1. Lecture 3 : Growth and technological progress
Key issues
The role of technological progress in growth – the long run tendency towards a steady state or balanced growth i.e. where the growth rate of output is equal to the rate of population growth plus the rate of technological change
The role of Research and Development (R&D) in determining technological progress
Discussing the empirical experience with regard to the rate of technological progress

2. Structure of lecture
Theoretical overview on technological progress and growth
Drivers of technological progress and entrepreneurship
Empirical discussion – indentifying technological progress in overall growth data

3. 1. Theoretical overview on technological progress and growth
Technological progress has many dimensions. It may mean:
Larger quantities of output e.g. new lubricant that allows machines to run at higher speed
Better products e.g. improvements in car safety over time
New products e.g. cell phones, digital/downloadable music and movies
A larger variety of products e.g. wide variety of consumer products (cereal bars, chocolate milk)
Technological progress leads to increases in output for given amounts of capital and labor. In essence, consumers receive more services, which is the equivalent of increased output.

4. Technological Progress and the Production Function
Let’s denote the state of technology by A and rewrite the production function as:
A modified and more convenient form is:
Where output is dependent on capital and on labour multiplied by the sate of technology, which implies:
Technological progress (A) reduces the number of workers ((N) needed to produce a given output (Y)
Technological progress (A) increases the output (Y) produced by a given number of workers (N)
Therefore, AN gives the amount of effective labour in the economy

5. What is effective labour?
The amount of effective labour (sometimes called labour in efficiency units) is indicated by:
technology (A) x the quantity of labour (N) = (AN) in the production function:
If the state of technology doubles (2A) it is as if the economy has twice as many workers (2AN)
Therefore, we think of output as being produced by two factors: Capital (K) and Effective Labour (AN)
Again, constant returns to scale apply: or

6. Effective labour (cont)
For the production function:
We also assume decreasing returns to factors (for each of the two factors) i.e.
Given a certain level of effective labour (AN) an increase in capital (K) increases output (Y) at a decreasing rate, or
Given a certain level of capital (K) an increase in effective labour (AN) increases output (Y) at a decreasing rate
Therefore, having set up the modified production function it is convenient to advance our analysis on the basis of output per effective worker and capital per effective worker (as in the steady state both output per effective worker and capital per effective worker are constant):

7. Output per effective worker depends on capital per effective worker
The relation between output per effective worker and capital per effective worker is:
which we can redefine as (see Fig 12.1):
Therefore:
Output per effective worker is a function of capital per effective worker.

8. Output per effective worker
Output per Effective Worker versus Capital per Effective Worker
Figure
Because of decreasing returns to capital, increases in capital per effective worker lead to smaller and smaller increases in output per effective worker.

9. Interactions between Output and Capital
As in Fig 12.2, the dynamics of output and capital per effective worker involve:
Output per effective worker increases with capital per effective worker (Blue):
Investment is given by the level of savings (as I=sY), which divided by the number of effective workers (AN) gives (Green):
Required investment – the level of investment per effective worker that is required to maintain a level of capital per effective worker is given by (Red):

10. Required investment (cont.)
Case 1
Where there is no technological change: the stock of capital is constant (K*/N) where the flow of investment (and savings) is equal to the rate of depreciation (δ) i.e.
Case 2
Where there is technological change: A increases over time (so AN increases over time), therefore to maintain the ratio of capital to effective workers (K/AN)* requires an increase in the capital stock (K) proportional to the increase in effective workers (AN), where:
the rate of depreciation = δ
the growth of population and number of workers (ratio of employment to total population assumed constant) = gN
the rate of technological progress = gA
this implies that the growth rate of effective labour (AN) = gA + gN
Therefore, the level of investment required to maintain a given level of capital per effective worker is given by:

11. Required investment (cont.)
Numerical example
if the rate of depreciation = δ = 10%
if the growth of population and number of workers = gN = 1%
if the rate of technological progress = gA = 2%
then based on Or
investment must equal (10% + 1% + 2%) 13% of the capital stock to maintain a constant level of capital per effective worker
division by AN gives the required level of investment per effective worker (red line in Fig 12.2)

12. Interactions between Output and Capital
The Dynamics of Capital per Effective Worker and Output per Effective Worker
Figure
Capital per effective worker and output per effective worker converge to constant values in the long run.

13. Dynamics of Capital and Output –tendency towards balanced growth
At (K/AN)0 actual investment (AC) exceeds the investment level required to maintain the existing level of capital per effective worker (AD) AC>AD, therefore K/AN increases
At Fig 12.2, from (K/AN)0 the economy moves to the right, with the level of capital per effective worker increasing over time (to the left actual inv is below required inv)
In the long run, where required investment (red) and actual investment (green) intersect, capital per effective worker reaches a constant level at (K/AN)*, and so does output per effective worker (Y/AN)*, this is the steady state
This implies that output (Y) is growing at the same rate as effective labor (AN). Because effective labour grows at the rate gN + gA output growth in the steady state must equal gN + gA and capital also grows at gN + gA
Conclusion: in a steady state growth rate of output (balanced growth) equals the rate of population growth plus the rate of technological progress (and is independent of the savings rate)

14. Comparison – limits to growth
Case 1 No technological progress Economy tends to steady state and cannot sustain positive output growth because decreasing returns to capital would require that a larger an larger portion of output be devoted to capital accumulation Case 2 With technological progress Economy tends towards balanced growth where, due to decreasing returns to capital, larger portions of output would have to be continuously devoted to capital accumulation in order to sustain output growth higher than the growth of effective labour given as gN + gA

15. Standard of living
To understand the impact on the standard of living we must look at the output per worker and not output per effective worker
Output grows a the rate gN + gA
The number of workers grows at the rate gN
Therefore output per worker grows at the rate gA
Conclusion: When the economy is in a steady state, output per worker grows at the rate of technological progress

16. Characteristics of balanced Growth
In a steady state - Output, capital and effective labour all grow at the same rate gN + gA
As a result this is also called a state of balanced growth
In a steady state – output and the two inputs K and AN grow a the same rate (hence “balanced growth”)
The characteristics of a steady state/balanced growth/long run are as follows (see Table 12.1):
Capital per effective worker and output per effective worker are constant (Fig 12.2)
Capital per worker and output per worker are growing at the rate of technological progress
Labour is growing a the rate of population growth
Capital and output are growing at the rate of population growth plus technological progress

17. Characteristics of balanced growth
Table The Characteristics of Balanced Growth
Rate of growth of: 1
Capital per effective worker 2
Output per effective worker 3
Capital per worker gA 4
Output per worker 5
Labor gN 6
Capital
gA + gN 7
Output

18. Effects of the saving rate
The Saving rate effects the level of output (per effective worker) but not the long run growth rate of output
Long-run effect
In Fig.12.3 an increase in savings from s0 to s1 has the following long run (steady state) effects:
The investment relation shifts upwards
The level of capital per effective worker increases from (K/AN)0 to (K/AN)1
The level of output per effective worker increases from (Y/AN)0 to (Y/AN)1
Transitional or short run effect
In Fig. 12.4

19. The Effects of the Saving Rate
The Effects of an Increase in the Saving Rate: I
Figure
An increase in the saving rate leads to an increase in the steady-state levels of output per effective worker and capital per effective worker.

20. The Effects of the Saving Rate (short run)
Fig 12.4 plots output (at log scale) against time
At AA the economy is on a balanced growth path (slope gN + gA)
Savings rate increases from S0 to S1 a time t
Output grows faster for some time, but then returns to the original growth rate (slope gN + gA)
In the new steady state at BB the economy grows at the same rate but on a higher growth path (higher level of output per effective worker)

21. The Effects of the Saving Rate (short run)
The Effects of an Increase in the Saving Rate: II
Figure
The increase in the saving rate leads to higher growth until the economy reaches its new, higher, balanced growth path.

22. Summary of growth dynamics and balanced growth
In an economy with technological progress and population growth, output grows over time
In steady state output per effective worker and capital per effective worker are constant (no change)
In steady state, output per worker and capital per worker grow at the rate of technological progress (hence the improvement in living standards)
In steady state output and capital grow at the same rate as effective labour (which is a growth rate equal to the growth rate of the number of workers plus the rate of technological progress)

23. 2. Determinants of technological progress
Finding: growth rate of output per worker is determined by the rate of technological progress
Question: What determines the rate of technological progress?
Answer: “Technological progress” in modern economies is the result of firms’ research and development (R&D) activities. The outcome of R&D is fundamentally ideas. (ideas, unlike a specific machine can be used by many firms of the same time, so ideas must be protected or there will be no incenitve to generate new ideas)
The level of spending on R&D depends on:
The fertility of the research process, or how spending on R&D translates into new ideas and new products, and
the appropriability of research results, or the extent to which firms benefit from the results of their own R&D.

24. The Fertility of the Research Process
Research is fertile if R&D leads to many new products.
The determinants of fertility include:
The interaction between basic research (the search for general principles and results) and applied research (the application of results to specific uses) e.g. the invention of the transistor and the microchip has resulted in a revolution in information technology (See Moore’s Law – the number of resistors in a microchip would double every 18 to 24 months resulting in more powerful computers)
The country: some countries are more successful at basic research; others are more successful at applied research and development.
Time: It takes many years, and often many decades, for the full potential of major discoveries to be realised. (See process of diffusion of hybrid corn in the US (suited to local conditions and raising corn yield by up to 20%)
Good news: there is no sign that technological progress is slowing down, or that most discoveries have already been made.

25. Information Technology, the New Economy, and Productivity Growth
Figure 1
Moore’s Law: Number of Transistors per Chip, 1970 to 2000

26. The Diffusion of New Technology: Hybrid Corn
Figure 1
Percentage of Total Corn Acreage Planted with Hybrid Seed, Selected U.S. States, 1932 to 1956

27. The Appropriability of Research Results
If firms cannot appropriate the profits from the development of new products, they will not engage in R&D. Factors at work include:
The nature of the research process. Is there a payoff in being first at developing a new product? (or will other firms be able quickly to imitate the product)
Legal protection. Patents give a firm that has discovered a new product the right to exclude anyone else from the production or use of the new product for a period of time.
Question arises as to how best governments should design patent laws as there is a trade-off; protection is needed to create an incentive for R&D, but society would benefit if new ideas are widely dispersed without restriction (therefore time bound restrictions or pay innovators or incubate innovators)
Globalisation: countries that are less technologically advanced have poorer patent protection e.g. China is primarily a user rather than a producer of new technologies

28. 3. Empirical discussion on growth
A high rate of growth of output per worker may come from two sources:
A higher rate of technological progress. If gA is higher, balanced output growth (gN + gA) will also be higher
Adjustment of capital per effective worker, K/AN, to a higher level. In this case, there is a short-run transitional period in which the growth rate of output exceeds the rate of technological progress (as per Fig.12.3 and 12.4).
It is possible to identify which source of growth is predominant, as follows:
If the rate of growth of output per worker = the rate of technological progress then there is balanced growth (1st source)
If the rate of growth of output per worker > the rate of technological progress then there source of growth is due to the adjustment to a higher level of capital per effective worker (2nd source)
Empirically – growth since the 1950’s has been due to technological progress (See Table 12.2 where there is evidence of balanced growth i.e. rate of growth of output per worker (column 1) ≈ the rate of technological progress (column 2))

29. Table Average Annual Rates of Growth of Output per Capita and Technological Progress in Four Rich Countries since 1950
Rate of Growth of Output per Worker (%) 1950 to 2004
Rate of Technological Progress (%) 1950 to 2004
France
3.2
3.1
Japan
4.2
3.8
United Kingdom
2.4
2.6
United States
1.8
2.0
Average
2.9

30. Table 12-2 illustrates two main facts:
First, growth since 1950 has been a result of rapid technological progress, not unusually high capital accumulation. (This conclusion is based on the evidence of balanced growth i.e. rate of growth of output per worker (column 1) ≈ the rate of technological progress (column 2))
Second, convergence of output per worker across countries has come from higher technological progress, rather than from faster capital accumulation, in the countries that started behind. (This conclusion is based on ranking of the rates of technological progress (in the second column) with Japan at the top and the United States at the bottom)

31. Capital Accumulation versus Technological Progress in China since 1980
Going beyond growth in OECD countries, one of the striking facts in Chapter 10 was the high growth rates achieved by a number of Asian countries. This raises again the same questions we just discussed: Do these high growth rates reflect fast technological progress, or do they reflect unusually high capital accumulation?
To answer the questions, we focus on China because of its size and because of the astonishingly high output growth rate, nearly 10%, it has achieved since from 1983 to 2003
As outlined in Table 12.3
As the rate of growth of output per worker (8%) and the rate of technological progress (8,2%) are nearly equal, therefore we draw the conclusion that growth in China since the early 1980’s has been balanced and is driven by technological progress

32. How has China achieve such technological progress?
Firstly, urbanisation from country to city from low productivity areas to high productivity areas
Second, China has imported the technology from more advanced countries

33. Capital Accumulation versus Technological Progress in China since 1980
Table Average Annual Rate of Growth of Output per Worker and Technological Progress in China, 1983 to 2003
Rate of Growth of Output (%)
Rate of Growth of Output per Worker (%)
Rate of Technological Progress (%)
9.7
8.0
8.2
The nature of technological progress is likely to be different in more and less advanced economies. The more advanced economies, being by definition at the technological frontier, need to develop new ideas, new processes, and new products.
It is easier for the less advanced economies to imitate rather than innovate new technologies. This can explain why convergence, both within the OECD and in the case of China and other countries, typically takes the form of technological catch-up. (but not all countries can imitate technology)

34. Solow’s Measure of technological progress
Assumption: each factor of production is paid its marginal product (i.e. if a worker is aid R then his/her contribution to output is R and if worker increases working hours by 10% then the increase in output will be 10% of R30 000) Formally, ΔY=W/PΔN or ΔY/Y=WN/PYxΔN/N ΔY/Y is rate of growth of output = gY WN/PY is share of labour in output = α ΔN/N is rate of change of labour input = gN Therefore: gY = αgN The share of capital in output = 1 – α (and growth is gK) e.g. if capital grows by 5% and share of capital is 0,3 (because share of labour is 0,7) then the output growth due to the growth of capital is equal to 1,5%

35. Solow’s Measure of technological progress
Growth in output attributed to growth in labour and capital is equal to: αgN+(1-α) gK SOLOW’S CALCULATION: The growth due to technological progress is equal to the excess of actual growth of output gY over the growth attributable to growth of labour and the growth of capital Residual = gY – [αgN+(1-α) gK]

36. Solow’s Measure of technological progress
Example: If employment increases by 2%, capital stock grows by 5% and the share of labour is 0,7 (and capital share is 0,3), then the part of the growth attributed to growth of labour and capital = (0,7 x 2% + 0,3 x 5%) = 2.9% It actual output growth is equal to 4% then Solow’s residual is equal to 1,1% (growth due to technological progress) Note: The Solow residual is sometimes called the rate of growth of total factor productivity (or the rate of TFP growth)