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

Technologies  improve    at  very  different  rates

2

And  they  follow    predictable  trends

5

Key hypothesis

All technologies obey same random process – parameters vary across technologies !

What is the random process?

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

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

Cost follows a geometric random walk with drift

More  precise  formulation    of  generalized  Moore’s  law:

Change in log(cost) Drift Noise

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.

(Data are normalized by initial value; Learning Window = 6 years)

How good are the forecasts?

Forecasts without error bars are not very useful.

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)

This works surprisingly well

However, it is possible to do better by taking correlations into account

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

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

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

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

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)

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

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%

What is the probability that solar PV will be cheaper

than nuclear power?

Wright’s law (1936)

Theodore Paul Wright

Cost vs. cumulative production = power law y = x��

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

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

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

Aimee Bailey, Jan Bakker, Patrick McSharry, Dylan Rebois, J.D. Farmer

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.

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)

Power law of practice

Improvement with practice in time to add two numbers (Blackburn, 1936)

Ford’s model T

Wright’s law only works when reducing cost is main objective

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

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

Production vs. time

For technologies in this sample, also reasonable to postulate that production increases exponentially with time

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)

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

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?

Liberty Ships

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.

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.

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

Cost vs. time for recipe model

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

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

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

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?