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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 technology's past learning rate barely predicts its future one, with a correlation of 0.12. Pooled across every segment of the study's piecewise fits to the 87 technologies, learning rates project a median cost decline of about 20% per doubling of cumulative production, with one standard deviation spanning roughly −1% to 38%; however, an analysis of the study's data that fits one constant rate to each technology's whole record, weighted by record length, puts the median at about 22%, with one standard deviation spanning roughly 6% to 35%.

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?

We found that past learning rates are not good predictors of future learning rates. 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.

Pooling every learning-rate segment from the piecewise fits across all 87 technologies, the learning exponent is best described by a normal distribution with mean −0.33 and standard deviation 0.35 — a median of about 20% cost decline per doubling of cumulative production, with one standard deviation spanning roughly −1% to 38%, and about one segment in six showing costs that rise with production. The fitted parameters are given in Supplementary Table 2, on page 22 of the paper's Supplementary Material, which the main text cites only once, in its Methods (Section 2.4).

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.

Additional analysis

Not reported in the published paper

The paper's distribution of learning rates, in Supplementary Table 2, pools every segment of its piecewise fits and counts each segment equally, however short. A separate analysis (see link below) of the same published data, done for this web page, fits one constant rate to each technology's whole record instead.

Counting each technology once, it gives a median learning rate of about 18% per doubling of cumulative production, with one standard deviation spanning roughly 2% to 31%. Weighting each technology by the length of its record raises the median to about 22%, with one standard deviation spanning roughly 6% to 35%, because the technologies with the longest records learned faster on average. Leaving out nuclear electricity, whose costs rose with production, moves either result by less than one point.

Learning rates from one constant-rate fit per technology, with and without weighting by record length
All 87, unweightedWithout nuclear electricity (86), unweightedAll 87, weighted by record lengthWithout nuclear electricity (86), weighted by record length
Mean learning exponent β−0.285−0.300−0.354−0.362
Standard deviation of β0.2500.2060.2680.245
Median learning rate (at mean β)17.9%18.8%21.7%22.2%
Learning rate at mean β − 1 SD (faster)31.0%29.6%35.0%34.4%
Learning rate at mean β + 1 SD (slower)2.4%6.3%5.8%7.8%

Each technology's learning exponent β is fitted by ordinary least squares to its whole record of log unit cost against log cumulative production — Wright's model with one constant rate, as in the paper's Equations 1 to 3 — and converted to a learning rate as 100 × (1 − 2^β), the percentage cost decline per doubling of cumulative production.

Weighted columns count each technology in proportion to the length of its record, measured as the number of doublings of cumulative production it spans, which ranges from about 0.5 to 31. Unweighted columns count each technology once.

The median assumes β is normally distributed, so it is the mean β converted to a rate. It is not the average of the individual rates, which is 16.6% for all 87 unweighted, because the conversion from β is not a straight line; for the same reason the rates at ±1 SD sit unevenly around the median. A lower β means faster learning, so −1 SD gives the higher rate.

"Without nuclear electricity" drops the Nuclear_Electricity series, whose cost rose with production (β = +1.03, a learning rate of −104%). The OECD nuclear power series is kept.

These differ from the paper's own distribution (Supplementary Table 2, mean β −0.33, standard deviation 0.35), which pools every segment of the study's piecewise fits and counts each segment equally however short.

Analysis of the study's published data (Zenodo, doi:10.5281/zenodo.17179225, the authors' release v4.0) by the Conceptual Investigations Unit, 2026. Code, data, and outputs on GitHub.

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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