” rarely asserted,

(only “conditional” on all the “exogenous” factors).

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Convergence is one of the more unintuitive ideas in economics.

See Gerschenkron (1962).

Idea: there are relative returns to relative poverty:

leapfrogging

diminishing returns

learning from the mistakes of others.

using known technologies

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The Influence of Convergence

Two important (and unfortunate) implications for research:

First, it limits our focus to objects rather than processes. E.g.,

one country is more corrupt than another,

or less democratic,

or is imbued with a horrible work ethic,

or is prone to reproducing like rabbits,

or is intrinsically predisposed not to save,

and so on.

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At some level, valid, but mainly well-known circularities:

low incomes ⇒ low savings, high pop growth rates, corruption,. . .

Imperialist economists will see circularities everywhere:

Underdevelopment ⇒ politics, institutions, even “culture”.

Regressions: too much emphasis on objects and not the process

endogenous variable −→ economics −→ endogenous variable

Corollary: attitudes towards economic policy; ongoing vs one-time, shallow vs deep (Hoff and Stiglitz (2000)).

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Second unfortunate implication is almost linguistic, but no lessimportant: conditional convergence.

If so much conditioning needed, why not call a spade a spadeand switch the mindset to divergence?

More than just a linguistic issue.

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Some Facts About Cross-Country Growth

1960–2000, average per capita income (PPP) of richest 5%about 29 times corresponding figure for the poorest 5%.

(Huge. Compare with interstate differences in the U.S.)

Within the distribution:

Meteoric rise of East Asian economies: initially Japan, Korea,Taiwan, Singapore, Hong Kong, Thailand, Malaysia, Indonesia.

Over 1965–90: annual rate of 5.5%. (For entire dataset of 102countries, 1.9% p.a.)

And China! 8.6% over 1980–1990, 9.6% over 1990–2000.

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Languishing of Latin America during the 1980s. Only Chile andColombia with higher per capita income in 1990 than 1980.

With some notable exceptions (such as Chile, 5.7%, and Ar-gentina, 3.6%), annual per-capita growth still slow for Latin Amer-ica in the 1990s.

Similarly, much of Africa stagnated or declined over the 1980s.(Nigeria and Tanzania substantial declines, Kenya and Ugandabarely grew. )

Notable turnarounds in the 1990s have occurred in both di-rections, with alarming declines in countries such as the Congo,Rwanda and Burundi, and substantial progress in Uganda.

Use of mobility matrices, 1980–2000.

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(Thanks Liz!)

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Both very low and very high incomes extremely sticky. Middle-income countries have far greater mobility.

For instance, countries in category 1 (between half the worldaverage and the world average) in 1980 moved away to “right”and “left”: less than half of them remained where they were in1980.

88% of the poorest countries (category 1/4) in 1980 remainedwhere they were. Another 88% of the richest countries in 1980stayed here they were.

Look at the next-to-poorest category (those with incomes be-tween one-quarter and one-half of the world average in 1962).Almost half of them dropped to an even lower category. (Slipperyslope.)

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A longer view from Pritchett (1997):

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Pritchett continues:

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Summary

Over 1960–2000, the relative distribution of world income quitestable.

Lots of movement within the distribution however.

No ultimate traps to development.

Yet a history of wealth or poverty partly foretells the future.

Sticky ends, mobile middles.

As far as we can tell, long-run processes emphatically signaldivergence.

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Different attempts to reconcile the failure of convergence withtraditional theory:

Hardline View. Look for controls.

Multiplicity View. Abandon the convergence argument.

Interactive View. Agents/countries and markets.

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Hardline: The Calibration Game

Aggregate production function (labor normalized to 1):

yt = Atkθt ,

where At captures exogenous growth of TFP:

At = A(1 + γ)(1−θ)t,

(Interpret γ as the growth rate of labor productivity.)

Capital accumulation equation:

kt+1 = (1− δ)kt + xt,

Savings equation:xt = syt,

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Standard arguments show that kt converges to the path

(1 + γ)t(

sA

γ + δ

)1/(1−θ),

so that yt converges to the path

A(1 + γ)t(

sA

γ + δ

)θ/(1−θ).

Ratios

y1/y2 = (s1/s2)θ/(1−θ)

The effect of varying s depends only on the ratio θ/(1− θ).

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y1/y2 = (s1/s2)θ/(1−θ)

But this has small effects. Why?

θ is proxy for the share of capital. Lucas (1990) uses 0.4, sothat θ/(1− θ) ' 2/3.

This means that doubling s will only raise steady state per-capitaincomes by a factor of 22/3, around 60%.

Nowhere close to the inequalities we see around us.

Parente and Prescott (2000) impute 70% to labor income and5% to land, which leaves them with a capital share of 25%.

Even worse fit: a doubling of s only translates into a 25%variation in per-capita income.

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To add insult to injury: savings rates in the richest countriesnowhere close to double poor counterparts.

In 1993, industrialized s = 19.4%. LDC s = 23.3%. Even Africahad s = 18.8%.

TFP differentials give us a better chance: whereas

y1

y2=

(s1

s2

)θ/(1−θ),

for TFP differences more amplified:

y1

y2=

(A1

A2

)1/(1−θ).

When θ = 1/3, square root of s-ratios translate to income ratioswhile technology ratios are taken to the power 1.5.

So a doubling of TFP “explains” a ratio of 3. Better.

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Lucas (1990) approach: differentiate production function toget

r = Aθkθ−1,

or equivalently

r = θA1/θy(θ−1)/θ.

Once again take θ = 1/3, so

r1

r2=

(y2

y1

)2

.

Yields absurd numbers. If the per-capita income in the US is15 times larger than that of India, the rate of return on capital inIndia should be over 200 times higher! Even if θ = 0.4 (used byLucas), get a ratio of 60, lower but also absurd.

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Ways Out

Differences in Human Capital

Krueger (1968) makes productivity corrections across US andIndian workers.

Use US-based estimates of how age, education and sector affectproductivity.

Obtains ratio of one US worker = approx. 5 Indian workers.This means that the ratio income per effective capita is 3.

This too generates a rate of return differential between 5 (ifcapital’s share is 40%) and 9 (if that share is set lower at 1/3).Too large.

Topic recently revisited by Erosa, Koreshkova and Restuccia(2010).

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Differences in TFP

Implicit TFP ratios needed to equalize r and maintain per-(effective) capita income ratios around 3.

Equality of the two rates of return:

AIyθ−1I = AUy

θ−1U ,

yU

yI=

(AU

AI

)1/(1−θ)'

(AU

AI

)1.5

if θ ' 1/3.

AU

AI' 32/3 = 2.08.

Big or small? If the US and India put in the same amountsof capital and quality-corrected labor into production, the US willproduce twice as much as India. This may be a tall order.

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Externalities in Human Capital

[Lucas] Suppose that the externality is proportional to ha, wherea > 0. Then

AU

AI=

(hU

hI

)a.

Lucas estimates a ' 0.36, using Denision’s productivity compar-isons within the United States over 1909 and 1958, and combiningthem with human capital endowments over the same period.

Because 50.36 ' 1.8, this takes care of the problem as far asLucas is concerned.

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Misallocation of Capital

Generate productivity differences from the misallocation of cap-ital (Banerjee and Duflo (2004)).

Interesting tension here: misallocation implies small values of θ,bigger problem.

Important issue, but cannot provide a ready fix.

The Share of Capital

Is capital share (θ) underestimated? Parente and Prescott(2000, p. 44–55) discuss this route in some detail, by consid-ering intangible forms of capital and the possibility that physicalcapital is grossly mismeasured, but these adjustments are just notenough.

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Government Failure

Expropriation of new investors, while existing investors (whomay be unproductive) are overprotected.

A view in which incumbent elites are not necessarily the bestbusiness hands, yet they are in a position to control the entranceof others more efficient than they are.

Related to political-economy arguments made by Engerman-Sokoloff and Acemoglu-Johnson-Robinson.

Parente and Prescott consider a variant of this point of view, inwhich they regard the government as intervening excessively andthus lowering productivity.

Or can have lack of intervention, such as lax protection ofproperty rights. Certain types of long-run investment may thennot be made (see Besley, Bandiera, or Goldstein-Udry). Or free-rider problems in joint production, as also overexploitation of thecommons.

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Summary

Convergence relies on diminishing returns to “capital”.

But observed variation in income understated by orders of mag-nitude.

Hunt for other factors that might explain the difference:

Prosaic: human capital, technology, government, . . .

High-flying: corruption, democracy, religion, culture, . . .

Playing the calibration game too seriously reveals a particularworld-view. It suggests a fundamental belief that the world econ-omy is ultimately a great leveler.

Alternative: models not grounded in convergence to beginwith.

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Uneven Growth

Sources

theories of divergence (multiple equilibria, history-dependence)

sectoral change (demand composition, dualism)

globalization

Reactions

occupational choice

political economy

conflict

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