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Macroeconomic Analysis 2003
Convergence
or
Conditional Convergence
Lecture 7
1
Contents
•
•
•
•
•
•
•
•
•
Definition of Convergence and Divergence
Evidence of divergence among UK regions
Labour and capital mobility and convergence
Steady State in Autarky and Globalisation
Evidence for Conditional Convergence
Poverty Trap: why pigs cannot become elephants?
Does more trade lead to convergence?
Results of growth studies
Exercises
Lecture 7
2
Meaning of Convergence and Divergence
Prediction of convergence
Solow Model: Catching up
under Growing apart
High income
High income
Y/P
Income
Y/P
Divergence
Low ncome
Low income
Time
Time
Poor country should grow
at faster rate then a rich
country
Experience of African
countries
Lecture 7
3
Two concepts of Economic Convergence
Mean Differerence
Dispersion Measure


Convergence
g
g
Time
 ln y   ln  y 
i

R
R
R
ln Yt    0  1 t
LI
1
Low income regions should
grow faster than high income
region
2
t 

HI
1
Time
Standard Deviation
i ,t
Convergence
t
N  1
Lecture 7
4
Evidence for Lack of Sigma and Beta Convergence in the
Per capita Income among the UK Regions, 1993-1998
Ann.
Growth
rate %
1993
1994
1995
1996
1997
1998
United Kingdom
9,671
10,170
10,619
11,185
11,871
12,548
4.34
England
9,852
10,349
10,771
11,384
12,141
12,845
4.42
East Riding and North
Lincolnshire
9,289
9,680
10,130
10,920
11,490
11,759
Kingston Upon Hull, City of
9,319
9,787
10,325
10,886
11,538
11,850
4.00
East Riding of Yorkshire
8,268
8,487
8,741
9,799
9,996
10,051
3.26
10,236
10,741
11,325
12,059
12,939
13,402
London
14,110
14,798
15,251
15,885
17,158
18,566
4.57
Scotland
9,614
10,168
10,818
11,162
11,429
12,117
3.86
Northern Ireland5
7,610
8,114
8,654
8,964
9,507
9,754
4.14
Wales
7,978
8,393
8,900
9,240
9,562
10,063
3.87
1,934
2,210
2,537
North and North East
Lincolnshire
3.93
4.49
Sigma Convergence
Standard Deviation
1,806
1,894
Lecture 7
1,905
5
Marginal productivity of Capital in Rich and Poor Countries
and Capital Accumulation in Autarky
MPKP
MPKR
rp
rR
KR
Lecture 7
KP
6
Marginal productivity of Capital in Rich and Poor Countries
and Capital Accumulation After Globalisation
MPKP
MPKR
rP
rp
RG
rR
KR
Lecture 7
KP
7
Marginal productivity of Labour in Rich and Poor Countries
Before and After Globalisation
MPLP
MPLR
wR
wR’
LR
LP’
LR’
Lecture 7
LP
8
Who Gain and Who Lose From Globalisation?
Capitalists in rich
countries and
workers in poor
countries gain.
rp
rR
MPKR
MPKP
wR
wR’
wp’
MPLR
MPLR’
wp
MPLP’
MPLP
Lecture 7
9
Savers
Households, Corporations and
Government
Intermediaries
Banks, Insurance Companies, Building Societies,
Trusts, Stock and Bonk Markets
Investors
Small, Medium and Large
Private, Public, Domestic
and Foreign
Lecture 7
10
Factor Mobility and Convergence


Yi  Ai K i Li
   1
KMobil
e
yes
Convergen
ce
No
no
convergenc
e
 1
and
0   1
0  1
and
 1
Lmobile
KMobile
Lmobile
KMobile
Lmobile
yes
no
yes
yes
Yes
no
yes
no
no
no
Lecture 7
11
Factors Promoting Convergence
• Domestic factors
–
–
–
–
–
–
• Global factors
Saving
Investment
Population growth rate
Human capital
Technology
Development of
infrastructure
– Sound economic policy
– Homogenous and stable
society
– Transparent rules and
regulations
– Trade of goods and services
– Inflow and outflow of
capital
– Emigration or immigration
of skilled and unskilled
labour
– Adoption of better
technology
– Growth of the global
economy
– Peace/Oil prices
Lecture 7
12
Autarky and Saving and Capital
(Gartner (2003:262) has similar example)
Country A
Country B
YA  K A0.5 L0A.5
 A  0.1
YB  K B0.5 L0B.5
s A  0.2
sB  0
 B  0.1
What is the capital stock in the
steady state in A in Autarky?
How much do workers get?
How much do owners of
capital get?
sK A0.5 L0A.5   A K A
0.2 K A0.5 10  0.1K A

K A  400
What is the capital stock in the
steady state in B in Autarky?
How much do workers get?
How much do owners of
capital get?
0.0 K B0.5 10  0.1K B
 K B  0 YB  0
 Becomes a beggar country.
YA  200
Lecture 7
13
Impacts of Globalisation in Output and Income
What is the capital stock in the steady state in A and B
if there is a free mobility of capital?
Country A
Country B
K A  KB  K
K A  KB  K
Country A saves for both
countries. It receives rental
income from country B.
Country B does not save
but can borrow capital from
country A.


0.2 10K 0.5  0.5  10K 0.5  0.1K  K 
K  15  225
YB  K 0.5 L0B.5  2250.5  10  150
2
YA  K 0.5 L0A.5  2250.5  10  150
GNP in country B =
GDP+Investment Receipts
GNPA = 150+75 = 225
Capitalists gain and
workers lose in country A.
Lecture 7
Country B need to pay
capital income to Country
A.
GNP in country B = GDPInvestment Payments
GNPB = 150-75 = 75
Country B gains from the
capital transfers.
14
Evidence for Beta-Convergence in Europe: Growth
Rate of Per Capita Income and Its level in 1960
Evidence of Converngence in Europe
4.500
Annual growth rate of per cap income
4.000
gr
Power (gr)
3.500
3.000
2.500
2.000
1.500
1.000
0.500
0.000
0
5000
10000
15000
Lecture
7
Per capita income in 1960
20000
25000
30000
15
GDP per capita (constant 1995 US$)
1960
2000 Y00/Y60 growth rate (1960-2000)
Austria
10596
32763 3.092016
2.822
Belgium
10335
30830 2.983067
2.732
Denmark
16287
38521 2.365138
2.152
Finland
9769
32024 3.278125
2.968
France
10611
29811 2.809443
2.582
Greece
3818
13105 3.432425
3.083
Hungary
1514
5425 3.584302
3.191
Ireland
5462
27741 5.079002
4.063
Italy
6606
20885 3.161663
2.878
Luxembourg 15772
56372 3.574182
3.184
Netherlands
11999
30966 2.580715
2.370
Norway
11322
37954 3.352235
3.024
Portugal
2735
12794 4.678735
3.858
Spain
4620
17798 3.852798
3.372
Sweden
13165
31206 2.370376
2.158
Switzerland
26245
46737 1.780796
1.443
United Kingdom 9496
21667 2.281698
2.062
Lecture 7
16
Lack Evidence of Convergence among Middle and Low
Income Countries:Average Annual Growth Rate of Per Capita
Income (%) and Its level in 1960
1960 angrrate
Central African Republic
457 -0.746708
Chad
290 -0.713465
Ghana
450
-0.2145
Haiti
547 -0.997717
Madagascar
383 -1.106759
Nicaragua
638 -0.785382
Niger
386 -1.606578
Senegal
670 -0.238649
Sierra Leone
223 -1.041848
Venezuela, RB 3720 -0.299503
Zambia
648 -1.256572
1960 agrrate
China
112 4.989179
Hong Kong, China
3008 5.214552
Ireland
5462 4.062741
Korea, Rep.
1325 5.720737
Japan
8399 4.186912
Malta
1177 5.404178
Portugal
2734 3.858026
Singapore
2676 5.890155
Thailand
465 4.492804
Conditional Convergence
Lecture 7
17
Results from Cross Country Growth Studies -1
A low initial level of income is associated with
higher growth rate in subsequent period when other
variables are held constant.
Growth rates are higher when the ratio of investment
to GDP is higher.
Growth rates are higher in countries which have
larger stock of human capital per capita. These are
reflected in terms of enrolment in the primary and
secondary schools.
Population growth rates are negatively associated
with growth rates.
Lecture 7
18
Results from Cross Country Growth Studies -2
Countries with distorted markets have lower growth
rates. Distortions occur in exchange rates and prices
or by impediments to a free and fair trade.
Countries with efficient financial system have higher
growth rates. Size of the financial markets is
measured as a ratio of liquid assets to the GDP.
Countries with political instability have lower growth
rates. Frequency of revolutions, wars and coups are
used to measure political instability.
Lecture 7
19
Economic Convergence Acrross Major Industrial Countries
Japan had lower income in the
beginning and had an astonishing
growth rate from 1960 to 1990
and it overtook
all OECD countries in per capita income
50,000
40,000
France
35,000
Italy
Japan
United Kingdom
United States
30,000
25,000
20,000
15,000
France, Germany UK and USA
show significant process of
convergence
10,000
5,000
Lecture 7
00
20
98
19
96
19
94
19
92
19
90
19
88
19
86
19
84
19
82
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80
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78
19
76
19
74
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72
19
70
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68
19
66
19
64
19
62
19
60
0
19
Per Capita Income in 1995 US dollars
45,000
20
Disparity in GNP Per Capita at Purchasing Power
Parity,2001 (US $): A Lot of Divergence
35000
GNP at Purchasing Pow er Parity,2001
30000
25000
20000
15000
10000
5000
0
h
Hi
g
id
dl
e
M
Lo
w
W
or
ld
US
A
21
UK
G
ha
na
an
za
ni
a
Ug
an
da
Ne
pa
l
ta
n
ak
is
ga
po
re
Ja
pa
n
ng
Ko
ng
Ch
i
na
Lecture 7
Evidence for Convergence of Output Gap Among Major Industrail Countries
(IMF)
6
Output gap% =100*[(Trend GDP-Actual GDP)/Actual GDP]
4
2
19
79
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
Percent of GDP
0
-2
-4
-6
FRANCE
GERMANY
JAPAN
UNITED KINGDOM
UNITED STATES
-8
Lecture 7
-10
22
Evidence for Conditional Convergence Across All Countries
Low income countries grow slower
than middle income countries, which
grow faster than high
income countries.
Conditional Convergence
Lecture 7
23
Why the investment rate is not the same across all
OECD Countries? Feldstien-Horioka Puzzle
Lecture 7
24
Openness and Growth: Evidence from the OECD Countries 1980-2000
Average annual growth rate of py
6.00
5.00
Series1
Poly. (Series1)
4.00
3.00
2.00
1.00
0.00
0.00
50.00
100.00
150.00
200.00
250.00
Ratio of Trade Volume to GDP
Lecture 7
25
Conditional convergence
1. There is no relation between initial GDP (most studies take
1960 as the base year) and the growth rates if both
developed and developing economies are taken together.
2. Many studies suggest evidence for convergence among
OECD countries(so called rich country club), states of the
US, provinces of Canada and prefectures of Japan.
3. There are arguments suggesting that developing
economies have different steady state than of developed
economies.
Why?
Story of squirrel and elephant.
Lecture 7
26
Poverty Trap
Productivity of capital does not only depend upon the
amount of capital but depends upon amount of
human capital.
Countries with lower human capital are in danger of
being caught in poverty trap.
MPK
e
cost
Capital stock
Marginal product of capital is less than the cost of
capital and capital stock gradually diminishes before
point e. Cost is less than MPK after e more capital is
accumulated.
Lecture 7
27
Is this caused by the barriers to adopt a good
technology? Or by Lauddites?
Lecture 7
28
Can a Penguin become a Cat or a Pig
become an Elephant?
Lecture 7
29
Increasing Return, Poverty Threshold and Stability
of the Steady State
y=f(k)
y
I =(n+d)k
Points b and o
are unstable
steady states
a
sy
b
Big Push
o
k0
Poor SS
k2
Poverty TH
Lecture 7
k1
30
yH
Critical Capital Stock for Control in Population Growth Rate
y  k
y
Y
L
i   n   k
H  H

b
i   n   k
L  L 
S  sy  sk
a
yL
nH > nL
KH
PovTH
Low ss trap
Lecture 7
Kss
k
K
L
31
Economic Growth Policies







Increase in public and private saving
Development of human capital
Removal of distortions in investment
Institutional reform (rule of law)
Macroeconomic stability
Carefully designed redistribution policy
Social security reform
Lecture 7
32
Policy Issues:
Tax, Saving and Consumption
• What is the impact in consumption and saving in the
above model
– If there is a 20 percent tax on interest income?
– If there is a 20 percent subsidy in it?
– What sort of tax system is better for increasing the
ratio of saving? Does a higher rate of VAT promote
saving or consumption?
– Does a higher rate of tax on labour income
encourage or discourage saving?
– Does a higher rate of tax on pension income
increase saving or consumption?
Lecture 7
33
Exercises
• Calculate annual growth rates between 1960
and 2000 across G7 and for countries with
growth miracles and growth disasters
• Calculation of positive externality and
economic growth (Spill-over Effects).
• Closing the productivity gap
• Conditional convergence
Lecture 7
34