"Do Real-Output and Real-Wage Measures Capture Reality? The History of Lighting Suggests Not"

Filed under interpretation in canon/proposals.md; written here as idea, and the refiling is the first thing this entry has to defend.

The paper contains two separable things. One is a method: to price a service, measure the thing the buyer actually wants — lumen-hours, not lamps — and divide by the wage, so that the answer comes out in hours of work and no deflator is involved. The other is an interpretation: the claim that because the method finds a bias of three orders of magnitude in lighting, measured real-wage growth since 1800 understates the truth by a factor of three to fifteen.

The house test for idea, argued out in human-computers and applied there to de Prony's computing office, is that the thing is implementable, and built on rather than argued about. The method passes cleanly and has the citations to prove it: Fouquet and Pearson rebuilt the whole series for the United Kingdom back to 1300 on it, Nordhaus himself ran it again on computing power in 2007, and Tsao and Waide used it to explain three centuries of world lighting demand. The interpretation, by contrast, is the part that was argued about — Charles Hulten attacked it in the same volume, in print, on the facing pages — and it is the part that has held up least well. Filing this entry as interpretation would hang it on its weakest claim. Filing it as idea hangs it on the part three separate research programmes were built out of, and lets section 3 grade the interpretation honestly instead of having to defend it.

The citation occasion proposals.md attaches to the id points the same way. It says twice that what a reading needs is the fix: "measure the outcome in hours of work rather than the goods in currency." That is a procedure, not a reading of events.

On the year field. 1994 is the Cowles Foundation discussion-paper date (No. 1078). The paper was published in January 1996 as chapter 1 of The Economics of New Goods, Bresnahan and Gordon eds., NBER Studies in Income and Wealth vol. 58, pages 27–70 — and it is also cited in the literature as Nordhaus 1997, which is what Fouquet and Pearson call it. All three years refer to one document. The id's 1994 is the date the work was finished and is kept.

On descends_from. Empty, and not for lack of ancestors — for lack of ancestors in this canon. The real ones are the hedonic-price tradition (Griliches, Triplett, Rosen), Cole et al.'s 1986 quality-adjusted price index for computer processors, which Hulten names as the result Nordhaus generalised, and Adam Smith, whom Nordhaus quotes in his conclusion. None of them is a canon entry, and inventing an id for them would be worse than leaving the field empty. Two entries that already exist are siblings rather than ancestors, and a reading using this one will often want them: sen-capability-approach, which attacks the same target — a single money figure standing in for how people live — from the access side rather than the price side, and goodharts-law-1975, which is about what happens to a measure under pressure, where this is about a measure being quietly wrong with nobody pushing on it at all.

What it is

Nordhaus set out to test whether the official record of two centuries of economic growth is any good, and he picked lighting because lighting has a service characteristic that does not change. A lumen in 1800 is a lumen in 1992. Almost nothing else in the consumption basket has that property — a car is not a faster horse, a photocopier is not better carbon paper — so lighting is the rare case where "the same thing" can be priced across two hundred years without argument about what the same thing means.

The construction has three steps and they are all simple:

1. Measure the efficiency of each lighting technology in lumen-hours per thousand Btu, or lumens per watt. 2. Divide the price of the fuel by that efficiency to get the price of the service — cents per thousand lumen-hours — rather than the price of the good. 3. Divide that by the wage to get the price in hours of work.

Step 1 is the labour of the paper, and where the data ran out Nordhaus made it himself. The appendix records that he burned 21 pounds of firewood in a standard home fireplace, measured the result with a Minolta TL-1 illuminance meter, got 3.4 hours of light at 2.1 foot-candles, and derived 0.69 lumen-hours per thousand Btu for an open fire. For the Babylonian case he bought a Roman terra-cotta lamp from a dealer in Minneapolis, fuelled it with "100 percent Hunza pure cold-pressed sesame oil" and a wick pulled out of a modern candle, and burned a quarter cup for 17 hours to get 17.5 lumen-hours per thousand Btu. The rest comes from documents — most importantly Benjamin Silliman Jr.'s 1855 photometric tests of town gas, sperm oil, camphene and rock oil, done as a consultancy for the Pennsylvania oilmen and suppressed on commercial grounds until 1870, which Nordhaus calls "probably the best single source of data on both prices and efficiency available before this century."

The numbers the entry exists to carry

Efficiency, in lumens per watt (his table 1.3): open wood fire 0.00235; Neolithic animal-fat lamp 0.0151; Babylonian sesame-oil lamp, 1750 B.C., 0.0597; tallow candle, 1800, 0.0757; town gas with a Welsbach mantle, 1916, 0.8685; Edison's carbon filament, 1883, 2.6; tungsten filament, 1920, 11.8; first-generation compact fluorescent bulb, 1992, 68.2778. From the Babylonian lamp to the compact fluorescent is a factor of about twelve hundred. From the 1800 candle to the 1992 bulb is a factor of about nine hundred, which Nordhaus converts to 3.6 percent per year — against 0.04 percent per year from Babylon to 1800, and 0.01 percent per year from the Palaeolithic to Babylon.

Price, in hours of work per thousand lumen-hours (his tables 1.4 and 1.6):

| era | hours of work per 1,000 lumen-hours | |---|---| | open fire, from earliest time | 58 | | Neolithic lamp | 50 | | Babylonian sesame-oil lamp, 1750 B.C. | 41.5 | | tallow candle, 1800 | 5.387 | | town gas, Welsbach mantle, 1916 | 0.012 | | filament lamp, 1950 | 0.00188 | | compact fluorescent, 1992 | 0.00012 |

That last figure is about four-tenths of a second of work. The fall from 1800 is a factor of roughly forty-five thousand (my arithmetic: 5.387 ÷ 0.00012), and from Babylon a factor of about 346,000, which is the source of his line that "an hour's work today will buy about 350,000 times as much illumination as could be bought in early Babylonia." His most vivid version: a hundred-watt bulb burning three hours a night produces 1.5 million lumen-hours a year; getting that much light in 1800 meant burning seventeen thousand candles, and "the average worker would have had to toil almost one thousand hours to earn the dollars to buy the candles." In 1992, twenty-two kilowatt-hours, "about ten minutes' work."

Then the comparison that gives the paper its point. Nordhaus assembled the price index a statistical agency would actually have produced — patched from Warren and Pearson's wholesale "fuel and light" series, Hoover's nineteenth-century consumer prices, the BLS wholesale index, and the CPI for gas and electricity — and set it against the true price. Deflated, the true price of light fell to 0.029 on a 1800 = 100 base. The two traditional indexes fell to roughly a quarter of the overall CPI over the same period. The ratio of traditional to true is 910 on his better series and 1,632 on the other. The abstract's summary: traditional indexes "overstate price growth, and therefore understate output growth, by a factor between 900 and 1,600 since the beginning of the nineteenth century."

The mechanism is not exotic and this matters for transferring it. Traditional indexes went wrong in three ways, only one of which is the famous one: wrong weights (minor); failure to track efficiency, so that a Btu of gas in 1850 and a Btu of electricity in 1950 are treated as delivering the same service; and late linking of new goods, so that a technology enters the index only after its introductory price collapse is over. Nordhaus's own worked example: from 1883 to 1993 the fuel prices moved by a factor of 10 up (kerosene) and 3 down (electricity), while the true price of electric light fell by 75 — and an index built on the wrong fuel weights overstates by a factor of 750 all on its own.

The claim he then built on top, which is a different claim

Section 1.6 is a Gedankenexperiment, and Nordhaus labels it as one. He sorted 1991 US consumption into three bins: run-of-the-mill sectors where quality change is small (home-cooked food, cotton shirts, haircuts, furniture, printed matter) at 27.7 percent; seismically active sectors, recognisable since 1800 but transformed (housing, watches, financial services, education) at 35.8 percent; and tectonic shifts, where "the entire nature of the production process has changed radically" (appliances, medical care, utilities including lighting, transportation, electronics) at 36.6 percent. He then assumed the bias in each bin was some fraction of lighting's 3.6 percent per year, and recomputed real wages.

Measured real wages grew by a factor of 13 between 1800 and 1992. On his low-bias assumption, 40. On his high-bias assumption, 190. This is the sentence the paper is usually cited for, and it is the sentence section 3 has to grade.

Why a reading would cite it

The token is the lamp. The completed task is the light. The occasion is already in this project's record. The 2026-08-19 midday reading carried Artificial Analysis's measurement of GLM-5.3: the API price per million tokens was unchanged from the previous version, $1.40 in and $4.40 out, while the measured cost of completing their index rose from about $0.44 to about $0.68 a task, because the newer model is more verbose. A price index built on tokens says the price of AI held flat. A price index built on the service says it rose by half. Those are the traditional and the true index of light, a hundred and seventy years later, in the same table — and the reading's own comment, "flat token prices are not flat workload prices," is Nordhaus's thesis restated without knowing it. This entry is what lets a later reading say that in one clause with a citation instead of rediscovering it.

When a price collapse is offered as evidence of abundance. Epoch AI's measurement — that the price to reach a fixed benchmark score has fallen between 9x and 900x per year over three years, 40x per year for GPT-4-level performance on PhD-level science questions — is the correct shape of measurement, and it is the shape Nordhaus invented. Citing him here does two jobs at once: it says the instrument is the right one, and it says what the instrument does not show. It does not show what share of income goes to the service, who has it, or whether the collapse in unit price was consumed rather than banked. On lighting, all three of those went the way that complicates the story, and the entry carries those findings (section 3) rather than only the happy number.

When a price of zero is read as a price. The 2026-08-20 midnight reading recorded three of the largest consumer platforms moving an assistant to free or to the desktop on one afternoon. Nordhaus's construction is a frontier index — the cost of the best available technology, and, as he says plainly, "this obviously would not apply to the backwoods farmer." A frontier price of zero is a statement about the frontier. It is not a measurement of what is being paid, and the paper is unusually clear about which question its number answers.

And for the project's own instrument. METHODOLOGY.md §2 records the decision that the abundance pole is to be measured in real terms via hours of median work, "ideally with no price index at all," and names this paper as the precedent. That makes the entry load-bearing twice: a reading may cite it about the world, and the project's own measurement stands on it. Which is exactly why the grading below matters more here than it would for an entry the project only quotes.

Where this entry does not reach. It is not evidence that today's statistics are understating AI. That is a specific empirical claim about a specific period, it has been tested by people who wanted to believe it, and section 3 records that it failed the test. Anyone reaching for Nordhaus to explain away a disappointing productivity number is using the entry against its own record.

What it got right, and what it got wrong

Not a prediction, so there is no due date to grade against — but the paper made dated, checkable claims and later work checked them. Graded, claim by claim.

Claim: lighting efficiency rose by a factor of about nine hundred between 1800 and 1992, at 3.6 percent a year. Made 1994. Held, and understated by the passage of time. The compact fluorescent he used as the endpoint at 68 lumens per watt was superseded within twenty years by white LEDs; the US Department of Energy's programme documents cool-white LED packages moving from roughly 25 to over 160 lumens per watt, and commercial high-efficacy parts are quoted above 200. The 1994 endpoint is now about a third of the frontier. Nothing about the method broke; the series simply kept going.

Claim: traditional price indexes overstate the price of light by a factor between 900 and 1,600 since 1800. Held, and independently replicated on different data in a different country. Fouquet and Pearson rebuilt the series for the United Kingdom from 1300, explicitly "building on Nordhaus's pioneering approach," and found that by 2000, with UK GDP per capita at 15 times its 1800 value, "lighting services cost less than one three thousandth of their 1800 value." That is the same order of magnitude reached from British parish, college and hospital accounts rather than American ones. A replication that far from the original data is the strongest evidence in this entry.

Claim: real wages since 1800 grew by a factor of 40 to 190, not 13. Not held. This is the part to be careful with, and Nordhaus half-said so himself — he called the estimates "highly speculative" in the paper. Charles Hulten, whose comment is printed immediately after the chapter in the same volume, ran the arithmetic backwards: deflate 1991 US personal income per capita of about $17,200 by Nordhaus's low-bias factor and 1800 income comes out at $430; by the high-bias factor, $90. Hulten's verdict: "It is hard to imagine anyone wanting to live in modern America with an income of $90; it is only just imaginable that anyone would want to live with an income at the upper end of the Nordhaus range." Taken literally the high case says the average American colonial was poorer than the average resident of the poorest country in the world today, which is not what the physical and demographic record says.

Some arithmetic of my own, to size the disagreement rather than leave it rhetorical. Nordhaus's low case implies an annual bias of about 0.59 percent in the deflator over 1800–1992; his high case about 1.40 percent. The Boskin Commission, reporting two years after this paper with Robert Gordon — co-editor of the volume it appeared in — among its five members, put total CPI bias at 1.1 percentage points a year, of which quality change and new goods contributed about 0.6. So Nordhaus's low case is roughly the number the profession converged on for the quality-and-new-goods channel he was studying, and his high case exceeds the entire estimated bias from all four sources combined. The low case is inside the consensus. The high case never got in, and the paper is nonetheless usually cited at the high end.

Claim: "it is possible that by the very nature of their construction, price indexes miss the most important technological revolutions in economic history." Held as a proposition about method, and it changed practice. When Nordhaus wrote, only two hedonic adjustments were used routinely in the entire US price statistics apparatus — computers and housing. The Boskin report and the work around it moved BLS practice substantially. The general point is now orthodoxy.

But the specific modern application of it failed its test, and this is the grading that matters most for an AI reading. From about 2010 the mismeasurement argument was widely used to explain away the post-2004 productivity slowdown: the gains are real, the statistics just cannot see them. Byrne, Fernald and Reinsdorf tested it in 2016 and found the opposite of what the story needs — mismeasurement of IT was substantial before the slowdown and, if anything, larger in the fast-growth 1995–2004 period than after, so it cannot explain a change that begins in 2004. Chad Syverson piled on in 2017 with four independent challenges: the slowdown hit dozens of countries with no relationship to their ICT intensity; every published estimate of digital consumer surplus falls far short of the $2.7 trillion of missing output; the implied ICT-sector growth rates would have to be multiples of the measured ones; and the gap between gross domestic income and product predates the slowdown and shows up as capital income, not labour income. A method can be right about the eighteenth century and still not rescue the twenty-first. Nordhaus's instrument is sound; the inference "and therefore today's numbers are wrong in my favour" has been checked and did not survive.

What the method showed that its enthusiasts rarely quote. Two findings from the work built on it point the other way from abundance. Fouquet and Pearson found that UK per-capita light use rose 6,500-fold and total consumption 25,000-fold between 1800 and 2000 — the price collapse was spent, not banked, which is the rebound effect in its cleanest historical form. And Tsao and colleagues found that the price and income elasticities of demand for light are both close to one, with the consequence that "over the past three centuries, and even now, the world spends about 0.72% of its GDP on light" — the same share in Britain in 1700, in the modern off-grid world, and in the developed world using the best technology available. Measured in hours per lumen-hour, light became effectively free. Measured as a share of income, nothing whatsoever happened. Both are correct. A project intending to draw an abundance pole from hours-of-work prices needs to have decided, in advance, which of those two facts it is claiming.

Commonly misused as

Not required for idea, but this entry earns the section, because the method has a house style of misuse and the project is about to adopt the method.

Misused as: a general-purpose proof that everything is getting better. The paper has been adopted as the technical backbone of a genre — "time prices," most prominently in Marian Tupy and Gale Pooley's Superabundance (2022) and the Human Progress site, where the light series is extended to LEDs and reported as a time-price drop of 99.99932 percent since 1830. The arithmetic in that genre is usually right and the selection is the problem: the method is applied to goods whose service characteristic is invariant and cheap to produce, which is the class Nordhaus deliberately chose because it is tractable, not because it is representative. He was explicit that lighting sits in the extreme "tectonic" bin, that about 28 percent of consumption is run-of-the-mill where he assumed little or no bias, and that food — the fixed star of every long-run index — is the case where the goods really are superficially the same. Housing, healthcare and education are the ones where the hours price has moved the wrong way, and a basket assembled only from the tractable cases is a rigged basket.

Misused as: a licence to disbelieve any statistic that disagrees with you. The paper is an argument that a particular class of error is large and identifiable, produced by doing hundreds of hours of measurement to replace the bad number with a better one. It is not an argument that official series are unreliable in general, and the section 3 record — Byrne/Fernald/Reinsdorf, Syverson — is what happens when the suspicion is stated as a hypothesis and tested rather than deployed. The honest use is: build the better series. The dishonest use is: the real number is whatever I need it to be, and Nordhaus proved it.

Misused as: proof that measuring the characteristic always beats measuring the good. Hulten's comment, printed in the volume and rarely quoted alongside the paper, makes the case that a characteristics index can overstate welfare. His argument is satiation and complementarity: if the marginal value of the tenth doubling of a characteristic is far below the first because the rest of the package is fixed, an index tracking the characteristic linearly will book a threefold gain where the real gain is 60 percent. His two examples are "maximum available horsepower" for cars and "million instructions per second" for computers, and he names lumens as a third. He adds a second failure mode: if the new bulb is four times as efficient and four times as expensive, a characteristics index built on energy saving alone records an improvement that did not occur. Both objections transfer to AI without modification. Tokens per dollar is a MIPS number. Benchmark score per dollar is a MIPS number. Nordhaus avoided the first objection only because lumens really are what people want from lamps, and avoided the second only by excluding capital costs — which brings us to the last one.

Misused as: a complete price. Nordhaus states three restrictions on his own number and they are usually dropped in transmission. It is a frontier price — the best available technology, not what anyone was actually paying. It counts only the marginal fuel cost: "Other costs, including capital, risk, labor, and environmental costs, are omitted primarily because of lack of data." And it tracks one of six service characteristics he lists for light, setting aside wavelength, reliability, convenience, safety and durability. The capital exclusion is the sharpest one for the 1992 endpoint: at a candle, fuel was substantially the whole cost, but a first-generation compact fluorescent bulb was an expensive object, and pricing it at its electricity alone flatters the last data point in the series by an amount the paper does not quantify. A reading using an hours-price of AI needs to say whether it is pricing the frontier or the median, the marginal call or the subscription and the hardware, and one characteristic or all of them. Nordhaus said which he was doing. The genre built on him mostly does not.

Sources

Read directly, as rendered page images.

• **William D. Nordhaus, "Do Real-Output and Real-Wage Measures Capture Reality? The History of Lighting Suggests Not," ch. 1 of The Economics of New Goods, Bresnahan and Gordon eds., NBER Studies in Income and Wealth vol. 58, University of Chicago Press, January 1996, pp. 27–70 — the NBER PDF at nber.org/system/files/chapters/c6064/c6064.pdf, read as page images, the whole chapter including the appendix, references and Hulten's comment**. Source for everything attributed to the paper above: tables 1.1 through 1.9, the efficiency and labour-price figures, the 900–1,600 ratio, the 3.6 percent annual bias, the 1883–1993 factor-of-750 example, the three-bin Gedankenexperiment and the 13 / 40 / 190 real-wage factors, the "backwoods farmer" and omitted-costs caveats, the six service characteristics, the thousand-hours-of-candles passage, and the appendix account of the firewood and sesame-oil measurements with the Minolta TL-1 meter. Also the source for the Hulten comment quoted in sections 3 and 4 — the $17,200 / $1,300 / $430 / $90 reductio, the horsepower-and-MIPS satiation argument, and the four-times-efficient-four-times-costlier case.
• **J. Y. Tsao, H. D. Saunders, J. R. Creighton, M. E. Coltrin and J. A. Simmons, "Solid-state lighting: an energy-economics perspective," J. Phys. D: Appl. Phys. 43 (2010) 354001** — the copy at web.mit.edu/2.813/www/readings, read as page images, pages 1–3. Source for the 0.72 percent of world GDP figure and its constancy across the UK in 1700, the modern off-grid world and the modern developed world, and for the proportionality of light consumption to GDP ÷ cost of light.
• **Roger Fouquet and Peter J. G. Pearson, "Seven Centuries of Energy Services: The Price and Use of Light in the United Kingdom (1300–2000)," The Energy Journal 27(1) (2006): 139–177** — the copy at csbg.ca, read as page images, pages 139–141. Source for the verbatim abstract figures (GDP per capita 15×, lighting services below one three-thousandth, per-capita use 6,500×, total consumption 25,000×), for their explicit statement that they build on "Nordhaus's pioneering approach," and for their own warning about "rebound and saturation effects." I did not read the eleven-section body, so nothing here is attributed to their technology-by-technology series.

Established by search against primaries, without reading the full document. For each of these I can vouch for the fact and the citation and not for having read the source end to end.

• Cowles Foundation Discussion Paper No. 1078 (1994), via the RePEc record at ideas.repec.org/p/cwl/cwldpp/1078.html — source for the discussion-paper year and for the abstract's "factor between 900 and 1,600" wording, which matches the published chapter.
• David M. Byrne, John G. Fernald and Marshall B. Reinsdorf, "Does the United States Have a Productivity Slowdown or a Measurement Problem?", Brookings Papers on Economic Activity, Spring 2016 — the finding that mismeasurement of IT was substantial before the slowdown and cannot explain a break beginning in 2004.
• **Chad Syverson, "Challenges to Mismeasurement Explanations for the US Productivity Slowdown," Journal of Economic Perspectives 31(2) (2017): 165–186** — the four challenges, including the international evidence, the $2.7 trillion shortfall, and the capital-income timing point.
• **Advisory Commission to Study the Consumer Price Index (Boskin Commission), Toward a More Accurate Measure of the Cost of Living, 4 December 1996** — the 1.1 percentage point total bias and the roughly 0.6 point quality-and-new- goods component, and Robert Gordon's membership.
• **William D. Nordhaus, "Two Centuries of Productivity Growth in Computing," Journal of Economic History 67(1) (March 2007): 128–159** — the same method applied to computation, with performance-based improvement of between 1.7 and 76 trillion-fold since manual computing and price declines "markedly larger than those reported in the official statistics."
• Epoch AI, "LLM inference prices have fallen rapidly but unequally across tasks," epoch.ai/data-insights/llm-inference-price-trends — 9x to 900x per year depending on benchmark and score, 40x per year for GPT-4-level GPQA Diamond performance, across six benchmarks over three years, with their own caveat that "the fastest price drops in that range have occurred in the past year, so it's less clear that those will persist."
• US Department of Energy solid-state lighting programme documents — cool-white LED package efficacy rising from roughly 25 to above 160 lumens per watt. Used only to establish that the series continued past Nordhaus's 1992 endpoint.

Attributed, not endorsed.

• **Marian L. Tupy and Gale L. Pooley, Superabundance (2022), and the Human Progress "time prices" series**, including the 99.99932 percent time-price drop since 1830 and the 228 lumens-per-watt LED comparison. These are cited in section 4 as the example of the method's characteristic misuse. The organisation publishes with an explicit thesis, the arithmetic is theirs and I did not check it, and the figures appear here as a description of the genre rather than as findings this entry stands behind.

What I could not verify, and left out.

• The exact month of Cowles Discussion Paper 1078. RePEc gives the year only.
• Whether anyone has published a full extension of the true-price-of-light series through the LED era in a peer-reviewed venue. The LED efficacy numbers are solid; a continuous post-1992 hours-price series from a source of Fouquet and Pearson's standard is something I looked for and did not find, which is worth knowing if this project intends to build one.
• Nordhaus's own later view of the Gedankenexperiment's high case. He returned to the measurement questions repeatedly, including in "Are We Approaching an Economic Singularity?" (NBER 2015; AEJ: Macroeconomics 2021), where he tested for runaway growth in the data and did not find it — but I did not read that paper here and am not attributing a retraction to him.

On the boundary. This entry names sen-capability-approach, goodharts-law-1975 and human-computers, all of which exist in canon/, and creates no ids. It places no needle, deposits nothing in history/, and refers to the 2026-08-19 and 2026-08-20 readings by date only. Nothing here is evidence.