posts_gdocs: 1THmmJVzdsf_Bl2xyf9xlYG4YZBamhvhD7SrlEmzOKlU
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| id | slug | type | content | published | createdAt | publishedAt | updatedAt | publicationContext | revisionId | breadcrumbs | markdown | title |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1THmmJVzdsf_Bl2xyf9xlYG4YZBamhvhD7SrlEmzOKlU | learning-curve | article | {
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"text": "Technologies that follow Wright\u2019s Law get cheaper at a consistent rate, as the cumulative production of that technology increases.",
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"text": "The best way to explain what this means is to look at a concrete example.",
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"text": "Solar technology: an example of a technology that follows Wright\u2019s Law",
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"text": "The time series in the chart shows the deployment of solar panels on the horizontal axis and the price of solar panels on the vertical axis. The orange line that describes the relationship between these two metrics over time is called the ",
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"text": "learning curve",
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"text": " of that technology.",
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"text": "As the cumulative installed capacity increased, the price of solar ",
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"text": "declined exponentially",
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"text": ". Solar technology is a prime example. For more than four decades, the price of solar panels declined by 20% with each doubling of global cumulative capacity.",
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"text": "The fact that both metrics changed exponentially can be nicely seen in this chart because both axes are logarithmic. On a logarithmic axis, a measure that declines exponentially ",
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"text": "follows a straight line",
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"text": "That more production leads to falling prices is not surprising \u2013 such \u2018economies of scale\u2019 are found in the production of many goods. If you are already making one pizza, making a second one isn\u2019t that much extra work.",
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"text": "What is exceptional about technologies that follow a learning curve is that this effect persists, and ",
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"text": "the rate at which the price declines stays roughly constant",
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"text": ". This is what it means for a technology to follow Wright\u2019s Law.",
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"text": "The relationship between the laws of Gordon Moore and Theodore Paul Wright",
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"text": "Solar power is not the only technology where we see trends of exponential change. The most famous case of exponential technological change is Moore\u2019s Law \u2013 the observation of Intel\u2019s co-founder Gordon Moore who noticed that the number of transistors on microprocessors doubled every two years.",
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"text": "We have another article on Moore\u2019s Law on Our World in Data: ",
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"text": "What is Moore\u2019s Law?",
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"text": "Integrated circuits are the fundamental technology of computers, and Moore\u2019s Law has driven a range of changes in computer technology in recent decades \u2013 computers became rapidly cheaper, more energy efficient, and faster.",
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"text": "Moore\u2019s Law, however, is not given in the same way that we just looked at for solar prices. Moore\u2019s Law describes technological change as a function of ",
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"text": "time. ",
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"text": "In the example of solar technology we looked at price changes not as a function of time, but of ",
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"text": "experience",
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"text": " \u2013 measured as the cumulative amount of solar panels that were ever installed.",
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"text": "This relationship that each doubling in experience leads to the same relative price decline was discovered earlier than Moore\u2019s Law by aerospace engineer Theodore Paul Wright in 1936.",
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"text": " It\u2019s called ",
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"text": "Moore\u2019s observation of the progress in computing technology can be seen as a special case of Wright\u2019s Law.",
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"text": "Solar panels are not the only technologies that follow this law. Look at ",
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"text": "our visualization",
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"text": " of the price declines of 66 different technologies and the research referenced in the footnote",
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"text": "The learning rate",
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"text": "The relative price decline associated with each doubling of cumulative experience is the ",
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"text": "learning rate",
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"text": " of a technology.",
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"text": "The learning rate of solar panels is 20%. This means that with each doubling of the installed cumulative capacity, the price of solar panels declined by 20%.",
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"text": "In the footnote, you can find more information about the scientific literature on the learning rate in solar technology, and an example of how the learning rate is calculated.",
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"text": "The high learning rate meant that the price of solar declined dramatically. As the chart above showed, the price declined from $106 to $0.38 per watt in these four decades. A decline of 99.6%.",
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"text": "How is this possible? And is the relationship between experience and price causal?",
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"text": "That the price of technology declines when more of that technology is produced is a classic case of learning by doing. Increasing production gives the engineers the chance to learn how to improve the process.",
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"text": "This effect creates a virtuous cycle of increasing demand and falling prices. More of that technology gets deployed to satisfy increasing demand, leading to falling prices. At those lower prices, the technology becomes cost-effective in new applications, which in turn means that demand increases. In this positive feedback loop, these technologies power themselves forward to lower and lower prices.",
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"text": "The specifics, of course, differ between the different technologies. For more information on what is behind the price reduction of solar panels, see the footnote.",
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"text": "How do we know that increasing experience is causing lower prices? After all, it could be the other way around: production only increases after costs have fallen.",
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"text": "In most settings, this is difficult to disentangle empirically, but researchers Fran\u00e7ois Lafond, Diana Greenwald, and Doyne Farmer found an instance where this question can be answered. In their paper \u201cCan Stimulating Demand Drive Costs Down?\u201d, they study the price changes at a time when reverse causality can be ruled out: the demand for military technology in the Second World War. In that case it is clear that demand was driven by the circumstances of the war, and not by lower prices.",
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"text": "They found that as demand for weapons grew, production experience increased sharply, and prices declined. When the war was over and demand shrank, the price decline reverted back to a slower rate. It was the cumulative experience that drove a decline in prices, not the other way around.",
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"text": "What can we learn from the learning curve of a technology?",
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"text": "If you want to know what the future looks like, one of the most useful questions to ask is which technologies follow a learning curve.",
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"text": "Most technologies do not follow Wright\u2019s Law \u2013 the prices of bicycles, fridges, or coal power plants do not decline exponentially as we produce more of them. But those which do follow Wright\u2019s Law \u2013 like computers, solar panels, and ",
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"text": " \u2013 are the ones to look out for. In their infancy, they might only be found in very niche applications, but a few decades later they are everywhere.",
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"text": "This means that if you are unaware that a technology follows Wright\u2019s Law, you can get your predictions very wrong. At the dawn of the computer age in 1943, IBM president Thomas Watson famously said, \"I think there is a world market for maybe five computers.\"",
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"text": " At the price point of computers at the time, that was perhaps perfectly true, but what he didn\u2019t foresee was how rapidly the price of computers would come down. From their initial niche computers expanded to more and more applications, and the virtuous cycle meant that the price of computers declined continuously. The exponential progress of computer technology expanded their use from a tiny niche to the defining technology of our time.",
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"text": "Solar panels are on the same trajectory as we\u2019ve seen before. At the price of solar panels in the 1950s, it would have sounded quite reasonable to say, \u201cI think there is a world market for maybe five solar panels.\u201d But as a prediction for the future, this statement too, would have been ",
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"text": "To get our expectations about the future right, we are well-advised to take the exponential change of Wright\u2019s Law seriously. Doyne Farmer, Fran\u00e7ois Lafond, Penny Mealy, Rupert Way, Cameron Hepburn, and others have done important pioneering work in this field. A central paper of their work is Farmer\u2019s and Lafond\u2019s \u201cHow predictable is technological progress?\u201d.",
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"text": " The focus of this research paper is the price of solar, so that we avoid repeating Watson\u2019s mistake with renewable energy. They lay out in detail what I discussed here: how solar panels decline in price, how demand drives this change, and how we can learn about the future by relying on these insights.",
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"text": "To get our expectations for the future right, we need to pay particular attention to the technologies that follow learning curves. Initially, we might only find them in a few high-tech applications, but the future belongs to them.",
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"text": "As one would expect, the exact learning rate for a given technology differs slightly across studies, mostly due to differences in the chosen data source, the chosen proxy measure for \u2018experience\u2019, the geographic location or the considered time-span.",
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"text": "To give the fairest estimate and avoid relying on one unusual data point I am therefore reporting an average across several experience curve studies for PV that was conducted by de La Tour et al. 2013. The authors find an average learning rate over many studies of 20.2% (see Table 1 of their publication).",
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"text": "The learning rate implied by the data that I\u2019m presenting here is very similar (19.3%) and can be calculated as follows:",
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"text": "The number of doublings of the capacity is: log2(578,553 / 0.3)=20.879",
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"text": "The rate of change of the price at each doubling is: (106.09 / 0.37725) ^ (1/(20.879)) - 1=0.31=",
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"text": "So the learning rate is 1-2^(-0.31)=0.193399911=",
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"text": "According to the research cited below it involved: larger, more efficient factories are producing the modules; R&D efforts increase; technological advances increase the efficiency of the panels; engineering advances improve the production processes of the silicon ingots and wafers; the mining and processing of the raw materials increases in scale and becomes cheaper; operational experience accumulates; the modules are more durable and live longer; market competition ensures that profits are low; and capital costs for the production decline. A myriad of small improvements across a large collective process drives this continuous price decline.",
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"text": "Kavlak, Goksin and McNerney, James and Trancik, Jessika E. (2017) \u2013 Evaluating the Causes of Cost Reduction in Photovoltaic Modules (August 9, 2017). In Energy Policy, 123:700-710, 2018, ",
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"text": "Theodore Paul Wright (1936) \u2013 Factors affecting the cost of airplanes. J. Aeronaut. Sci., 3 (4) (1936), pp. 122-128",
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"text": "Plausibly, it isn\u2019t just the passing of time that drives the progress in computer chips, but there too it is the learning that comes with continuously expanding the production of these chips. Lafond et al (2018) explain that the two laws produce the same forecasts when cumulative production grows exponentially, which is the case when production grows exponentially. More precisely, if production grows exponentially with some noise/fluctuations, then cumulative production grows exponentially with very little noise/fluctuations. As a result, the log of cumulative production is a linear trend and therefore predicting cost by the linear trend of time or the linear trend of log cumulative production give the same results.",
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1 | 2024-02-01 18:33:45 | 2023-04-18 00:57:56 | 2024-02-06 17:45:11 | listed | ALBJ4LtHeAkDHQkgfKPot7q2dhTS8mHJzqukfeko69AxjvBDaGxNkIFra7o6HfLwibt5UnKN63AhhSVIS3Vz0Q | Technologies that follow Wright’s Law get cheaper at a consistent rate, as the cumulative production of that technology increases. The best way to explain what this means is to look at a concrete example. # Solar technology: an example of a technology that follows Wright’s Law The time series in the chart shows the deployment of solar panels on the horizontal axis and the price of solar panels on the vertical axis. The orange line that describes the relationship between these two metrics over time is called the _learning curve_ of that technology. <Image filename="solar-pv-prices-vs-cumulative-capacity.png" alt=""/> As the cumulative installed capacity increased, the price of solar _declinedexponentially_. Solar technology is a prime example. For more than four decades, the price of solar panels declined by 20% with each doubling of global cumulative capacity. The fact that both metrics changed exponentially can be nicely seen in this chart because both axes are logarithmic. On a logarithmic axis, a measure that declines exponentially [follows a straight line](https://blog.datawrapper.de/weeklychart-logscale/). That more production leads to falling prices is not surprising – such ‘economies of scale’ are found in the production of many goods. If you are already making one pizza, making a second one isn’t that much extra work. What is exceptional about technologies that follow a learning curve is that this effect persists, and _the rate at which the price declines stays roughly constant_. This is what it means for a technology to follow Wright’s Law. # The relationship between the laws of Gordon Moore and Theodore Paul Wright Solar power is not the only technology where we see trends of exponential change. The most famous case of exponential technological change is Moore’s Law – the observation of Intel’s co-founder Gordon Moore who noticed that the number of transistors on microprocessors doubled every two years. We have another article on Moore’s Law on Our World in Data: [What is Moore’s Law?](https://ourworldindata.org/moores-law) Integrated circuits are the fundamental technology of computers, and Moore’s Law has driven a range of changes in computer technology in recent decades – computers became rapidly cheaper, more energy efficient, and faster. Moore’s Law, however, is not given in the same way that we just looked at for solar prices. Moore’s Law describes technological change as a function of _time. _In the example of solar technology we looked at price changes not as a function of time, but of _experience_ – measured as the cumulative amount of solar panels that were ever installed. This relationship that each doubling in experience leads to the same relative price decline was discovered earlier than Moore’s Law by aerospace engineer Theodore Paul Wright in 1936.1 It’s called _Wright’s Law_, after him. Moore’s observation of the progress in computing technology can be seen as a special case of Wright’s Law.2 Solar panels are not the only technologies that follow this law. Look at [our visualization](https://ourworldindata.org/grapher/costs-of-66-different-technologies-over-time) of the price declines of 66 different technologies and the research referenced in the footnote3 # The learning rate The relative price decline associated with each doubling of cumulative experience is the _learning rate_ of a technology. The learning rate of solar panels is 20%. This means that with each doubling of the installed cumulative capacity, the price of solar panels declined by 20%. In the footnote, you can find more information about the scientific literature on the learning rate in solar technology, and an example of how the learning rate is calculated.4 The high learning rate meant that the price of solar declined dramatically. As the chart above showed, the price declined from $106 to $0.38 per watt in these four decades. A decline of 99.6%. # How is this possible? And is the relationship between experience and price causal? That the price of technology declines when more of that technology is produced is a classic case of learning by doing. Increasing production gives the engineers the chance to learn how to improve the process. This effect creates a virtuous cycle of increasing demand and falling prices. More of that technology gets deployed to satisfy increasing demand, leading to falling prices. At those lower prices, the technology becomes cost-effective in new applications, which in turn means that demand increases. In this positive feedback loop, these technologies power themselves forward to lower and lower prices. The specifics, of course, differ between the different technologies. For more information on what is behind the price reduction of solar panels, see the footnote.5 How do we know that increasing experience is causing lower prices? After all, it could be the other way around: production only increases after costs have fallen. In most settings, this is difficult to disentangle empirically, but researchers François Lafond, Diana Greenwald, and Doyne Farmer found an instance where this question can be answered. In their paper “Can Stimulating Demand Drive Costs Down?”, they study the price changes at a time when reverse causality can be ruled out: the demand for military technology in the Second World War. In that case it is clear that demand was driven by the circumstances of the war, and not by lower prices.6 They found that as demand for weapons grew, production experience increased sharply, and prices declined. When the war was over and demand shrank, the price decline reverted back to a slower rate. It was the cumulative experience that drove a decline in prices, not the other way around. # What can we learn from the learning curve of a technology? If you want to know what the future looks like, one of the most useful questions to ask is which technologies follow a learning curve. Most technologies do not follow Wright’s Law – the prices of bicycles, fridges, or coal power plants do not decline exponentially as we produce more of them. But those which do follow Wright’s Law – like computers, solar panels, and [batteries](https://ourworldindata.org/battery-price-decline) – are the ones to look out for. In their infancy, they might only be found in very niche applications, but a few decades later they are everywhere. This means that if you are unaware that a technology follows Wright’s Law, you can get your predictions very wrong. At the dawn of the computer age in 1943, IBM president Thomas Watson famously said, "I think there is a world market for maybe five computers."7 At the price point of computers at the time, that was perhaps perfectly true, but what he didn’t foresee was how rapidly the price of computers would come down. From their initial niche computers expanded to more and more applications, and the virtuous cycle meant that the price of computers declined continuously. The exponential progress of computer technology expanded their use from a tiny niche to the defining technology of our time. Solar panels are on the same trajectory as we’ve seen before. At the price of solar panels in the 1950s, it would have sounded quite reasonable to say, “I think there is a world market for maybe five solar panels.” But as a prediction for the future, this statement too, would have been [ridiculously wrong](https://ourworldindata.org/explorers/energy?tab=chart&facet=none&uniformYAxis=0&country=~OWID_WRL&Total+or+Breakdown=Select+a+source&Energy+or+Electricity=Electricity+only&Metric=Annual+generation&Select+a+source=Solar). To get our expectations about the future right, we are well-advised to take the exponential change of Wright’s Law seriously. Doyne Farmer, François Lafond, Penny Mealy, Rupert Way, Cameron Hepburn, and others have done important pioneering work in this field. A central paper of their work is Farmer’s and Lafond’s “How predictable is technological progress?”.8 The focus of this research paper is the price of solar, so that we avoid repeating Watson’s mistake with renewable energy. They lay out in detail what I discussed here: how solar panels decline in price, how demand drives this change, and how we can learn about the future by relying on these insights. To get our expectations for the future right, we need to pay particular attention to the technologies that follow learning curves. Initially, we might only find them in a few high-tech applications, but the future belongs to them. Theodore Paul Wright (1936) – Factors affecting the cost of airplanes. J. Aeronaut. Sci., 3 (4) (1936), pp. 122-128 Plausibly, it isn’t just the passing of time that drives the progress in computer chips, but there too it is the learning that comes with continuously expanding the production of these chips. Lafond et al (2018) explain that the two laws produce the same forecasts when cumulative production grows exponentially, which is the case when production grows exponentially. More precisely, if production grows exponentially with some noise/fluctuations, then cumulative production grows exponentially with very little noise/fluctuations. As a result, the log of cumulative production is a linear trend and therefore predicting cost by the linear trend of time or the linear trend of log cumulative production give the same results. Fracois Lafond, Aimee G. Bailey, Jan D. Bakker, Dylan Rebois, Rubina Zadourian, Patrick McSharry, and [J. Doyne Farmer](http://www.doynefarmer.com/) (2018) – [How well do experience curves predict technological progress? A method for making distributional forecasts](https://francoislafond.files.wordpress.com/2015/11/wrightslawpaper20.pdf) In Technological Forecasting and Social Change 128, pp 104-117, 2018. [arXiv](https://www.arxiv.org/abs/1703.05979), [Publisher](http://www.sciencedirect.com/science/article/pii/S0040162517303736), [Data](https://www.dropbox.com/sh/w7jvzijblb4nkex/AAC2R-ml3JvIjFfBZtUTPlkta?dl=0), [Code](https://francoislafond.files.wordpress.com/2019/12/forecast_tech_progress-1.zip). See also Nagy B, Farmer JD, Bui QM, Trancik JE (2013) Statistical Basis for Predicting Technological Progress. PLoS ONE 8(2): e52669. [https://doi.org/10.1371/journal.pone.0052669](https://doi.org/10.1371/journal.pone.0052669) Wright’s Law for solar PV modules has also been given its own name; some call it [Swanson’s Law (Wiki)](https://en.wikipedia.org/wiki/Swanson%27s_law). Nagy B, Farmer JD, Bui QM, Trancik JE (2013) Statistical Basis for Predicting Technological Progress. PLoS ONE 8(2): e52669. https://doi.org/10.1371/journal.pone.0052669 Many more references can be found in Doyne Farmer and Fracois Lafond (2016) – How predictable is technological progress? Research Policy. Volume 45, Issue 3, April 2016, Pages 647-665. [https://doi.org/10.1016/j.respol.2015.11.001](https://doi.org/10.1016/j.respol.2015.11.001) The price of Ford’s Model T followed Wright’s Law: each doubling of cumulative production led to the same relative decline in prices. What’s fascinating is that this decline hasn’t stopped until today. An 8hp car, as the Model T, costs what you’d expect: See Sam Korus (2019) – [Wright’s Law Predicted 109 Years of Auto Production Costs, and Now Tesla’s](https://ark-invest.com/analyst-research/wrights-law-predicts-teslas-gross-margin/) As one would expect, the exact learning rate for a given technology differs slightly across studies, mostly due to differences in the chosen data source, the chosen proxy measure for ‘experience’, the geographic location or the considered time-span. To give the fairest estimate and avoid relying on one unusual data point I am therefore reporting an average across several experience curve studies for PV that was conducted by de La Tour et al. 2013. The authors find an average learning rate over many studies of 20.2% (see Table 1 of their publication). de La Tour, A., Glachant, M. & Ménière, Y. (2013) – [Predicting the costs of photovoltaic solar modules in 2020 using experience curve models](https://www.sciencedirect.com/science/article/abs/pii/S0360544213007883). In _Energy_ 62, 341–348. The learning rate implied by the data that I’m presenting here is very similar (19.3%) and can be calculated as follows: Cumulative capacity – in 1976 0.3 MW – in 2019 578,553 MW Module Cost ($ per W) – in 1976 106.09 – in 2019 0.377 The number of doublings of the capacity is: log2(578,553 / 0.3)=20.879 The rate of change of the price at each doubling is: (106.09 / 0.37725) ^ (1/(20.879)) - 1=0.31=**31%** So the learning rate is 1-2^(-0.31)=0.193399911=**19.3%** According to the research cited below it involved: larger, more efficient factories are producing the modules; R&D efforts increase; technological advances increase the efficiency of the panels; engineering advances improve the production processes of the silicon ingots and wafers; the mining and processing of the raw materials increases in scale and becomes cheaper; operational experience accumulates; the modules are more durable and live longer; market competition ensures that profits are low; and capital costs for the production decline. A myriad of small improvements across a large collective process drives this continuous price decline. Kavlak, Goksin and McNerney, James and Trancik, Jessika E. (2017) – Evaluating the Causes of Cost Reduction in Photovoltaic Modules (August 9, 2017). In Energy Policy, 123:700-710, 2018, [http://dx.doi.org/10.2139/ssrn.2891516](https://dx.doi.org/10.2139/ssrn.2891516) Lafond, Francois and Greenwald, Diana Seave and Farmer, J. Doyne, Can Stimulating Demand Drive Costs Down? World War II as a Natural Experiment (June 1, 2020). [http://dx.doi.org/10.2139/ssrn.3519913](http://dx.doi.org/10.2139/ssrn.3519913) The first reference to Watson saying this is in an article from Der Spiegel from 26th May 1965 – [Sieg der Mikrosekunde](https://www.spiegel.de/spiegel/print/d-46272769.html) Doyne Farmer and Fracois Lafond (2016) – How predictable is technological progress? Research Policy. Volume 45, Issue 3, April 2016, Pages 647-665. [https://doi.org/10.1016/j.respol.2015.11.001](https://doi.org/10.1016/j.respol.2015.11.001) See also: de La Tour, A., Glachant, M. & Ménière, Y. (2013) – [Predicting the costs of photovoltaic solar modules in 2020 using experience curve models](https://www.sciencedirect.com/science/article/abs/pii/S0360544213007883). In _Energy_ 62, 341–348. | Learning curves: What does it mean for a technology to follow Wright’s Law? |