Basic facts of growth. Solow growth model – a quick reminder
Advanced Macroeconomics
Joanna Siwińska-Gorzelak
• Most graphs in these slides are from Acemoglu: „Introduction do Modern Economic Growth”
• See: http://press.princeton.edu/chapters/s8764.pdf
Small differences in growth rates have great implications
Source: T.Picketty; http://piketty.pse.ens.fr/files/capital21c/en/Piketty2014FiguresTablesLinks.pdf
Distribution of world GDP, 2012
Source: T.Picketty; http://piketty.pse.ens.fr/files/capital21c/en/pdf/T1.1.pdf
Poverty
• While poverty rates have declined in all regions, progress has been uneven:
• The reduction in extreme poverty was mainly driven by East Asia and Pacific: China & India.
• Half of the extreme poor live in Sub-Saharan Africa.
• A vast majority of the global poor live in rural areas and are poorly educated, mostly employed in the agricultural sector.
The Solow model
• The Solow model is remarkable for its simplicity
• The Solow model is a good starting point and a springboard for further models
• At the centre of the model is the neoclassical production function
• We will analyze it in continuous time (i.e. we make the time units - the difference between t and t+1 - as small as possible
• From now on, a dot over a variable means the change of this variable over time:
tt x
dt
dx
Neoclassical production function
Yt =F(Kt, AtNt)
• Where K denotes capital, A – technology; N – labour force (population)
• Neoclassical production function is characterised by
1. Constant returns to scale
2. Positive and diminishing marginal products of capital and labour
3. Inada conditions
Neoclassical production function
• 1. Constant returns to scale
• 2. Marginal product of K & N – positive and diminishing
• 3. Inada conditions (what happens at „extremes”)
MPNMPN
MPKMPK
dNdMPNMPN
dLdY
dKdMPKMPK
dKdY
ccNAcKFcY
NN
KK
0
0
lim0lim
lim0lim
.3
00
00
.2
0);(
.1
Further assumptions of the Solow model
• Y=C+I, so that G=0 and NX=0
• The produced good is homogenous and it can change from consumption into investment good at no cost
• The rate of saving is constant and is equal to s, so that S=sY.
• Since Y=C+I, hence sY=I
• The depreciation rate of capital is constant and is equal to d
• The rate of population growth is „n” and the rate of technological progress is „g”
gA
An
N
N
The Solow model
• If we define:
• Then we can express the production function as:
)ˆ(ˆtt
kfy
y
nN
Ng
A
A
AN
Kk
AN
Yy
ˆˆ
Capital accumulation
tt
ttttt
dKsYK
KdKsYKdKIK
1
111
•The increase in capital stock depends on (among others) investment •Note, however that we are more interested in the bahaviour of capital per „effective worker”
Cobb-Douglas production function – an example
11
`1
ˆ
ˆ
0ˆ
ˆ)(ˆˆ
ˆ)(ˆˆ
gnd
sk
s
gndk
k
kgndksk
kgndysk
Modifications
• A famous modification is due to Mankiw, Romer, Weil: ”A Contribution to the Empirics of Economic Growth”, QJE, 1992 (MRW), who have stressed the role of human capital
• Human capital accumulation is a very similar process to the accumulation of k
hky
ANHKY
ˆˆˆ
)( 1
hgndyshH
ˆ)(ˆˆ
Empirics
)(1
)ln(1
)ln(1
)ln(ln
)(1
)ln(1
)ln(ln
)(1
)ln(1
)ln(ln
*1
1
gndssAy
gndsAy
gndsAy
gnd
sAy
HK
t
•This approach has been followed by MRW
Empirics - convergence
• Note that Solow model predicts convergence – a very important phenomenon, which we will discuss later
What have we learnt from the Solow model?
• We have a simple framework that allows us to study implications of capital accumulation and technological progress
• This framework is already quite useful in thinking about the world
• But on the other hand, we have not learn that much
• Technological progress is a black box; so is the saving rate
• Solow model is good at laying out the questions
• We need to dig deeper in order to answer them
• That’s our job for the next 4 weeks.
What are the fundamentals of growth
• Culture
• Climate
• Institutions
• Luck
• Acemolgu: institutions!
• Institutions: „are the rules of the game in a society or are the humanly devised constraints that shape human interactions
Institutions
• Acemoglu argues: • North and South Korea • The colonization of many countries by Europeans after 1492
(large scale natural experiment) • Europeans transformed the institutions of all the conquered
nations • Historical evidence „shows that there has been a remarkable
reversal of fortune in economic prosperity within former European colonies”
• Aztecs, Incas, societies of India were among the richest in the world; now the nations that exist in these boundaries are among the poorest