1. Chapter 6
A Simple Model
of Growth and
Development
Charles I. Jones

2. Next Step: Technology Diffusion
A review of the growth models:
Technological progress is always the key.
Solow models take technological progress to be exogenous.
Romer and Schumpeterian models endogenize growth by providing microeconomic underpinnings to innovation.
The next step is to show how technology gets diffused across countries, and to explain why some countries’ level of technological development is still low.

3. Basic Model The basic setup is very similar to the Romer model.
Firms produce output Y using labor L and a range of capital goods The “number” of capital goods is limited by the skill level h.
The production function is
Low-skilled workers use spades, high-skilled workers use both spades and excavators.
Key distinction: this time, new designs of capital goods due to innovation are already available from the more developed part of the world. Think of this model as discussing a less developed economy.

4. Capital Goods Production
As before, one unit of raw capital good produces exactly one unit of the intermediate capital good.
Total capital stock in the economy must equal to the total stock of capital goods:
Intermediate goods are treated symmetrically: for all j.
The aggregate production function then takes the following form that treats skill level exactly as a labor-augmenting productivity factor:

5. Capital Accumulation
Capital stock changes with time due to savings/investments and capital depreciation in a standard way:
In chapter 3, the skill level h was the number of schooling years.
In this model, skill h is defined as the range of the intermediate goods an individual has learned how to use.

6. Learning to Use Advanced Goods
Workers progress from using hoes and oxen to using tractors and fertilizers according to
Here u is the amount of time an individual spends accumulating skill instead of working. A is the best-practice frontier.
Spending additional time (u) accumulating skill will increase the skill level proportionally (why?).
The change in skill is a geometrically weighted average of the frontier skill level A and the individual skill level h (why?).

7. Skill Accumulation
Let us rewrite the skill accumulation equation like this:
The closer the skill level h is to the frontier A (i.e. the lower the value of , the harder it is to learn a new skill.
Computers were difficult to learn when they just appeared compared to today when they are common, i.e. far from the frontier.
The technological frontier is assumed to evolve because of investment in research by the advanced countries:

8. Balanced Growth Path We assume that and u are constant and exogenous.
We also assume that , where n is also constant and exogenously given.
Since the skill level h is entering the production function like A enters it in Chapter 3, the growth rate in h will determine the growth rates of and
The growth rate will be constant if is constant, which means A and h must grow at the same rate.
Along the balanced growth path then,

9. Steady State
The growth rate of the less developed economy is determined by the growth in the skill level, which in turn is determined by the rate of growth of the world’s technological frontier.
The steady state capital-output ratio is given by
Substituting it into the production function, we obtain:
The more time individuals spend learning skills, the closer the economy is to the best-practice technological frontier:

10. Evolution of Output per Worker
Output per worker in our economy is evolving with time and is a function of exogenous parameters and the evolution of the world’s best practice technological frontier:
In this model, economies grow because they learn how to use new ideas developed throughout the world.
Investing more increases growth, while rapidly growing population produces a downward pressure on growth.
Economies that spend more time accumulating skills will be closer to the technological frontier.
Differences in the technological level are explained by differences in u, the amount of time individuals invest in accumulating skills.

11. The TFP Problem
In our model, Total Factor Productivity is the same in all countries.
However, one of the stylized facts we examined says that the TFP levels vary considerably across countries.
The possible explanations for TFP differences are
Lack of economic institutions that allocate labor and capital to their most productive uses
State intervention may result in productive inefficiencies
Firms may be reluctant to invest in skill accumulation

12. Technology Transfer
The key assumption so far was that the intermediate capital goods are readily and freely available for use from the more advanced countries. However:
Steering wheel may need to be placed on the other side
Electric appliances might need to conform to a different standard
Movies may need to be modified even for the same language (e.g. Australian vs American English)
Patents
Property rights protection is necessary to ensure innovation
Do patents issued in one country get enforced in another?
If yes, innovation is stimulated even more
However, in this case one has to pay for the intermediate goods

13. Effects of International Property Rights Protection
Consider a model of two countries:
The North, at the technological frontier
The South, far below the frontier, imitating the designs invented in the North
If international property rights are respected in the South, imitation is more difficult, so it reduces in equation for skills growth:
Along the balanced growth path, the reduction of growth rate of skills leads to a reduction in the ratio of skills to technological level:

14. Effects of International Property Rights Protection
However, better protection of the international property rights will induce the North to innovate since every new idea results in higher profits, so more labor in the North is engaged in research: the Northern share of researchers will go up.
This increases the level of A.
Since in the South, the balanced-growth path output per capita is determined by , the decrease in and an
increase in A will have mutually offsetting effects.
Helpman (1993) finds that the net effect is negative: more innovation in the North is not enough to offset slower imitation in the South

15. The Case of Appropriate Technology
In some countries, imitation only makes sense once an appropriate level of technological development is reached.
Computers are useless without electricity network
Bullet trains are not needed in a country with no railroads
In case the South is not sufficiently developed to adopt the Northern technologies, the A in the South will be lower.
However, if the North modifies its technologies for use in the South due to the international property rights protection in the South, the level of A will be higher due to more incentives to innovate in the North, so that the net effect will be positive.

16. Recent Developments
TRIPS: Agreement on Trade-Related Aspects of Intellectual Property Rights
As off 1995, ratifying TRIPS became compulsory for anyone willing to join the WTO (World Trade Organization)
The frontier countries (US, Europe) pushed for TRIPS
Developing countries negotiated a delay in the adoption of this agreement
In 2005, the window to implement TRIPS ended for the less developed countries, but it was extended until 2013 for the least developed countries.

17. Globalization and Trade
One of our stylized facts was that openness to the international trade is positively associated with growth.
Let us modify the production function to account for this link:
becomes
The number of intermediate goods varieties is equal to h, those goods produced at home, PLUS m varieties imported from other countries.

18. The Capital Stock Identity
Let z be the number of units of each of the h types of intermediate goods that a country has learned how to make.
The value of domestically produced capital will be
Since the domestic final-goods sector uses units of each of the h intermediate goods, the country keeps for domestic production.
As a result, the country can pay for the intermediate goods produced abroad.
Since there are m different types imported, and x(t) units of each imported variety use, the following identity hods:

19. Interpreting the Capital Stock Identity
Since , it follows that
Net intermediate goods produced domestically are shipped as exports to foreign countries in exchange for imports of mx in foreign intermediate goods.
Alternatively, we can invoke the FDI (foreign direct investment) reasoning: the home country owns K units of capital, but only hx of those are located inside the country, while the other mx units are located abroad.
Intel’s chip plant in Costa Rica
An equivalent amount of foreign capital is invested in home country:
Toyota’s assembly plant in Tennessee

20. Production Function with Trade
The capital stock identity can be rearranged to obtain
Combining with the modified production function, we can write:
The term h+m enters as a labor-augmenting technology.
More foreign inputs increase output.
Rearranging slightly, we obtain:
This is a familiar aggregate production function augmented by the ratio of foreign to domestic inputs.

21. Balanced Growth Path with Trade
Since mathematically the aggregate production function is similar to the one analyzed at the beginning of the chapter, all familiar conclusions apply. In particular, along the balanced growth path,
In case the economy is closed, i.e. m=0, we are back to the solution we obtained earlier in this chapter.

22. Trade Openness and Growth
Ratio of imports to GDP can act as a crude measure of the country’s openness:
As the ratio increases (e.g. think of increasing m with fixed h), the ratio of imports to GDP goes up, too.
From the production function ,
an increase in acts in the same way as an increase in education u or savings rate , by increasing the level of technology A.
After opening up, growth will be higher, and extent of openness will be higher, too. That is explaining the stylized fact on trade and growth.

23. Trade Openness and Growth Miracles
Korea: imports accounted for 13% of GDP in 1960, rising to 54% by 2008.
China: imports are 3% of GDP in 1960, but they are 27% in 2008.
Both countries have substantially increased the amount of foreign-produced intermediate parts in their production factor mix.
South Korea
Cell phone parts
Automobile parts

24. Foreign-Produced Inputs and Growth
Along the balanced-growth path, h is growing at the rate g.
Unless m is growing at the same rate or higher, the ratio will be falling.
Broda, Greenfield and Weinstein (2010) document the following:
A median country increased the number of imported intermediate inputs from in 1993 to by 2003.
That translates into a growth rate of about 3.5% per year
92% of the increase in the value of imports is accounted for by the increase in the variety of imported goods rather than the volume of the already imported goods
The empirical model implies that an increase in the variety of imported inputs increases median growth from 2% to 2.6% with the increased growth effects in place for 75 years!

25. Same Long-Run Growth Rate?
Technology diffusion model implies that in the long run each country’s growth rate will be the same and equal to the rate of expansion of the best-practice technological frontier A.
Belgium and Singapore are good examples of countries that grow by actively borrowing the best-practice ideas from the rest of the world (both have small populations).
Our stylized facts, though, say that average growth rates vary enormously across countries.
Large variation in growth rates are explained by transition dynamics. Different growth rates are possible while countries are changing their position within the world’s income distribution.

26. Different Growth Rates and the Steady State
We know that countries that are below their steady state will grow faster than average, while being above the steady state slows down growth.
What makes countries be away from their steady states?
Shock to capital stock (e.g. war)
Policy reform affecting investment
Policy reform affecting educational system

27. United States and United Kingdom
: US grows at 1.7% per year > 0.9% for UK
After 1950: US and UK grow at 2.03% and 2.17%, respectively
We have to be careful interpreting average growth figures over long periods of time!

28. Transition Dynamics and Technology Diffusion
Transition dynamics in the Solow models is a feature of capital accumulation equation.
In the model of technology diffusion, transition dynamics involves not only capital accumulation, but also technology diffusion in
Suppose a country reduces import tariffs, which increases the rate of growth in the skill level h, and the level of steady-state level of income
The principle of transition dynamics says that, since the economy is now below its steady-state level of per capita income, it will start growing faster.