Transcript grad-Macroeconomics-ISET5

Macroeconomics
BGSE/UPF
LECTURE SLIDES SET 5
Professor Antonio Ciccone
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III. Economic Growth with
Human Capital and
Externalities
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Outline
1.
THE IMPORTANCE OF THE ROLE PLAYED BY
CAPITAL IN PRODUCTION
2.
A SIMPLE MODEL OF ENDOGENOUS GROWTH
3.
EXTERNALITIES AND GROWTH
4.
HUMAN CAPITAL AND GROWTH
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1. THE IMPORTANCE OF THE ROLE
PLAYED BY CAPITAL IN PRODUCTION
Let us return to the Solow model
•
•
Savings a constant fraction s of income
Depreciation rate of capital is 
•
•
Population growth n
Rate of echnological progress a
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PRODUCTION FUNCTION with DECREASING
RETURNS TO CAPITAL
F ( K , L)  K  ( AL)1
0    1  DECREASING RETURNS TO CAPITAL
 CLOSE TO ZERO: STRONG DECREASING
RETURNS
 CLOSE TO UNITY: WEAK DECREASING
RETURNS
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COBB-DOUGLAS PRODUCTION FUNCTION
Y  K  ( AL)1
MPK   K  1 ( AL)1   k  1
MPK K
MPK k

 (1   )
K MPK
k MPK
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STRONG AND WEAK DECREASING RETURNS TO CAPITAL
MPK
WEAK
DECREASING
RETURNS
STRONG
DECREASING RETURNS
TO CAPITAL
k
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Effect of savings rate on BGP income/capital
under STRONG and WEAK decreasing
returns to capital
k BGP
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1
s




At Lt
  n  a 
K BGP,t
K BGP ,t s
1

s K BGP ,t 1  
• STRONG DECREASING RETURNS TO CAPITAL
Small BGP effects of savings rate
• WEAK DECREASING RETURNS TO CAPITAL
 Large BGP effects of savings rate
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
1
s
yBGP  k BGP  



n

a


YBGP,t s


s YBGP,t 1  
• STRONG DECREASING RETURNS TO CAPITAL
Small BGP effects of savings rate
• WEAK DECREASING RETURNS TO CAPITAL
 Large BGP effects of savings rate
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How much of international
income differences explained by
“propensity of countries to
accumulate”?
Depends on strength of decreasing
returns to capital
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Convergence to the BGP under WEAK and
STRONG decreasing returns to capital
EQUILIBRIUM CAPITAL ACCUMULATION
EQUATION
K  sF(K, L)   K
K
F(K, L)
s

K
K
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CONVERGENCE UNDER STRONG DECREASING RETURNS TO CAPITAL

Kt
Kt
F (K , L )
s
K

K*
K (t )
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CONVERGENCE AND WEAK DECREASING RETURNS TO CAPITAL

Kt
Kt
F ( K , L)
s
K

K*
K (t )
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INCOME CONVERGENCE EQUATION (CLOSE to
balanced growth path)
yt
 a  (1   )(n    a)(ln y *  ln yt )
yt
yt
 a  (1   )(n    a)ln y *
yt
 (1   )(n    a)ln yt
growth between t and t  T 
f (determinants of BGP income)
  convergence parameter  ln(initial income)
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Speed of convergence
• STRONG decreasing returns to
capitalFAST convergence to BGP
• WEAK decreasing returns to
capitalSLOW convergence to BGP
EMPIRICALLY, using cross-country data
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REMEMBER THAT IN THE SOLOW MODEL
Elasticity of output with respect to capital

= Capital income share
= 1/3 (empirically)
=STRONG DECREASING RETURNS:
 Fast convergence to BGP
Small BGP level effects of savings rate
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2. A SIMPLE MODEL OF
ENDOGENOUS GROWTH
Return to the Solow model
• Savings a constant fraction s of income
• Depreciation rate of capital is 
• No population growth
• No technological change
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BUT BUT BUT NO DECREASING RETURNS TO CAPITAL(!)
Y  AK
where A is a CONSTANT
which implies
MPK  A  constant
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THIS PRODUCTION FUNCTION ALSO IMPLIES
THAT
Elasticity of output with respect to capital
1
= Capital income share
• which is evidently in CONTRADICTION with
empirical observation
• but let’s see where it leads us
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EQUILIBRIUM CAPITAL ACCUMULATION EQUATION
K  sAK   K
K   sA    K
-- if sA>, CAPITAL per WORKER and therefore
OUTPUT per WORKER grow forever, even if there is
NO TECHNOLOGICAL PROGRESS
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PERPETUAL CAPITAL ACCUMULATION WITHOUT
TECHNOLOGICAL CHANGE
Y  AK
sAK
K
K (t )
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Is there a BALANCED GROWTH PATH?
(path where all variables grow at constant rate)
From equilibrium accumulation equation

K t  sAK   K
To growth rate of capital

K
 sA  
K
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To growth rate of output
Y=AK 
Y K
  sA  
Y K
Hence in this ENDOGENOUS GROWTH MODEL
1) long run growth in absence of technological progress
2) a higher savings rate means FASTER GROWTH IN
the SHORT, MEDIUM, and LONG run
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Moreover,
Y
 sA  
Y
- Implies that the growth rate of capital does
NOT fall as economies accumulate capital
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GROWTH RATE OF CAPITAL (AND OUTPUT) STAYS
CONSTANT IN TIME
Y
AK
s s
 sA
K
K


Kt Yt

Kt Yt

K (t )
 same macro fundamentals (s,A,), same growth rate, no
matter what initial conditions !!
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MAIN RESULTS:
• perpetual accumulation-driven growth:
capital accumulation alone can be the
“engine of economic growth”
• savings rate has long-run growth effects: an
increase in the savings rate increases the
growth rate of capital and output forever
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Endogenous growth and
convergence
The AK model has two interesting features:
(A) a poor economy will NOT achieve the
income per capita of a rich economy even if
has the same macro fundamentals
(B) holding deep parameters or macro
fundamentals constant as economies
become richer, growth does not slow down
 are these two linked? NO!
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Endogenous growth model where GROWTH RATE OF
CAPITAL FALLS IN TIME
Y
s
K
Kt
Kt

Kt
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Endogenous growth and
convergence
(A) a poor economy will NOT achieve the
income per capita of a rich economy
even if has the same macro
fundamentals
(B) holding deep parameters or macro
fundamentals constant as economies
become richer, growth MAY STILL slow
down
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The problem with the AK model?
• Capital share too large
• Back to the Solow model?
-- externalities
-- human capital
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3. EXTERNALITIES AND
ENDOGENOUS GROWTH
In the Solow model we have
• perfect competition
• no externalities
As a result
Y
 MPK  r  
K
Y K
(r   ) K
 " " 
 CAPITAL INCOME SHARE
K Y
Y
1
which we said was around
3
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Why
Y K
 CAPITAL INCOME SHARE
K Y
?
Because the RESULTS of INVESTMENT are assumed to be
– EXCLUDABLE (only the INVESTOR benefits directly)
But sometimes investments by one particular firm yields
results that are
– NON-EXCLUDABLE
– NON-RIVAL
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Rivalry and excludability
EXCLUDABLE?
YES
NO
RIVAL? YES --Banana for personal
-- Crowded highway in Germany
consumption
-- Clean air in city
--Truck for production
NO -- NON-crowded highway --Car design
in Italy (for pay)
--New form of organization for
-- PAY TV
production
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What if investment has a non-rival, non excludable element?
Y
K
Y
K
 r 
PRIVATE
 r 
ECONOMY WIDE (SOCIAL)
Y K
1
 CAPITAL INCOME SHARE=
K Y
3
Externalities:
 real world has SLOWER convergence than Solow model, but not
as slow as in endogenous growth model
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Non-excludability, non-rivalry in
the Solow model?
• Technological progress!
• But fell from heaven; or to put it
differently COMES WITH THE
PASSAGE OF TIME, not with
investment
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The Solow model with
externalities
• Capital income share reflects the
internal return to capital
• Elasticity of aggregate output wrt to
capital reflects the social return to
capital (private plus external return)
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Solow model with externalities
 
F (K f , L f )  K f

1
( EL f )
where f is an index for firms: f=1,…,N
E  Ak

where A grows at rate a; and there are positive externalities
to aggregate capital accumulation if and only if  > 0
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Solve:
• Optimal behavior of each firm (rental of
capital and labor)
• Aggregate production as a function of
aggregate inputs (capital and labor)
• Solow and non-Solow dynamics
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4. HUMAN CAPITAL AND
ENDOGENOUS GROWTH
In the Solow model we have
•
•
•
perfect competition
no externalities
only ONE TYPE OF CAPITAL: PHYSICAL CAPITAL
As a result
Y K
 CAPITAL INCOME SHARE
K Y
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But what about HUMAN CAPITAL?
What is human capital?
• knowledge in people that makes them more
productive
In many ways similar to physical capital
• first INVEST (go to school; get some training)
• then GET A RETURN (higher wage)
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Y
BroadCapital
1
 CAPITAL INCOME SHARE=
BroadCapital
Y
3
Human capital (like capital externalities):
• real world has SLOWER convergence than Solow
model, but not as slow as in endogenous growth
model
• capital and savings explains more of international
differences in income than in the Solow model
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Level and growth effects of HC
• Level effect of HC: more HC raises
output (“neoclassical view of HC”)
• Growth effect: human capital may
determine the rate of technological
progress:
 may affect growth rate in BGP
 or have transitional growth effects only
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Growth effects of HC (A)
• Lucas, JME, 1988: human capital can
produce output or “technology”:
ac ,t 
Ac ,t
Ac ,t
"
  c h( HC "c ,LEARNING
)
t
 increasing HC allocated to learning may therefore increase the
BGP growth rate
(the downside is that output is reduced in the short and medium
run)
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“Growth” effects of HC (B)
Nelson and Phelps, AER, 1966
ac,t
BGP:
a frontier ,t
 A frontier ,t  Ac ,t 
 h( HCc ) 

 A frontier ,t 
ac,t  a frontier ,t

Ac,t 
 h( HCc ) 1 
 
 A frontier ,t 
Ac
A frontier
 1
a frontier
h( HCc )
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Empirical work on link between
human capital and growth
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The human capital “level” effect
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FROM ELASTICITIES to AGGREGATE RATES OF RETURN
TO SCHOOLING
Much of the aggregate work estimates:
1% increase in average years of schooling
income per capita growth(?)
Formally:
increase y
y
elasticity=
increase in S
S
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Something that is easier to interpret intuitively would be:
1 YEAR increase in average years of schooling
income per capita growth(?)
increase y
y
Aggr. Return=
*S
increase in S
S
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Elasticity
0.1
0.2
0.3
0.4
0.5
0.7
1
1.2
Aggr. Return
1.25%
2.5%
3.75%
5%
6.25%
8.75%
12%
15%
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HUMAN CAPITAL QUALITY
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Human capital externalities
Moretti, AER 2004
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Estimating
externalities:
PLANT
INDUSTRY
CITY
-- does output IN THE PLANT
(controlling for inputs in plant and industry)
INCREASE with THE SHARE OF COLLEGE WORKERS
outside of INDUSTRY but inside CITY?
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Estimating equation:
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Data:
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Benchmark results:
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Physical capital externalities?
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