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Standard Evidence for Learning Curves isn't Good Enough

Why a tight correlation between cumulative experience and declining costs doesn't really prove anything.

Published onMar 04, 2021
Standard Evidence for Learning Curves isn't Good Enough

In economic models of “learning-by-doing,” technological progress is an incidental outcome of production: the more a firm or worker does something, the better they get at it. In its stronger form, the idea is formalized as a “learning curve” (also sometimes called an “experience curve” or “Wright’s Law”), which asserts that every doubling of total experience leads to a consistent decline in per-unit production costs. For example, every doubling of the cumulative number of solar panels installed is associated with a 20% decline in their cost, as illustrated in the striking figure below (note both axes are in logs).

Learning curves have an important implication: if we want to lower the cost of a new technology, we should increase production. The implications for combating climate change are particularly important: learning curves imply we can make renewable energy cheap by scaling up currently existing technologies.

But are learning curves true? The linear relationship between log costs and log experience seems to be compelling evidence in their favor - it is exactly what learning-by-doing predicts. And similar log-linear relationships are observed in dozens of industries, suggesting learning-by-doing is a universal characteristic of the innovation process.

But what if we’re wrong?

But let’s suppose, for the sake of argument, the idea is completely wrong and there is actually no relationship between cost reductions and cumulative experience. Instead, let’s assume there is simply a steady exponential decline in the unit costs of solar panels: 20% every two years. This decline is driven by some other factor that has nothing to do with cumulative experience. It could be R&D conducted by the firms; it could be advances in basic science; it could be knowledge spillovers from other industries, etc. Whatever it is, let’s assume it leads to a steady 20% cost reduction every two years, no matter how much experience the industry has.

Let’s assume it’s 1976 and this industry is producing 0.2 MW every two years, and that total cumulative experience is 0.4 MW. This industry faces a demand curve - the lower the price, the higher the demand. Specifically, let’s assume every 20% reduction in the price leads to a doubling of demand. Lastly, let’s assume cost reductions are proportionally passed through to prices.

How does this industry evolve over time?

In 1978, cost and prices drop 20%, as they do every every two years. The decline in price leads demand to double to 0.4 MW over the next two years. Cumulative experience has doubled from 0.4 to 0.8 MW.

In 1980, cost and prices drop 20% again. The decline in price leads demand to double to 0.8 MW per decade. Cumulative experience has doubled from 0.8 MW to 1.6 MW.

In 1982… you get the point. Every two years, costs decline 20% and cumulative experience doubles. If we were to graph the results, we end up with the following:

In this industry, every time cumulative output doubles, costs fall 20%. The result is the same kind of log-linear relationship between cumulative experience and cost as would be predicted by a learning curve.

But in this case, the causality is reversed - it is price reductions that lead to increases in demand and production, not the other way around. Importantly, that means the policy implications from learning curves do not hold. If we want to lower the costs of renewable energy, scaling up production of existing technologies will not work. 

This point goes well beyond the specific example I just devised. In any demand curve with a constant elasticity of demand, it can be shown constant exponential progress yields the same log-linear relationship predicted by a learning curve. And even when demand doesn’t have a constant elasticity of demand, you can frequently get something that looks pretty close to a log-linear relationship, especially if there is a bit of noise.

But ok; progress is probably not completely unrelated to experience. What if progress is actually a mix of learning curve effects and constant annual progress? Nordhaus (2014) models this situation, and also throws in growth of demand over time (which we might expect if the population and income are both rising). He shows you’ll still get a constant log-linear relationship between cost and cumulative experience, but now the slope of the line in such a figure is a mix of all these different factors.

Using Learning Curves to Predict With Real Data

In principle, there is a way to solve this problem. If progress happens both due to cumulative experience and due to the passage of time, then you can just run a regression where you include both time and total experience as explanatory variables for cost. To the extent experience varies differently from time, you can separately identify the relative contribution of each effect in a regression model. Voila!

But the trouble is precisely that, in actual data, experience does not tend to differ from time. Most markets tend to grow at a steady exponential rate, and even if they don’t, their cumulative output does. This point is made pretty starkly by Lafond et al. (2018), who analyze real data on 51 different products and technologies. For each case, they use a subset of the data to estimate one of two forecasting models: one based on learning curves, one based on constant annual progress. They then use the estimated model to forecast cost for the rest of the data and compare the accuracy of the methods. In the majority of cases, they tend to perform extremely similarly. 

To take one illustrative example, the figure below forecasts solar panel costs out to 2024. Beginning in 2015 or so, the dashed line is their forecast and confidence interval for a model assuming constant technological progress (which they call Moore’s law). The red lines are their forecasts and confidence intervals for a model assuming learning-by-doing (which they call Wright’s law). The two forecasts are nearly identical. 

The main point is that consistent declines in cost whenever cumulative output doubles is not particularly strong evidence for learning curves. Progress could be 100% due to learning, 100% due to other factors, or any mix of the two, and you will tend to get a result that looks the same.

But that doesn’t mean learning curves are not true - only that we need to look for different evidence. The article “Learning curves are tough to use” reviews some of this evidence.

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Cited in the above

Knowledge spillovers are a big deal

Learning curves are tough to use

Cites the above

How to accelerate technological progress

Are technologies inevitable?

Learning curves are tough to use

Articles cited:

Thompson, Peter. 2012. The Relationship between Unit Cost and Cumulative Quantity and the Evidence for Organizational Learning-by-Doing. Journal of Economic Perspectives 26(3): 203-224.

Nordhaus, William D. 2014. The Perils of the Learning Model for Modeling Endogenous Technological Change. The Energy Journal 35(1): 1-13.

Lafond, François, Aimee Gotway Bailey, Jan David Bakker, Dylan Rebois, Rubina Zadourian, Patrick McSharry, and J. Doyne Farmer. 2018. How well do experience curves predict technological progress? A method for making distributional forecasts. Technological Forecasting and Social Change 128: 104-117.

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