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![Page 1: Economic growth theory: How does it help us to do applied growth work? Elena Ianchovichina PRMED, World Bank Joint Vienna Institute, Austria June, 2009.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649dea5503460f94ae57d8/html5/thumbnails/1.jpg)
Economic growth theory:How does it help us to do applied
growth work?
Elena Ianchovichina
PRMED, World Bank
Joint Vienna Institute, Austria
June, 2009
![Page 2: Economic growth theory: How does it help us to do applied growth work? Elena Ianchovichina PRMED, World Bank Joint Vienna Institute, Austria June, 2009.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649dea5503460f94ae57d8/html5/thumbnails/2.jpg)
Why the focus on growth? 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 What can poor countries do to catch up? What should rich countries do to maintain their high
living standards?
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Solow’s theory of growth The centerpiece of Solow’s neoclassical model is
the production function: Y=AF(K, L), where 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 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
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Emphasis on capital accumulationand strong assumptions
The neoclassical model emphasizes growth through capital accumulation: where I is investment, δ is the rate of capital depreciation
Expressing in units of labor and assuming that I=sY we have
where s is the saving rate, n is the rate of population growth, and all
parameters are exogenous.
KIK
knksAfk )()(.
![Page 5: Economic growth theory: How does it help us to do applied growth work? Elena Ianchovichina PRMED, World Bank Joint Vienna Institute, Austria June, 2009.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649dea5503460f94ae57d8/html5/thumbnails/5.jpg)
Economy in a steady state In the steady state, the ratio of capital per unit
of labor is stable: or, using a “*” to denote a steady-state value,
is determined by: where is steady-state income
0.k
** )()( knksAf **)( ykAf
y
k
(n+δ)k
sAf(k)
k*
y*
![Page 6: Economic growth theory: How does it help us to do applied growth work? Elena Ianchovichina PRMED, World Bank Joint Vienna Institute, Austria June, 2009.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649dea5503460f94ae57d8/html5/thumbnails/6.jpg)
Predictions I
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
k
(n+δ)k
sA0f(k)
k*
y*(0)
sA1f(k)y*(1)
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Predictions II 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
k
(n(0)+δ)k
S(0)Af(k)
k*(0)
y*(0)
y*(1)S(1)Af(k)
(n(2)+δ)k
y*(2)
k*(1)k*(2)
![Page 8: Economic growth theory: How does it help us to do applied growth work? Elena Ianchovichina PRMED, World Bank Joint Vienna Institute, Austria June, 2009.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649dea5503460f94ae57d8/html5/thumbnails/8.jpg)
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
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Critiques
Critique 1: model assumes technology is exogenous We know income per capita grows as technology improves
Critique 2: countries use the same production function Countries can be considered at different points on the same
production function
y
k
(n1+δ)k
sAf(k)
k*(1)
y*(1)
k*(2)
y*(2)
(n2+δ)k
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Is the assumption of exogenous savings a problem? Not really
In the optimal growth literature savings are endogenously determined
Two basic approaches In a OLG model (Samuelson and Diamond) In a infinitely lived representative agent (Ramsey, Cass,
Koopmans) Both approaches yield results similar to Solow
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
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From theory to empirics Practical growth analysis has relied on
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 The production function in Solow is the basis for these
and other approaches
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Growth accounting 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: where is the share of capital in income.
Taking logs and time derivatives, leads to:
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
)1( LAKY
ALKY ˆˆ)1(ˆˆ
![Page 13: Economic growth theory: How does it help us to do applied growth work? Elena Ianchovichina PRMED, World Bank Joint Vienna Institute, Austria June, 2009.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649dea5503460f94ae57d8/html5/thumbnails/13.jpg)
Speed of convergence to steady state
In the Solow model income converges to its steady-state level at the same rate as capital:
where is the capital share
The convergence equation holds for any type of production function
)( *.
yyy ))(1( gn
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Cross-country empirical analysis Solow’s model is the basis for cross-country growth
work as it predicts international income differences and conditional convergence 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 statey
t
y*(s1,n1)
y*(s2,n2)y2=A2f(k2)
y1=A1f(k1)
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Determinants of long-term growth 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:
Structural policies and institutions Education, financial depth, trade openness, government inefficiency,
infrastructure, governance Stabilization policies
Fiscal and monetary policies (inflation, cyclical volatility) Monetary and exchange rate policies (real exchange rate overvaluation) Regulatory framework for financial transactions
External conditions Terms of trade shocks Period specific shifts associated with changes in global conditions: recessions,
booms, technological innovations
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Cyclical output movements
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
y
t
y*(s,n) y1=A1f(k1)
![Page 17: Economic growth theory: How does it help us to do applied growth work? Elena Ianchovichina PRMED, World Bank Joint Vienna Institute, Austria June, 2009.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649dea5503460f94ae57d8/html5/thumbnails/17.jpg)
Other approaches Ramsey preceded Solow
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)
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Simple Ramsey optimal growth model 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:
Subject to:
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
(1) ))(exp()(
s
ts dtstzcuU
(2) ),,,( tttttt
t kxgfnkdt
dkc
![Page 19: Economic growth theory: How does it help us to do applied growth work? Elena Ianchovichina PRMED, World Bank Joint Vienna Institute, Austria June, 2009.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649dea5503460f94ae57d8/html5/thumbnails/19.jpg)
First-order conditions
Firms use CRS technology and maximize profits Complementary factors x and taxes θ are exogenous First-order conditions for profit maximization imply:
Government spending is assumed to be fixed exogenously Wages are given as w
(3) ),,,( ttttt rkxgf
(4) ),,,(),,,( tttttttttt wkxgfkkxgf
![Page 20: Economic growth theory: How does it help us to do applied growth work? Elena Ianchovichina PRMED, World Bank Joint Vienna Institute, Austria June, 2009.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649dea5503460f94ae57d8/html5/thumbnails/20.jpg)
Keynes-Ramsey rule Maximizing (1) subject to (2) and (3), and carried out by setting up a
Hamiltonian results in the following Keynes-Ramsey rule:
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
)),,()(( tttttt
t xgrcc
c
![Page 21: Economic growth theory: How does it help us to do applied growth work? Elena Ianchovichina PRMED, World Bank Joint Vienna Institute, Austria June, 2009.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649dea5503460f94ae57d8/html5/thumbnails/21.jpg)
Keynes-Ramsey rule In the case of balanced growth equilibrium:
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 HRV-type binding-constraints to growth analysis
)),,()(( tttttt
t
t
t xgrcc
c
k
k