Convergence and Divergence
Two Views of Underdevelopment
Debraj Ray, NYU
University of Oslo lecture, March 2015
Convergence and Divergence
The Solow model has had enormous impact on development economics
and macroeconomics.
Rich countries grow slower than poor countries
Main idea: diminishing returns to capital
Tendency for countries to converge.
Huge literature, including many papers that test for convergence.
Convergence in Two Flavors
Basic Solow model predicts unconditional convergence:
The incomes of countries move ever closer to one another
(Assumes parameters are similar across countries)
Does this assertion fit the data?
Option 1. Small number of countries, long horizon.
Option 2. Large number of countries, short horizon.
Testing Unconditional Convergence
1. Baumol (AER 1986): 16 countries, among the richest in the world today.
In order of poorest to richest in 1870: Japan, Finland, Sweden, Norway,
Germany, Italy, Austria, France, Canada, Denmark, the United States, the
Netherlands, Switzerland, Belgium, the United Kingdom, and Australia.
Angus Maddison: per-capita incomes for 1870.
Idea: regress 1870–1979 growth rate on 1870 incomes.
ln yi1979 − ln yi1870 = A + b ln yi1870 + i
Unconditional convergence ⇒ b ' −1.
Get b = −0.995, R2 = 0.88.
What’s wrong with this picture?
De Long critique (AER 1988):
Add seven more countries to Maddison’s 16.
In 1870, they had as much claim to membership in the “convergence club”
as any included in the 16: Argentina, Chile, East Germany, Ireland, New
Zealand, Portugal, and Spain.
New Zealand, Argentina, and Chile were in the list of top ten recipients of
British and French overseas investment (in per capita terms) as late as 1913.
All had per capita GDP higher than Finland in 1870.
Strategy: drop Japan (why?), add the 7.
Slope still negative, though loses significance.
Correct for measurement error, game over.
2. More Countries
2a. Updated Maddison dataset 2013, 60 countries:
log"per1capita"income"growth,"187012010"
4"
3"
2"
1"
5.8"
6.3"
6.8"
7.3"
log"per1capita"income,"1870"(in"1990"dollars)"
7.8"
2b. Even More Countries.
Barro (QJE 1991): 100+ countries over 1960–1985.
2c. Even More Countries + Long Time Horizon (Pritchett)
What about more countries and more time?
Problem: no data going back to 1870.
Pritchett assumption: no country can fall below $250 per capita (1985 PPP)
Defense 1: lowest 5-year average ever is Ethiopia $275 (1961–5).
Defense 2: below extreme nutrition-based poverty lines actually used in
poor countries (see Ravallion, Dutt and van de Valle 1991, or nutrition lines
at 2000Kcal)
Defense 3: at any lower income, population too unhealthy to grow. Child
mortality rate estimated to climb well above barrier of 600 per 1000.
Claim: the $250 bound “proves” divergence over long-run.
The US grew four-fold from 1870 to 1960.
Thus, any country whose income was not fourfold higher in 1960 than it
was in 1870 grew more slowly than the United States.
42 out of 125 countries in the PWT have pcy below $1,000 in 1960.
Or try this:
extrapolate back so poorest country in 1960 hits exactly $250 in 1870.
US: use actual figures.
preserve the relative rankings of all other countries (see footnote 11 of
Pritchett)
Conditional Convergence
Simply no evidence for unconditional convergence.
Second line of defense: the parameters are not the same across countries.
So convergence is conditional. 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.
Three Objections to Conditional Convergence
I. At some level, perfectly valid, but not very deep.
It doesn’t explain why the conditioning variables are different.
E.g., low incomes can provoke low savings rates, or high population growth
rates, or high corruption.
Example: The Endogeneity of s
s
y1*
y2*
y*
Blue line: How s is affected by steady state income y ∗ .
Red line: How y ∗ is determined by s (as in Solow model).
Example: The Endogeneity of n
n
y1*
y2*
y*
Blue line: How n is affected by steady state income y ∗ .
Red line: How y ∗ is determined by n (as in Solow model).
II. If so much conditioning needed, why not call a spade a spade?
Maybe the status quo is divergence, not convergence?
II. If so much conditioning needed, why not call a spade a spade?
Maybe the status quo is divergence, not convergence?
III. Conditioning using the Solow model doesn’t take us very far.
Calibration game:
II. If so much conditioning needed, why not call a spade a spade?
Maybe the status quo is divergence, not convergence?
III. Conditioning using the Solow model doesn’t take us very far.
Calibration game:
Per-capita production function:
yt = At ktθ ,
where At is TFP growth: At = A(1 + γ )(1−θ )t .
Capital accumulation and savings equations:
kt+1 = (1 − δ )kt + xt ;
xt = syt .
Standard argument: yt converges to the path
A(1 + γ )t
sA
γ+δ
θ/(1−θ )
.
So for two countries 1 and 2 with same TFP,
y1
=
y2
s1
s2
θ/(1−θ )
.
Standard argument: yt converges to the path
A(1 + γ )t
sA
γ+δ
θ/(1−θ )
.
So for two countries 1 and 2 with same TFP,
y1
=
y2
s1
s2
θ/(1−θ )
.
θ is share of capital: 0.25 (Parente-Prescott) – 0.40 (Lucas), so optimistically
θ/(1 − θ ) ' 2/3.
Doubling s ⇒ income ratio approx 22/3 , around 60%.
Standard argument: yt converges to the path
A(1 + γ )t
sA
γ+δ
θ/(1−θ )
.
So for two countries 1 and 2 with same TFP,
y1
=
y2
s1
s2
θ/(1−θ )
.
θ is share of capital: 0.25 (Parente-Prescott) – 0.40 (Lucas), so optimistically
θ/(1 − θ ) ' 2/3.
Doubling s ⇒ income ratio approx 22/3 , around 60%.
1960–2000, average per capita income (PPP) of richest 5% about 29 times
corresponding figure for the poorest 5%.
Hardline View. Never mind.
Keep conditioning, and keep looking for conditional convergence:
Human capital, technology, government, misallocation
Corruption, democracy, religion, culture, . . .
Very, very hard to explain the differences.
Hardline View. Never mind.
Keep conditioning, and keep looking for conditional convergence:
Human capital, technology, government, misallocation
Corruption, democracy, religion, culture, . . .
Very, very hard to explain the differences.
But then what is the point of “conditional convergence”?
Based on a fundamental belief that life is fair.
And too little emphasis on cumulative traps
endogenous variable −→ economics −→ endogenous variable
Hardline View. Never mind.
Keep conditioning, and keep looking for conditional convergence:
Human capital, technology, government, misallocation
Corruption, democracy, religion, culture, . . .
Very, very hard to explain the differences.
But then what is the point of “conditional convergence”?
Based on a fundamental belief that life is fair.
And too little emphasis on cumulative traps
endogenous variable −→ economics −→ endogenous variable
Alternative: theories built for divergence “from the start”.
Mobility matrix, 1982–2009
Cat 1: income < 1/4 world av; Cat 2: between 1/4 and 1/2 world av; Cat
3: between 1/2 world av and world av; Cat 4: between world av and twice
world av; Cat 5: income > twice world av.
Obs Cat À
Á
Â
Ã
Ä
À 84 13 3
0
0
32
21
Á 43 43 14 0
0
26
Â
0 27 50 23 0
20
Ã
0
0 20 70 10
29
Ä
0
0
0
3 97
Graphical representation (diagram from Quah 1993)
Two Approaches to Divergence
Two Approaches to Divergence
A. Underdevelopment as an equilibrium trap
B. Underdevelopment as history-dependence
A. Underdevelopment As An Equilibrium Trap
Rosenstein-Rodan (1943), Myrdal (1944, 1957), Hirschman (1958)
Complementarities:
When more people taking an action leads to a bigger tendency for any one
person to take that same action.
rW
rF
rW
rF
E
Using FDR
Using West Side Highway
rD
rQ
A
rD
C
B
Using Dvorak
rQ
Using QWERTY
Examples
Technology. Macs vs PCs.
Network externalities.
Infrastructure. Public sector covers fixed and variable cost:
p(n) = v + (F /n).
Finance. Thicker financial market ⇒ higher diversification.
⇒ Easier for individual to invest ⇒ thicker market.
Social Capital. Mobility destroys traditional social networks.
All sorts of effects including a mobility feedback.
Corruption.
Society with limited auditing capacity
Only a fraction of “corrupt” people can be investigated.
Norms
Throwing garbage in public spaces
The use of contraceptives
Waiting one’s turn, queueing, joining a revolution
Currency Crises
Herding versus the fundamentals.
Discrimination and Group Reputations
Discriminated groups don’t “invest”, discrimination continues.
Inter-Industry Links (Rosenstein-Rodan [1943], Hirschman [1958])
Joining the Revolution
People indexed from 0 to 1, thinking of joining the revolution.
Benefits and costs:
If the revolution succeeds: B (x) to person indexed by x, x ∈ [0, 1].
If the revolution fails: L (independent of x-index for simplicity).
Probability of success p(n), where n is # joining revolution.
p(n)
B(x)
1
0
1
n
0
1
x
The Revolution, contd.
If n people expected to join, how many want to join?
Find largest x in [0, 1] such that p(n)B (x) − [1 − p(n)]L ≥ 0:
B (x) ≥
1 − p(n)
L.
p(n)
Example 1: multiple equilibrium:
B (x) = B > 0, while p(0) = 0 and p(1) = 1.
Example 2: generically unique equilibrium:
B (x) = (1 − x)/x and p(n) = n.
At 0 if L > 1, and at 1 if L < 1.
Example 3: B (x) = (1 − x)/x and p(n) = n2 . See Ch. 5 Update.
Questions of Transition
How does history enter the picture?
Multiple equilibrium theories often too nondeterministic.
What connects equilibria over time?
Why is QWERTY stickier than fashion?
Percentage of adopters (x)
Why does a transition follow a logistic path?
xt
Why History Matters (No one wants to go first)
rN, rO
rN
rN (y)
rO
rN (x)
x
y
% in the new sector
Lagged externalities
Who moves from x to y, if the returns take time to build up?
B. Underdevelopment as History-Dependence
Increasing returns
Fixed costs for setting up a business, learning by doing
Culture (including norms)
culture ⇒ economic progress (or lack thereof) ⇒ culture.
Status quo bias
Will affect the direction of change
Legal systems
Influences contract enforcement.
Inequality (more if we have time).
Political systems (more if we have time).
Example: The Growth Model With Increasing Returns
y = f (k ), but f has two techniques built in.
f1 (k ) = Akα and f2 (k ) = Bkβ − C. B A and C is a fixed cost.
f2(k)
(1+n)k
(1-d)k
f1(k)
K
k
+ sf(k)
k1*
k2*
k
Example: Status Quo Bias
based on Fernández and Rodrik (1991).
Consider a society of 100 people.
Proposed project pays off +1 to a beneficiary and -1 to a loser.
It is known that 70 individuals will be beneficiaries.
Under symmetry, expected payoff is
7
(1)
10
+
3
(−1)
10
> 0.
So all vote yes.
But if 45 people are commonly known to benefit, then the remaining 55
vote no! (Why?)
The project (once in) wouldn’t be voted out. But if not there, not voted in.
⇒ History-dependence.
Example: Increasing Returns in a New Business
(a) IRS (b) gradual switching, and (b) imperfect capital markets
Example: Milestone Utility and the Distribution of Wealth
Utility depends on “goal achievement”; e.g., people overtaken.
Simple example: utility equals rank in the wealth distribution.
Going from w to w0 exhibits increasing marginal cost.
Then high inequality associated with low rates of growth.
Model: utility given by
A(w − x)α + F
x[1 + r ]
1+g
,
where everyone growing at rate g and F is the cdf of wealth.
Explain (a) steady state and (b) F and g are endogenous.
Inequality and growth negatively correlated.
Political Economy, Institutions and History Dependence
Institutions:
Ambient rules (formal or informal) for conducting economic, social and
political transactions.
E.g., institutions that protect property rights (law enforcement)
Or provide old age pensions (social security)
Or provide insurance against a banking crisis (FDIC)
Or enable financial holdings in companies (the stock market)
Or guarantee that contracts will be upheld (courts)
Or oversee safe and fair elections (Electoral Commissions)
Or norms of reciprocity and sanctions (informal).
Good economic institutions promote investment and growth
But institution creation is deeply conditioned by history
Indeed, bad institutions (such as autocracies) may self-generate or generate worse institutions (dictatorships) as the beneficiaries struggle to keep
their benefits.
Sokoloff and Engerman (JEP 2000) argue that this lies at the difference
between North and South America:
Initially: “Voltaire, for example, considered the conflict in North America
between the French and the British during the Seven Years War (1756-63) to
be madness and characterized the two countries as ‘fighting over a few acres
of snow.’ The victorious British were later to engage in a lively public debate
over which territory should be taken from the French as reparations — the
Caribbean island of Guadeloupe (with a land area of 563 square miles) or
Canada.”
South America: Huge mineral riches, lots of native labor
Extractive economies (mine rights, tribute-taking, etc.).
Or plantation economies which used slave labor; again, relatively few
large landowners.
Rights assigned in controlled, restricted way.
E.g. strict restrictions on migration to the New World.
⇒ unequally situated elite, which tried to hold on to power.
Restrictions on commerce and political participation; e.g., need to own
substantial land in order to vote.
North America: US and Canada
No large amounts of native labor
No appropriate climate for sugar except in the South (but even here, size
of sugar plantations relatively small)
Laborers of European descent, equality in human capital
Relatively small landholdings, open immigration
Hard to create institutions with unequal political power.
Even though voting restricted at the beginning, franchise was rapidly extended.
Sokoloff and Engermann conclude:
“These early differences in the extent of inequality across New World economies
may have been preserved by the types of economic institutions that evolved
and by the effects of those institutions on how broadly access to economic opportunities was shared. This path of institutional development may in turn
have affected growth. Where there was extreme inequality, and institutions
advantaged elites and limited the access of much of the population to economic opportunities, members of elites were better able to maintain their elite
status over time, but at the cost of society not realizing the full economic potential of disadvantaged groups . . . [S]uch biases in the paths of institutional
development likely go far in explaining the persistence of inequality over the
long run in Latin America and elsewhere in the New World.”
Sokoloff and Engermann conclude:
“These early differences in the extent of inequality across New World economies
may have been preserved by the types of economic institutions that evolved
and by the effects of those institutions on how broadly access to economic opportunities was shared. This path of institutional development may in turn
have affected growth. Where there was extreme inequality, and institutions
advantaged elites and limited the access of much of the population to economic opportunities, members of elites were better able to maintain their elite
status over time, but at the cost of society not realizing the full economic potential of disadvantaged groups . . . [S]uch biases in the paths of institutional
development likely go far in explaining the persistence of inequality over the
long run in Latin America and elsewhere in the New World.”
Tests of this hypothesis:
Acemoglu, Johnson and Robinson (2000), Banerjee and Iyer (2005)
and many others
Summary
Initial history conditions subsequent development.
That happens when history affects behavior in persistent ways.
Diminishing returns is one leading example in which this does not happen.
But it is about the only example.
We showed how increasing returns resurrects history.
So do institutions, the status quo, and the social determinants of preferences.
History-dependence is the rule rather than the exception.
Understanding this in specific contexts is key to understanding underdevelopment.