Chapter8 ec 222

8
C H A P T E
R

Economic Growth II:
Technology, Empirics, and Policy

8-1 Technological Progress in the Solow Model
8-2 From Growth Theory to Growth Empirics
8-3 Policies to Promote Growth
8-4 Endogenous Growth Theory

In this chapter, you will learn…

 how to incorporate technological progress in the
Solow model
 about policies to promote growth
 about growth empirics: confronting the theory with
facts
 two simple models in which the rate of technological
progress is endogenous

Chapter 8: Economic Growth II ECON 100A: Intermediate Macro Theory slide 2

Introduction

In the Solow model of Chapter 7,
 the production technology is held constant.
 income per capita is constant in the steady state.
Neither point is true in the real world:
 1904-2004: U.S. real GDP per person grew by a factor
of 7.6, or 2% per year.
 examples of technological progress abound
(see next slide).


Examples of technological progress
 From 1950 to 2000, U.S. farm sector productivity nearly
tripled.
 The real price of computer power has fallen an average of
30% per year over the past three decades.
 Percentage of U.S. households with ≥ 1 computers:
8% in 1984, 62% in 2003
 1981: 213 computers connected to the Internet
2000: 60 million computers connected to the Internet
 2001: iPod capacity = 5gb, 1000 songs. Not capable of
playing episodes of Grey’s Anatomy.
2006: iPod capacity = 80gb, 20,000 songs. Can play
episodes of Grey’s Anatomy.

Technological progress in the Solow
model
 A new variable: E = labor efficiency
 Assume:
Technological progress is labor-augmenting:
it increases labor efficiency at the exogenous rate g:

∆E
g =
E


model
 We now write the production function as:
Y = F (K , L ×E )
 where L × E = the number of effective
workers.
 Increases in labor efficiency have the
same effect on output as increases in
the labor force.


model
 Notation:
y = Y/LE = output per effective worker
k = K/LE = capital per effective worker
 Production function per effective worker:
y = f(k)
 Saving and investment per effective worker:
s y = s f(k)


model
(δ + n + g)k = break-even investment:
the amount of investment necessary
to keep k constant.
Consists of:
 δ k to replace depreciating capital
 n k to provide capital for new workers
 g k to provide capital for the new “effective”
workers created by technological progress


model
Investment, ∆ k = s f(k) − (δ +n +g )k
break-even
investment
( δ +n + g ) k

sf(k)

k* Capital per
Chapter 8: Economic Growth II worker, k
ECON 100A: Intermediate Macro slide 9
Theory

Steady-state growth rates in the
Solow model with tech. progress
Steady-state
Variable Symbol
growth rate
Capital per
k = K/(L×E ) 0
effective worker
Output per
y = Y/(L×E ) 0
effective worker

Output per worker (Y/ L) = y×E g

Total output Y = y×E×L n+g
Chapter 8: Economic Growth II ECON 100A: Intermediate Macro slide 10
Theory

The Golden Rule

To find the Golden Rule capital stock,
express c* in terms of k*:
In the Golden
In the Golden
c = y
* *
− i *
Rule steady state,
Rule steady state,
= f (k* ) − (δ + n + g) k* the marginal
the marginal
product of capital
product of capital
c* is maximized when net of depreciation
net of depreciation
MPK = δ + n + g equals the
equals the
pop. growth rate
pop. growth rate
or equivalently, plus the rate of
plus the rate of
MPK − δ = n + g tech progress.
tech progress.

Growth empirics:
Balanced growth
 Solow model’s steady state exhibits
balanced growth - many variables grow
at the same rate.
 Solow model predicts Y/L and K/L grow at the same
rate (g), so K/Y should be constant.
 This is true in the real world.
 Solow model predicts real wage grows at same rate
as Y/L, while real rental price is constant.
 This is also true in the real world.

Growth empirics: Convergence
 Solow model predicts that, other things equal, “poor”
countries (with lower Y/L and K/L) should grow faster
than “rich” ones.
 If true, then the income gap between rich & poor
countries would shrink over time, causing living
standards to “converge.”
 In real world, many poor countries do NOT grow faster
than rich ones. Does this mean the Solow model fails?


Growth Empirics: Convergence
 Solow model predicts that, other things equal, “poor”
countries (with lower Y/L and K/L) should grow faster
than “rich” ones.
 No, because “other things” aren’t equal.
 In samples of countries with
similar savings & pop. growth rates,
income gaps shrink about 2% per year.
 In larger samples, after controlling for differences in
saving, pop. growth, and human capital, incomes
converge by about 2% per year.

Growth empirics: Convergence
 What the Solow model really predicts is
conditional convergence - countries converge
to their own steady states, which are determined by
saving, population growth, and education.
 This prediction comes true in the real world.


Growth empirics: Factor accumulation vs.
production efficiency
 Differences in income per capita among countries can
be due to differences in
1. capital – physical or human – per worker
2. the efficiency of production
(the height of the production function)
 Studies:
 both factors are important.
 the two factors are correlated: countries with higher
physical or human capital per worker also tend to
have higher production efficiency.

Growth empirics: Factor accumulation vs.
 Possible explanations for the correlation between
capital per worker and production efficiency:
 Production efficiency encourages capital
accumulation.
 Capital accumulation has externalities that raise
efficiency.
 A third, unknown variable causes
capital accumulation and efficiency to be higher in
some countries than others.


Growth empirics:
Production efficiency and free trade
 Since Adam Smith, economists have argued that free
trade can increase production efficiency and living
standards.
 Research by Sachs & Warner:
Average annual growth rates, 1970-89

open closed
developed nations 2.3% 0.7%
developing nations 4.5% 0.7%

Growth empirics:
Production efficiency and free trade
 To determine causation, Frankel and Romer exploit
geographic differences among countries:
 Some nations trade less because they are farther
from other nations, or landlocked.
 Such geographical differences are correlated with
trade but not with other determinants of income.
 Hence, they can be used to isolate the impact of trade
on income.
 Findings: increasing trade/GDP by 2% causes GDP per
capita to rise 1%, other things equal.

Policy issues
 Are we saving enough? Too much?
 What policies might change the saving rate?
 How should we allocate our investment between
privately owned physical capital, public infrastructure,
and “human capital”?
 How do a country’s institutions affect production
efficiency and capital accumulation?
 What policies might encourage faster technological
progress?

Policy issues:
Evaluating the rate of saving
 Use the Golden Rule to determine whether
the U.S. saving rate and capital stock are too high,
too low, or about right.
 If (MPK − δ ) > (n + g ),
U.S. is below the Golden Rule steady state
and should increase s.
 If (MPK − δ ) < (n + g ),
U.S. economy is above the Golden Rule steady state
and should reduce s.


Policy issues:
To estimate (MPK − δ ), use three facts about the U.S.
economy:
1. k = 2.5 y
The capital stock is about 2.5 times one year’s GDP.
2. δ k = 0.1 y
About 10% of GDP is used to replace depreciating
capital.
3. MPK × k = 0.3 y
Capital income is about 30% of GDP.


Policy issues:
1. k = 2.5 y
2. δ k = 0.1 y
3. MPK × k = 0.3 y

To determine δ , divide 2 by 1:

δk 0.1y 0.1
k
=
2.5 y
⇒ δ = = 0.04
2.5


Policy issues:
1. k = 2.5 y
2. δ k = 0.1 y
3. MPK × k = 0.3 y

To determine MPK, divide 3 by 1:
MPK × k 0.3 y 0.3
k
=
2.5 y
⇒ MPK = = 0.12
2.5

Hence, MPK − δ = 0.12 − 0.04 = 0.08

Policy issues:
 From the last slide: MPK − δ = 0.08
 U.S. real GDP grows an average of 3% per year,
so n + g = 0.03
 Thus,
MPK − δ = 0.08 > 0.03 = n + g
 Conclusion:
The U.S. is below the Golden Rule steady state:
The U.S. is below the Golden Rule steady state:
Increasing the U.S. saving rate would increase
Increasing the U.S. saving rate would increase
consumption per capita in the long run.
consumption per capita in the long run.

Policy issues:
How to increase the saving rate
 Reduce the government budget deficit
(or increase the budget surplus).
 Increase incentives for private saving:
 reduce capital gains tax, corporate income tax,
estate tax as they discourage saving.
 replace federal income tax with a consumption tax.
 expand tax incentives for IRAs (individual
retirement accounts) and other retirement savings
accounts.


Policy issues:
Allocating the economy’s investment
 In the Solow model, there’s one type of capital.
 In the real world, there are many types,
which we can divide into three categories:
 private capital stock
 public infrastructure
 human capital: the knowledge and skills that
workers acquire through education.
 How should we allocate investment among these
types?

Policy issues:
Allocating the economy’s investment
Two viewpoints:
1. Equalize tax treatment of all types of capital in all
industries, then let the market allocate investment to
the type with the highest marginal product.
2. Industrial policy:
Govt should actively encourage investment in capital
of certain types or in certain industries, because they
may have positive externalities
that private investors don’t consider.


Possible problems with
industrial policy
 The govt may not have the ability to “pick winners”
(choose industries with the highest return to capital or
biggest externalities).
 Politics (e.g., campaign contributions) rather than
economics may influence which industries get
preferential treatment.


Policy issues:
Establishing the right institutions
 Creating the right institutions is important for
ensuring that resources are allocated to their best
use. Examples:
 Legal institutions, to protect property rights.
 Capital markets, to help financial capital flow to the
best investment projects.
 A corruption-free government, to promote
competition, enforce contracts, etc.


Policy issues:
Encouraging tech. progress
 Patent laws:
encourage innovation by granting temporary
monopolies to inventors of new products.
 Tax incentives for R&D
 Grants to fund basic research at universities
 Industrial policy:
encourages specific industries that are key for rapid
tech. progress
(subject to the preceding concerns).

CASE STUDY:
The productivity slowdown
Growth in output per person
(percent per year)
1948-72 1972-95
Canada 2.9 1.8
France 4.3 1.6
Germany 5.7 2.0
Italy 4.9 2.3
Japan 8.2 2.6
U.K. 2.4 1.8
U.S. 2.2 1.5
Theory

Possible explanations for the
productivity slowdown
 Measurement problems:
Productivity increases not fully measured.
 But: Why would measurement problems
be worse after 1972 than before?
 Oil prices:
Oil shocks occurred about when productivity
slowdown began.
 But: Then why didn’t productivity speed up when
oil prices fell in the mid-1980s?


Possible explanations for the
productivity slowdown
 Worker quality:
1970s - large influx of new entrants into labor force
(baby boomers, women).
New workers tend to be less productive than
experienced workers.
 The depletion of ideas:
Perhaps the slow growth of 1972-1995 is normal, and
the rapid growth during 1948-1972 is the anomaly.


Which of these suspects is the culprit?

All of them are plausible,
All of them are plausible,
but it’s difficult to prove
but it’s difficult to prove
that any one of them is guilty.
that any one of them is guilty.


CASE STUDY:
I.T. and the “New Economy”
Growth in output per person
(percent per year)
1948-72 1972-95 1995-2004
Canada 2.9 1.8 2.4
France 4.3 1.6 1.7
Germany 5.7 2.0 1.2
Italy 4.9 2.3 1.5
Japan 8.2 2.6 1.2
U.K. 2.4 1.8 2.5
U.S. 2.2 1.5 2.2

Theory

CASE STUDY:
I.T. and the “New Economy”
Apparently, the computer revolution did not affect
aggregate productivity until the mid-1990s.
Two reasons:
1. Computer industry’s share of GDP much
bigger in late 1990s than earlier.
2. Takes time for firms to determine how to
utilize new technology most effectively.

The big, open question:
 How long will I.T. remain an engine of growth?


Endogenous growth theory

 Solow model:
 sustained growth in living standards is due to tech
progress.
 the rate of tech progress is exogenous.
 Endogenous growth theory:
 a set of models in which the growth rate of
productivity and living standards is endogenous.


A basic model
 Production function: Y = A K
where A is the amount of output for each unit
of capital (A is exogenous & constant)
 Key difference between this model & Solow:
MPK is constant here, diminishes in Solow
 Investment: s Y
 Depreciation: δ K
 Equation of motion for total capital:
∆K = s Y − δ K

A basic model
∆K = s Y − δ K
 Divide through by K and use Y = A K to get:
∆Y ∆K
= = sA − δ
Y K

 If s A > δ , then income will grow forever,
and investment is the “engine of growth.”
 Here, the permanent growth rate depends
on s. In Solow model, it does not.

Does capital have diminishing returns or
not?
 Depends on definition of “capital.”
 If “capital” is narrowly defined (only plant &
equipment), then yes.
 Advocates of endogenous growth theory
argue that knowledge is a type of capital.
 If so, then constant returns to capital is more
plausible, and this model may be a good description
of economic growth.


A two-sector model

 Two sectors:
 manufacturing firms produce goods.
 research universities produce knowledge that
increases labor efficiency in manufacturing.
 u = fraction of labor in research
(u is exogenous)
 Mfg prod func: Y = F [K, (1-u )E L]
 Res prod func: ∆E = g (u )E
 Cap accumulation: ∆K = s Y − δ K

A two-sector model
 In the steady state, mfg output per worker and
the standard of living grow at rate
∆E/E = g (u ).
 Key variables:
s: affects the level of income, but not its
growth rate (same as in Solow model)
u: affects level and growth rate of income
 Question: Would an increase in u be
unambiguously good for the economy?


Facts about R&D
1. Much research is done by firms seeking profits.
2. Firms profit from research:
 Patents create a stream of monopoly profits.
 Extra profit from being first on the market with a new
product.
3. Innovation produces externalities that reduce the
cost of subsequent innovation.
Much of the new endogenous growth theory
Much of the new endogenous growth theory
attempts to incorporate these facts into models
attempts to incorporate these facts into models
to better understand technological progress.
to better understand technological progress.

Is the private sector doing enough R&D?

 The existence of positive externalities in the creation
of knowledge suggests that the private sector is not
doing enough R&D.
 But, there is much duplication of R&D effort among
competing firms.
 Estimates:
Social return to R&D ≥ 40% per year.
 Thus, many believe govt should encourage R&D.

Economic growth as “creative
destruction”
 Schumpeter (1942) coined term “creative destruction”
to describe displacements resulting from technological
progress:
 the introduction of a new product is good for
consumers, but often bad for incumbent producers,
who may be forced out of the market.
 Examples:
 Luddites (1811-12) destroyed machines that
displaced skilled knitting workers in England.
 Walmart displaces many “mom and pop” stores.

Lecture 5, Part II Summary

1. Key results from Solow model with tech progress
 steady state growth rate of income per person
depends solely on the exogenous rate of tech progress
 the U.S. has much less capital than the Golden Rule
steady state

2. Ways to increase the saving rate
 increase public saving (reduce budget deficit)
 tax incentives for private saving

Chapter 8: Economic Growth II ECON 100A: Intermediate Macro Theory
slide 47


3. Productivity slowdown & “new economy”
 Early 1970s: productivity growth fell in the U.S. and
other countries.
 Mid 1990s: productivity growth increased, probably
because of advances in I.T.
4. Empirical studies
 Solow model explains balanced growth, conditional
convergence
 Cross-country variation in living standards is
due to differences in cap. accumulation and in
slide 48


5. Endogenous growth theory: Models that
 examine the determinants of the rate of
tech. progress, which Solow takes as given.
 explain decisions that determine the creation of
knowledge through R&D.

slide 49

Chapter8 ec 222

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