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Escaping Stagnation
Sang Yoon (Tim) Lee
Universität Mannheim
May 4, 2015
last updated: May 4, 2015
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
1 / 24
Review from Last Week
Malthusian model of stagnation
Productivity differences mainly result in population density differences
(not in income per capita)
Predictions of the model pre-industrialization fit historical events
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
2 / 24
This Week and Next
1
Escaping from stagnation
2
Rise of industrial sector (two sector model)
3
Demand for food and development failures
4
Quantity-Quality trade-off for children and fertility decline
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
3 / 24
Source of Stagnation
Income per capita in Malthus model:
At X α
yt =
Nt
In the model (in continuous time),
˙
A˙
N
y˙
=α
−
y
A N
Empirically (in discrete time),
log(yt+1 ) − log(yt ) = α {[log(At+1 ) − log(At )] − [log(Nt+1 ) − log(Nt )]}
⇒ Stagnation happens because growth rate of N cancels growth rate of A.
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
4 / 24
Escaping Stagnation
Based on this, there are three potential ways to escape stagnation:
1
Acceleration in growth of At with bounds to fertility growth
2
Exogenous decrease in population growth
3
Need something outside current model - introduce something new
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
5 / 24
Exogenous Demographic Change?
Fertility growth cannot be unbounded
Also, maybe people change birth behavior
This would cause escape from stagnation
But that would mean decline in population growth leads to escape.
⇒ Both in Europe and subsequent development scenarios, industrialization
began by exploding population ⇒ slowdown began much later.
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
6 / 24
Technology growth outruns fertility growth?
Fertility growth cannot be unbounded
Suppose max number of children a couple can have is 10 (per year)
Then population increases by 5-fold every 25 years or so...
If technology grows faster, we can escape stagnation:
1 + g > 51/25 ≈ 1.07
⇒ But no one grew this fast (7% per year were called “growth miracles”)
⇒ No one has such a high level of fertility after development
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
7 / 24
Structural Change
So, let’s first think about escaping from stagnation, then demographics.
Maybe land (X) becomes less important factor in production?
I
Consider the agricultural production function
Y = BXαt N1−αt
I
If αt → 0 over time, we get sustained growth. (similar question in homework)
This is reasonable (land does seem to be less important these days), but
then why did it become less important?
When does αt start changing? If it was always changing, can’t explain
stagnation...
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
8 / 24
Two sector model
Instead of saying a parameter suddenly starts changing, build model with
two production sectors:
Yta = (Aat X)α (Nta )1−α
Yti = (Ait )α Nti ,
where “a” stands for agricultural, “i” stands for industrial.1
We don’t want to say we just start transitioning from one function to the
other
We will create conditions where industrial production is never used, until
Ait meets a certain threshold
1 Note
that there are different levels of technology for each sector, but it doesn’t matter even if
we assume At ≡ Aat = Ait , the results will be qualitatively the same.
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
9 / 24
Rest of the two sector model
Agricultural and Industrial output:
Yta = (Aat X)α (Nta )1−α
Yti = (Ait )α Nti ,
with the following assumptions:
Nt = Nta + Nti
A˙ at
= ga
Aat
A˙ it
= gi
Ait
˙t
N
= log(yt /2p)
Nt
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
10 / 24
Which technology to use?
Basic principle of economics: more efficient technology will be used!
Marginal product of labor in agriculture
a α
∂Yta
At X
=
(
1
−
α
)
∂Nta
Nta
Marginal product of labor in industry
∂Yti
= (Ait )α
∂Nti
Note that, as Nta grows, MPL in agriculture falls, but not in industry!
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
11 / 24
Transition threshold
Stagnation is when only agricultural is used (Nt = Nta ) - it will be same as
the Malthus model!
a α
At X
> (Ait )α
(1 − α )
Nt
If we are in the stagnation BGP the LHS is
(1 − α)2p exp(ga ) > (Ait )α
The LHS is constant while RHS is growing. When enough time passes so
that
(1 − α)2p exp(ga ) ≤ (Ait )α
transition to the industrial sector begins!
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
12 / 24
Optimal Allocation of Labor
After industrial production begins,
a 1
At X
= Ait
(1 − α ) α
Nta
1
Nta = (1 − α) α ·
Aat X
Ait
and the rest will work in the industry.
If gi > ga , Nti → Nt in the limit - never actually happens.
However, productivity growth will no longer suppress income per capita
- as transition accelerates, income per capita will start to grow!
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
13 / 24
A story using the two sector model
Let’s assume Aa0 >> Ai0 and ga < gi .
Malthusian stage when population and (industrial) technology are at
very low levels
Eventually, reach the stagnation BGP
Industrial technology continues growing and crosses threshold
Eventually, agriculture continues to shrink
As this happens, income per capita eventually grows at rate gi (in the
limit)
But if ga >> gi , transition may not occur at all!
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
14 / 24
Shortcomings of the model
Agricultural consumption is not the same as industrial consumption!
Even though we escape stagnation, population growth will continue to
explode
After transition, since income per capita grows even faster, population
grows even faster, food production would decline (and we would starve
to death!)
⇒ Now, have to think about food!
Differentiate food and industrial goods (food is necessity)
Then incorporate demographic transition
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
15 / 24
Demand for food
Assume a food production constraint:
fNt < (Aat X)α (Nta )1−α
If not binding, nothing changes
If binding,
fNt = (Aat X)α (Nta )1−α
1
1− α
fNt
a
Nt =
a
α
( At X )
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
16 / 24
Role of the constraint:
In original model...
Aat and Nti are negatively correlated
If Aat is high, transition occurs more slowly
If Aat is low, transition occurs more quickly (and consequently we starve!)
With the constraint binding,
If Aat is high, transition occurs more quickly - first need to eat, then
develop!
If Aat is low, transition occurs more slowly! Because we need to eat! In the
extreme case, transition will not occur!
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
17 / 24
Evidence
The industrial revolution was not just about industry, but agriculture
became much more productive as well
In England, there were sharp increases in agriculture ⇒ need less
workers, so workers transitioned to industry!
England had abundant farmland colonies!
ALL other European countries industrialized much later....
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
18 / 24
The Employment Share of Agriculture in European
Countries
60%
50%
40%
30%
20%
10%
0%
1790
1810
France
1830
Germany
1850
1870
United Kingdom
1890
Sweden
1910
Italy
Still (more?) shortcomings
With the food constraint, unchecked population growth becomes an even
larger problem
Since population grows even faster after transition, food demand
increases - in the end people starve to death: maximum sustainable
g
population at At is
g
fNtmax = (At X)α (Ntmax )1−α
1
g
Ntmax = f − α At X
so whenever Nt reaches Ntmax , those people will die...
Why would people keep having more children that are going to starve to
death?
In reality,
1
2
people stopped starving to death
then they stopped having children
Need to transition to a different fertility choice! (next week)
Tim Lee (U Mannheim)
Economic Growth
May 4, 2015
20 / 24
The Total Fertility Rate in England
6
5.5
Total Fertility Rate
5
4.5
4
3.5
3
2.5
2
1.5
1
1800
1820
1840
1860
1880
1900
1920
The Total Fertility Rate in European Countries
6
Total Fertility Rate
5
4
3
2
1
1851-1855
France
1876-1880
Netherlands
1901-1905
England and Wales
1926-1930
Germany
1951-1955
Norway
Sweden
1976-1980
Finland
The Crude Birth Rate in European Countries
C rude B irth R ates
(pe r10 00)
42
38
34
30
26
22
18
167 0
1720
England
177 0
Fra nce
1820
Swed en
1 870
F inla nd
192 0
G erman y
The Crude Death Rate in European Countries
40
C r u d e D e a th R a(p
tee r1 0 0 0)
36
32
28
24
20
16
12
1725
1775
E n g la n d
F ra n c e
1825
S we d e n
1875
F in la n d
1925
G erma ny