the predictability of technological progress€¦ · metal products non-metallic mineral products...
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The predictability of !technological progress
!
Oxford Energy Mee.ng on Transforma.ve Change University of Oxford
June 17, 2014
J. Doyne Farmer & Francois Lafond Ins.tute for New Economic Thinking at the Oxford Mar.n School
and Mathema7cal Ins7tute External Professor, Santa Fe Ins.tute
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Technologies improve at very different rates
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And they follow predictable trends
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Key hypothesis
All technologies obey same random process – parameters vary across technologies !
What is the random process?
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Data for 48 different technologies
7 1940 1960 1980 2000
1e−0
81e−0
51e−0
21e
+01
1e+0
4
log(
cost
)
ChemicalEnergyHardwareConsumer GoodsFood
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Moore’s law (1965)
Originally a statement about density of transistors We will use to refer to the hypothesis that technological
performance improves exponentially with time. (Koh and Magee, 2006), (Nagy, Farmer, Bui, Trancik, 2013)
Gordon Moore
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Cost follows a geometric random walk with drift
More precise formulation of generalized Moore’s law:
Change in log(cost) Drift Noise
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Test for predictability using hind casting
Pretend to be at a given time in the past
Use given method to forecast each future year
Repeat for all past dates
Score methods based on forecasting errors
Make hypothesis that improvement process is the same for all technologies, except for parameters.
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(Data are normalized by initial value; Learning Window = 6 years)
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How good are the forecasts?
Forecasts without error bars are not very useful.
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Predicted forecasting error assuming normally distributed IID noise
38
E = yt+τ − yt+τ
yt+� = prediction for time t + �
K = estimated noise amplitude
m = number of points used to estimate µ
t = Student’s “t” distribution
1√A
!EK
"∼ t(m− 1)
A = τ(1 + τ/m)
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This works surprisingly well
However, it is possible to do better by taking correlations into account
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Random process with correlated noise
40
yt+1 � yt = µ + vt + �vt�1
vt = noise at time t
� = parameter describing correlation
1�A�
�EK
�� t(m � 1)
A� = 2nd degree polynomial in �
whose coe�cients depend on � and m
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5,973 annual forecasts, all with
Comparison to empirical data for 48 different technologies
41
−15 −10 −5 0 5 10 15
2e−04
1e−03
5e−03
2e−02
1e−01
5e−01
X
Pr(E
>X)
IMA(1,0)IMA(1,1)
Cumulative distributions for positive and negative errors plotted separately
Red takes correlation into account!Black does not
� < 20τ
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42
−10 −5 0 5 10
0.002
0.005
0.020
0.050
0.200
0.500
X
Pr(E
>X)
o
11220
Comparison to empirical distribution for 48 technologies
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Errors vs. forecast horizon
43
1 2 5 10 20
1e−0
11e
+00
1e+0
11e
+02
1e+0
3
Forecast horizon o
real datamean simulation[0.05,0.95] simulation
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Comparison of errors vs forecast horizon
44
1 2 5 10 20
15
1050
500
o
(EK)
2
real datam < 1m < 3
o(1 + o m)
mean simulation IMA(1,0)
[0.05,0.95] simulation IMA(1,0)
mean simulation, IMA(1,1)
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Innovation noise amplitude vs. improvement rate
45
0.02 0.05 0.10 0.20 0.50
0.02
0.05
0.10
0.20
< µ
K
ChemicalEnergyHardwareConsumer GoodsFood
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Distributional forecast of solar PV assuming business as usual
46
●●●●
●●●●●●●●●●●●
●●●●●●●●●●
●●●
●
●●
1980 1987 1994 2001 2008 2015 2022 2029
0.05
0.14
0.37
12.72
7.39
20.09
●●●●
●●●●●●●●●●●●
●●●●●●●●●●
●●●
●
●●
80%90%99%
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What is the probability that solar PV will be cheaper
than nuclear power?
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Wright’s law (1936)
Theodore Paul Wright
Cost vs. cumulative production = power law y = x��
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1e+01 1e+03 1e+05 1e+07 1e+09
1e-08
1e-05
1e-02
1e+01
Wright
Total cumulative production (# of units)
Ave
rag
e u
nit p
rice
(re
al $
)
Transistor
Photovoltaics
HardDiskDrive
Ethanol
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Moore’s law as a geometric random walk with drift
Time series models
Change in log(cost) Drift Noise
Wright’s law as random walk with drift dependent on cumulative production
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Compatibility of wright and Moore (Sahal, 1987)
If production expands exponentially and costs drop exponentially, Wright’s law will hold.
!
!
!
x(t) = exp(at)y(t) = exp(�bt)y(x) = x�b/a
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Aimee Bailey, Jan Bakker, Patrick McSharry, Dylan Rebois, J.D. Farmer
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Policy implications
The policy implications of Moore’s law and Wright’s law are quite different:
Moore’s law: Progress is inexorable, policy doesn’t matter.
Wright’s law: If causality is from production to cost, increased production accelerates improvement. Feed in tariffs should be effective.
Skeptic: Perhaps cost => production, not prod => cost.
WWII suggests otherwise.
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What causes technologies to improve at such different rates?
• Physics/Engineering/Manufacture
- inherent properties
- learning + economies of scale - (See Funk and Magee, 2014)
• Demand (economics)
• Tropic structure of economy (McNerney, Caravelli, Farmer)
• Increase in combinatorial possibilities
• Population growth (Romer, 1999) Interpreting cumulative production as number of search trials, simple theory for search gives power law (Wright).
- (McNerney, Farmer, Redner, Trancik, PNAS, 2011)
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Power law of practice
Improvement with practice in time to add two numbers (Blackburn, 1936)
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Ford’s model T
Wright’s law only works when reducing cost is main objective
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1970 1980 1990 2000
1e-08
1e-05
1e-02
1e+01
Moore
Time (years)
Avera
ge u
nit p
rice (
real $)
Transistor
Photovoltaics
HardDiskDrive
Ethanol
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1e+01 1e+03 1e+05 1e+07 1e+09
1e-08
1e-05
1e-02
1e+01
Wright
Total cumulative production (# of units)
Ave
rag
e u
nit p
rice
(re
al $
)
Transistor
Photovoltaics
HardDiskDrive
Ethanol
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Production vs. time
For technologies in this sample, also reasonable to postulate that production increases exponentially with time
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1970 1980 1990 2000
1e+00
1e+03
1e+06
1e+09
Production volume
Time (years)
Ye
arly p
rod
uctio
n (
# o
f u
nits)
Transistor
Photovoltaics
HardDiskDrive
Ethanol
(Nagy, Farmer, Bui, Trancik, PlosOne, 2013)
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0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Empirical validation of Sahal's identity: alpha = b/a
b/a
alpha A
A
A
A
A
B
B
B
C
C
C
C
C
D
E
E
E
E
EE
E
E
F
F
G
H
H
LL
M
M
M
M
M
N
O
O
PP
P
P
P
PP
P
P
P
P
P
R
S
S
S
T
T
U
V
V
W
W
W
A
A
A
A
A
B
B
B
C
C
C
C
C
D
E
E
E
E
EE
E
E
F
F
G
H
H
LL
M
M
M
M
M
N
O
O
PP
P
P
P
PP
P
P
P
P
P
R
S
S
S
T
T
U
V
V
W
W
W
(Nagy, Farmer, Bui, Trancik, PlosOne, 2013) Bela Nagy
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Summary of Results: Wright’s law vs. Moore’s law
Wright’s law forecasts based on production better than Moore’s law based on time at long horizons Production history more useful than time. Suggestion: Costs can be driven down by stimulating production (feed-in tariffs). Need “artificial experiments”, such as WWII, to test properly (correlation v.s causation).
Does production drive cost down, or does cost drive production up? Or both?
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Liberty Ships
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Generality of Wright’s law
• Holds at the level of products, firms, industries, or best technology performing a given function.
• Explanation must be correspondingly general.
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Recipe MODEL OF technological improvement
Muth (Management Science, 1987)
Engineers generate new solutions at random, accept them if they are better. Single component: Implies Wright’s law with exponent = -1.
Auerswald, Kauffman, Lobo and Shell (JEDC, 2000)
Multiple components that depend on each other. Accept improvements only if sum score improves.
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Recipe MODEL (CONTINUED)
McNerney, Farmer, Redner, Trancik (PNAS, 2011)
simplified and solved recipe model
generates power law with exponent -(1/d), where d = “design complexity”, which depends on DSM. For homogeneous networks d is in-degree of DSM.
for heterogeneous networks there are typically bottleneck components, d is more complicated to compute, and progress typically occurs via a sequence of punctuated equilibria
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Cost vs. time for recipe model
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Need to go beyond recipe model
• Nice start, but only part of story
• Anecdotally: Innovations in one industry often drive innovations in others
- solar PV, laser printers, digital cameras, ...
• Interactions between technologies are key
- must model evolution of entire technological ecology to understand a single technology
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Physics matters to economics
• Evolutionary search finds physical processes capable of rapid improvement
• Interaction between physics, which determines what is possible, and economics, which determines what is wanted
• Physics is key determinant of technological improvement (Funk and Magee)
• Migration toward “good physics” can result in dramatic improvements
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Electricity, gas, & water
Coke, petroleum products,& nuclear fuel
Mining Research & development
Pharmaceuticals
Health & social work
Transport & storage
Renting of machinery
Public administration& defense
Real estate activities
Paper & publishing
Education
Community, social,& personal services
Computer activities
Other business activities
Post & telecommunications
Finance, insurance
Wholesale& retail trade, repairs
Aircraft & spacecraft
Office, accounting,& computing machinery
Medical, precision,& optical instruments
Radio, TV,& communication equipment
Railroad & transportequipment
Motor vehicles
Ships & boats
Non-ferrous metals
Electrical machinery
Machinery & equipment NEC
Iron & steelFabricatedmetal products
Non-metallicmineral products
ConstructionWood products
Manufacturing NEC,recycling
Textiles
Rubber andplastics
Chemicals
Hotels & restaurants
Agriculture& forestry
Food products
self-flow
community membership
throughflow
10 $11
10 $12 10 $11
10 $10
McNerney, Fath, Silverberg (2013)U.S. industry network, 1997
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local minima implied by Wright unit cost
production
old technology
new technology
Question: Do new technologies enter with lower y intercept or steeper slope? (for moment assume lower y intercept)
What influences rate at which new technologies enter?