Macroeconomics

Chapter 6 Part 2:
Long-Run Economic Growth

ECON2220 Intermediate Macroeconomics

Wataru Miyamoto
Spring 2024

Copyright © 2024 Pearson Education Ltd. 1

Review
• What causes economic growth?
• Investment causes growth?
• Can GDP grow in the long run?

• The Solow model says no!

• Investment cannot sustain a positive growth of output in the long run
• Can keep a positive growth rate for some time
• Why? Diminishing marginal returns to capital

• What if we change something in this economy? Can this economy

grow in the long run?
2
The Solow Model
• Let’s consider these candidates
• The saving rate 𝑠

• Population growth 𝑛

• Productivity 𝐴

3
The Solow Model
• The saving rate
• Higher saving rate means higher capital per capita 𝑘, higher output per capita
𝑦
1
𝑠𝐴 1−𝑎
𝑘∗ =
𝑛+𝑑

• Can this mechanism generate growth in the long run?

4
Figure 6.6: The effect of an increased saving rate on the
steady-state capital–labor ratio
1 + 𝑛 ∆𝑘𝑡+1 = 𝑠𝐴𝑘𝑡𝑎 − 𝑛 + 𝑑 𝑘𝑡

5
The Solow Model
• The saving rate
• Can we sustain a positive growth rate of output per capita by raising the
saving rate?
• No, 𝑠 ≤ 1
• We can increase output per capita 𝑦 to some extent

• Should a policy goal be to raise the saving rate?

• Not necessarily, since the cost is lower consumption in
the short run (i.e., during the transition)
• There is a trade-off between present and future consumption
𝑐𝑡 = 𝑦𝑡 − 𝑖𝑡 = 1 − 𝑠 𝐴𝑘𝑡𝑎
• Even in the long run (i.e., at the steady state), not clear if we can increase 𝑐 by
raising 𝑠

• Q: What is the level of saving rate that maximizes consumption per capita at
the steady state?
6
The Solow Model
• Consumption at the steady state
𝑐∗ = 1 − 𝑠 𝐴 𝑘∗ 𝑎
1
𝑠𝐴 1−𝑎
where 𝑘∗ = . Thus,
𝑛+𝑑 𝑎
𝑠𝐴 1−𝑎
𝑐∗ = 1−𝑠 𝐴
𝑛+𝑑

• We want to maximize 𝑐 ∗ by changing 𝑠

• As usual, we take the derivative of 𝑐 ∗ with respect to 𝑠 and set it
equal to zero

7
The Solow Model
𝑎
𝑠𝐴 1−𝑎
∗
𝑐 = 1−𝑠 𝐴
𝑛+𝑑
Taking the derivative of 𝑐 ∗ with respect to 𝑠 and set it equal to zero yields,
𝑎 𝑎
𝑠𝐴 1−𝑎 𝑠𝐴 1−𝑎 𝑎 1
−𝐴 + 1−𝑠 𝐴 =0
𝑛+𝑑 𝑛+𝑑 1−𝑎𝑠
Solving for 𝑠, we get
𝑠=𝑎

𝑑𝑓 𝑥 𝑔 𝑥 𝑑𝑓 𝑥 𝑑𝑔 𝑥
• Note: = 𝑔 𝑥 +𝑓 𝑥 . Here 𝑓 𝑥 = 1 − 𝑠 and
𝑑𝑥 𝑎 𝑑𝑥 𝑑𝑥
𝑠𝐴 1−𝑎
g 𝑥 =𝐴
𝑛+𝑑

8
The Solow Model
• This saving rate 𝑠 is called Golden Rule saving rate
• Balancing the trade-off between present and future consumption
𝑐𝑡 = 1 − 𝑠 𝑦𝑡

• Using the previous numerical example, let’s think about the situation where 𝑠
suddenly goes up from 0.1 to Golden rule saving rate level 𝑠 = 𝑎 = 0.3
• Suppose the economy is at the steady state initially (first 10 years)
𝑠 = 0.1, 𝐴 = 1, 𝑛 = 0.02, 𝑑 = 0.08, 𝑎 = 0.3
• Let’s plot the transition dynamics to the new steady state

9
Figure: Capital and consumption per capita over time

New 𝑘 ∗
New 𝑐 ∗

Old 𝑐 ∗

Old 𝑘 ∗
10
The Solow Model
• Raising the saving rate
• Trade-off
• Lower current consumption vs higher future consumption
• Golden rule 𝑠 maximizes 𝑐 ∗ at the steady state
• You need to pay attention to the transition dynamics too

• Should the government try to target a particular saving rate such as the Golden Rule
saving rate?
• If the private market is efficient, the government shouldn’t
• Households decide the amount of saving optimally, considering the tradeoff between
current consumption and future consumption

• But if tax laws (tax on interest rates)/inefficient financial sector cause an inefficiently low
level of saving, government policy to raise the saving rate may be justified

• Q: What is the saving rate that maximizes output per capita?

11
The Solow Model
• Population growth
• Higher population growth means a lower capital per capita 𝑘, lower output
per capita 𝑦, and lower consumption per capita 𝑐
1
𝑠𝐴 1−𝑎
𝑘∗ =
𝑛+𝑑

• What is the intuition behind this?

12
Figure 6.7: The effect of a higher population growth rate
on the steady-state capital–labor ratio
1 + 𝑛 ∆𝑘𝑡+1 = 𝑠𝐴𝑘𝑡𝑎 − 𝑛 + 𝑑 𝑘𝑡

13
The Solow Model
• Population growth
• Should a policy goal be to reduce population growth?
• Doing so will raise consumption per capita
• But it will reduce total output and consumption, affecting a nation’s ability to
defend itself or influence world events
• Changes in cohort sizes may cause problems for social security systems and areas
like health care
• You cannot sustain a negative population growth rate in the long run

14
The Solow Model
• Productivity growth
• The key factor in economic growth is productivity improvement
• Productivity improvement raises output per capita 𝑦 for a given level of the
capital per capita 𝑘
1
𝑠𝐴 1−𝑎
𝑘∗ =
𝑛+𝑑

15
Figure 6.8: An improvement in productivity

16
The Solow Model
• Productivity growth
• In equilibrium, productivity improvement increases the capital per capita 𝑘,
output per capita 𝑦, and consumption per capita 𝑐
• Why?
• Productivity improvement directly improves the amount that can be produced at
any capital–labor ratio 𝑘
• The increase in output per capita increases the supply of saving, causing the
long-run capital-labor ratio to rise

17
Figure 6.9: The effect of a productivity improvement on
the steady-state capital–labor ratio
1 + 𝑛 ∆𝑘𝑡+1 = 𝑠𝐴𝑘𝑡𝑎 − 𝑛 + 𝑑 𝑘𝑡

18
The Solow Model
• Productivity growth
• Can output/consumption per capita grow indefinitely?
• The saving rate can’t rise forever (it peaks at 100%) and
the population growth rate can’t fall forever
• But productivity and innovation can always occur, so
output can rise continuously

• The rate of productivity improvement is the dominant factor determining how

quickly living standards rise
• 𝐴 can sustain a positive growth of output in the long run
• Consistent with Growth Accounting and cross-country difference in 𝐴 using
production function

19
Summary 8:The Fundamental Determinants of Long-
Run Living Standards

Causes long-run output,

consumption, and capital
An increase in per worker to Reason
The saving rate, s Rise Higher saving allows for more
investment and a larger capital stock.

The rate of Fall With higher population growth more

population growth, n output must be used to equip new
workers with capital, leaving less
output available for consumption or
to increase capital per worker.

Productivity Rise Higher productivity directly increases

output; by raising incomes, it also
raises saving and the capital stock.

20
The Solow Model
• Problem of Solow model
• Exogenous growth
• Technical progress yields growth in per capita income in the Solow model
• But technical progress is given exogenously
• Model does not explain growth in the long run
• For that we would need a theory of A

• More recent research focuses on the model where 𝐴 is explained

endogenously in the model (called endogenous growth theory)

21
The Solow Model
• Endogenous growth theory—explaining the sources of productivity
growth

• Constant MPK
• Human capital
• Knowledge, skills, and training of individuals
• Human capital tends to increase in the same proportion as physical capital

𝑌 = 𝐴𝐾 𝑎 𝐻𝑁 1−𝑎
and 𝐻 = 𝐾

• Aggregate production function

𝑌 = 𝐴𝐾
• Increases in human capital offsets the decline in MPK from having more
capital

22
Figure: Average U.S. Educational Attainment, Persons
Aged 25 and Over

23
The Solow Model
• Implications of endogenous growth (AK model)
• Mathematically, this is the Solow model when 𝑎 = 1
• Fundamental equation becomes
1 + 𝑛 𝑘𝑡+1 − 𝑘𝑡 = 𝑠𝐴𝑘𝑡 − 𝑛 + 𝑑 𝑘𝑡
∆𝑘𝑡+1
• Then, 1 + 𝑛 = 𝑠𝐴 − 𝑛 + 𝑑
𝑘𝑡
• If 𝑠𝐴 > 𝑛 + 𝑑 , capital per person keeps on growing
∆𝑦 ∆𝑘
• Since output is proportional to capital, = , so
𝑦 𝑘

∆𝑦 𝑠𝐴 − 𝑛 + 𝑑
=
𝑦 1+𝑛
• Thus, the saving rate affects the long-run growth rate (not true in Solow
model)

24
The Solow Model
• Endogenous growth theory
• Research and development programs
• 𝑁𝑡𝑅 : Number of researchers

𝐴𝑡+1
= ℎ 𝑁𝑡𝑅
𝐴𝑡
• Increased technical knowledge offsets the decline in MPK from having more
capital

25
Figure: Research Intensity in the G-5 Countries

26
The Solow Model
• Summary
• Endogenous growth theory attempts to explain, rather than assume, the
economy’s growth rate
• In the AK model, the growth rate depends on many things, such as the saving
rate, that can be affected by government policies

27
The Solow Model
• Practice questions
• The economy is at the steady state initially
• (1) An earthquake occurs and some capital is destroyed. What is going to
happen to capital per person, output per person over time?
• 𝐾 drops. What would happen to 𝑘 and 𝑦 over time (the transition dynamics and
the steady sate)?
• 𝑘 drops but recovers in the long run

• (2) Instead, some people died due to the earthquake. What is going to
happen to capital per person, output per person over time?
• 𝑁 drops. What would happen to 𝑘 and 𝑦 over time?
• 𝑘 goes up but goes back to the steady state in the long run

28
The Solow Model
• Testing the Solow model

• Destruction of Capital in a War

• Many 20th century wars caused the destruction of a large part of the
capital stock of the countries involved
• What does the Solow model tell us about the effect of such a “shock”
on:
• Output in the short run
• Output in the long run

29
The Solow Model
• Destruction of Capital in a War
• Assume 𝐾 drops in the Solow model
• What would happen to 𝑦 over time?
• Without the change in 𝐴
• 𝑦 drops and then grows temporarily
• After it reaches the steady state, it stops growing
• In practice, 𝐴 grows over time as the Growth Accounting suggests. So, …

30
Figure: Log GDP per Person for Germany

31
Figure: Log GDP per Person for Japan

32
Figure: Log GDP per Person for the US

33
The Solow Model
• Growth miracles in the Solow model
• What does the Solow model suggest as an explanation for high growth rates
of East Asian Tigers?
• In the Solow model:
• Countries below their steady state grow fast
• Further below, faster grow
• Countries above their steady state grow slow (contract)
• Perhaps this may explain differences in growth rates across countries
• Asian Tigers: Below steady state at the beginning (1960s), so experienced high
growth for some time until they reach their steady state

• In the next figure, we consider two countries: Country A has initially a lower
level of capital per capita than country B. Thus, A is poorer.
• Country A will have a higher growth rate than country B
34
Figure: Capital per capita over time

Country B

𝑘 ∗ =1

Country A

35
Figure: Growth Rates in the OECD (frontier countries)
1960-2007

36
Figure: Growth Rates around the World 1960-2007

37
The Solow Model
• Convergence in the Solow model
𝑎
𝑠𝐴 1−𝑎
∗
𝑦 =𝐴
𝑛+𝑑
• Output should converge if 𝐴, 𝑠, 𝑛, 𝑑 are the same
• Perhaps this is more true for OECD countries than countries more
generally

• Where is it even more likely to be true?

• Within countries

38
Figure: Convergence Across US States

39
Figure: Convergence Across Japanese Prefectures (1930-
1990)

40
Figure: Convergence Across 90 Regions in Europe (1950-
1990)

41
The Solow Model
• Strong convergence across
• OECD countries
• US states
• Japanese prefectures
• European regions

• (Barro and Sala-I-Martin, 1999, Economic Growth)

42
The Solow Model
• Convergence in the Solow model
𝑎
𝑠𝐴 1−𝑎
∗
𝑦 =𝐴
𝑛+𝑑
• What if 𝐴, 𝑠, 𝑛, 𝑑 are not the same?
• We can control for differences in 𝐴, 𝑠, 𝑛, 𝑑
• Collect data for each country
• Countries that are further from their steady state should grow faster
• Testing “Conditional convergence”
• Countries converge to their own steady states
• “Unconditional (absolute) convergence”

43
Figure: Conditional Convergence

44
Summary: The Solow Model
• Growth in Solow model
• Investment: Still no growth in per capita output
• TFP Growth: Yields growth in per capita output
• But it is exogenous (model doesn’t explain growth)

• Convergence
• Unconditional convergence: If 𝐴, 𝑠, 𝑛, 𝑑 are the same
• Does not hold for all countries
• Conditional convergence: If 𝐴, 𝑠, 𝑛, 𝑑 differ
• Holds to some extent
• Some empirical evidence supporting the Solow model
• Recovery from wars, cross-country/states convergence, conditional convergence

45
The Economics of Ideas
• Solow model and key questions
• What determines the growth of the “frontier”?
• Capital accumulation not a source of long run growth
• TFP growth accounts for more than half of US growth
• TFP growth exogenous in Solow model
• Solow model not helpful in thinking about frontier
• Why are some countries so far behind the frontier?
• Temporarily below due to history but converging
• Lower steady state. Why? What’s behind 𝐴, 𝑠, 𝑛, 𝑑 associated with lower steady
state?

• Next, let’s think about “𝐴”

• What does 𝐴 include? Technology?
• If so, why does 𝐴 keep on growing in the “frontier”?

46
The Economics of Ideas
• The growing frontier
• Why is our productive capacity “𝐴” 50 times greater than 200 years ago?

• Common answer: We have accumulated a huge amount of new knowledge

• Perhaps production of knowledge is fundamental engine of growth
• Solow model taught us that production of capital is not fundamental engine
of growth

• Is there something special about production of knowledge?

47
The Economics of Ideas
• What are the characteristics of 𝐴?
• Recipes, technology, inventions, formulas
• e.g., information technology, microchips, the Wal-Mart approach to retailing,
Ford’s assembly lines, mathematical formula, etc.

• Do not confuse ideas with R&D

• Broader concept
• Only 8% through formal R&D

• How can we measure 𝐴?

• Growth accounting (Solow residual)

48
The Economics of Ideas
• What is special about ideas?
• Non-rival goods
• One’s consumption does not diminish consumption by others
• Capital and labor are rival goods, but ideas are not
• Rival
• Food, capital, labor
• Non-rival
• Patent, the Wal-Mart approach to retailing, mathematical formula, design for
cloths
• This is important for growth as everybody in the economy can use the same
idea
• Replication argument
• 2𝑌 = 𝐴𝐹 2𝐾, 2𝐿 4𝑌 = 2𝐴𝐹 2𝐾, 2𝐿
• 𝑌 = 𝐴𝐹 𝐾, 𝐿 2𝑌 = 2𝐴𝐹 𝐾, 𝐿
• 𝑌 = 𝐴𝐹 𝐾, 𝐿 2𝑌 = 2𝐴𝐹 𝐾, 𝐿
49
The Economics of Ideas
• Key questions about 𝐴
• Does the market system work well in producing knowledge?

• Does the government need to encourage the production of knowledge?

• Grant “patents” to inventors
• Subsidize basic research

• Why do we need these policies?

• What is the market failure?

• What are the downsides of these policies?

50
The Economics of Ideas
• Consider the production of a new drug
• Drug development costs $800 million

• Once invented: Constant returns to scale

• Standard replication argument

• Factory uses 𝐾 and 𝑁 to produce 𝑌 doses per day

• To double production: Build another identical factory

• Suppose, once created marginal cost is $10

• Marginal cost $10 per dose on first million doses and also on second million
doses.
51
The Economics of Ideas
• Efficient use of new drug
• Once created marginal cost: $10
• How do we bring about efficient use of drug?
• Price must equal marginal cost! 𝑝 = $10
• A competitive market would bring this about
• What is the problem with this?
• Inventor can’t recoup initial $800 million investment
• Inventor will thus not spend resources inventing

• Conclusion: Policy of placing new knowledge in the “public domain” and

relying on competitive markets yields insufficient incentives to create
knowledge
• What is the market failure?

52
The Economics of Ideas
• Market failure in market for ideas
• If we don’t grant rights over ideas,
• Inventor can’t capture full benefits of his/her efforts and thus doesn’t have
strong incentives to engage in research
• Need “excludability”
• Excludability: One can charge a fee for using an idea
• Non-excludability: e.g., mathematical formula (taking the derivative of a
function), national defense, etc.
• Outcome: Too little knowledge production

• Depending on the situation, some ideas can be excludable or non-

excludable
• New drugs, design, etc.
• Should we simply make ideas excludable when we can?

53
The Economics of Ideas
• Market failure in market for ideas
• Fully excludable invention: Will we get perfect competition?
• No!
• With perfect competition: price=marginal cost
• Firms can’t recoup initial investment
• Firms will stop entering market before we get to perfect competition
• We will have an “oligopolistic” market where price>marginal cost

• Not efficient outcome!

54
The Economics of Ideas
• Trade-off
• New ideas with economic distortions and higher prices than with perfect
competition
• Perfect competition with lower prices but no new ideas

• Market for ideas in practice

• Full excludability is not realistic
• Backward engineering always possible
• In practice, non-excludability is a serious issue
• Incentives to invest too low

55
The Economics of Ideas
• Market for ideas in practice
• Example: HIV drugs
• Have been invented. Marginal cost very low.
• Prices much higher than marginal costs.
• Many people in poor countries could pay marginal cost but not price. Priced out
of the market.
• Huge loss in welfare (People die!)
• However, with price=marginal cost, no pharmaceutical company will invest

• Can the government solve this problem?

56
The Economics of Ideas
• Time-consistency problem
• Ex-ante, we want to promise pharmaceutical companies that they will have
the monopoly of the vaccine

• Ex-post, we would like to replicate the vaccine in other companies in order to

have more competition and to lower the price

57
The Economics of Ideas
• Possible solution:
• Legal systems and patents
• A patent is a temporary right to have the monopoly of a product, so that the
company that has developed it can set prices higher than usual
• Enforces temporary full excludability
• But: Price>marginal cost
• e.g., Mathematical formula, marginal cost = 0
• Inefficiently low use of invention
• e.g., With positive price, people use the mathematical formula less
• Provide an incentive for knowledge production
• Turns out to be key to growth

58
The Economics of Ideas
• Other mechanisms for encouraging innovation
• Direct government support of research
• May work for mathematical formula (no excludability)
• Support scientific research, fund gov’t research facilities, provide grants to
researchers, give tax incentives, provide support for science education (human
capital), removing barriers to entry/entrepreneurship

• For the production of ideas, we need a legal system and a market

design that creates incentives for innovation
• Political decision of allocating money can be distorted easily
• Institution of the country matters

59
The Role of Institutions
• Two key questions about growth
• What determines the growth of the “frontier”?
• 𝐴, ideas/knowledge
• Market for ideas
• Importance of institution
• No patents, no strong incentive for new ideas long time ago, so slow growth until a
few hundred years ago

• Why are some countries so far behind the frontier?

• Barriers to riches

60
The Role of Institutions
• Why are some countries behind the frontier?
• Why 𝐴 and 𝑘 so low? Or 𝑠, 𝑛, 𝑑 associated with low level of 𝑦?

• What is the fundamental cause?

• Fundamental cause → 𝐴, 𝑠, 𝑛, 𝑑, 𝑘

• Especially, what does 𝐴 reflect?

61
The Role of Institutions
• Potential explanations
• Luck
• Culture
• Geography
• Institutions
• Education
• etc.

• Difficulty
• Need to find causality, not correlation
• Still ongoing research

• Let’s look at some of empirical evidence so far

62
The Role of Institutions
• Luck
• Great Man theory
• Some countries are lucky to have good leaders
• National leaders cause changes in growth in the countries they govern

• How can we bring evidence to bear on this causal inference question?

• Look at whether changes in leaders is systematically associated with changes

in growth (i.e., correlation)?

• But leadership transitions are not random

• Leader may be ousted because growth is bad (reverse causality)

63
The Role of Institutions
• We need to find a natural experiment
• Are there any leadership transitions that are random from the
perspective of growth?

• Jones and Olken (2005):

• Look at leadership transitions due to death of leaders while in office
• Deaths from natural causes and accidents (exclude assassinations)
• In these cases, the timing of the transition is random

64
The Role of Institutions
• How do we measure effect?
• For random deaths of leaders: Calculate difference in growth in 𝑇 years
before death and 𝑇 years after death

• Is change when leaders die unusually large?

65
Figure: Growth and Leader Deaths

66
The Role of Institutions
• China: Mao (Parkinson’s 1976)
• Deng Xiaoping moved country towards market oriented policies
• Mozambique: Samora Machel (Plane crash 1986)
• Nationalized private land. Portuguese settlers fled
• After Machel’s death, Joaquin Chissano moved country towards market
oriented policies
• Guinea: Sekou Toure (Heart Attack 1984)
• Totalitarian rule with violent purges
• Iran: Ayatollah Khomeini (Surgery compl. 1989)
• Prevented peace negotiations in Iran-Iraq war

67
The Role of Institutions
• Systematic results
• When leaders die, we observe unusually large changes in growth rates

• A one standard deviation increase in leader quality increases growth rate by

1.5% per year

• Effect only exists for autocratic regimes. Not for democracies. Larger for
countries with fewer constraints on executive power

• Countries may grow by luck

68
The Role of Institutions
• Culture
• Differences in beliefs, attitudes and preferences
• Religion, family ties, social norms etc.
• May affect adoption of new technologies, saving rate, attitudes towards
commerce and finance (hard work)
• German sociologist Max Weber:
• The origins of industrialization in Western Europe could be due to Protestantism
• Emphasized hard work and higher saving
• Asian values
• Hard working
• Difficult to find natural experiments
• Cultures change, but very slowly

69
The Role of Institutions
• Geography
• Exogenous differences in environment

• Weather, temperature, natural resource, etc.

• Much of the soil is not suitable for agriculture
• Daytime temperature is too high to work
• Transportation cost is too high

70
Figure: Latitude and log GDP per capita 1995

71
The Role of Institutions
• Geography and growth
• Latitude correlated with GDP

• What are potential channels?

• Tropical disease (malaria, dengue fever)
• Access to trade

• Hard to accumulate capital/human capital

• Countries may be permanently disadvantaged
• Though we are much better at controlling diseases

72
Figure: Growth and Disease

73
The Role of Institutions
• Institutions as a barrier to riches
• Humanly-devised rules shaping incentives (laws and regulations)
• Big differences in economic and political institutions across countries
• Enforcement of property rights
• Legal systems
• Corruption
• Entry barriers
• Democracy vs. dictatorship
• Unlike geography and culture, can be changed
• “Good” institutions create incentives to accumulate capital/human capital and
adopt new technologies
• All rich countries have “capitalist” institutions
• Private property, enforcement of contracts, freedom to engage in trade and to
choose jobs
• Let’s see the relationship between institutions and income levels
74
Figure: Protection against Risk of Expropriation and GDP
per capita

75
Figure: Control of Corruption and GDP per capita

76
The Role of Institutions
• Institutions as a barrier to riches
• Protection against risk of expropriation
• Control of Corruption
• Both positively correlated with GDP

• Is this convincing evidence?

• Couldn’t this be due to reverse causality?
• Couldn’t it be that luck (e.g., good leader) caused growth and that people
demand better institutions when they become richer?

• We need a natural experiment

77
The Role of Institutions
• Institutions as a barrier to riches
• Natural experiments
• e.g., North Korea vs. South Korea (Germany after WWII, Hong Kong vs.
Guangdong)
• Separation of North and South is random, with radically different political and
economic institutions
• Random in the sense that institutional outcomes not related to the economic,
cultural or geographic conditions in the North and the South
• Experiment where similar subjects are “treated” differently
• North: Central planning (markets were banned), private property rights not
respected, supported by the Soviet Union
• South: A market-based economy, though initially autocracy, supported by the US
• But this doesn’t rule out great man theory (Kim Il-sung vs. Park Chung-hee)

78
Figure: GDP per capita for South and North Korea

79
The Role of Institutions
• Colonization as a natural experiment
• Acemoglu, Johnson and Robinson (2005)

• Starting in 15th century Europeans conquered much of rest of the world

• Africa, Asia, Australasia, Latin America, and North America

• Imposed different institutions in different places

• Different institutions led to different economic performance today

80
The Role of Institutions
• Different institutions due to a profit motive
• (1)“Extractive states” with not much protection of property rights or against
government expropriation, where it is less attractive to European settlers (no
immunity to diseases like malaria) and more developed to extract resources
(gold, silver, agricultural surplus and labor): e.g. Congo

• (2)“Good institutions” where lower mortality rate (less disease), so they want
good institution for themselves: e.g. New Zealand, Canada, US

• In places where it was difficult to settle (measured using the mortality

of settlers) and more developed, an extractive state was more likely

81
The Role of Institutions
• What happened?
• The institutions persisted even after independence and affected income level
today
• Reversal of fortune
• North-East U.S., New Zealand, Australia were much less developed but now most
developed
• Many parts of South America , South Asia, North Africa and sub-Saharan Africa
were more developed than North America (e.g., Mughals, Aztecs and Incas
among richest outside Europe) but now among poorer societies

82
Figure: Reversal of Fortune

83
The Role of Institutions
• Mechanism
• Low settler mortality
• → Settlements
• → Built early “good” institutions
• → Current institutions
• → High income today

84
Figure: Mortality and GDP per capita

85
Figure: Mortality and Protection against Risk of
Expropriation

86
The Role of Institutions
• Potential problem of the approach
• Need settler mortality only affects current income through
institutions: Not so obvious
• Other channels
• Human capital of colonizers
• Direct effects of geography (disease)
• Though it may be hard to explain why the reversal of fortune happened

The authors control

the direct effect of disease
Lower settler mortality

Good institutions High income today

87
Summary
• Testing Solow model
• Absolute convergence
• Does not hold for all countries
• Conditional convergence
• Maybe holds to some extent
• Frontier countries: 𝐴 not explained
• Poor countries: Why low steady state?

• Theory of 𝐴: Ideas
• Non-rival goods
• Need excludability: Patent
• Trade-off
• Incentive to develop vs inefficiency due to monopoly
88
Summary
• Empirical evidence for a fundamental cause to explain why some
countries behind?
• Great man theory, culture, geography, institution, etc.

• You don’t need to remember/know all the details of this part

• But try to understand what the graphs say
• Causality or correlation

• Other important issues not discussed

• Income inequality within a country
• Increased compensation going to those with high skills in the US
• Rise in inequality leading to increased education gaps between rich and poor,
causing more future inequality
89
Review: The Solow Model
• Consider the Solow model discussed in class (Assume Cobb-Douglas
production function 𝑌𝑡 = 𝐴𝐾𝑡𝑎 𝑁𝑡1−𝑎 ).

(a) Solve for the steady-state values 𝑦 ∗ , 𝑘 ∗ , and 𝑐 ∗ .

(b) Explain, both mathematically and with a diagram, what happens to
𝑦 ∗ , 𝑘 ∗ , and 𝑐 ∗ if 𝐴 increases.

• Suppose that 𝑎 = 0.5 , 𝐴 = 2 , 𝑛 = 0.01 , and 𝑑 = 0.1.

(c) Find the value of 𝑠 that achieves 𝑦 ∗ = 10.
(d) Find the value of 𝑠 that maximizes 𝑐 ∗ .

90
Review: The Solow Model
(a) Solve for the steady-state values 𝑦 ∗ , 𝑘 ∗ , and 𝑐 ∗ .

• Recall the key equation in the Solow model:

1 + 𝑛 ∆𝑘𝑡+1 = 𝑠𝐴𝑘𝑡𝑎 − 𝑛 + 𝑑 𝑘𝑡

• By definition, 𝑘 ∗ satisfies
0 = 𝑠𝐴 𝑘 ∗ 𝑎 − 𝑛 + 𝑑 𝑘∗

• Solving for 𝑘 ∗ , we get

1
𝑠𝐴 1−𝑎
𝑘∗ =
𝑛+𝑑
91
Review: The Solow Model
(a) Solve for the steady-state values 𝑦 ∗ , 𝑘 ∗ , and 𝑐 ∗ .

• Thus,
𝑦∗ = 𝐴 𝑘∗ 𝑎
𝑎
𝑠𝐴 1−𝑎
=𝐴
𝑛+𝑑
and
𝑐∗ = 1 − 𝑠 𝑦∗ 𝑎
𝑠𝐴 1−𝑎
= 1−𝑠 𝐴
𝑛+𝑑

92
Review: The Solow Model
(b) Explain, both mathematically and with a diagram, what happens to
𝑦 ∗ , 𝑘 ∗ , and 𝑐 ∗ if 𝐴 increases.

• 𝑦 ∗ , 𝑘 ∗ , and 𝑐 ∗ increase
if 𝐴 increases. You can
see it from the figure on
the right. Also, note
𝑎
𝑠𝐴 1−𝑎
that 𝑦∗ =𝐴 is
𝑛+𝑑
increasing in 𝐴. Same
for 𝑘 ∗ , and 𝑐 ∗ (Check the
previous slides.).
93
Review: The Solow Model
(c) Find the value of 𝑠 that achieves 𝑦 ∗ = 10.

• Recall that
𝑎
𝑠𝐴 1−𝑎
∗
𝑦 =𝐴
𝑛+𝑑

• Plugging in 𝑦 ∗ = 10, 𝑎 = 0.5 , 𝐴 = 2 , 𝑛 = 0.01 , and 𝑑 = 0.1 and

solving for 𝑠, we get
𝑠 = 0.275

94
Review: The Solow Model
(d) Find the value of 𝑠 that maximizes 𝑐 ∗ .

• Recall that
𝑎
𝑠𝐴 1−𝑎
∗
𝑐 = 1−𝑠 𝐴
𝑛+𝑑

• Plugging in 𝑎 = 0.5 , 𝐴 = 2 , 𝑛 = 0.01 , and 𝑑 = 0.1, we get

∗
400
𝑐 = 𝑠 1−𝑠
11

95
Review: The Solow Model
(d) Find the value of 𝑠 that maximizes 𝑐 ∗ .

• Thus, the maximization problem is

400
max 𝑠 1−𝑠
𝑠 11

• The value of 𝑠 that maximizes 𝑐 ∗ , denoted by 𝑠 ∗ , satisfies the first-order

condition
400
−𝑠 ∗ + 1 − 𝑠 ∗ = 0
11

• Solving for 𝑠 ∗ , we get

𝑠 ∗ = 0.5
96