Technology learning curves predict green, low-cost energy future

At EXOGEN, we are on the lowest-cost path for energy. 

 The long-term trends provide a clue as to how this competition may be resolved: The prices of fossil fuels such as coal, oil, and gas are volatile, but after adjusting for inflation, prices now are very similar to what they were 140 years ago, and there is no obvious long-range trend. In contrast, for several decades the costs of solar photovoltaics (PV), wind, and batteries have dropped (roughly) exponentially at a rate near 10% per year. The cost of solar PV has decreased by more than three orders of magnitude since its first commercial use in 1958.

Rupert Way, Matthew Ives, Penny Mealy and J. Doyne Farmer


  • Empirically validated probabilistic forecasts of energy technology costs
  • Future energy system costs are estimated for three different scenarios
  • A rapid green energy transition will likely result in trillions of net savings
  • Energy models should be updated to reflect high probability of low-cost renewables


Future energy system costs will be determined by a combination of technologies that produce, store, and distribute eergy. Their costs and deployment will change with time due to innovation, competition, public policy, concerns about climate change, and other factors. To provide some perspective on the likely future energy system, Figure 1 shows how the energy landscape has evolved over the last 140 years. Figure 1A shows the historical costs of the principal energy technologies, and Figure 1B gives their deployment; both of which are on a logarithmic scale. As we approach the present in Figure 1A, the diagram becomes more congested, making it clear that we are in a period of unprecedented energy diversity, with many technologies with global average costs around $100/MWh competing for dominance.

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Figure 1Historical costs and production of key energy supply technologiesShow full captionView Large ImageFigure ViewerDownload Hi-res imageDownload (PPT)

Figure 1B shows how the use of technologies in the global energy landscape has evolved since 1880, when coal passed traditional biomass. It documents the slow exponential rise in the production of oil and natural gas over a century and the rapid rise and plateauing of nuclear energy. But perhaps the most remarkable feature is the dramatic exponential rise in the deployment of solar PV, wind, batteries, and electrolyzers over the last decades as they transitioned from niche applications to mass markets. Their rate of increase is similar to that of nuclear energy in the 1970s, but unlike nuclear energy, they have all consistently experienced exponentially decreasing costs. The combination of exponentially decreasing costs and rapid exponentially increasing deployment is different from anything observed in any other energy technologies in the past, and positions these key green technologies to challenge the dominance of fossil fuels within a decade.

How likely is it that clean energy technology costs will continue to drop at similar rates in the future? Under what conditions will this happen, and what does this imply for the overall cost of the green energy transition? Is there a path forward that can get us to net-zero emissions cheaply and quickly? We address these questions here by applying empirically tested, state-of-the-art cost forecasting methods to energy technologies.

Historically, most energy-economy models have underestimated deployment rates for renewable energy technologies and overestimated their costs, which has led to calls for alternative approaches and more reliable technology forecasting methods. Recent efforts have made progress in this direction, but they are largely deterministic in nature. The methods we use are probabilistic, allowing us to view energy pathways through the lens of placing bets on technologies. After all, powering modern economies requires betting on some technologies one way or another, be they clean technologies or more fossil fuels—the best we can do is make good bets. Which technologies should we bet on, and how likely are they to pay off? We focus on solar, wind, batteries, and electrolyzers, which we call here “key green technologies”, because they could play crucial roles in decarbonization and have strong progress trends that are well documented in publicly available datasets. We also consider the major incumbent energy technologies and compare our forecasts with projections made by influential energy-economy models. We investigate three different energy transition scenarios and discuss the implications for whole system costs and transition pathways.

Figure 1 provides a glimpse into the diverse nature of technological change as technologies rise and fall from dominance. It reflects how innovation and technological learning produce different outcomes for different technologies. The diversity of rates of technological improvement for energy technologies seen in Figure 1 is typical of technologies in general. Roughly speaking, technologies can be divided into two groups based on their rates of improvement. For the first group, comprising the vast majority of technologies, inflation-adjusted costs have remained roughly constant through time. Fossil fuels provide a good example: although there has been enormous progress in technologies for discovery and extraction, as easily accessible resources are depleted, it becomes necessary to extract less accessible resources, creating a “running-to-stand-still” dynamic in which prices have remained roughly constant for more than a century (this is true for all minerals). Another example of a non-improving technology is carbon capture and storage (CCS); despite significant effort, over its 50-year commercial history for enhanced oil recovery, costs have not declined at all.There are even cases, such as nuclear power, where costs have increased. By contrast, for a select group of improving technologies, costs have dropped roughly exponentially while deployment has increased exponentially.Rates of improvement for technologies such as optical fibers and transistors are as high as 40%–50% per year. Solar PV, wind, and batteries have behaved similarly but with improvement rates closer to 10% (see Document S1 section “The heterogeneity and persistence of technological change”). This makes unit costs for these technologies predictable, even if the specific technological innovations that lead to lower costs are not predictable.

Because the behavior of these two groups of technologies is so different, they require different cost forecasting models. Fossil fuels such as oil and gas are tradable commodities, and according to efficient markets theory, their prices should follow a random walk. This provides a useful approximation for roughly a decade, but over longer spans of time they display mean reversion. This makes autoregressive models a natural choice, and we use them to forecast oil, coal, and gas prices (see Experimental procedures and Document S1 sections “AR(1) process,” “Oil,” “Coal,” and “Gas”). For the select group of technologies that are improving, improvement rates are remarkably consistent. For these technologies there are two dominant methods for quantitatively forecasting costs based on historical data. The first is a generalized form of Moore’s law, which says that costs drop exponentially as a function of time (i.e., at a fixed percentage per year). The second is Wright’s law, which predicts that costs drop as a power law of cumulative production.

 This relationship is also called an experience curve or learning curve, and cumulative production is also called experience. (For a discussion of challenges and caveats concerning Wright’s law, see Document S1 section “Wright’s law caveats.”) Multifactor models have been proposed using additional input variables, such as patenting activity and research and development (R&D) expenditures, but data are limited and they require additional parameters. This can lead to overfitting, resulting in poor out-of-sample forecasts (see Document S1 section “Bias-variance trade-off”). Multifactor models have so far not been properly tested, and we do not use them here.

Successful technologies tend to follow an “S-curve” for deployment, starting with a long phase of exponential growth in production that eventually tapers off due to market saturation. Under Wright’s law, during the exponential growth phase costs drop exponentially in time, as they do for Moore’s law, but when production growth eventually slows, cost improvement also slows. Improving technologies often spend many decades in the exponential growth phase, making it hard to distinguish between Moore’s law and Wright’s law. Forecasts using the two models have similar accuracy in backtesting experiments.

This brings up the important question of responsiveness to investment. Under Moore’s law, costs are assumed to change exogenously over time, independent of policy and investment. Under Wright’s law, costs depend on experience. Although experience does not directly cause costs to drop, it is correlated with other factors that do, such as level of effort and R&D, and has the essential advantage of being relatively easy to measure.

 For comparison, the historical time series displayed in Figure 1 are plotted as experience curves in Figure S17. The same heterogeneity of improvement rates seen in Figure 1 is evident for Wright’s law—the fact that fossil fuel prices have not dropped historically means that experience had no net effect—in stark contrast to key green technologies. In this paper, we focus on Wright’s law because it satisfies the basic intuition that exerting greater effort induces greater effects. (We repeated all our modeling experiments using Moore’s law and found that the qualitative conclusions are similar; see Document S1 section “Moore’s law results.” For a more thorough discussion of causality, see Document S1 section “Discussion on questions of causality.”) Wright’s law has usually been used to generate point forecasts, meaning that the forecast is a deterministic function of experience, with no estimate of the error of the forecast. Early attempts at introducing error bars did not provide a priori functional forms, which made the data requirements for out-of-sample testing prohibitive. More recently, a priori error estimates were derived that predict forecasting accuracy as a function of historical improvement rates and volatility, and the number of data points available for forecasting.

Based on comprehensive backtesting, this method was shown to generate reliable probabilistic estimates of future costs. This was done by selecting reference dates in the past and then, using only the data available at the time, making forecasts over all time horizons up to 20 years into the future with respect to each reference date. Using historical data for 50 different technologies, based on roughly 6,000 forecasts, the empirically observed forecast accuracy closely matched the a priori derived estimates on all time horizons up to 20 years ahead.

 Our main contribution in this paper is to systematically apply this method—which we call the stochastic experience curve or stochastic Wright’s law—to the energy transition.