Transcript Document
Lesson 2
“First Generation” theories of economic
growth
The Harrod-Domar Model
The Solow “Neoclassical” Growth Model
Convergence
Developed by Sir Roy Harrod (1939) and
Evsey Domar (1946)
Economic growth is the result of sacrificing
current consumption
Households save from current income =>
firms invest these savings => creation of
capital goods => production of output
increases => economic growth
National income, Y(t), is either spent on
consumption goods, C(t), or saved, S(t):
Y(t)=C(t)+S(t)
In a closed economy, the supply of savings
must equal the demand for investment, I(t):
S(t)=I(t)
Investment increases the economy’s stock of
capital, while replacing the part of this stock that
is wearing out:
K (t ) I (t ) K ( t )
Notation:
x(t ) dx(t ) dt
K (t ) : the economy's stock of capital goods
: the rate of depreciation of capital
Assumptions of the model:
Savings is a fixed fraction of income:
S (t ) sY (t ), 0 s 1
The capital-output ratio is constant:
K (t ) Y (t )
The savings rate, s, and the capital-output ratio,
, are the two key variables in the model
The key equation in the Harrod-Domar model
is:
g
s
Where, g Y (t ) Y (t ) : the growth rate of output
Note: Details of the above equation to be derived
in class
Adding population growth (n) to the model,
we get:
s
g n
g* is now the rate of growth of per-capita output
This growth equation was instrumental in
shaping policies in socialist countries such as
India and the Soviet Union in the 1950s and
1960s
The key variables in the Harrod-Domar model
are:
The savings rate
The population growth rate
The capital-output ratio
All these variables are assumed to be
exogenous, which is unrealistic
What determines these variables?
There is evidence to suggest that the savings rate (s)
rises with income:
Poor people or countries close to subsistence do not or
cannot save much
As income rises, there is more room for savings; but the
very rich have less need for savings
Some inequality might also affect the savings rate: middle
class saves more than poor or rich
This implies that poor and rich countries should have
low growth rates, compared to middle-income
countries
Huge body of evidence suggests that population growth changes
with the level of development: Demographic Transition
At low levels of per-capita income, death rates are very high. This
leads to high birth rates too. Combined effect is a low rate of
population growth
As per-capita income rises, living standards improve and death rates
fall sharply. But birth rates don’t. So population growth is high
At very high levels of per-capita income, birth rates fall as well, and
population growth declines
Relationship between per-capita income and population growth:
“inverse-U”
Developed by Nobel Prize winning
economist, Robert Solow (1955)
Extends the Harrod-Domar story in a very
important direction:
Endogeneizes the capital-output ratio, .
Based on the Law of Diminishing Returns
The capital-output ratio depends on the relative
endowments of capital and labor in the economy
Rate of capital accumulation (per-capita):
k(t ) sy(t ) ( n)k (t )
Where,
k (t ) K (t ) / L(t ) capital per unit of labor
y (t ) Y (t ) / L(t ) per - capita output
L(t ) Size of labor force
Key difference from Harrod-Domar story: Production
function: per-capita output is a function of per-capita
capital stock:
y f k , f 0, f 0
Over the long-run, due to diminishing returns, the
per-capita stock of capital stops eventually stops
growing:
k(t ) 0 as t
This situation (stationary per-capita capital stock) is
called the steady-state equilibrium:
~
~
sf (k ) nk
Given the parameters , s, and n, we can determine
~
the unique steady-state per-capita stock of capital, k
There is no per-capita growth in output in the
steady-state (due to diminishing returns to
capital)
Total output and capital grow at the rate of
population growth:
Y K
n
Y K
An increase in the population growth rate (n):
Lowers the steady-state level of per-capita output
Increases the growth rate of total output
Why the “dual” effect?
Labor is both an input in production as well as a consumer
of final goods
Growth Effect: changes the growth rate of a variable
Level Effect: changes the level of a variable, but
leaves its growth rate unchanged
In the previous version, growth of per-capita
output cannot be sustained indefinitely
Economy eventually converges to a stationary
equilibrium (constant per-capita output)
What happens if we introduce technical
progress?
Production function shifts upwards over time as new
knowledge and efficiency is gained and applied
Does this outweigh the effect of diminishing returns?
The answer is …
Assumption: Labor-augmenting technical progress
Technical progress enhances the efficiency or productivity
of the labor force
Let E(t) denote the level of labor productivity and let
denote its growth rate
Then, the effective labor force is defined as:
E(t)L(t)
Note that the effective labor force is growing at the
rate (n + )
Now, define all quantities in terms of units of
effective labor (not per-capita):
kˆ K EL : capital per effective worker
yˆ Y EL : output per effective worker
The accumulation of capital per effective
worker is then given by:
kˆ syˆ n kˆ
At the steady state, there is no growth in
capital per effective worker: kˆ 0 as t
The level of the capital stock per effective
worker is stationary (constant) in the steadystate, and solves:
sf (kˆ) n kˆ
If the capital stock per effective worker is
constant in the steady state, then it must be
the case that:
Per-capita output (and capital) is growing at the
rate of technical progress, .
Total output (and capital) is growing at the rate
(n + )
Unconditional Convergence:
If structural parameters are identical across countries,
then all countries must converge to a common level of
per-capita income, irrespective of initial conditions
Poor countries have higher marginal product of
capital than rich countries, and therefore grow faster
(“catching-up”)
History does not matter for the long run
This is one of the strongest predictions of the
Solow model
Baumol (1986)
Examined growth rates of the world’s richest 16
countries, using data from 1870-1979
Horizontal axis: plot per-capita income in 1870
(initial condition)
Vertical axis: plot per-capita income growth from
1870-1979
Prediction of the model: inverse relationship
Countries in Baumol’s sample:
Richest countries in 1979
Japan, Finland, Sweden, Norway, Germany, Italy, Austria,
France, Canada, Denmark, USA, Netherlands, Switzerland,
Belgium, UK, Australia
But in 1870, Japan was not one of the richest countries;
Argentina, East Germany, and Portugal were rich, but are
excluded from the sample
Only those countries that were successful at the end
of the sample were chosen
Selection Bias: using wisdom after the event
A good test should look at a set of countries
that, ex-ante, seemed likely to converge to
high per-capita GDP levels over time
Use countries with similar initial conditions,
and not similar terminal conditions
De Long (1988) addressed this problem by
extending Baumol’s dataset to include 23
countries, but excluded Japan
Use a large set of countries, but over a short
time horizon
Parente and Prescott (1993)
Studied 102 countries over the period 1960-85
Each country’s per-capita GDP is expressed as a
fraction of US per-capita GDP in a given year
Standard deviation of relative GDP for each year is
calculated
If convergence hypothesis is true, then standard
deviations should decline over time
Structural parameters (technology, population
growth, savings) differ across countries
Countries converge to their own steady states, and
not to a common steady state
Although long-run levels of per-capita income can
vary across countries, there could be convergence in
growth rates, if technological progress is identical
In testing for convergence, one must control for all
the factors that are different across countries