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Variability of technology learning rates

Angelo Carlino, Alicia Wongel, Lei Duan, Edgar Virgüez, Steven J. Davis, Morgan R. Edwards, and Ken Caldeira · Advances in Applied Energy 20, 100252 · 2025

Key finding. Across the 87 technologies in the Performance Curve Database, a model allowing stepwise changes in the learning rate fits better than a constant rate for 58 of them, and a technology's learning rate in the first half of its history predicts its rate in the second half hardly at all — a Pearson correlation of 0.12, not distinguishable from zero.

Two panels. Panel a plots unit cost relative to its initial value, on a logarithmic axis spanning ten orders of magnitude, against cumulative production relative to initial, for 87 technologies coloured by sector. Every trace falls, but at visibly different and changing slopes; nuclear electricity rises. Panel b is a scatter of each technology's future learning rate against its past learning rate, both in per cent, with a dashed 1:1 line. The points form a diffuse cloud centred well above the line rather than lying along it, spanning about minus 20 to plus 50 per cent on both axes.
If a learning rate were a fixed property of a technology, panel b would be a line. Instead the points scatter across the plane — the correlation between a technology's past and future learning rate is 0.12, indistinguishable from zero — while panel a shows costs nonetheless falling almost everywhere. Costs do decline with production; the rate at which they decline is what will not stay put. Figure 2 from Carlino et al. (2025), Advances in Applied Energy 20, 100252. Reproduced under CC BY-NC-ND 4.0. Used unmodified, as the licence requires; the journal running head above the figure is excluded from the crop.

What question did this research address?

Almost every projection of what a low-carbon technology will cost rests on Wright's model — unit cost falls as a power law of cumulative production, so each doubling of output cuts cost by a fixed percentage. That percentage, the learning rate, is treated as a constant of the technology.

If it is not constant, then a forecast built by extrapolating an observed learning rate inherits an error nobody is accounting for. This paper asked how well the constant-rate assumption holds across the broadest available collection of technology cost histories, and what changes when it is dropped.

What did we find?

Splitting each technology's record in half and comparing the learning rate before and after gives a correlation of 0.12, which is not significantly different from zero at the 5% level. Points scatter well away from the identity line rather than along it.

More data does not fix this. The 44 longest series give a correlation of 0.07 and the 43 shortest 0.13, neither significant, and no individual sector's correlation differs significantly from zero either. Longer records make each estimate steadier without making it more predictive.

Comparing the standard first-difference Wright's model against piecewise regressions by the Bayesian Information Criterion, a model with at least two learning rates wins for 58 of the 87 technologies; the constant-rate model is best for 29. The Akaike criterion puts the figure at 60. Weighting sectors equally rather than by how many technologies each contributes gives 58%.

The breakpoints are not artefacts of the fitting. A non-parametric bootstrap with 500 resamples per technology agrees with the original number of breakpoints 74% of the time on average, with a median of 79%.

The three technologies that matter most for decarbonization behave the same way. Solar photovoltaics, wind power, and lithium-ion batteries all show learning rates that accelerate over time, with mismatches between the past and future rate reaching 10 percentage points for solar, 25 for wind, and 30 for batteries.

A forecasting model built on piecewise curves — trusting the most recent learning trend in the short run and expecting regression to the mean in the long run — gives errors equal to or significantly lower than the constant-rate model for 36 and 30 technologies respectively. It does this without technology-specific tuning, needing only the location of the last breakpoint.

Which model wins depends on the technology. Calibrated on data to 2000, the constant-rate model scores better for solar photovoltaics, the piecewise model better for lithium-ion batteries, and for wind power the piecewise model is better in recent years but worse over the whole validation period.

Why does it matter?

A learning rate read off history is routinely carried decades into the future in energy system and integrated assessment models. If past and future rates correlate at 0.12, that extrapolation is far weaker evidence than the precision of the resulting cost curve suggests, and the uncertainty being reported is too narrow.

The finding is not that costs fail to fall with production — they generally do. It is that the *rate* at which they fall shifts as demand, research effort, and policy support change, so a technology can enter a faster or slower learning phase without warning.

The practical implication the authors draw is about where to put money. Since which technology will get cheap fastest cannot be read off its past, investment in early-stage technologies already approaching cost-competitiveness — combined with techno-economic analysis and explicit decision-making under uncertainty — is more robust than betting on an extrapolated learning curve.

Citation

Angelo Carlino, Alicia Wongel, Lei Duan, Edgar Virgüez, Steven J. Davis, Morgan R. Edwards, and Ken Caldeira (2025). Variability of technology learning rates. Advances in Applied Energy 20, 100252.

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