1. Stylized Facts + Solow Growth Model

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Macroeconomic Topics in
Development & Transition
EC938
Sharun W. Mukand
1
Development Policy and Macroeconomics
2

Economic Growth

Globalization, Trade and Inequality

Political and Economic Crises: Currency Crises

Governance and Institutions

Political Economy of Policymaking

Foreign Aid, Corruption

Miscellaneous Topics
3

Background: Some stylized facts about
developing countries (macroeconomy)

Economic Growth….Theory + evidence
-- proximate versus ultimate causes
-- growth and policymaking.
Some stylized facts (Macro)….





4
In 1997 developing countries accounted for 32% of world
output.
132 of the 183 countries are developing countries.
Although most of production takes place in the industrial
countries, country-specific macroeconomic policy
formulation is carried out in a developing-country context.
Developing countries behave similarly to industrial
countries, but operate in a different environment.
Emphasis on politics, reputation, credibility, inequality,
exchange rate management, crises….
Stylized facts (contd…)
1. Developing economies tend to be more open to trade in

5
goods and services than are the major industrial countries.
Openness: trade share (sum of the shares of exports and imports)
in GDP.

First panel of Figure 1.2: developing nations tend to be more open
than the major industrial countries.

Mean value of the trade share is 45%, compared with about 25%
in the G-7 countries.
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2. Developing countries typically have little control over the
prices of the goods they export and import.
Exogeneity of the terms of trade is suggested both
 by their small share in the world economy;
 by the composition of their exports.
In 1990 developing nations accounted for about one quarter of
world exports and imports.
In 1991 over half of the exports of low- and middle-income
countries consisted of primary commodities.
Second panel of Figure 1.2: share of primary commodities in the
exports of a selected group of developing countries.
Third panel: two-thirds of the exports of the countries went to
industrial countries.

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8
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3. Extent of external trade in assets has been more limited in
developing countries, though this situation has recently begun to
change.



10
Developing countries have undergone an increase in their degree of
integration with the world capital market.
Integration occurred in the context of immature domestic financial
systems, limited policy flexibility, and fragile credibility.
This situation has caused to the capital inflow problem in some countries.
4. Majority of developing countries have neither adopted fully
flexible exchange rates nor joined monetary unions.

In developing countries officially determined rates predominate.

Exchange regimes in developing countries have evolved toward
greater flexibility since the collapse of the Bretton Woods system
in 1973.

This has meant that more frequent adjustments of an officially
determined parity rather than the adoption of market-determined
exchange rates.
11
Domestic Financial Markets
5. Financial markets in developing nations have been
characterized by the prevalence of rudimentary financial
institutions and by “financial repression.

Only some of the developing countries have developed large
equity markets.

Financial markets are dominated by commercial banks.

Equity markets tend to be dominated by a few firms and exhibit
very low turnover.
12
Macroeconomic Volatility
6. Macroeconomic environment in developing countries is much
more volatile.
Roots of macroeconomic instability are both external and internal:
 Volatility in the terms of trade and international financial
conditions.
 Inflexibility of domestic macroeconomic instruments and
political instability.
Figure 1.12:
 Latin America case.
 All components of the governments budget is less stable.

13
Politics Matters!

14
Policymaking in developing/transition countries
is vulnerable to political factors to a far greater
extent than in developed countries.
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15

Gavin and Perotti (1997): volatility in some Latin American
countries have been compounded by a procyclical fiscal policy
response:
 increase in government expenditure and fiscal deficits during
periods of expansion;
 fall during recessions.

Overall, boom and bust phenomena tend to be much more
common and more costly in developing countries. Why?
16
Economic Growth: the Questions
17

Why are some countries rich and
others poor?

What accounts for differences in
income levels and growth rates
across countries?

What is the role of political
factors in accounting for
differences in growth and income
across countries?

What is the role of policy
interventions and governance in
generating economic growth and
decreasing poverty?
18
Economic Growth
 Present a policy-oriented overview of the theory and empirical
evidence of economic growth


19
Trace linkages between economic growth and its main determinants:
(i) proximate: saving, investment, and economic efficiency
(ii) ultimate(?): Institutions, culture, geography….
Growing apart
Country B: 2% a year
GNP per capita
 Investment
 Efficiency
 Institutions
Threefold
difference after
60 years
 Policy
Country A: 0.4% a year
0
20
60
Years
21
National economic output
Economic growth:
The short run vs. the long run
Economic growth
in the long run
Potential output
Actual output
Upswing
Business cycles
in the short run
Downswing
Time
22
Botswana and Nigeria:
GNP per capita 1962-2001
3500
Botswana
3000
Nigeria
2500
2000
Current US$,
Atlas method
1500
1000
500
19
62
19
66
19
70
19
74
19
78
19
82
19
86
19
90
19
94
19
98
0
23
Spain and Argentina :
GNP per capita 1962-2001
18000
16000
Argentina
14000
Spain
12000
10000
Current US$,
Atlas method
8000
6000
4000
2000
19
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19
66
19
70
19
74
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78
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82
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86
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90
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94
19
98
0
24
Thailand and Burma….

25
TECHNICAL PRELIMINARIES (1)
1. The rate of change of a variable, say Y, with respect to time (t), is:
dY (t )
dt
2. The (continuous) rate of growth of Y is:
1 dY (t )
Y (t ) dt
3. From elementary calculus we know that:
1 dY (t ) d log Y (t )

Y (t ) dt
dt
NB Here “log” means the natural log, the log to the base e (= 2.7182818….).
26
26
Technical preliminaries (3)
Notation
The “dot” notation:
dY
Y
dt
So a growth rate is:
Y 1 dY

Y Y dt
The “hat” notation:
27
Y
ˆ
Y
Y
27
Technical preliminaries (4)
Growth rates of products
Eg if
V  PY
then
V P Y
 
V P Y
Growth rates of divisions
Eg if y  Y / L
y Y L
 
y Y L
28
28
Solow model:
overarching assumptions
1. One good (“corn”)
2. Constant returns to scale
3. Perfect competition in input and factor
markets
4. Population growth is exogenous
5. The capital stock decays at a constant rate
6. Output requires only labour and capital
29
29
Solow model:
simplifying assumptions
7. Production function is Cobb-Douglas
8. Households save a constant fraction of their
income
9. Households work a constant fraction of their
time
30
30
The Solow model: production
Production function:
 1
Y  F ( K , L)  K L ,
0   1
NB: Units for Y, K, and L are flows, ie quantities
per period
31
31
The Solow model: returns to inputs
(Monopoly) profits are:
where
Y  pK K  p L L
pK , pL are the real input prices: eg
pK = PK/P
Note that the price of capital is the rental price, not the asset price.
Firms are assumed to maximise profits.
32
32
The Solow model:
returns to inputs (2)
Profit maximisation implies that real input prices
are equated to marginal products:
 1
F
K
pK 
  
K
L
Y 
 
K

F
K
Y 
pL 
 (1   )    (1   )  
L
L
L
33
33
Implications
1. Input payments exhaust output (there is nothing left over):
pK K  p L L  Y
2.
The marginal product of capital (labour) declines as capital (labour) input
is increased, holding constant the other input
3. Input shares are constant:
pK K
pL L
 ,
 1
Y
Y
34
34
Solow model: evolution of capital
The capital stock grows through investment (I)
but also declines due to physical decay at the
constant rate d:
K  I  dK , d  0, K (0)  K 0
35
35
Solow model: household behaviour (1)
Households save a constant fraction of their income. To
save is to invest, so:
I  sY , s  0
Alternatively, because of the national income identity
Y CI
they consume a constant fraction of their income:
C  (1  s )Y
36
36
Solow model: household behaviour (2)
Population grows at a constant, exogenous rate
and households devote a constant fraction of
their time to work:
L(t )  L0ent
whence
L
n
L
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37
Solow model: equations
(1)
 1
Y K L
(2) I  sY
(3) K  I  dK , K (0)  K 0
(4) L / L  n, L(0)  L0
38
38
The set-up: summary
For the basic Solow model, we have the following
parameters:
 , d , s, n
α and d relate to technology, while s and n relate to
household behaviour.
There are also two initial conditions:
L(0)  L0 and K (0)  K0
39
39
Solving the model (1)
Substituting from equations (1) and (2) into (3)
and dividing through by K:
K
 1 1
 sK L  d
K
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40
Solving the model (2)
Now put all variables into per head terms:
y  Y / L, k  K / L
Also,
k K L K
   n
k K L K
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41
Solving the model (3)
The capital accumulation equation is:
K
 sK  1L1  d
K
and in per head terms (substitute in k*/k = K*/K – n)) this becomes:
k
 sk  1  (n  d )
k
42
42
For future reference
We wrote the production function as:
 1
Y K L
And we can re-write it in per head terms as:
y  k
43
43

The production function, y  k
y
0
k
44
44
Solving the model (4)
Back to the capital accumulation equation that we just derived:
k
 sk  1  (n  d )
k
The right hand side contains two terms. Let’s graph these as
functions of k.
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45
The basic Solow model
k /k
nd
k /k  0
0
k0
k /k  0
k*
sk  1 ( sy / k )
k
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46
Conclusions of the basic Solow model



The only possible equilibrium is one where output per head and
capital per head (y and k) are constant.
This equilibrium is stable --- if output and capital per head are
initially above (below) the equilibrium levels, then they will fall
(rise) till they are at the these equilibrium levels.
The long run (equilibrium) growth rate is zero.
47
47
Typical paths for k (and y)
log k
log k*
time
48
48
An important relationship
In steady state k  0, so from previous slides
sy   (n  d )k 
therefore the steady state capital-output ratio is
s
k


nd
y
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49
Equilibrium levels
Since y  k  ,
 s 
k 

d

n



 s 
y 

d

n



1
1
and

1
50
50
Alternative treatment
Take the capital accumulation equation:
k
 sk  1  (n  d )
k
Multiply through by k:
Now graph the two terms on the right hand side as functions of k:

k  sk  (n  d )k
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51
The Solow model
(alternative treatment)
(n+d)k
A
sy*
0
k*
sk  ( sy )
k
k* = the steady state level of capital
52
52

53
Output-capital ratio – low  rate of expansion of aggregate capital is low
population growth outstrips the rate of growth of capital – eroding per
capita capital stock.
The Solow model
(alternative treatment)
(n+d)k
dk/dt=0 at
point A
A
sy
y*
0
k*
k
54
54
Solow and Growth Rates…


55
We wanted a growth model, but the solution shows that in the long run the growth
rate is zero --- output per head and capital per head approach a constant level (y*
and k*).
For continuous per capita growth, capital must grow faster than population 
however, diminishing returns implies that the marginal contribution of capital to
output declines  decline in growth rate of output…

To get long run growth, we must have a motor of growth. In the Solow model this
is exogenous technical progress

…optimistic force of continuing technical progress has to outweigh the doom of
diminishing returns  indefinite economic growth

Relative growth rates observed (in the context of this model) have to be transitional
– i.e. occur during the transition to the steady state. (….can be shown that faster
growth occurs if a country is further away from its steady state…)
Population Growth in the Solow Model

56
Quantity of capital available per worker decreases with population growth
 capital dilution.
The Solow model
(Population growth rate increases)
(n2 + d)k
A
sy*
0
k* = the steady state level of capital;
k*
(n1+d)k
sk  ( sy )
k
Population growth rate increases from n 1 to n2.
57
57
The Solow Model: Income Differences – why are
some countries rich and others poor?


Differences in Investment Rates across countries:
[yi*/yj*]= (si/sj)α/(1-α)
Higher investment rates translate into correspondingly higher levels of income
across countries.

Why do investment rates across countries then….??

Savings rates perhaps?
Differences in savings rates may arise for reasons unrelated to their levels of
income per capita –
Govt. policy/ income inequality/culture….
Savings rate may be affected by income itself (i.e. endogenous).
(i)
(i)
58
Solow model  regardless of the initial per capita capital stock, two countries
with similar savings rates, depreciation rates and population growth rates will
converge to similar standards of living in the long run
Government and Growth: A First Take
59

Govt. policy affects the accumulation of physical capital

Govt policy and population growth…

Government encourages human capital formation

Tech…

Govt policy affects EFFICIENCY…
60

Govt and the RULE of LAW.

Taxation, Efficiency & the Size of Govt.

Why do Govts do things that are bad for economic growth?
Long Run Growth and Institutions: the Argument


Institutions---organization of society, “rules of the
game”--- are a major determinant of economic
performance and a key factor in understanding the vast
cross-country differences in prosperity.
Institutions are not exogenous, but there are potential
sources of exogenous variation in history.
–

61
.
Institutions are not typically chosen for the good of
society, but imposed by groups with political power for
their economic consequences.
Plan of the lectures (1)

Lecture 1: Institutional Causes of Economic
Performance.
–
–
–
–
–
–
–
–
–
62
Sources of prosperity.
What are institutions? Brief discussion.
Sources of cross-country differences in prosperity.
Geography versus institutions and the identification problem.
Learning from the Korean experiment.
The colonial experiment and the Reversal of Fortune.
Reassessing geography versus institutions.
Are British colonies different?
The role of culture.
Plan of the lectures (2)

Lecture 2: Towards a Theory of Institutions.
–
–
–
Different meta-theories: efficiency, history, ideology and
social conflict.
Economic institutions, political institutions and political power
Historical examples:
1.
2.
3.
–
–
–
Dynamics of political power and political institutions.
A theory of institutions.
Historical examples:
1.
2.
63
Land relations in the Dutch East Indies
Early financial development in the U.S. and Mexico
Price regulation in Ghana, Kenya and Colombia
Atlantic trade and rise of constitutional regimes.
Emergence of mass democracy in Western Europe.
Sources of prosperity (1)
64

Vast differences in prosperity across countries today.

Why?

Standard economic answers:
Sources of prosperity (2)

These are, however, proximate causes of differences in
prosperity.
–
–


The answer to these questions is related to the
fundamental causes of differences in prosperity.
Potential fundamental causes:
–
–
–
65
Why do some countries invest less in physical and human
capital?
Why do some countries fail to adopt new technologies and to
organize production efficiency?
Institutions (humanly-devised rules shaping incentives)
Geography (exogenous differences of environment)
Culture (differences in beliefs, attitudes and preferences)
What are institutions? (1)

Institutions: the rules of the game in economic, political
and social interactions.
–


North (1990, p. 3):
"Institutions are the rules of the game in a society or,
more formally, are the humanly devised constraints that
shape human interaction.“
Key point: institutions
–
–
–
66
Institutions determine “social organization”
are humanly devised
set constraints
shape incentives
What are institutions? (2)

A broad cluster including many sub levels:
–
–

economic institutions: e.g., property rights, contract enforcement, etc.
 shape economic incentives, contracting possibilities, distribution.
political institutions: e.g., form of gov., constraints on politicians and
elites, separation of powers, etc.
 shape political incentives and distribution of political power.
Important distinction between:
– Formal institutions: codified rules, e.g. in the constitution
– Informal institutions: related to how formal institutions are
used, to distribution of power, social norms, and equilibrium.


67
Constitutions in U.S. and many Latin American countries similar,
but the practice of politics, and constraints on presidents and
elites very different.
Why? Because distribution of political power can be very different
even when formal institutions are similar.
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