Wright’s Law vs Moore’s Law: Which Predicts Technology Better?

The argument over Wright’s law vs Moore’s law sounds like a quarrel between two curve fits, but it is really a question about cause. Does a technology get cheaper because the calendar moves, or because people keep building it? Moore’s law, in the broad sense forecasters use, says cost falls by a roughly fixed percentage every year. Wright’s law says cost falls by a roughly fixed percentage every time cumulative production doubles. For solar panels, batteries, electrolyzers and chips, the two rules usually give nearly the same answer looking backward. Looking forward, they can disagree by a factor of two, and the disagreement decides how much a subsidy, a factory or a climate policy is worth.

This article sets out what the published evidence actually shows, where the two laws are mathematically the same thing in disguise, and where they come apart. It ends with a small simulation built for this piece and a list of observations that would settle the question.

Two laws, stated precisely

Gordon Moore’s original observation concerned the number of components on an integrated circuit, a story told in our piece on whether Moore's law is dead. Forecasting researchers use the name more loosely. In the comparison by Nagy, Farmer, Bui and Trancik (2013), “Moore’s law” means any cost or performance measure that changes exponentially with time. Write it as log cost = a − m·t, where m is a constant annual rate of decline.

Wright’s law comes from Theodore Wright’s studies of airplane manufacturing. It ties cost to experience instead of time: log cost = b − w·log(cumulative production). The exponent w is usually reported as a learning rate, the fractional cost drop per doubling of output. An exponent of 0.32 corresponds to about 20 percent cheaper per doubling.

Those definitions matter because the two rules make different causal claims. Moore’s version is agnostic: progress arrives on schedule, from research, spillovers, or whatever else. Wright’s version names a lever. If you buy more, you push the technology down its curve faster. That is the logic behind deployment subsidies and behind much of the optimism in energy-transition modeling.

Why people keep asking

The question is not confined to journals. An ARK Invest essay by Brett Winton (2019) carries the headline “Moore’s Law Isn’t Dead: It’s Wrong – Long Live Wright’s Law” and argues that production volume, not time, is the real driver. IEEE Spectrum ran a piece titled “Wright’s Law Edges Out Moore’s Law in Predicting Technology Development“, and Design News asked in a battery-focused column whether Moore’s law was “the Wright one.” Those are the framings that turned up in a search for this article; the popular version of the question is usually “which one is right?”

That framing is slightly off. The more useful question is narrower: under what conditions do the two laws make different predictions, and has history supplied enough of those conditions to tell them apart?

What the evidence establishes

The landmark test is Nagy et al. (2013), published in PLOS ONE. The authors assembled annual cost and production series for 62 technologies, grouped into chemicals, hardware, energy and other categories, with records spanning 10 to 39 years. They fit several candidate laws on early data, forecast later years, and scored the errors. Their headline result is short:

“Wright’s law produces the best forecasts, but Moore’s law is not far behind.”

Nagy, Farmer, Bui & Trancik, 2013, PLOS ONE

The same paper explains why the race was close. When production grows exponentially, cumulative production also grows exponentially at the same rate, so log cumulative production is just a linear function of time. Plug that into Wright’s law and you get Moore’s law, with the annual rate equal to the Wright exponent times the production growth rate (m = w·g). The authors credit the insight to the economist Devendra Sahal:

“A combination of an exponential decrease in cost and an exponential increase in production would make Moore’s law and Wright’s law indistinguishable, as originally pointed out by Sahal.”

Nagy et al., 2013, abstract

Nagy and colleagues also checked this relationship empirically. Comparing the Wright exponent predicted from the Moore rate and production growth against the directly fitted one, they found the points sit close to the identity line and concluded that Sahal’s conjecture holds Two other candidates fared worse in their tests. Goddard’s rule, in which progress comes purely from economies of scale in annual production, was weaker at short horizons. A model attributed to Nordhaus overfit and was dropped.

Follow-up work tightened the statistics without overturning the verdict. Farmer and Lafond (2016), in Research Policy, modeled Moore’s law as a correlated geometric random walk with drift across 53 technologies and showed that hindcast errors at different horizons collapse onto one distribution, so a forecast can come with an honest error bar. Lafond and co-authors (2017 arXiv preprint, later published in Technological Forecasting and Social Change) built the same kind of distributional forecast for experience curves, using 51 products. Their conclusion is pragmatic:

“Moore’s law is more convenient and just as good for business as usual forecasts for a given time in the future.”

Lafond et al., arXiv:1703.05979

The same paper argues that Wright’s law is the more useful tool for policy, precisely because it carries a causal story about deployment. That argument was put to large-scale use by Way, Ives, Mealy and Farmer (2022) in Joule, who generated probabilistic cost forecasts for energy technologies, validated on data for more than 50 technologies, and concluded that a rapid clean-energy transition would likely yield trillions in net savings compared with continuing a fossil-fuel system. A commentary by Trutnevyte, Zielonka and Wen (2022) in the same journal noted that the work reopens debate about probabilistic methods in energy modeling.

So the established facts are modest. Over historical data, both laws forecast well, Wright slightly better. The reason they tie is known and has been verified. What has not been established is which variable is doing the causal work.

The competing answers, steelmanned

Answer 1: experience drives cost (Wright is causal)

The case for Wright rests on mechanism. Factories accumulate tacit know-how; suppliers scale; engineers redesign parts after watching thousands fail. Each of these is plausibly tied to units shipped, not to dates. The slight edge in the Nagy hindcasts fits this view, as does the fact that cost declines appear to speed up when demand jumps. Winton’s essay uses lithium-ion cells and electric vehicles as the example of a curve that re-accelerated once a new market opened.

The weakness is that the hindcast edge is small, and a small edge is exactly what you would also expect if cumulative production were merely a slightly better clock than the calendar.

Answer 2: time drives cost (Moore is enough)

Here progress comes from forces largely outside any one product: basic science, better tools borrowed from neighboring industries, cheaper inputs. Production rises because the technology got cheaper, not the other way round. Under this reading the arrow runs from cost to demand, and Wright’s correlation is reverse causation. Moore’s rule also needs one less forecast. To use Wright’s law you must predict future production, which is itself uncertain.

Its weakness is that it offers no account of why some technologies improve slowly or not at all while others race ahead. A purely exogenous clock says nothing about what policy can change.

Answer 3: the data cannot tell, and the learning model is risky

William Nordhaus pressed this point in an NBER working paper, later published in The Energy Journal (2014). His argument is that separating learning from exogenous technical change is a statistical identification problem, that the problem generally biases estimated learning coefficients upward, and that inflated learning rates lead optimization models to favor the wrong technologies. The abstract, as shown on RePEc/IDEAS, warns that this practice is riskier than most modelers realize.

This is the strongest objection, because it does not claim Moore is right. It claims the evidence used to favor Wright cannot, by itself, distinguish the two. If that holds, policy built on learning rates is resting on an assumption, not a finding.

Answer 4: both are shadows of something else

A fourth view treats both laws as summaries of a hidden process, such as cumulative R&D spending or the improvement rate of underlying components. Nagy’s tests included Goddard’s scale-based rule and a variant attributed to Sinclair, Klepper and Cohen, and neither beat Wright. That is evidence against those particular alternatives, not against the general idea.

A small simulation built for this article

To see the identification problem directly, I wrote a short Monte Carlo in Python. It simulates a technology for 30 years. Annual production grows 30 percent a year (with noise) for the first 20 years. True cost follows Wright’s law with exponent 0.32, about a 20 percent learning rate, plus random noise of 0.08 in log units. Each run fits Moore’s law and Wright’s law on years 1 to 20, then forecasts year 30. Five scenarios change what happens to production after year 20. In the last one, the truth is switched to Moore’s law instead. Every scenario was run 2,000 times with a fixed seed.

Two kinds of Wright forecast are reported. “Wright, production known” is handed the true future output, which is the honest way to test the law itself. “Wright, production extrapolated” must guess future output by extending the past trend, which is the situation a real forecaster faces.

import numpy as np
rng = np.random.default_rng(33)
T_IN, H, RUNS = 20, 10, 2000          # years of history, forecast horizon, Monte Carlo runs
G, W, SD = 0.30, 0.32, 0.08           # production growth/yr, Wright exponent (~20%/doubling), log-cost noise

def production(scen):
    t = np.arange(T_IN + H)
    g = np.full(T_IN + H, G)
    if scen in ("slow", "moore_slow"): g[T_IN:] = 0.0       # demand plateaus after year 20
    if scen == "half": g[T_IN:] = G / 2                        # demand growth halves
    if scen == "fast": g[T_IN:] = 2 * G                        # demand surge after year 20
    q = np.exp(np.cumsum(g) + rng.normal(0, 0.05, T_IN + H))   # annual output with noise
    return t, np.cumsum(q) + 1 / G                              # cumulative output (prior stock 1/G)

def run(scen):
    t, X = production(scen)
    if scen == "moore_slow":                                    # truth: cost driven by time only
        lc = -W * G * t + rng.normal(0, SD, t.size)
    else:                                                       # truth: Wright's law
        lc = -W * np.log(X) + rng.normal(0, SD, t.size)
    i, o = slice(0, T_IN), T_IN + H - 1
    m = np.polyfit(t[i], lc[i], 1); w = np.polyfit(np.log(X[i]), lc[i], 1)
    # Wright forecaster that must also extrapolate production at its past growth rate
    lq = np.polyfit(t[1:T_IN], np.log(np.diff(X[:T_IN])), 1)
    q_fut = np.exp(np.polyval(lq, t[T_IN:]))
    X_ext = X[T_IN - 1] + np.cumsum(q_fut)
    e_m = np.polyval(m, t[o]) - lc[o]
    e_w = np.polyval(w, np.log(X[o])) - lc[o]
    e_we = np.polyval(w, np.log(X_ext[-1])) - lc[o]
    Z = np.column_stack([np.ones(T_IN), t[i], np.log(X[i])])   # both regressors at once
    beta, res, *_ = np.linalg.lstsq(Z, lc[i], rcond=None)
    s2 = res[0] / (T_IN - 3); se = np.sqrt(s2 * np.linalg.inv(Z.T @ Z)[2, 2])
    return e_m, e_w, e_we, np.corrcoef(t[i], np.log(X[i]))[0, 1], m[0] / G, -w[0], se

for scen in ["steady", "half", "slow", "fast", "moore_slow"]:
    r = np.array([run(scen) for _ in range(RUNS)])
    rm = lambda c: np.sqrt(np.mean(r[:, c] ** 2))
    print(f"{scen:11s} RMSE10 moore={rm(0):.3f} wright_known={rm(1):.3f} wright_extrap={rm(2):.3f} "
          f"bias moore={r[:,0].mean():+.3f} wright={r[:,1].mean():+.3f} corr={r[:,3].mean():.4f} "
          f"implied_w_from_moore={-r[:,4].mean():.3f} wright_w={r[:,5].mean():.3f} SE_w_joint={r[:,6].mean():.3f}")

Errors are the root-mean-square difference between forecast and actual log cost at year 30. A value of 0.10 means a typical miss of about 11 percent; 0.58 means a typical miss of about 78 percent.

Four results stand out. First, with steady exponential growth the three forecasts are effectively identical (about 0.10). In the 20-year training window, the correlation between time and log cumulative production averaged 0.9999, and the Wright exponent implied by the fitted Moore rate (m/g) averaged 0.324 against a true 0.32. That is Sahal’s identity, reproduced.

Second, the laws diverge only when production growth changes. If demand plateaus and Wright’s law is true, a Moore forecast is too optimistic: actual cost ends up about 1.8 times the forecast. If demand surges, Moore is too pessimistic by a factor of about 2.2.

Third, the practical advantage of Wright vanishes when future production must be guessed. Extrapolating past output growth gave errors almost exactly as large as Moore’s in every divergent scenario. A Wright forecast is only as good as its production forecast.

Fourth, and most telling for the identification debate: when both regressors were fitted together on the 20-year window, the standard error of the Wright exponent averaged about 0.88, nearly three times the size of the true value of 0.32. The training data contain almost no information about which variable matters. The last row shows the mirror case. If the truth is Moore’s law and production stalls, a Wright forecast with perfect production knowledge misses by a factor of about 1.8.

What this does not show: it uses invented parameters, not the Nagy dataset, and its noise is independent year to year rather than the persistent random walk Farmer and Lafond found in real series. It says nothing about which law is true for any real technology. It shows only where the evidence would have to come from.

The author’s reading

This section is opinion. My reading is that the published record supports a narrow claim and is often used to support a broad one. The narrow claim, well established, is that both laws forecast historical costs about equally well and that Wright’s law holds a small edge. The broad claim, that buying more of a technology causes it to get cheaper at a measurable rate, is plausible, has good mechanistic support, and has not been cleanly demonstrated with the time-series data usually cited for it.

For practical forecasting with no change in demand growth expected, I would use Moore’s form with Farmer-Lafond style error bars; it requires one fewer guess. For policy questions, where the whole point is to change production, Wright’s law is the only one of the two that even attempts an answer, but its learning rate should carry a wide uncertainty band, as Nordhaus warned. Energy readers will recognize the stakes from our look at the math behind balcony solar and from large projects such as the PowerChina molten-salt plant in Qinghai: cost forecasts for those technologies lean heavily on learning rates.

What would settle it

The simulation points to the natural experiment that matters: a break in production growth that is not caused by a change in cost. Several kinds of evidence would qualify, and each yields a falsifiable prediction.

• Demand shocks from outside the market. A sudden mandate, war-time procurement, or a trade barrier that changes production without changing technology. Wright predicts the cost trend bends with output within a few years; Moore predicts it does not.
• The same product, two production histories. Identical technologies made by firms or countries whose cumulative output diverged. Wright predicts cost gaps that track the output gaps; Moore predicts converging costs, since time passes equally for both.
• Saturating markets. Products whose output has flattened. If Wright holds, the annual rate of cost decline should slow roughly in proportion to the slowdown in production growth (m = w·g).
• Pre-registered forecasts. Publishing Wright-based and Moore-based forecasts for energy technologies today, with production assumptions stated, and scoring them in a decade. The Way et al. framework is detailed enough to make this practical.
• Instrumental-variable estimates of learning rates. Using policy-driven deployment as an instrument would address the Nordhaus objection directly. A learning rate that survives such a test would be far more credible than one fitted to a smooth trend.

A specific prediction: if Wright’s law is causal with a 20 percent learning rate, a technology whose annual production growth falls from 30 percent to zero should see its annual cost decline shrink from roughly 9 percent toward a fraction of that within a decade. A technology that keeps falling at 9 percent a year despite flat output would count against Wright.

Common questions

Is Wright’s law the same as the learning curve or experience curve?

Mostly. Terminology varies, and some authors reserve “learning curve” for labor hours inside one plant, but the learning curve and the experience curve both use the power-law form linking cost to cumulative output. Forecasting papers generally treat them as one model.

If both laws predict equally well, why does the choice matter?

Because they answer different questions. For a forecast of cost in a given year under business as usual, either works. For a policy that changes how much gets built, only Wright’s law predicts any effect, so the assumed learning rate drives the estimated benefit.

Does Moore’s law in this debate mean transistor counts?

Not exactly. Researchers use the name for any quantity that improves exponentially with time, including cost per unit of a solar module or a chemical. Moore’s original chip observation is one example of the pattern.

Which law should I use for solar or battery prices?

For a plain forecast, either one with a realistic error band. The research reviewed here suggests the bigger risk lies not in picking the wrong law but in false precision. If your scenario assumes production growth will change sharply, Wright’s law is the relevant tool, and your production assumption becomes the main source of uncertainty.

References

1. Nagy, B., Farmer, J. D., Bui, Q. M., & Trancik, J. E. (2013). Statistical basis for predicting technological progress. PLOS ONE, 8(2), e52669. https://doi.org/10.1371/journal.pone.0052669
2. Farmer, J. D., & Lafond, F. (2016). How predictable is technological progress? Research Policy, 45(3), 647–665. https://doi.org/10.1016/j.respol.2015.11.001
3. Lafond, F., Bailey, A. G., Bakker, J. D., Rebois, D., Zadourian, R., McSharry, P., & Farmer, J. D. (2017). How well do experience curves predict technological progress? A method for making distributional forecasts. arXiv:1703.05979 (preprint); published in Technological Forecasting and Social Change, DOI 10.1016/j.techfore.2017.11.001. https://arxiv.org/abs/1703.05979
4. Way, R., Ives, M. C., Mealy, P., & Farmer, J. D. (2022). Empirically grounded technology forecasts and the energy transition. Joule. https://doi.org/10.1016/j.joule.2022.08.009
5. Trutnevyte, E., Zielonka, N., & Wen, X. (2022). Crystal ball to foresee energy technology progress? Joule, 6(9), 1969–1970. https://doi.org/10.1016/j.joule.2022.07.007
6. Nordhaus, W. D. (2014). The perils of the learning model for modeling endogenous technological change. The Energy Journal, 35(1). DOI 10.5547/01956574.35.1.1. Working paper version: NBER Working Paper 14638 (2009), https://www.nber.org/papers/w14638; abstract via RePEc/IDEAS.
7. Winton, B. (2019, January 2). Moore’s Law isn’t dead: It’s wrong – Long live Wright’s Law. ARK Invest. https://ark-invest.com/articles/analyst-research/wrights-law-2/
8. IEEE Spectrum. Wright’s law edges out Moore’s law in predicting technology development. https://spectrum.ieee.org/wrights-law-edges-out-moores-law-in-predicting-technology-development
9. Design News. Engineering fundamentals: Is Moore’s Law the Wright one? Battery tech hopes so. https://www.designnews.com/electronics/engineering-fundamentals-is-moore-s-law-the-wright-one-battery-tech-hopes-so