Macroeconomics

1
Performance of World Economies
Gavin Cameron University of Oxford
OUBEP 2006
2
introduction

• Is there some action a government of India could
  take that would lead the Indian economy to grow
  like Indonesias or Egypts? If so, what,
  exactly? If not, what is it about the nature of
  India that makes it so? The consequences for
  human welfare involved in questions like these
  are simply staggering Once one starts to think
  about them, it is hard to think about anything
  else, Robert Lucas, 1988.

3
important elements of long-run growth

• Technical Change (q.v. Smiths pin factory)
• Over time, technology becomes more advanced, and
  hence output per worker rises
• Factor Accumulation (q.v. Ramsey on saving)
• Over time, with sensible property rights, people
  accumulate capital assets (physical, human and
  environmental), even though factors are typically
  subject to diminishing returns
• Factor Substitution (cf. Ricardo on land)
• Over time, factors cannot earn economic rents
  unless their supply is restricted, even then,
  other factors can be used as substitutes
• Product Substitution (q.v. Schumpeter on creative
  destruction)
• Over time, new varieties and qualities of
  products are developed, which replace previous
  types.

4
Kaldors stylised facts

• Per capita output grows over time and its growth
  rate does not tend to diminish the same is true
  of real wages
• Physical capital per worker grows over time
• The rate of return to capital is nearly constant
• The ratio of physical capital to output is nearly
  constant
• The shares of labour and physical capital in
  national income are nearly constant
• The growth rate of output per worker differs
  substantially across countries.

5
Source Robert J Gordon (2005)
6
diminishing returns
Output per worker (K/L)
Output per worker, Y/L
Output is produced using a diminishing returns
production technology. As more capital is added,
the additional increment to output gets smaller.
The shape of the curve reflects the production
technology it gets flatter as the output
elasticity of capital falls, and steeper as it
rises.
Capital per worker (K/L)
7
... a constant saving rate
Output per worker (K/L)
Some constant fraction, s, of output is saved.
This saving takes the form of new capital goods.
Saving per worker, sY/L
Capital per worker (K/L)
8
and a constant depreciation rate
Output per worker (K/L)
Required Investment per worker, (nd)K/L
Gross investment is required each year, since the
stock of capital per worker falls because of
physical depreciation and because of labour force
growth.
Capital per worker (K/L)
9
the Solow model
Output per worker (K/L)
Output per worker, Y/L
The economy is in equilibrium when net investment
is zero.
Required Investment per worker, (nd)K/L
Saving per worker, sY/L
Rate of convergence is an increasing function of
s, and a decreasing function of nd and the
output elasticity of capital
Capital per worker (K/L)
K/L
10
a rise in the saving rate
Output per worker (K/L)
Output per worker, Y/L
Required Investment per worker, (nd)K/L
sY/L
sY/L
The increase in investment raises the growth rate
temporarily as the economy moves to a new
steady-state. But once the new higher
steady-state level of income is reached, the
growth rate returns to its previous level.
Capital per worker (K/L)
11
faster population growth
Output per worker (K/L)
Output per worker, Y/L
Required Investment per worker
(nd)K/L
(nd)K/L
The rise in population growth means that more
workers need to be equipped with capital each
time period, which means that less is available
for replacing depreciated equipment. This leads
to a fall in the steady-state level of capital.
Capital per worker (K/L)
12
the golden rule
Output per worker (K/L)
Output per worker, Y/L
Required Investment per worker, (nd)K/L
C/L
The goal of a social planner might be to maximise
consumption per capita (where consumption is
largest relative to investment per worker). This
occurs where the slope of the output per worker
curve is the same as the slope of the
depreciation per worker curve. The implied
saving rate is likely to be different from the
market outcome.
I/L
Capital per worker (K/L)
13
the poverty trap - industrialisation
Output per worker (K/L)
Required Investment per worker, (nd)K/L
high income industrial
Saving per worker
medium income mixed
low income agricultural
Capital per worker (K/L)
14
the poverty trap endogenous fertility
Output per worker (K/L)
Required Investment per worker, (nd)K/L
Saving per worker
high income low fertility, low mortality
medium income low fertility, high mortality
low income high fertility, high mortality
Capital per worker (K/L)
15
the AK model
Output per worker, Y/L
Output per worker (K/L)
If there are constant returns to broad capital,
net investment might always be positive, so there
is no equilibrium level of output per worker.
Saving per worker, sY/L

Required investment per worker, (nd)K/L
Capital per worker (K/L)
16
Solow vs AK

• The Solow model model has two main predictions
• For countries with the same steady-state, poor
  countries should grow faster than rich ones.
• An increase in investment raises the growth rate
  temporarily as the economy moves to a new
  steady-state. But once the new higher
  steady-state level of income is reached, the
  growth rate returns to its previous level there
  is a levels effect but not a growth effect.
• However, the AK model yields the opposite
  predictions there is no convergence, and policy
  changes can have permanent effects.

K/L
Solow world
levels effect
K/L
catch-up
t
K/L
AK world
growth effect
no catch-up
t
17
Source OMahony and Van Ark (2003)
18
twin peaks
number of countries
Since the 1960s, the distribution of world log
income has tended to become more twin-peaked than
before. Danny Quah argues that open economies
tend to be in the higher peak.
1960
1990
income
19
the sources of economic growth

• Growth of output weighted growth of inputs
  growth of total factor productivity
• Growth of labour productivity weighted growth
  of capital per worker growth of total factor
  productivity
• Growth of inputs
• Capital and labour
• Materials and energy
• Growth of total factor productivity
• Higher quality products
• New varieties of products
• Better ways to use existing inputs

20
growth accounting
Output per worker (K/L)
Output per worker, Y/L
C
B
Output per worker, Y/L
A
A rise in technology raises the steady-state
level of output per capita. Part of this rise
(AB) is the pure effect of technical change
(TFP), the other part (BC) is due to ensuing
capital accumulation.
Capital per worker (K/L)
21
Source OMahony and Van Ark (2003), table 1.4b.
22
Source OMahony and Van Ark (2003), table III.14.
23
Source OMahony and Van Ark (2003), table III.5.
24
high productivity countries

• Institutions that favour production over
  diversion low corruption, private property, good
  institutions
• Low rate of government consumption (i.e. spending
  excluding investment transfers)
• Open to international trade
• Well-educated workforce
• International language
• Temperate latitude away from the equator
• Easy access to coast and ports.

25
long-run growth

• Unemployment and business cycles are important in
  explaining short and medium run growth, but play
  almost no rôle in the long-run in the long-run,
  national output is determined by supply.
• In the long-run, the main source of rising living
  standards is rising output per worker.
• Rising output per worker is due to the steady
  accumulation of capital (human, physical, social,
  environmental) and technological progress,
  promoted by a supportive economic environment.
• The simple Solow model shows that there is an
  equilibrium level of capital per worker in the
  absence of technological progress. Recent
  post-neoclassical endogenous growth models
  attempt to explain technological progress.

26
summary

• Productivity Growth isnt everything, but in the
  long-run, it is almost everything, Paul Krugman,
  1990.

27
syndicate topics

• How do an increased saving rate or an increased
  population growth rate affect the Solow model?
• Should we expect poor or large countries to grow
  faster than rich or small ones?
• Assess the relative importance of investment,
  competition, enterprise, innovation, and skills
  on productivity growth.
• What factors do you think explain the above five
  drivers?
• Why are some countries rich and others poor?
• Does faster growth mean higher unemployment?

28
optional spreadsheet task

• The country of Davymania starts with 100 units of
  capital and 30 workers. The working population
  grows at 2 per annum and capital depreciates at
  8 per annum. Output is produced according to
  the production function YvK.vL and the saving
  rate is 20.
• Use a spreadsheet to show how capital, labour,
  and output grow over time.
• What are the equilibrium ratios of capital per
  worker, and output per worker in this economy?
• Plot the response of capital per worker over time
  to (a) a change in the saving rate, (b) a change
  in the population growth rate, (c) a rise in
  efficiency that allows output to be 10 higher
  for any given level of capital and labour, (d) a
  production function of YK¼.L¾.
• Hard What is the half-life of the gap between
  any given level of capital per worker and the
  equilibrium? What saving rate would maximise
  consumption per worker in equilibrium?