334 neoclassical growth model 2013(1)
TRANSCRIPT
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
1/21
Economics 334:
Approaches to Economic Growth
The Solow Growth Model
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
2/21
Source: OECD - Maddison (2001) The World Economy: A Millennial Perspective
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
3/21
Real GDP per capita growth rates, selected countries
1820-1998
Country 1820-70 1870-1913 1913-1950 1950-73 1973-98
United Kingdom 1.26 1.01 0.92 2.44 1.79
Germany 1.09 1.63 0.17 5.02 1.60
France 0.85 1.45 1.12 4.05 1.61
Italy 0.59 1.26 0.85 4.95 2.07
Western Europe 1.00 1.33 0.83 3.93 1.75
United States 1.34 1.82 1.61 2.45 1.99
Canada 1.29 2.27 1.40 2.74 1.60
Japan 0.19 1.48 0.89 8.05 2.34
China -0.25 0.10 -0.062 2.86 5.39
Source: OECD - Maddison (2001) The World Economy: A Millennial Perspective
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
4/21
Theories of Economic Growth
Classical Economists: David Hume (1711-1776)
Adam Smith (1723-1790)
Thomas Malthus (1766-1834)
David Ricardo (1772-1823)
Karl Marx (1818-1883)
Twentieth Century
David Harrod-Evsey Domar 1940s (Keynesian) Robert Solow 1950s (Neo-classical)
Paul Romer 1980s (Endogenous Growth)
4
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
5/21
SOLOW, R. M. (1957)Technical Change and the
Aggregate Production Function,Review of Economics
and Statistics, Vol 39, No 3, pp. 312-320
The problem:What explains growth?
A case study of the U.S. economy between 1909 and 1949.
During this period, the economy grew approximately 80percent.
What explains this average annual growth rate? Howmuch is due to:
growth in the labour force?
capital accumulation?
technological change?
The growth accounting framework has developed fromSolows model and is widely used to determine the relativecontribution of these factors in economic growth
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
6/21
(1)
His argument:
That the amount of output produced by a given K(t) and L(t) increases
over time as technology A(t) grows.
How does Solow make his case?
He doesn't have data for A(t) but he argues that growth in technology can
be inferred from the growth in output capital and hours worked. To do this
he brings in a more general economic framework, a production functionwith constant returns to scale. (Recall the definition of constant returns to
scale?)
The most convenient (and widely accepted) way to illustrate the growth
accounting framework is to use a Cobb-Douglas production function:
Y =AKL
where Y=output, A="technical progress", K=capital stock, L=labour supply,
and represent the shares of capital and labour in production.
See Diagram I
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
7/21
ExtensiveGrowth
Y=Af(K)
sY=sAf(K)
Capital (K)
Output (Y)
Y2
Y1
K1 K2
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
8/21
But we want to disaggregate the contribution of each
of the factors of production and technology to growth
in output, Y over time. This can be accomplished by a mathematical
manipulation of the Cobb-Douglas production function
(taking the logarithm and differentiating with respect to
time*) to get the equation in linear form. (Why wouldwe want to do this?)
A simple representation of the results of this
manipulation is:Y
Y=
AA
+ KK
+ (1 ) LL
;
Where represents "change", eg. L2 -L1; So,L
L=growth rate of labour and so on.
This equation represents
"extensive growth"
* For those of you who may wish to know, .
The mathematics behind the derivation of the growth accounting equation is not necessary for this
course.ln(xy)
=
lnx+
lny
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
9/21
The contribution of technical progress can bedetermined by subtracting the contribution of theother factors from output growth.
This is the Solow Residual.
That is,A
A=
YY
KK
(1 ) LL
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
10/21
But what about "intensive growth?" We are
interested in growth in per capita incomes.
To get to the intensive form of the growth accounting equation we divide (1) byL:
where y=output per capita (or per worker) and k=capital tolabour ratio.
Taking the logarithm and derivative with respect to time once again, we have:
So growth in per capita income is a function of technological change andcapital accumulation. But if capital is subject to diminishing returns, then in thelong run growth in output is determined by technological change.
Solow's findings: 7/8ths of output growth in the period 1909-1949 was due to"technological progress."
y
y=
AA
+ kk
Y
L=A
K
L
L
L
This gives us y =Ak
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
11/21
Another way to represent the model:
Formal refinements of this model take into accountdepreciation, dand population growth, n.
Firms must invest sufficient capital to replace wornout machinery and equipment
And to keep growing, an economy must provide thegrowing labour force with capital
- That is, to maintain the capital to labour ratio thatallows the growth of per capita income to remainat its desired rate
Taking into account depreciation only we canrepresent this mathematically as : K
(Investment)=sF(K,L)-dK Taking into account both depreciation and population
growth in extensive form:
K=sF(K,L)-(d+n)K or K=sY-(d+n)K
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
12/21
Again, we are interested in intensive growth:
That is, we are interested in determining the savingsnecessary to maintain the desired growth in per capita
income after taking in to account the depreciation of
capital and population (work force) growth.
- the STEADY STATE level of capital accumulation
is such that....
sy=(d+n)k
THAT IS, WHERE SAVINGS PER CAPITA IS JUST
SUFFICIENT TO COVER DEPRECIATION AND
POPULATION GROWTH
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
13/21
We can represent these relationships
graphically:
y*
THE ECONOMY WILL
TEND TOWARD THESTEADY STATE RATE
OF GROWTH.
k*k1* k2*
sy=sf(k)
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
14/21
What if the population growth rate falls?
9
y*
y2*
k* k2*
sy=sf(k)
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
15/21
What if the savings rate rises?
So increasing theproportion ofincome allocatedto savings, raises
per capita income.
....But whatdetermineswhether themembers of a
society raise theshare of savingsfrom income(individually or inaggregate)?
k2*
sy2=s2f(k)y2
*
sy=sf(k)
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
16/21
How would we represent the Solow model with
technological change graphically?
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
17/21
two issues to think about here:
Firstly, that it is usually the case that when technologicalchange occurs, further investment in capital is required to
implement the change
That links to a second assumption, that technical change
tends to be labour augmenting(that it makes each worker
more productive)
Y=f(K,AL)
We can now think of capital per worker in terms of
capital per effective worker, since now each worker
is made more productive by technological change.
Note: for a good mathematical representation of this model, see jones, c. (2001) Introduction to Economic
Growth. For a nice tutorial on the neoclassical growth model with some interactive pages see
www.Fgn.Unisg.Ch/eurmacro/tutor/neoclassicalgrowth-index.Html .
http://www.fgn.unisg.ch/eurmacro/tutor/neoclassicalgrowth-index.htmlhttp://www.fgn.unisg.ch/eurmacro/tutor/neoclassicalgrowth-index.htmlhttp://www.fgn.unisg.ch/eurmacro/tutor/neoclassicalgrowth-index.htmlhttp://www.fgn.unisg.ch/eurmacro/tutor/neoclassicalgrowth-index.html -
8/13/2019 334 Neoclassical Growth Model 2013(1)
18/21
Secondly, if population is growing at the rate of n, and
technology is growing at the rate of a, then the required
investment to maintain the steady state rate growth of output,
output per worker (now effective worker), and consumption percapita is (n+d+a)k.
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
19/21
This is why technology is seen to be crucial to increasing
the standard of living. Without technological change, thesteady state growth rate of output is just sufficient to keep
up with population growth (n) and depreciation (d). With
technological change, output per worker will rise and
potentially incomes as well. What determines whether
workers incomes will rise?
Question: If technological change is labour augmenting
and the rate of population growth is falling, what
implications does this have for economic growth? What
are the options available to an economy characterized bythis situation (Europe and other industrialized countries)?
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
20/21
Question: If the nature of existing technological
change is labour augmenting and the birth ratesare falling, what implications does this have for
economic growth?
What are the options available to an economy
characterized by this situation (Europe and
some other industrialized countries)?
-
8/13/2019 334 Neoclassical Growth Model 2013(1)
21/21