A Consumer-Producer Model for Induced Technological Progress

1. 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

2. Learning curve x : cumulative output C(x) : cost at cumulative output L : learning parameter LR = 1 – 2-L : learning rate

3. 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.

4. Offshore wind 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.

5. Learning curve caveats (I) • 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…

6. Learning curve caveats (II) • 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).

7. Work in progress • Hence ongoing efforts to explore the caveats of learning curves and propose new models for better understanding them.

8. Nordhaus • (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.

9. Wene • 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.

10. Component learning x : cumulative output C(x) : cost at cumulative output L : learning parameter LR = 1 – 2-L : learning rate α : 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.

11. 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.

12. 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.

13. Alternative to learning curve Exponential relations can be used to simulate the evolution over time of cumulative production and costs: The elimination of time gives a relation de facto equivalent to the learning curve: 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.

14. 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.

15. Unpacking the learning curve • 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) • Aim: investigate the consequences for energy policy as well as induced technical change in energy scenario models.

16. New model (I) Relation between costs C and investments I with elasticity Ec: Relation between production y and costs C with (price-demand) elasticity Ex:

17. New model (II) Let’s assume that: so that: Substituting in the elasticity equations and integrating, we get: and

18. New model (III) For cumulative production then also (approximately) applies: From which it can then be shown that: which is the expression for the learning curve.

19. New Model (IV) • 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.

20. 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: • 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.