Transcript Economic Growth

Economic Growth
Growth Facts
Solow Growth Model
Optimal Growth
Endogenous Growth
Readings
• Williamson, Ch 6, p 200-222 (Solow Growth)
• Williamson, Ch 7 (Endogenous Growth)
Table 6.1 Economic Growth in
Eight Major Countries, 1870–2005
Growth Facts
• Before Industrial Revolution (1800) standards of
living was very similar across countries.
• Large differences in per-capita incomes across
countries appeared after IR.
• Positive correlation between per capita output
and per capital investment.
• Negative correlation between per capita output
and population growth.
• Rich countries:
Convergence
• Poorest countries: No Convergence
Figure 6.2 Output per Worker vs.
Investment Rate
Figure 6.3 Output per Worker vs. the
Population Growth Rate
Figure 6.5 Convergence
Among the Richest Countries
Figure 6.6 No Convergence
Among the Poorest Countries
• Questions:
(1) What explains differences in economic
growth and standard of living among
countries?
(2) How do factors like saving, population, and
technology affect economic growth and
productivity?
(3) What does CE model say about optimal
growth?
(4) How does the accumulation of “human
capital” contribute to economic growth?
(4) Policy implications?
• Two key variables of interest:
(1) yt = Yt/Nt = output per person or average
labor productivity. Also can measure
standard of living.
(2) ΔY/Y = growth rate of Y.
Solow Growth Model
• Robert Solow (MIT) – 1989 Nobel Winner
• A constant returns to scale production function
says
F(xK,xN) = xF(K,N)
• Notice that from CRTS production function we
can write
Yt
yt 
 zt f ( kt )
Nt
where kt = Kt/Nt.
• Per-capita GDP (y) depends only on the capital–
labor ratio (k).
• Competitive Market-Clearing:
Yt = Ct + It
• Assume proportional aggregate savinginvestment rate:
(Yt - Ct)= It = sYt
• Population grows at rate n:
Nt+1 = (1+n)Nt
• Population = Labor Force = Nt
• Definition of (Net) Investment:
I t  Kt 1  (1   ) Kt
kt 1 (1  n)  szt f (kt )  (1   )kt

kt 1  kt  szt f (kt )  (n   )kt  kt
• A steady state equilibrium is where k and y are constant
(no pressure to change): kt 1  kt  k* or k  0

szf (k*)  (n   )k *
• In the steady state k = K/N and y = Y/N are
constant. Therefore
* y = k = 0
* Y K N
Y

K

N
n
• Saving Rate (s)
Increase s  increases k* and y*
(i) Permanent increase in standard of living (y*)
(ii) Temporary increase in economic growth.
• Productivity/Technology (z)
Increase z  increases k* and y*
(i) Perm increase in standard of living
(ii) One time inc. in z  temp increase in
economic growth.
(iii) Sustained inc. in z  perm inc. in growth
Figure 6.15 Effect of an Increase in the
Savings Rate on the Steady State Quantity of
Capital per Worker
6-16
Figure 6.16 Effect of an Increase in
the Savings Rate at Time T
6-17
Figure 6.23 Natural Log of the Solow
Residual, 1948–2001
• Population growth (n)
increase n  decreases k* and y*
(i) Permanent decrease in standard of living
(ii) Permanent increase in economic growth
• Application – The convergence hypothesis:
Economic growth and output per person in
countries with similar levels of technology,
savings and population growth should converge.
• Application/Evidence
* Growth convergence among developed
countries.
* Japanese/German “miracle” after WWII
* Non-convergence among poor countries
Explanation: Barriers to Technological
Adoption.
(i)
Trade Restrictions
(ii) Intellectual Property Rights /
Monopolies
Figure 7.2 Convergence in Income per
Worker Across Countries in the Solow
Growth Model
Figure 7.3 Convergence in Aggregate
Output Across Countries in the Solow
Growth Model
Productivity Levels in Selected Countries
Country
GDP/ Labor 1973
(% of US)
GDP/Labor 1998
(% of US)
Growth Rate
US
100
100
1.5%
France
76
98
2.5%
UK
67
79
2.2%
Germany
62
77
2.4%
Ireland
41
78
4.1%
Argentina
45
39
0.9%
Mexico
38
29
0.5%
Peru
26
15
-0.7%
Brazil
24
23
1.2%
Figure 6.4 No Convergence
Among All Countries
Figure 7.4 Differences in Total Factor
Productivity
Optimal Growth
• How much should a growing economy consume and
save?
(i) What’s the “best” s?
(ii) What’s the “best” k*?
• Two Responses:
(1) Maximize Steady State Consumption
(Solow Model)
(2) Maximize PDV of discounted household
utility. (Optimal Growth Model)
Solow - The Golden Rule
• Steady-state per capita consumption:
Ct
Y
S
Y sY
 c*  t  t  t  t  (1  s) y *
Nt
Nt Nt Nt Nt
c*  zf (k*)  (n   )k *
OR
• Golden-Rule: The optimal kGR* maximizes c*
“treat others (future generations) as you would
like to be treated”:
FOC 
zf ' (kGR *)  n  
Figure 6.17 Steady State
Consumption per Worker
6-28
Policy
• Public policies to increase saving rate (s)
(1) Reduce budget deficit (government
spending)
(2) Encourage private saving (IRA accounts,
Social Security reform)
• Public policies to increase productivity (z)
(1) Infrastructure
(2) Human capital (R&D)
(3) Industrial policies
The Optimal Growth Model –
Modified Golden Rule
• Optimal Growth Model  Basic CE model w/
* exogenous/inelastic labor supply
* representative consumer so all variables
are already in per-capita terms.
• The saving rate (s) is endogenous in Optimal
Growth Model.
• Recall that CE Model  Pareto Optimal

t 1
max

u (ct )
• Social Planner’s Objective:

t 1
subject to
c  I  y  zf (k )
t
t
t
t
I t  kt 1  (1   )kt
• State Variable: k t
• Control Variable: ct
• Bellman Equation:
V (kt )  Max u (ct )  V (kt 1 )
ct
subject to
kt 1  zt f (kt )  (1   )kt  ct
• First Order Condition:
u' (ct )  u' (ct 1 )zf ' (kt 1 )  (1   )
• Steady State (Modified Golden Rule):
zf ' (k MG R )  (1/  1)  
*
where   1/(1r) and r is rate of time preference.
• Is this level of capital k*MGR accumulation
socially optimal?
• Social Efficiency (Solow Growth):
zf ' (kGR *)  n  
• Individual Efficiency (Optimal Growth):
zf ' (k MG R )  r  
*
as steady state implies r* = rate of time preference = r.
(i) n = r = r  kGR= kMGG
 Dynamic Efficiency
(ii) n > r = r  kGR < kMGR
 over accumulation
(iii) n < r = r  kGR > kMGR
 under accumulation
Endogenous Growth
• Solow Model can only explain non-convergence
via barriers to technological adoption.
• In Solow Model sustained growth is due to
exogenous forces. Does not explain where
growth comes from.
• Endogenous growth models attempt to explain
economic growth from society’s choice of human
capital accumulation:
Human Capital = Stock of Knowledge and Skills
A Simple Example
• Definitions:
Labor Supply
Education
Human Capital Stock
Efficiency Units of Labor
Real Wage per Efficiency Unit
• Budget Constraint for t = 1,2:
ct  wt ut Ht  t
= ut
= (1-ut)
= Ht
= utHt
= wt
(BC)
• Investment in Human Capital:
Ht 1  b(1  ut ) Ht
(HC)
• Production Function:
Yt  z(ut H t )
• Representative Household: Given H1 and wt,
max U(c1,c2, …) subject to (BC) and (HC).
• Representative Firm: Maximize t = Yt – wtutHt.
• Market-Clearing: Yt = ct
• General Case: In a steady state equilibrium where ut =
ut+1 = u,
Yt 1 zut 1b(1  ut ) H t
H t 1

b(1  u ) 
Yt
zut H t
Ht
Output Growth = Consumption Growth
= Human Capital Growth = b(1-u) – 1 > 0 if b(1-u) > 1.
Implications
• Sustained economic growth can be explained by
endogenously by human capital accumulation.
• Higher rates of growth can be attained by
(i) Greater time allocation to education (1-u)
(ii) More efficient educational systems (b)
• Countries with identical u and b will experience
same growth rate but levels of output and
standard of living may never converge.
Figure 7.9 Growth and
Education
Figure 7.10 Income per
Worker and Education
Figure 7.8 No Convergence in
the Endogenous Growth
Model
• Policy Implications:
(i) There is a potential role for governments to
subsidize education/worker retraining or
encourage efficiency (increasing b /
decreasing u).
(ii) There are externalities to human capital
accumulation  too little private
investment.
Private Marginal benefit = MC
< Society Marginal Benefit
• (iii) Optimal Human Capital Accumulation:
* Social MB = MC
* Short-Run Marginal Cost of Lost
Consumption = Long Run MB of increased
future consumption.
Figure 7.7 Effect of a Decrease in u on the
Consumption Path in the Endogenous Growth
Model