A Consumer-Producer Model for
Induced Technological Progress
IEW, University of Cape Town, South Africa, 19-21 June 2012
Francesco Ferioli and Bob van der Zwaan
www.ecn.nl
Learning curve
 x
C ( x)  C ( x0 ) 
 x0 
x:
C(x) :
L:
LR = 1 – 2-L :
L
cumulative output
cost at cumulative output
learning parameter
learning rate
Learning rate
Ferioli, F., K. Schoots and B.C.C. van der Zwaan, “Use and Limitations of Learning Curves for Energy
Technology Policy: a Component-Learning Hypothesis”, Energy Policy, 37, 2009, pp.2525-2535.
Offshore wind
Specific cost (€(2010)/kW)
10000
Offshore wind
Specific park cost
Monopiles only
2008
1991
1000
2005
lr = 3%
R² = 0.49
lr = 5%
R² = 0.57
Costs corrected for commodity price fluctuations
Data from 1991 to 2008
Data from 1991 to 2005
100
1
10
100
1000
Cumulative capacity (MW)
10000
van der Zwaan, B.C.C., R. Rivera-Tinoco, S. Lensink, P. van den Oosterkamp, “Cost Reductions for
Offshore Wind Power: Exploring the Balance between Scaling, Learning and R&D”, Renewable Energy,
41, 2012, pp.389-393.
Learning curve caveats (I)
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Different analysts working on the same technology may get very
different results (data, cost/price, currency, inflation, regression).
R&D, economies-of-scale, automation: cost reduction mechanisms
that are often included in learning curves and obscure true learning.
‘True’ learning-by-doing refers to acquisition of experience: seminal
papers by Wright (1936) and Arrow (1962).
Learning-by-manufacturing, learning-by-using, learning-by-copying,
forgetting-by-not-doing…
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Learning curve caveats (II)
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Statistical significance of learning rates varies substantially over
different technologies.
Technology system boundaries may be different, which may explain
differences between analysts.
Technologies that do not learn, have ceased learning, have exited
the market or perished, are not considered.
For PV, the accumulation of experience only weakly explains overall
cost reductions (plant size, module efficiency and cost of silicon).
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Work in progress
•
Hence ongoing efforts to explore the caveats of learning curves and
propose new models for better understanding them.
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Nordhaus
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(1) Learning curves are widely used to estimate cost functions in
manufacturing models.
(2) They have also been introduced in policy models of energy and
climate change economics.
Nordhaus argues that, while (1) may be useful, (2) may be a
dangerous strategy, by elaborating three main points:
– A fundamental identification problem exists in trying to separate learning from
exogenous technical change, so that learning rates are biased upwards;
– Empirical tests illustrate the potential bias and show that learning rates are not
robust to alternative specifications;
– Overestimating learning rates provides incorrect estimates of the marginal cost
of output and biases policy models towards the corresponding technologies.
Nordhaus, W.D., 2008, The Perils of the Learning Model for Modeling Endogenous Technological
Change, Yale University, 15 December 2008.
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Wene
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Wene considers the learning system as a non-trivial machine and
attempts to ground learning curves in cybernetic theory.
He assumes operational closure and feedback regulation, which
allows calculating eigenvalues for a self-reflecting system.
The eigenvalues correspond to the learning rates of the system, with
values of 20% (zero mode) and <8% (higher modes).
This cybernetic approach thus reproduces the overall features of
technology learning.
It provides a framework for understanding gradual improvements
and radical innovations for (energy) technologies.
This approach towards technology learning systems needs
complementary analysis.
Wene C. O., 2007, “Technology learning system as non-trivial machines”, Kybernetes 36 (3/4), 348-363.
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Component learning
 x
C ( x)  C ( x0 ) 
 x0 
x:
C(x) :
L:
LR = 1 – 2-L :
α:
L
 (1   )C ( x0 )
cumulative output
cost at cumulative output
learning parameter
learning rate
cost share of learning component at t=0
Ferioli, F., K. Schoots and B.C.C. van der Zwaan, “Use and Limitations of Learning Curves for Energy
Technology Policy: a Component-Learning Hypothesis”, Energy Policy, 37, 2009, pp.2525-2535.
Growth and time
Ferioli, F. and B.C.C. van der Zwaan, “Learning in Times of Change: a Dynamic Explanation for
Technological Progress”, Environmental Science and Technology, 43, 11, 2009, pp. 4002-4008.
Costs and time
Ferioli, F. and B.C.C. van der Zwaan, “Learning in Times of Change: a Dynamic Explanation for
Technological Progress”, Environmental Science and Technology, 43, 11, 2009, pp. 4002-4008.
Alternative to learning curve
Exponential relations can be used to simulate the evolution over time
of cumulative production and costs:
x(t )  x0 et
C (t )  C0 e  t
The elimination of time gives a relation de facto equivalent to the
learning curve:
 x
C ( x)  C0  
 x0 



Ferioli, F. and B.C.C. van der Zwaan, “Learning in Times of Change: a Dynamic Explanation for
Technological Progress”, Environmental Science and Technology, 43, 11, 2009, pp. 4002-4008.
Stochastic learning curve model
Ferioli, F. and B.C.C. van der Zwaan, “Learning in Times of Change: a Dynamic Explanation for
Technological Progress”, Environmental Science and Technology, 43, 11, 2009, pp. 4002-4008.
Unpacking the learning curve
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Goal: continue our work attempting to understand the economic
dynamics behind technology learning curves.
Observation: an expansion cycle appears to exist between: cost
reductions & production growth, growth & market investments, and
investments & cost reductions.
Key parameters of our model:
– investment-cost elasticity (producer side).
– price-demand elasticity (consumer side)
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Aim: investigate the consequences for energy policy as well as
induced technical change in energy scenario models.
New model (I)
Relation between costs C and investments I with elasticity Ec:
C
I
  Ec
C
I
Relation between production y and costs C with (price-demand) elasticity Ex:
y
C
  Ex
y
C
New model (II)
Let’s assume that:
I (t )  I 0 e
gt
so that:
dI
 gI
dt
Substituting in the elasticity equations and integrating, we get:
C  C0 e  Ec gt
and
y  y0 e E x Ec gt
New model (III)
For cumulative production then also (approximately) applies:
x  x0 e
E x Ec gt
From which it can then be shown that:
C  x
  
C0  x0 

1
Ex
which is the expression for the learning curve.
New Model (IV)
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Of course, the real world is more complex than one explanatory
variable (investments I).
It can easily be shown, however, that exogenous cost reducing
factors – as long as they are exponential as well – can be added
while the corresponding expressions for C and x still generate the
learning curve (in line with Nordhaus’ suggestions).
We have thus obtained a new model that introduces time in the
learning curve methodology (like our previous paper) plus adds a
level of deeper meaning of what learning really may be.
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Working paper
•
Ferioli, F. and B.C.C van der Zwaan, “A Consumer-Producer Model
for Induced Technological Progress: Market Investments, Cost
Reductions and the Learning Curve”, in progress.
Conclusions:
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For many technologies and under many different circumstances
exponential growth and cost reduction appear the mechanisms
behind learning curves.
Further statistical testing of our model is required, allowing to
determine the relative usefulness, practicality and ‘truthfulness’ of
different approaches proposed to unpack learning.
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