Download Output per effective worker

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
Structure of lecture
1. Theoretical overview on technological
progress and growth
2. Drivers of technological progress and
entrepreneurship
3. Empirical discussion – indentifying
technological progress in overall
growth data
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.
Technological Progress and the
Production Function
Let’s denote the state of technology by A and rewrite the production
function as:
Y  F ( K, N , A)
(+ + +)
A modified and more convenient form is:
Y  F ( K, AN )
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
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:
Y  F ( K, AN )
• 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:
2Y  F (2K , 2 AN )
or
xY  F ( xK , xAN )
Effective labour (cont)
Y  F ( K, AN )
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):
Y
 K
 F
,
AN
 AN

1

Output per effective worker depends on
capital per effective worker
The relation between output per effective worker and
capital per effective worker is:
Y
 K
 F
,
AN
 AN

1

which we can redefine as (see Fig 12.1):
Y
 K 
 f

AN
 AN 
Therefore:
Output per effective worker is a function of capital per effective worker.
Output per effective worker
Figure 12 - 1
Output per Effective
Worker versus Capital
per Effective Worker
Because of decreasing returns
to capital, increases in capital
per effective worker lead to
smaller and smaller increases
in output per effective worker.
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):
Y
 K 
 f


AN
AN 
 Investment is given by the level of savings (as I=sY), which
divided by the number of effective workers (AN) gives (Green):
I
 Y 
 s

 AN 
AN
Y
 K 
 f

 AN 
AN
I
 K 
 sf 

 AN 
AN
 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):
I
K
 (  gA  gN )
AN
N
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.
K*
K
sf (
)  ( )
N
N
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:
I  K (gA  gN )K
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
I  K (gA  gN )K
I  (  gA  gN )K
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) I
K
AN
 (  gA  gN )
N
Interactions between Output and Capital
Figure 12 - 2
The Dynamics of Capital
per Effective Worker and
Output per Effective
Worker
Capital per effective worker
and output per effective worker
converge to constant values in
the long run.
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)
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
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
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
Characteristics of balanced growth
Table 12-1
The Characteristics of Balanced Growth
Rate of growth of:
1
Capital per effective worker
0
2
Output per effective worker
0
3
Capital per worker
gA
4
Output per worker
gA
5
Labor
gN
6
Capital
gA + gN
7
Output
gA + gN
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
The Effects of the Saving Rate
Figure 12 - 3
The Effects of an
Increase in the Saving
Rate: I
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.
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)
The Effects of the Saving Rate (short run)
Figure 12 - 4
The Effects of an
Increase in the Saving
Rate: II
The increase in the saving rate
leads to higher growth until the
economy reaches its new,
higher, balanced growth path.
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)
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.
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.
Information Technology, the New Economy,
and Productivity Growth
Figure 1 Moore’s Law: Number of Transistors per Chip, 1970 to 2000
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
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
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))
Table 12-2
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
2.9
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)
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
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
Capital Accumulation versus
Technological
Progress in China since 1980
Table 12-3
Average Annual Rate of Growth of Output per Worker and
Technological Progress in China, 1983 to 2003
Rate of Growth
of Output (%)
9.7
Rate of Growth of
Output per Worker (%)
8.0
Rate of Technological
Progress (%)
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)
Solow’s Measure of technological progress
Assumption: each factor of production is paid its marginal
product (i.e. if a worker is aid R30 000 then his/her
contribution to output is R30 000 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%
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]
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)