1. Economic growth theory: How does it help us to do applied growth work?
Elena Ianchovichina
PRMED
March 23, 2009

2. 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?

3. 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

4. Emphasis on capital accumulation and 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.

5. 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 y
(n+δ)k y*
sAf(k) k* k

6. 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
sA1f(k)
(n+δ)k
y*(1)
sA0f(k)
y*(0) k* k

7. 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
(n(2)+δ)k
(n(0)+δ)k
S(1)Af(k)
y*(1)
S(0)Af(k)
y*(0)
y*(2) k
k*(2)
k*(0)
k*(1)

8. 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

9. 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
(n1+δ)k
(n2+δ)k
y*(1)
sAf(k)
y*(2)
k*(2)
k*(1) k

10. 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

11. 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

12. 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

13. 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

14. 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 state y
A1y*(s1,n1)
y1=A1f(k1)
A2y*(s2,n2)
y2=A2f(k2) t

15. 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

16. 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
Ay*(s,n)
y1=A1f(k1) t

17. 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)

18. 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

19. 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

20. 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

21. 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

22. Theory of second best
Welfare may decline if reforms tackling some distortions are implemented as long as other distortions remain
In formal terms,
u is welfare; τi is a distortion in activity i
λi is the Lagrange multiplier corresponding to the constraint associated with the distortion in activity i;
the distortion associated with the biggest multiplier effect is the binding constraint
represents the net marginal valuations of activity i by society s, and by private agents
The direct effect is always welfare improving, but the indirect effect may not be, implying that welfare may decline if the indirect effect is negative and larger than the direct effect