Technological
Progress
Chapter 6
Students should be expected to:




Use the rule of 70 to calculate how fast a variable
doubles.
Use the Cobb-Douglas production function to calculate
labor productivity growth as a function of technology
growth and the average productivity of capital.
Calculate the steady-state capital productivity as a
function of capital fundamentals. Calculate the growth
rate of labor productivity when capital productivity is at a
steady state.
Describe the dynamics of labor and capital productivity,
real wages and returns to capital over the different
stages of growth.
Why was productivity growth so
fast in Asia?
Some of the fastest economic growth has
occurred in East Asia during the post-war
period.
 Reason for this growth has been attributed
to the rapid increases in the utilization of
the factors of production.
 Does this matter for the future?

Average Growth GDP per capita 1966-1990
Rule of 70
If GDP is growing at G% per year, then
GDP doubles every 70/G years.
 South Korea growing at a rate of 7% per
year will double every 10 years.
 USA growing at a rate of 2% per year will
double every 35years.

In 1960 no obvious signs that this region would perform so well
East Asian economies tended to have extremely high
investment rates
And increases in labor per person.
Growth Breakdown 1966-90 for Asian Dragons
Main explanation for large increase in output is a
large increase in inputs
Singapore financed huge capital accumulation
by compulsory pension scheme
50
40
30
Employee
20
Employers
1990
1988
1986
1984
0
1982
10
Central Provident Fund Contributions
% of Wages
East Asian Growth: Myth or Miracle
East Asian economies were able to
achieve very high (miraculous) increases
in standard of living.
 East Asian economic growth was achieved
through rapid capital accumulation and
relatively average technology/TFP growth.

 What
is the implication for the future?
Exogenous Growth
We assume that the technology level
grows over time as a natural and costless
by-product of economic activity.
 Assume a constant growth rate of
technology:

Z t 1  Z t
 gZ
Zt
Growth Rate of Productivity

The growth rate of productivity in the
Cobb-Douglas case is a weighted average
of capital per worker growth and
technology growth.

1


gdpt  (kt )  (Zt )
g
GDP
t
 a  g  (1  a ) g
k
t
k
t
Labor Productivity Growth Rate

This implies that the growth rate of output
and the growth rate of capital is a function
of the average productivity of capital.
K t 1  (1  d ) K t  I t  (1  d ) K t  sGDPt  K t 1  s  GDPt  dK t
g
K
t 1
K t 1
GDPt
GDPt
k
K

s
 d  gt 1  gt 1  n  s
 (d  n )
Kt
Kt
Kt
g
GDP
t 1
 GDPt

 a s
 (d  n)   (1  a) g Z
 Kt

Implications



If the growth rate of capital per worker is faster
than the growth rate of technology, the growth
rate of capital per worker will be higher than the
growth rate of labor productivity.
This, in turn, will imply that capital productivity
(the ratio of output to capital) will fall.
This will in turn imply that labor productivity
growth & capital per worker growth will slow
down.
Capital Productivity & Growth
gk
ggdp
gZ
[gdp/k]SS
GDP
K
Two Phases of Growth


Transition Path – Emerging economy with high
capital productivity experiences capitalinvestment led growth in which the growth rate
of labor productivity is increasing faster than the
world frontier of technology. Along the transition
path, capital is growing faster than output and
capital productivity is falling.
During much of the post-war period, Korea was
on its transition path.
Two Phases of Growth pt. 2



Balanced Growth Path – On the balanced
growth path, labor productivity and capital per
worker are each growing at the same rate as the
world technology frontier.
During the post-war period, the US was on its
balanced growth path.
All balanced growth paths should increase at the
same rate (the growth rate of world technology
frontier, gZ). However the positions of labor
productivity on the growth path may be different.
US and Brazil



Since the early 1970’s, the US and Brazil have
grown at roughly the same rate.
US labor productivity have been maintained at a
level approximately 3 times the level in Brazil.
Capital productivity has been roughly constant in
Brazil (though this has had more ups and downs
than in the US). Capital productivity has stayed
at a higher level in Brazil than the US.
Labor Productivity
Labor Productivity (logged)
11.2
10.8
10.4
10.0
9.6
9.2
8.8
8.4
50
55
60
65
70
75
Brazil
80
85
USA
90
95
00
Capital Productivity
0.9
0.8
0.7
0.6
0.5
Brazil
0.4
USA
0.3
0.2
0.1
19
89
19
87
19
85
19
83
19
81
19
79
19
77
19
75
19
73
19
71
19
69
19
67
19
65
0
Capital Productivity and Labor
Productivity

Holding technology constant, there is a negative
relationship between capital productivity and
labor productivity.


gdpt   kt  ( Zt )


1
 gdpt
1
 kt 
 gdpt 
1

 ( Zt )  gdpt  

 gdpt 
 kt 

1
Zt
Holding tech. constant, if you have a high ratio of
machines to workers, capital productivity will be
low and worker productivity high. If you have a
high ratio of workers to machines, the reverse
will be true.
Balanced growth path capital
productivity

We can solve for capital productivity along
the balanced growth path.
g Z    s[ gdp ]SS  (d  n)   (1   ) g Z
k


(d  n  g Z )
gdp
gdp
SS
SS
 s[
]  ( d  n)  [
] 
k
k
s

Different countries are likely to have
different investment growth rates and labor
force growth rates. Thus, they will have
different capital productivity levels.
Determinants of Long-term Capital
Productivity

Investment Rates: When economies invest a
high percentage of their output, they can
“support” a high level of capital per worker.
 To
maintain a steady level of capital per worker,
investment must be done in every period to replace
depreciated equipment and equip new workers.
 If investment levels are high, a high level of
depreciated capital can be replaced.

A high ratio of capital to labor implies a low level
capital productivity and a relatively high level of
labor productivity.
Factor Prices




How do real wages and real capital rental rates behave
over the long-term?
Factor prices (under Cobb-Douglas) are proportional to
average productivity.
Real wages are proportional to labor productivity. Along
the transition path, real wages will grow faster than
technology but slower than real capital per worker. Along
the balanced growth path, real wages will grow at the
same rate as technology.
Capital productivity will fall along the transition path due
to diminishing returns to capital. Along the balanced
growth path capital returns will remain constant as
capital productivity is constant.
Will poor countries catch up with
rich countries?



If all countries share the same technology, Zt,
countries will converge to a balanced growth
path along which they will grow at the same rate.
The position of that balanced growth path is
determined by capital productivity which is
determined in steady-state by investment and
population growth rates.
If a poor country has the same s and n, it will
catch up with the rich countries!
World Technology Frontier?
There are two problems with the modeling of Z as
some common level of technology available in the
world which drives the long-run growth path.
1.
As a matter of theory, we haven’t really explained longterm growth. Long-term growth occurs through the
costless (and exogenous magic of) technology.
This might be important since:
Some countries on the balanced growth path seem to
have grown at different rates (for example, US labor
productivity growth has been faster over the 20th
century than British.
There have been long periods of relatively slow
technology growth in developed countries, such as the
productivity slowdown of 1975-1995.

Where does technology growth
come from?



In OECD, a substantial share of GDP goes to
investment in Research and Development.
The production of this sector goes to producing
technology growth.
Knowledge is different than other capital in that it
is non-rival. Because one person is using
knowledge puts no limit on its use by others.
 Governments
issue patents to reward inventors to
give an incentive to R&D.
Rich and Large Countries More
Likely to Spend on R&D
R&D per Capita, 1997 (US$, PPP)
900
800
700
600
500
400
300
200
100
0
EU
North
Total
US
UK
Turkey
Sweden
Spain
Portugal
Poland
Norway
New
Netherlands
Mexico
Korea
Japan
Italy
Ireland
Iceland
Hungary
Greece
Germany
France
Finland
Denmark
Czech Rep.
Canada
Belgium
Austria
FDI

How does technology advance in
developing economies?
 Imitation
 Foreign
Direct Investment by R&D intensive
multi-national corporations.

Close to 50% of China’s exports are produced by
multi-national corporations.
FDI to China
CN: BoP: FA Balance: Direct Investm ent
USD m n
50000
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
-5000
-10000
1982
1984
1986
Net
1988
1990
1992
Abroad
1994
1996
1998
In Reporting Economy
2000
2002
Technology Differences Across
Countries


Empirical studies show that different countries
have very different levels of TFP.
Why is technology that different countries use so
different in efficiency.
 Difference
in Education levels that allow for different
levels of technology adoption.
 Restraints on competition which do not allow or
encourage adoption of new technology.
 Regulations
Productivity Slowdowns and
Acceleration




Over long periods of time, the rate of technology
growth will accelerate or slowdown.
During 1950’s and 1960’s most countries in the
world enjoyed very fast labor productivity growth.
During 1970’s and 1980’s, productivity growth
slowed down dramatically in every country in the
world.
After 1995, technology growth began to
accelerate in the USA and other developed
economies.
Why might technology growth vary
across time.
During Industrial age, economies have
experienced major technological
breakthroughs referred to as
macroinventions. (steam power, assembly
line, electrical grid).
 These inventions offer opportunities for
exceptional advances in productivity.

IT: Macroinventions

Information technology (computers, etc.)
are the current macroinvention being
exploited.
 Often
takes substantial number of years
between macro-tech breakthroughs and
efficient utilization.
 Solow Paradox: In mid-1990’s Nobel Laureate
Robert Solow said “Computers show up
everywhere except the data”/
Source: Dale Jorgenson, Harvard
Economic Growth in the
Information Age
Sources of U.S. Labor Productivity Growth
3.0
2.5
Annual Contribution (%)
2.0
1.5
1.0
0.5
0.0
1977-1989
1989-1995
1995-2000
-0.5
Labor Quality
Non-IT Capital Deepening
IT Capital Deepening
TFP
Midterm Exam

Thursday, May 4th
 6:30-8:30pm
Room 3007
 Prices and Quantities, Financial Concepts,
Production Functions, Capital
Accumulation, Technological Progress,
Money and Prices
