Economic growth theory:
How does it help us to do applied
growth work?
Elena Ianchovichina
PRMED, World Bank
Joint Vienna Institute, Austria
June, 2009
Why the focus on growth?
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Most policymakers worry about growth and
employment
Yet, theory offers little advice on how to generate
growth in a specific country
Growth is a fairly recent phenomenon in the period
1000-present
Large income differences between poor and rich
countries
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What can poor countries do to catch up?
What should rich countries do to maintain their high
living standards?
Solow’s theory of growth
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The centerpiece of Solow’s neoclassical model is
the production function: Y=AF(K, L), where
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Y is output, K is capital, L is labor, and A is a
productivity parameter
Assuming CRS, we can rewrite the production
function as: y=Af(k), where
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y=Y/L (output per unit of labor), k=K/L (capital per
unit of labor), and f(k)=F(k,1)
Output per capita y increases because of increases in
capacity k and improvements in technology A
Emphasis on capital accumulation
and strong assumptions
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The neoclassical model emphasizes growth
through capital accumulation: K  I  K
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where I is investment, δ is the rate of capital depreciation
Expressing in units of labor and assuming that
I=sY we have
.
k  sAf (k )  (n   )k
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where s is the saving rate, n is the rate of population growth, and all
parameters are exogenous.
Economy in a steady state
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In the steady state,. the ratio of capital per unit
of labor is stable: k  0
or, using a “*” to denote a steady-state value,
*
*
is determined by: sAf (k )  (n   )k
*
*
where Af (k )  y is steady-state income
y
(n+δ)k
y*
sAf(k)
k*
k
Predictions I
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The steady state rate of growth of real income per capita
y depends only on g and does not depend on s or n
Real income Y grows at the rate of growth in
technology and population (g+n)
If reform increases productivity, then income per capita
would rise from
y*(0) to y*(1)
y
(n+δ)k
sA1f(k)
y*(1)
sA0f(k)
y*(0)
k*
k
Predictions II
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In the long run the economy approaches a steady
state that is independent of initial k
In the steady state, k grows at the same rate as y, so
k/y = s/(n+δ)
The steady state income y* depends on s and n. The
higher s, the higher y*; the higher n, the lower y*
y
(n(2)+δ)k
(n(0)+δ)k
S(1)Af(k)
y*(1)
S(0)Af(k)
y*(0)
y*(2)
k*(2)
k*(0) k*(1)
k
Predictions III
• In the steady state, the marginal product of capital is
constant
– MP(K*)=(n+δ)/s=Af’(k*)
• In the steady state, the marginal product of labor
grows at the rate of technical change g
– MP(L*)=A(f(k)-kf’(k))
• These predictions are broadly consistent with
experience in the US
Critiques
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Critique 1: model assumes technology is exogenous
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We know income per capita grows as technology improves
Critique 2: countries use the same production function
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Countries can be considered at different points on the same
production function
y
y*(1)
(n2+δ)k
(n1+δ)k
sAf(k)
y*(2)
k*(2)
k*(1)
k
Is the assumption of exogenous
savings a problem? Not really
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In the optimal growth literature savings are
endogenously determined
Two basic approaches
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In a OLG model (Samuelson and Diamond)
In a infinitely lived representative agent (Ramsey, Cass,
Koopmans)
Both approaches yield results similar to Solow
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The economy reaches a steady state with a constant saving
rate
This steady state has the same characteristics as the steady
state in the Solow model
From theory to empirics
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Practical growth analysis has relied on
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Growth accounting
Growth regressions
Macro models (e.g. CGE and others)
Complemented by microeconomic analyses at the firm
level
What is the link between the neoclassical model and
these techniques
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The production function in Solow is the basis for these
and other approaches
Growth accounting
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Follows the standard Solow-style procedure to decompose
output growth into contributions of capital K, labor L and
productivity A
Production function represented for simplicity represented as a
Cobb-Douglas function: Y  AK  L(1 )
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where  is the share of capital in income.
Taking logs and time derivatives, leads to:
Yˆ  Kˆ  (1   ) Lˆ  Aˆ
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where “^” denotes percentage changes over time, capital growth
consists of investment net of depreciation, and labor growth stands for
the expansion of the working-age population
The production function in Solow is used to assess future
potential growth output
Speed of convergence to steady state
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In the Solow model income converges to its steadystate level at the same rate as capital:
.
y   ( y  y * )
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where   (1   )(n  g   )
 is the capital share
The convergence equation holds for any type of
production function
Cross-country empirical analysis
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Solow’s model is the basis for cross-country growth
work as it predicts international income differences
and conditional convergence
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Steady-states differ by country depending on their rates of
saving s and population growth n
Growth rates differ depending on country’s initial
deviation from own steady state
y
y*(s1,n1)
y*(s2,n2)
y1=A1f(k1)
y2=A2f(k2)
t
Determinants of long-term growth
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Cross-country growth regressions are used to assess the importance of the
main factors determining steady state per capita
The literature is huge (Barro, 1995 and many others)
Three sets of factors are typically included in these regressions:
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Structural policies and institutions
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Stabilization policies
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Education, financial depth, trade openness, government inefficiency,
infrastructure, governance
Fiscal and monetary policies (inflation, cyclical volatility)
Monetary and exchange rate policies (real exchange rate overvaluation)
Regulatory framework for financial transactions
External conditions
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Terms of trade shocks
Period specific shifts associated with changes in global conditions: recessions,
booms, technological innovations
Cyclical output movements
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Fatas (2002) shows that
Business cycles cannot be considered as temporary
deviations from a trend
Countries with more volatile fluctuations display
lower long-term growth rates
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y
y*(s,n)
y1=A1f(k1)
t
Other approaches
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Ramsey preceded Solow
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Ramsey developed a rigorous yet very simple
general-equilibrium model of optimal growth
This model offers an entry into the growth
diagnostic approach of HRV (2005)
Simple Ramsey optimal growth model
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Households have perfect foresight
Need to decide how much L and K to rent to firms, and how much to save
or consume by maximizing their individual utility:

U s   u (ct ) exp(  z (t  s)) dt
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Subject to:
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(1)
s
ct 
dkt
 nkt  f ( g t ,  t , xt , kt ) (2)
dt
c is consumption per capita
n is population growth;
k is capital per worker; there is no depreciation
g is technological progress
θ is a distortion such as a tax
x is availability of complementary factors of productions
z is the rate of time preference
First-order conditions
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Firms use CRS technology and maximize profits
Complementary factors x and taxes θ are exogenous
First-order conditions for profit maximization imply:
f ( gt ,t , xt , kt )  rt
(3)
f ( gt ,t , xt , kt )  kt f ( gt ,t , xt , kt )  wt
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(4)
Government spending is assumed to be fixed exogenously
Wages are given as w
Keynes-Ramsey rule
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Maximizing (1) subject to (2) and (3), and carried out by setting up a
Hamiltonian results in the following Keynes-Ramsey rule:
ct
  (ct )( rt ( g t ,  t , xt )   )
ct
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In this equation, σ is the elasticity of substitution between consumption at
two points in time, t and s, and ρ(z) is the real interest rate
The Keynes-Ramsey rule implies that consumption increases, remains
constant or declines depending on whether the marginal product of
capital net of population growth exceeds, is equal to or is less than the
rate of time preference
The larger the elasticity of substitution, the easier it is, in terms of utility,
to forgo current consumption in order to increase consumption later for a
given difference between the rate of return and the cost of capital
Keynes-Ramsey rule
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In the case of balanced growth equilibrium:
kt ct
   (ct )( rt ( g t , t , xt )   )
kt ct
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The Keynes-Ramsey rule implies investment increases,
remains constant or declines depending on whether the
return to capital net of population growth exceeds, is
equal to or less than the cost of capital
This equation is the starting point for the empirical HRVtype binding-constraints to growth analysis
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