lecture 12 economic growth. slide 1 economic growth explain improvements in standards of living (gdp...
TRANSCRIPT
Lecture 12Economic Growth
slide 2
Economic Growth
Explain improvements in standards of living (GDP per capital) along time
Explain differences across countrieslearn how our own growth rate is
affected by shocks and our government’s policies
Solow Growth Model
slide 3
some statistics
In Uganda, 96% of people live on less than $2/day. (data link)
2.8 billion people live on less than $2/day (1.1 billion under $1/day)
GDP per capita Chad in 1960: $1212, in 2000: $908 Venezuela in 1960: $7840, in 2000: $6420 Korea in 1960: $1495, in 2000: $15875 H.K. in 1960: $3090, in 2000: $26698
slide 4
Huge effects from tiny differences
1,081.4%243.7%85.4%
624.5%169.2%64.0%
2.5%
2.0%
…100 years…50 years…25 years
percentage increase in standard of living after…
annual growth rate of income per capita
slide 5
Long term growth effect
Rule of 72: 1% growth rate, approximately takes 72 years to double GDP
What will happen if China keeps 10% growth rate and US keeps 3% growth rate (US per capita GDP $42,000 China $6800)
slide 6
World Distribution of Income
6
slide 7
World Income Map
7
slide 8
South vs. North
8
slide 99
slide 10
Real GDP per capita, 1975–2003
10
slide 11
Life Expectancy and Income (Preston, 1976)
11
slide 1212
slide 13
Heights of Males and Females in China1
551
601
65
1920 1940 1960 19801920 1940 1960 1980
1 2
95% CI Fitted values
cohort
Graphs by 1=URBAN SITE(U) 2=RURAL SITE(R)13
slide 14
Happiness and Income
14
slide 15
The Solow Model due to Robert Solow,
won Nobel Prize for contributions to the study of economic growth
a major paradigm:widely used in policy makingbenchmark against which most
recent growth theories are compared
looks at the determinants of economic growth and the standard of living in the long run
slide 16
How Solow model is different from Chapter 3’s model
1. K is no longer fixed:investment causes it to grow, depreciation causes it to shrink.
2. L is no longer fixed:population growth causes it to grow.
3. The consumption function is simpler.
4. No G and T
slide 17
Production
Initially assume constant population (L) and no technology change
Production of goods and services:
Constant Returns to Scale:
),( LKFY
),( zLzKFzY
slide 18
Production
Letting z = 1/L, we get the production function in per capita terms:
y = Y/L = output per workerk = K/L = capital per worker
Constant Returns to Scale size of the economy does not affect the relationship between capital per worker and output per worker
)()1,/(/ kfyLKFLY
slide 19
Production
Decreasing MPK:
This implies the following shape for the production function:
)(/ kfKFMPK
0)( kf
slide 20
Production
MPK is the slope of this curve.k
yf(k)Low MPK
High MPK
slide 21
Production
Cobb-Douglas case:
1LAKY
AkLKALAKLLAK
LYy
)/(
1
Aky
slide 22
Demand
Assume a closed economy with no government: NX = G = 0
Assume that people save a fraction s of their income (and therefore consume 1 – s),
LILCLYICY /// icy
yscYsC )1()1( 10 s
slide 23
Demand
Substituting:
In equilibrium:
iysicy )1(
syi
)(ksfi
)(kfy
slide 24
Capital Accumulation
Two elements determine how the capital stock changes over time:
Investment: addition of new plants and equipment (makes capital stock rise)
Depreciation: wearing out of existing capital stock (makes capital stock fall)
slide 25
Capital Accumulation
In other words:
Stock Capitalin Change Investment onDepreciati
k )(ksf k
slide 26
Capital Accumulation
k
f(k)
sf(k)c
iy
slide 27
Capital Accumulation
Investment higher than depreciation capital stock increases
Depreciation higher than investment capital stock increases
0)( kkksf
0)( kkksf
slide 28
Capital Accumulation
Steady-state capital stock (k*):
Steady state output, consumption, investment:
**)( kksf
*)(***)()1(*)1(*
*)(*
ksfsyikfsysc
kfy
slide 29
Determining the capital–labor ratio in the steady state
29
slide 30
Capital Accumulation
Low k high MPK high returns from investment capital stock grows
High k low MPK low returns from investment capital stock decreases
In both cases, the economy converges to the steady state (long-run equilibrium)
0)(*111
kkksfkk
0)(*222
kkksfkk
slide 31
Capital Accumulation
Cobb-Douglas:
In steady state:
Akkf )(
**)(*)( kkAksf
)1/(1)1/(11 **)(
sAsA
ksA
k
slide 32
Increase in Savings Rate
k
s1f(k)
k
s2f(k)
*1
k *2
k
slide 33
Increase in Savings Rate
Higher s means that more resources will be dedicated to investment higher capital stock in steady state
Therefore, output per capita will be also higher
slide 34
Golden Rule
What is the relationship between steady-state consumption and savings rate?
Two conflicting forces:Higher s higher output higher the
amount of resources available for consumption c*
Higher s lower the proportion of income allocated to consumption c*
*)()1(* kfsc
slide 35
Golden Rule
For low values of s, c* increases with s
For high values of s, c* decreases with s
Golden Rule: capital stock implied by the savings rate such that c* is maximized
slide 36
Golden Rule
More formally:
But in steady state:
*)(*)(*)()1(* ksfkfkfsc
**)( kksf
**)(* kkfc
slide 37
Golden Rule
Golden Rule: find k* such that c* is maximized
**)(*max*
kkfck
)*(0)*(*d*d
gg kfkfkc
MPK
slide 38
Golden Rule
k
k
f(k)
*gk
MPK =
slide 39
Golden Rule
sg is the savings rate that implies kg*:
k
k
f(k)
*gk
MPK =
sgf(k)
slide 40
The relationship of consumption per worker to the capital–labor ratio in the steady state
40
slide 41
Golden Rule
Cobb-Douglas case:
Golden Rule: MPK =
Akkf )(
1)( kAkfMPK
)1/(1)1/(1
1 *)*(
AA
kkA gg
slide 42
Golden Rule
In steady state: *)*( ggg kkAs
A
AA
AAk
s gg
1)1/(11)*(
gs
slide 43
Transition to Golden Rule
Case 1: s > sg, i.e., steady-state capital too high. Decrease s in order to reach sg
k
sgf(k)
s2f(k)
*gk *k
k
slide 44
Transition to Golden Rule
t
t t
k y
c
k*
kg*
y*
yg*
c*cg*
i*
ig*
ti
slide 45
Transition to Golden Rule
Case 2: s < sg, i.e., steady-state capital too low. Increase s in order to reach sg
k
sf(k)
sgf(k)
*k *gk
k
slide 46
Transition to Golden Rule
t
t
k y
c
k*
kg* y*
yg*
c*
cg*
i*
ig*i
t
t
slide 47
Transition to Golden Rule
If the economy begins above the golden rule (s too high), consumption increases in all future periods decrease in s leads to welfare improvement
If the economy begins below the golden rule (s too low), consumption falls during transition there is a tradeoff between consuming today or in the future
slide 48
Egypt
Chad
Pakistan
Indonesia
ZimbabweKenya
India
CameroonUganda
Mexico
IvoryCoast
Brazil
Peru
U.K.
U.S.Canada
FranceIsrael
GermanyDenmark
ItalySingapore
Japan
Finland
100,000
10,000
1,000
100
Income per person in 1992(logarithmic scale)
0 5 10 15Investment as percentage of output (average 1960–1992)
20 25 30 35 40
International Evidence on Investment Rates and Income per Person
slide 49
Population Growth
Assume that the population--and labor force-- grow at rate n. (n is exogenous)
Ln
L
EX: Suppose L = 1000 in year 1 and the population is growing at 2%/year (n = 0.02).
Then L = n L = 0.02 1000 = 20,so L = 1020 in year 2.
slide 50
Break-even investment
( + n)k = break-even investment, the amount of investment necessary to keep k constant.
Break-even investment includes: k to replace capital as it wears out
n k to equip new workers with capital(otherwise, k would fall as the existing capital stock would be spread more thinly over a larger population of workers)
slide 51
The equation of motion for k
With population growth, the equation of motion for k is
k = s f(k) ( + n) k
break-even
investment
actual investme
nt
slide 52
The Solow Model diagram
Investment, break-even investment
Capital per worker, k
sf(k)
( + n ) k
k*
k = s f(k) ( +n)k
slide 53
The impact of population growth
Investment, break-even investment
Capital per worker, k
sf(k)
( +n1) k
k1*
( +n2) k
k2*
An increase in n causes an increase in break-even investment,leading to a lower steady-state level of k.
slide 54
Prediction:
Higher n lower k*.
And since y = f(k) , lower k* lower y* .
Thus, the Solow model predicts that countries with higher population growth rates will have lower levels of capital and income per worker in the long run.
slide 55
Chad
Kenya
Zimbabwe
Cameroon
Pakistan
Uganda
India
Indonesia
IsraelMexico
Brazil
Peru
Egypt
Singapore
U.S.
U.K.
Canada
FranceFinlandJapan
Denmark
IvoryCoast
Germany
Italy
100,000
10,000
1,000
1001 2 3 40
Income per person in 1992(logarithmic scale)
Population growth (percent per year) (average 1960–1992)
International Evidence on Population Growth and Income per Person
slide 5656
slide 57
Clark 2005, p1308 Fig 1
slide 58
The Golden Rule with Population Growth
To find the Golden Rule capital stock, we again express c* in terms of k*:
c* = y* i*
= f (k* ) ( + n) k*
c* is maximized when MPK = + n
or equivalently, MPK = n
slide 59
Technology Progress
Rewrite the production function to incorporate technology change:
E = efficiency of labor
E L = effective workers
Assume: Technological progress is labor-augmenting: it increases labor efficiency at the exogenous rate g:
),( ELKFY
slide 6060
Technology Progress
Assume that E grows at rate g
Therefore E L grows at rate n + g
Redefine all variables in terms of effective workers:
k = K/EL = capital per effective worker
slide 6161
Technology Progress
Then y = Y/EL (= output per effective worker) is given by:
Similarly for consumption and investment:
)()1,/(/ kfyELKFELY
icyELIELCELYICY ///
yscELYsELCYsC )1(/)1(/)1( syiELsYELIsYI //
slide 6262
Technology Progress
Therefore, the equations are the same as before
The only change is in the law of motion for k. Capital per effective worker: Increases with investment Decreases with physical depreciation Also decreases because there are more
effective workers to share the existing capital (higher L and E)
slide 6363
Technology Progress
Then:
In steady-state, capital per effective worker is fixed:
kgnksfkgnik )()()(
0k*)(*)( kgnksf
slide 6464
Technology Progress
k
sf(k)
( +n+g)k
k*k1 k2
slide 6565
Technology Progress
In steady state, income, consumption and investment per effective worker are also constant over time:
*)(***)()1(*)1(*
*)(*
ksfsyikfsysc
kfy
slide 6666
Technology Progress
Therefore capital, income, consumption and investment per worker grow at the rate g in steady-state:
*/*/**
*/*/**
*/*/**
*/*/**
EiLIELIi
EcLCELCc
EyLYELYy
EkLKELKk
slide 67
slide 67
Steady-State Growth Rates in the Solow Model with Tech. Progress
n + gY = y E L Total output
g(Y/ L ) = y E Output per worker
0y = Y/ (L E )Output per effective worker
0k = K/ (L E )Capital per effective worker
Steady-state growth rate
SymbolVariable
slide 6868
Technology Progress
This follows since steady-state variables are constant and E is growing at the rate g
Therefore, the inclusion of technology progress in the Solow model can generate sustained long-run growth
slide 6969
Technology Progress
Moreover, total capital, output, consumption and investment grow at the rate n+g in steady state:
Given that steady-state variables are constant and EL is growing at the rate n+g
** ,**** *,*
iELIcELCyELYkELK
slide 7070
Consumption per effective worker in steady state:
Golden Rule: find k* s.t. c* is maximized:
Golden Rule
*)(*)(*)(*)(*)()1(* kgnkfksfkfkfsc
*)(*)(*max*
kgnkfck
gnMPKkfgnkfkc
gg )*(0)()*(*d*d
slide 71
Government Policies to raise the rate of productivity growth
Improving infrastructure Would increased infrastructure spending increase
productivity?• There might be reverse causation: Richer countries
with higher productivity spend more on infrastructure, rather than vice versa
• Infrastructure investments by government may be inefficient, since politics, not economic efficiency, is often the main determinant
slide 72
Government Policies to raise the rate of productivity growth
Building human capital• There’s a strong connection between productivity and
human capital• Government can encourage human capital formation
through educational policies, worker training and relocation programs, and health programs
• Another form of human capital is entrepreneurial skill• Government could help by removing barriers like red tape
Encouraging research and development• Government can encourage R and D through direct aid to
research
slide 73
Why is technological breakthroughs progress so unequal across countries?
What determined whether/when new technology adopted?Geography view: importance of ecology,
climate, disease environment, geography, in short, factors outside human control.
Institutions view: importance of man-made factors; especially organization of society that provide incentives to individuals and firms.
History’s accidents: some countries are unlucky and trapped in underdevelopment.
73
slide 74
The Geography Factor
74
slide 75
The Institutions Factor
75
slide 76
Institutions and Economic Performances
76
slide 77
Institutions and Economic Performances
77
slide 78
But institutions are complicated: identification problem
Good institutions are correlated with many other good things. Theories about institutions are thus very difficult to test.
The study of the causal role of institutions on economic growth is therefore complicated by concerns about endogeneity.
For example, the United States is rich; it has good institutions; it has high levels of education; it has a common law heritage; it has a temperate climate.
Good institutions are difficult to pin down precisely. We want to be very careful to disentangle different causal effects and isolate the effect of interest.
78
slide 79
But institutions are also endogenous
Institutions could vary because underlying factors differ across countries: Geography, ecology, climate
Montesquieu’s story:
– Geography determines “human attitudes”
– Human attitudes determine both economic performance and political system.
– Institutions potentially influenced by the determinants of income
79
slide 8080
Factor Prices
So far, we solved the model without any reference to wages and rental rates (factor prices)
We just focused on how income is generated, but not on how it is distributed
Assume that a competitive firm hires capital and labor to generate output
slide 8181
Factor Prices
Assuming Cobb-Douglas technology:
Then the problem for this firm is given by:
KRLwELPAKLK
..)(max 1,
1)(),( ELAKELKFY
slide 8282
Factor Prices
First-order condition for K implies that:
In steady-state, the real rental rate is fixed (since k is fixed)
11
11
)/(/
)(//
kAELKAPR
ELKAKFMPKPR
slide 8383
Factor Prices
First-order condition for L implies that:
In steady-state, the real wages increase at the rate g (since k is fixed and E grows at the rate g)
EkAEELKAPw
EELKALFMPLPw
)1()/)(1(/
)(//
slide 8484
Factor Prices
Assume that capital is initially below the steady-state. Then k will evolve according to the following path:
t
k
k*
slide 8585
Factor Prices
Rental rate:initially high (low k implies high MPK)decreases over time as capital
accumulates and MPK decreases
t
R/P
slide 8686
Factor Prices
Define wage in terms of efficiency units as:
Then : initially low (low k implies low MPL labor
abundant relative to capital) increases over time as capital accumulates
and MPL increases constant in steady state
kAE
Pww )1(/~
w~
slide 8787
Factor Prices
This means that real wages (w/P):Grow faster than g during the
transitionGrow at the rate g in steady-state
t
w~
slide 88
Growth Accounting
Want to be able to explain why and how countries grow
There are many sources of growth First step is to decompose aggregate
growth into its components:Growth in the labor forceGrowth in capitalGrowth in productivity
88
slide 8989
Sources of Economic Growth
Assume Cobb-Douglas Production Function
Take log and differentiating
1Y zK L
(1 )dY dz dK dL
Y z K L
slide 90
Computing TFP
z: Total Factor Productivity (TFP) or “Solow Residual”
Y is GDP, K is aggregate capital, N is number of workers
Need to know α
90
slide 9191
What is “z”
Human Capital (Education) Technological Progress Externality: environmental Issues Institutional Effect
Firm OrganizationPatent ProtectionCorruptions
slide 92
Labor Share in the Cobb-Douglas Production Function
Firm optimization:
First-order condition with respect to N:
Labor share is wN/Y. Here:
92
1max( )zK N wN rK
(1 )w zK N
1/ (1 ) / 1wN Y zK N Y
slide 93
Result
Can use average labor share as measure of Labor share (total wages divided by
GDP) in the U.S. is about 64%Estimate α to be 0.36
Can now compute TFP as:
93
1
.36 .64/ ( )z Y K N
slide 94
Total Factor Productivity in the U.S.
94
slide 95
Decomposing Growth Rates
Taking logs of production function:
The same applies to log differences:
Log differences are approximately equal to percentage changes:
95
log log 0.36log 0.64logY z K N
log log 0.36 log 0.64 logY z K N
% % 0.36% 0.64%Y z K N
slide 96
Growth Decomposition for the U.S.
96
slide 97
Growth Decomposition for the Asian Tigers
97
slide 98
Growth Accounting for China
slide 99
Human Capital in China
99
slide 100
Human Capital in China
100
slide 101
Innovation
New Goods
Patents
Technology in China
101
slide 102
102
02
46
mea
n o
f p
ate
ntt
ot
1 1.5 2 2.5 3 3.5 4 4.5
Management and ProductivityP
aten
ts
1996
-200
4
Management ScoreNote: European firms only as uses the European Patent Office database
slide 103
103
Policies to promote growth
Saving Rate Human capital investment Encouraging technological progress Right Institutions
slide 104
104
Growth empirics: Confronting the Solow model with the facts
Solow model’s steady state exhibits balanced growth - many variables grow at the same rate. Solow model predicts Y/L and K/L grow at
same rate (g), so that K/Y should be constant.
This is true in the real world.
Solow model predicts real wage grows at same rate as Y/L, while real rental price is constant.
Also true in the real world.
slide 105
105
Convergence Solow model predicts that, other things
equal, “poor” countries (with lower Y/L and K/L ) should grow faster than “rich” ones.
If true, then the income gap between rich & poor countries would shrink over time, and living standards “converge.”
In real world, many poor countries do NOT grow faster than rich ones. Does this mean the Solow model fails?
slide 106
106
Convergence
No, because “other things” aren’t equal. In samples of countries with similar savings
& pop. growth rates, income gaps shrink about 2%/year.
In larger samples, if one controls for differences in saving, population growth, and human capital, incomes converge by about 2%/year.
slide 107
107
Convergence
What the Solow model really predicts is conditional convergence - countries converge to their own steady states, which are determined by saving, population growth, and education. And this prediction comes true in the real world.