Haute Lumière
Commerce · V.11 · MMXXVI · daylight
TEN CONCEPT BRIEFS · Chapter V.11 — When Flourishing and Output Diverge
One page each. A reader who reads only these ten pages has the chapter.
BRIEF 1 — The Easterlin Paradox, Stated Precisely
The idea. Richard Easterlin (1974) put three findings side by side rather than choosing one, and the tension between them is the paradox.
- Within a country, at one moment: richer people report higher happiness. The gradient is steep and it has never been in serious dispute.
- Across countries: the relationship looked weaker than that gradient predicted.
- Over time, within a country: average reported happiness in the United States had not risen with income.
The paradox is that (1) and (3) cannot both be simple. If income buys happiness for a person, why does fifty years of it not buy any for a nation?
What he actually claims now. Easterlin, McVey, Switek, Sawangfa and Zweig (2010) took it to 37 countries — seventeen developed, nine developing, eleven transition — and reported that over the long term, meaning ten years and more, the relation between growth in happiness and growth in income is nil.
The figure. Note the window. Ten years and more is the claim. Hold that number; Brief 5 is entirely about it.
What it is not. It is not a claim that income does not matter to people. It is not an argument against growth. Easterlin has never said either, and a reader who has been told he did has been told wrong.
You already know this because you have had a year in which your circumstances improved measurably and you did not feel a great deal different by December — and you have also known, with total clarity, that you would rather have the better circumstances than not.
BRIEF 2 — The Stevenson–Wolfers Reply, and What It Actually Claims
The idea. In 2008 Betsey Stevenson and Justin Wolfers brought a far wider income range — the Gallup World Poll spans roughly $840 to $127,000 a head, about 150 to one — and found a clean relationship between subjective well-being and income with three properties.
- It is log-linear: well-being rises with the logarithm of income.
- It shows no satiation point. They went back in 2013 specifically to look for one at the top of the distribution and did not find it.
- The within-country and between-country slopes are similar, which is the finding that dissolves Easterlin's second point.
What they did not claim. They did not claim Easterlin's numbers were wrong. They claimed that a different functional form, read across a much wider range, gives a different reading of the same underlying relation.
Why that matters enormously. A dispute about functional form is settled by computing. It is one of the very few arguments in economics where both sides can be handed the same spreadsheet and the disagreement will resolve into a number they both accept. Brief 3 is that number.
You already know this because you have seen two people look at the same chart and disagree, and discovered the disagreement was about whether the axis should be linear or logarithmic — at which point it stopped being an argument about the world and became an arithmetic question.
BRIEF 3 — Log Income, and Why Functional Form Is the Whole Dispute
The idea. If well-being is linear in the logarithm of income, then a constant absolute gain in well-being requires a constant proportional gain in income. That single sentence generates everything else in this chapter.
The computation. Twenty-four countries, Cantril ladder 0–10 against the natural log of GDP per head at purchasing power parity:
ladder = -3.34 + 0.92 · ln(GDP per capita)
R² = 0.86Eighty-six percent of the variance in national average well-being, across a hundred-and-fiftyfold income range, from one line. Every row and every term is printed in lib/verify/V_11.py.
And the specification that follows. Hold health, social support and freedom constant, as the World Happiness Report's own model does, and the coefficient falls to about 0.35 — a factor of 2.6. That is not a refutation. It says most of what income buys, it buys by buying those three things, which is the most actionable sentence in the brief.
The residuals worth knowing. Costa Rica sits 0.60 points above the line, Finland 0.99 above, Singapore 0.92 below, the United States 0.15 below. The line explains most of the variance and the residuals are where the interesting countries live.
You already know this because you understand that a pay rise of £5,000 is transformative on £20,000 and barely noticed on £200,000, and that is exactly what "linear in the log" means.
BRIEF 4 — The Price of One Ladder Point
The idea. A slope in logs is not a rate of gain. It is a price, and the price is proportional. Read it that way and the number becomes usable.
The arithmetic. From b = 0.92 ladder points per natural log unit:
gain per doubling of income b · ln 2 = 0.64 ladder points
income multiple for one point exp(1 / b) = 2.9 xAt the controlled slope of 0.35: 0.24 points per doubling, and 17 times income for one point.
In the unit an economy actually spends — time:
| Real growth | Years to buy one ladder point out of ten |
|---|---|
| 1 %/yr | 109 (287 at the controlled slope) |
| 2 %/yr | 55 (144) |
| 3 %/yr | 37 (97) |
Read it both ways, because both readings are honest. Income buys well-being, reliably, with no ceiling — true. One point of ten costs fifty-five years of two-percent growth — also true, same coefficient.
Why it matters. The most common way to be wrong about this literature is to treat a strong correlation as a fast one. A relationship can be tight, clean, unbounded and extremely slow, all at once.
You already know this because compound interest is the same shape: a rate that is undeniably real and undeniably slow, and the argument about whether it is "a lot" is always really an argument about the horizon.
BRIEF 5 — The Observation Window
The idea. This is where the paradox dissolves, and it dissolves into arithmetic rather than into a winner.
Run the Stevenson–Wolfers slope forward inside Easterlin's window. Two percent real growth, which is a good century for a rich country:
| Window | Income | Predicted ladder gain | Share of the scale |
|---|---|---|---|
| 10 years | ×1.22 | 0.18 pts | 1.8 % |
| 20 years | ×1.49 | 0.37 pts | 3.7 % |
| 30 years | ×1.81 | 0.55 pts | 5.5 % |
| 50 years | ×2.69 | 0.92 pts | 9.2 % |
Easterlin's long run starts at ten years. The log-linear relation said to refute him predicts, over his own window, a gain of under two percent of the scale. He looked, correctly, and found approximately nothing — which is approximately what the other camp's model says is there.
The United States, his own series. Real GDP per head went from about $27,000 in 1972 to about $62,000 in 2022 — 2.30×, or 1.20 doublings. Predicted gain: 0.77 ladder points on the bivariate slope, 0.29 on the controlled one.
Why it matters. Neither camp is careless. They are measuring the same coefficient over different windows and disagreeing about whether fifty-five years is a long time — which is a question about institutions and patience, not about data.
You already know this because you have watched a child grow and seen nothing day to day and everything in a photograph from three years ago. Same rate, two windows, two honest reports.
BRIEF 6 — Resolution, and Why Running the Survey Again Settles Nothing
The idea. An effect can be real, statistically detectable, and still undecidable — because the thing that limits you is not sampling error.
The arithmetic. The controlled-slope prediction for the US over fifty years is 0.29 ladder points. On the General Social Survey's three-point happiness item that is 0.058 of a scale point — 2.9 percent of that scale's whole range.
Against sampling error alone it is visible:
n = 1,500 · sd = 0.65
standard error of the mean = 0.65 / √1,500 = 0.0168
t = 0.058 / 0.0168 = 3.5And that is the trap. t = 3.5 says sampling error is not the binding constraint. What is binding is everything not in that standard error: fifty years of changes in question order, survey mode, response rate, and who answers the telephone. Any one of those can move a mean by three percent of a scale.
The consequence, which is the useful part. Running the survey again does not settle it. More respondents shrink the wrong error term. What would settle it is a design change — a fixed anchoring vignette, a behavioural measure that cannot drift, a mode-held panel — and that is a research programme somebody could actually fund.
You already know this because you have weighed yourself on two scales and got different answers, and understood immediately that weighing yourself more times on either one would not help.
BRIEF 7 — Stock, Flow, and Which One Leads
The idea. The operating rule of the chapter, and it is short enough to carry.
Output is a flow. Flourishing measures the condition of the stock the flow is drawn from. A flow can always be raised for a period by drawing the stock down, and no flow measure can tell you whether that is what happened.
It is S = D / (R · r) from Volume I, arriving through the payroll rather than the fixed asset register.
The two diagnoses.
- Output up, flourishing down → output is the suspect. You are probably looking at a withdrawal reported as income. Test it against overtime, deferred maintenance, unfilled vacancies, postponed training, a rise in hours worked. The stock measure is your leading indicator and the flow expires, typically inside four to six quarters.
- Flourishing up, output down → flourishing is the suspect, unless you can name the stock being rebuilt. That clause is the whole brief. A genuine rebuild is nameable and measurable: training delivered, vacancies filled, maintenance backlog falling, leave debt paid down.
Worked. A unit beats plan by 6 percent while voluntary turnover rises 3 points and overtime rises 18 percent. That is not a good quarter with a people problem attached. It is one quarter of next year's capacity, sold forward.
You already know this because you have had a productive fortnight on four hours' sleep a night and know exactly what the following fortnight cost.
BRIEF 8 — The Three Conditions Under Which Flourishing Is the Artefact
The idea. Flourishing measures fail in three specific, recognisable ways. Knowing them is what lets you trust the measure the rest of the time.
1. Self-reported and not anonymous. A survey whose results reach a line manager measures the relationship with the line manager. Fix: third-party administration, published response rate, and treat a rising score with a falling response rate as a falling score.
2. No anchor, and running long enough to adapt. Hedonic adaptation is real: Brickman, Coates and Janoff-Bulman (1978) found lottery winners and people with severe spinal injury converging far closer to baseline than anyone expected. A pure self-report series drifts toward its own mean regardless of conditions. Fix: pair it with a behavioural measure — turnover, absence, internal applications — that cannot adapt.
3. In somebody's bonus, with no denominator. Any measure that pays somebody and states no denominator will improve. Fix: publish what the measure did not look at, in the same table.
And the honest limit on adaptation, because the adaptation literature has its own honest negative. Lucas, Clark, Georgellis and Diener (2004) followed people through unemployment in a fifteen-year panel and found life satisfaction did not return to baseline even after re-employment. Set-point theory is wrong in the one case where being wrong matters most. Never use adaptation as a reason to discount a fall.
You already know this because you have filled in a survey knowing who would read it, and you have noticed how much of the answer that knowledge wrote.
BRIEF 9 — The Divergence Trigger, and Why It Must Be Gated
The idea. A rule that fires on the sign of a disagreement is worthless. The arithmetic proving it is one line long and it is the most practical number in the chapter.
Two series that are doing nothing at all.
P(they move in opposite directions in one period) = 0.50
P(that happens two periods running) 0.5² = 0.25 = 25 %A quarter of all periods, on pure noise. Everybody learns to ignore the alarm and the mechanism is dead inside a year.
Now add a materiality gate: both moves must clear one standard deviation of their own trailing series.
one-tailed normal, |move| > 1 sd 1 − Φ(1) = 0.1587
P(opposite AND both material) 2 × 0.1587² = 0.0503
P(that twice running) 0.0503² = 0.00253 = 0.25 %Roughly once in four hundred, and the false-trigger rate improves by about ninety-nine times — for one sentence of drafting.
The policy choice, stated. One standard deviation is a choice; 1.5 or 2 are equally defensible and will fire less. What is not defensible is a trigger on sign alone, and now you have the number to say so with.
You already know this because you have muted a notification that went off too often, and the thing it was warning you about did not stop being real.
BRIEF 10 — Permanent Divergence, and Who Bears It
The idea. Some divergences are not measurement problems and not design problems. They are real, they are permanent, and somebody carries the cost. A volume about flourishing that ends without naming that somebody has not finished.
Three, with the arithmetic.
Shift work. A plant can run 168 hours a week; a day shift runs 40 — a 4.2× multiple on capital utilisation, unobtainable without somebody awake at four in the morning. The IARC classifies shift work involving circadian disruption as probably carcinogenic, Group 2A (2007, reaffirmed 2019). Who bears it: the night-shift worker, in health, for a premium generally around a tenth to a fifth of base pay — a price nobody has established is right.
Unpaid care. The ILO (2018) counted 16.4 billion hours of unpaid care work a day — 2.05 billion full-time equivalents at an eight-hour day — worth about 9 percent of global GDP, some $11 trillion at 2011 PPP. Women do 76.2 percent: 12.5 billion hours a day, 1.56 billion full-time equivalents. Who bears it is that last number, and it appears in no set of national accounts.
Commuting. Stutzer and Frey (2008) found long commutes are not compensated by wages or rents; an hour each way needs about 40 percent more income to leave a person as well off. On a £45,000 salary that is £18,000 a year against 460 commuting hours — £39 an hour that nobody pays. Who bears it: the commuter, uncompensated, which is what makes it a paradox rather than a trade.
And one that went the right way, invisibly. US annual hours per worker fell from about 3,100 in 1870 to about 1,760 in 2019 — 43 percent given up. At today's hourly productivity and 1870's hours, output per worker would be 1.76× what it is. That is not lost output. It is flourishing already bought and paid for, and GDP records none of it.
You already know this because you have never once thought of a Saturday as foregone GDP, and you are right not to.
All figures in these briefs are computed in lib/verify/V_11.py, which prints its inputs and its intermediate terms, and labels every figure that is reported by a named source rather than derived.