Knowledge Stocks by Distance to Frontier:
Linking Low Education Inequality to High Growth in
Developing Economies
Kevin J. Bowman, Ph.D.
Journal of Asian Economics 18(4), p. 613-635, Aug. 2007
I. Introduction: Inequality and Growth
New Growth Theory Model build to address:
Why does inequality slow growth in LDCs,
but not in advanced countries?
A) [Background Info.]: Long Run Growth and New Growth Theory
The importance of technological change.
- More from the same inputs.
- Provides ability & added incentive to further invest.
The Virtuous Cycle of Development
I. Introduction: Inequality and Growth (continued)
B. [Background Info.]: The Kuznets Curve
- Early Development: Rising Inequality
- Later Development: Falling Inequality
The Kuznets Curve
INEQUALITY
Early
Late
DEVELOPMENT
II. The Puzzle
- Why does the Kuznets curve seem appropriate for advanced countries,
but not for many less developed countries (LDCs)?
A. Empirical Findings: High Inequality Slows Subsequent LDC Growth:
- Wealth inequality slows economic growth
sample: rich and poor countries.
[Alesina and Rodrik (1994); Persson and Tabellini (1994); Perotti (1996).]
- Above studies criticized for their linear specifications
[Krueger and Lindhal (2001)].
- Income inequality slows growth for poor countries,
but speeds growth for rich countries.
[Barro (2000)].
II. The Puzzle (cont.)
B. Previous Theories are Lacking but Useful
i. Political-Economy Growth Models
Theory: High inequality => high taxes => discourages investment.
[Alesina and Rodrik, 1994; & Persson and Tabellini, 1994]
Problems relying only on this technique:
1. Redistribution can be positively related to growth in LDCs
[Easterly and Robello, 1993; & Perotti, 1996]
2. More unequal societies tend to have either no more or actually less
redistribution than more equal societies. [Benabou, 2000]
An explanation for (2) despite (1)
[Benabou, 2000]
- Assume the rich are more politically active/enfranchised.
- Redistribution can:
HURT rich through higher taxes, but can potentially
HELP them through faster growth.
The higher the inequality…
II. The Puzzle
B. Previous Theories are Lacking but Useful
I. Political-Economy Growth Models (continued)
Case Studies: Latin America Vs.
The High Performance Asian Economies (HPAEs)
[Benabou (1996); Campos and Root (1996)]
- Both regions started with similar Per Capita GDP in 1960, but:
1. Latin America
high initial inequality => grew slowly
2. The HPAEs
low initial inequality => grew fast
- Although miliarty coups in both regions:
- pro-growth policies (including…)
more consistent in HPAEs.
II. The Puzzle:
B. Previous Theories are Lacking but Useful (continued)
ii. The Importance of Human Capital Investment
Theory: High wealth & income inequality =>
poor households can’t afford to invest in skills
lacking collateral for borrowing
=> lower average education level
[Galor and Zeira (1992)]
1. Suggests a positive correlation between:
wealth inequality & education inequality.
I find this is true [in this study].
2. Galor and Zeira do not model the source of tech change.
Why doesn’t the greater skills among the elite provide positive
externalities for others when they create or adapt techs?
I find (empirically): initial education inequality => slower LDC growth,
controlling for average education levels.
III. Knowledge Stocks By Distance to Frontier (novelty of this paper)
A. The Three Forces of Technological Change:



INVENTION: new ideas/techs. with potential to ↑output with given labor.
most skill-intensive.
INNOVATION: early apps of inventions that ↑ output with given labor.
moderately skill-intensive.
DIFFUSION: later apps of innovation across more industries.
least skill-intensive
but still requires…
Examples
Late 1800s/Early 1900s
Late 1900s/Early 2000s
Invention
electricity
computer technologies (DOS)
Innovation
early plant redesigns
& electrified equipment
Microsoft Office software
& early business applications.
Diffusion
the spread of more electric
equipment and plant designs
More user-friendly and sectorspecific Office applications
III. Knowledge Stocks By Distance to Frontier (continued)
B. Theory Why Inequality May Slow Growth in LDCs
• Invention is necessary for technology leaders but not for today’s LDCs.
High wage inequality => advanced country benefits with…
(and country has minimum education…)
• For LDCs, higher education inequality:
 importation of overly sophisticated technologies used by elite, but
does not diffuse.
 high relative wage
• Limited diffusion prohibits low-skilled families to finance schooling
(of their children)...
• Example.
BRAZIL: high inequality & making autos.
Vs. TAIWAN: low inequality while initially making furniture.
III. Knowledge Stocks By Distance to Frontier (continued)
B. Why Inequality May Slow Growth in LDCs (continued)
The Model is Consistent with these Empirical Facts:
1) INCOME inequality slows growth for LDCs BUT
not for advanced countries,
[Barro]
2) REDISTRIBUTION does NOT always occur
even when potentially helpful
[Easterly and Robello]
3) high initial EDUCATION inequality slows subsequent growth, in LDCs
(especially during skill-biased technological change)
[This study]
4) INCOME and EDUCATION inequality are positively correlated,
(helps explain why inequality in general is bad for LDCs).
[This study]
IV. The Formal Model
A) Model Setup
3 Levels of Skill:
- High (H)
3 Countries:
- Moderate (M)
&
Their Workers
- Low (L)
Example
- one advanced (*)……..….H & M…………College + & High School (H.S.)
- two LDCs
Equal LDC (E)……..M & L…………H.S. & Primary (6 yrs.)
Unequal LDC (U)…..M & L…………Associates & 4 Years of Ed.
5 Knowledge Stocks:
Assumed: The Greater the Skill the Greater the Access to Knowledge
more
sophisticated
- frontier (V)
- adaptive (A)
- standardized (S)
- traditional (T)
accessed by H
accessed by M
accessed by L
accessed by L
IV. The Formal Model
. B) The Model Setup (continued)
Workers Maximize Lifetime Utility
Option
Time 1
Time 2
Relatively
i) Study as a Pupil
i) Work as Higher Skilled
High Skilled
ii) Borrow
ii) Pay back loan
iii) Consume
iii) Consume.
Relatively
i) Work as Lower-Skilled i) Retire
Low Skilled
ii) Save
ii) Consume
iii) Consume
A Result:
If benefits of schooling > costs, more get an education
=> drives up the interest rate
=> raises the cost of education
until:
MB = MC of education
IV. The Formal Model
. B) The Model Setup (continued)
Case * (Advanced Economy):
• Let w = wage, C= Quantity of consumption good, ∆ = change
Inventive Sector (I):
Invention = ∆V = f(V*, H*I)
i) invention financed by human capital investment.
ii) higher ed. students are trained to use the latest stock of V*
iii) tuition depends on the wage of high skilled trainers/researchers
Innovative Sector (N):
C*N = ∆A = f(V*, H*N, M*N)
i) innovative ideas also require H, but build on older processes using M.
ii) Spillover to Adaptive Knowledge (∆A)
By innovating, innovators show lower skilled how to use inventions.
Adaptive Sector (D):
C*D = f(A*, M*D)
i) uses more general adaptive knowledge, A*, and M* to produce C*.
IV. The Formal Model
. B) The Model Setup (continued)
Less Developed Countries (LDCs):
- Relatively higher ed. allows for importation of adaptive knowledge
Equal LDC (E):
- Local Adaptive Sector (a):
CA,t = ∆St = f(A, Ma,, La)
With a Spillover to Standardized Knowledge
- Local Standard Sector (S):
CS,t = f(St, LS,t)
Unequal LDC (U):
- Local Adaptive Sector:
CA,t = f(At, Ma)
- Local Traditional Sector:
CT,t = f(Lt)
V. Theoretical Results
A. Simultaneous Steady-State Propositions:
(Long-run equilibrium with constant growth)
Proposition 1.
- Growth rates will be the same for:
The EQUAL LDC and The ADVANCED Country
The low-skilled sector has adequate capability to learn
from what is occurring in relatively high-skilled sector.
- Let g = the economic growth rate:
gss* = gEsss = %∆V* = %∆A* = %∆AE = %∆SE
V. Theoretical Results
A. Simultaneous Steady-State Propositions (continued):
Proposition 2.
- Case U:
gUsss = 0.
The importation of adaptive technologies
=> increases the productivity of higher-skilled sector.
But the gap in skills is too great.
=> lower-skilled sector stagnates.
=>Wage inequality grows
=> Poorer households can’t afford higher education
(recall: cost of education depends on…
& low-skilled wages are not keeping pace)
=> The country stagnates because it cannot accumulate skills.
Recall the Example:
Brazil Vs. Taiwan
VI. Empirical Results
1. Income Inequality and Education Inequality are Positively Correlated
2. High Initial Education Inequality Slows Subsequent Growth in LDCs
(especially in times of skill-biased tech. change) consistent with the theory.
VI. Empirical Results (continued)
3. Results hold in the earlier period, but are not as strong.
Consistent with theory…tech change less skill-biased 1960-75.
Conclusion:
• The tradeoff between Invention and Diffusion
- LDCs vs. Advanced Countries…
• The danger of high inequality for LDCs…
• Related to the Kuznets curve…
Policy Recommendation:
• Governments of poor countries must invest broadly
• The World Bank should consider incentivizing broad investment
when there are domestic, political obstacles in the unequal LDC