Care as Infrastructure

Volume V — Labour, Value, Flourishing

THE PLATE

A woman in a linen robe standing by a window, looking out, morning light on the wall beside her. — Plate V.04The Hour Before the Shift.Every road in a country is on a balance sheet somewhere. The hour that gets the worker to the road is not.

THE LETTER

Here is a sentence that will survive any argument about economics: nothing in your firm's output would exist if somebody had not fed, washed, taught, nursed and calmed the people who produced it. That work happens. It happens at a scale we can measure, in hours we can count, and the value of it is not small — the International Labour Organization puts it at nine percent of world output, and that is the low estimate, priced at minimum wage.

You did not need convincing of this. The reason it belongs in a book about economics is not moral. It is structural. Care is the only piece of infrastructure a modern economy runs on that it neither depreciates, nor maintains, nor books. A bridge gets an inspection schedule. A turbine gets a maintenance reserve. The stock of human capacity that walks into work every Monday gets neither, because the accounts have no line for it — and a stock with no maintenance reserve is a stock that is being drawn down.

This chapter does four things. It gives you the real magnitudes, in hours and in money, from the statistical offices that actually publish them. It shows you the two accepted ways of valuing an unpaid hour and why they disagree by more than half. It runs the employment arithmetic of care investment against construction and manufacturing, using the input-output work rather than the slogan. And it computes, properly, the fiscal return on a childcare programme — including the tax recovery that makes several of them self-funding, and the one assumption that decides whether yours is.

It also tells you where this fails, because the strongest evidence for care investment comes from small, expensive, beautifully staffed pilots, and the record of taking those to scale is genuinely mixed. Anyone who hands you the Perry Preschool return without handing you the Tennessee follow-up is selling something.

You will finish with a costed instrument and a break-even number you can check.

— The Editors

DISCOVERY

What is already working

The first thing that is working is the measurement itself, and it is more advanced than most people in business realise.

The national statistical offices already keep the account. This is not a proposal. It is a published series.

The Office for National Statistics in the United Kingdom publishes a household satellite account. For 2016 it valued unpaid household service work at £1,240 billion, against a UK GDP of £1,968 billion — 63.0 percent of recorded output, produced entirely outside it. The largest single component was childcare, at £352 billion: 28.4 percent of the unpaid total and 17.9 percent of GDP on its own. Childcare, unpaid, is larger than most of the sectors that get their own trade association.

The Bureau of Economic Analysis in the United States has done the same exercise back to 1965. Household production would have added 39 percent to US GDP in 1965 and 26 percent in 2010. Read that fall correctly: it is not that less care happened. It is that a great deal of it moved across the production boundary as women entered paid work, so it began to be counted — and 13 percentage points of national output appeared without anybody making anything new.

The ILO did it globally. Sixteen point four billion hours a day of unpaid care work — the equivalent of 2.05 billion people working full time without pay, or 5.99 trillion hours a year. Valued at each country's hourly minimum wage, that is US$11 trillion, nine percent of world output. Check the implied figure: eleven trillion over nine percent implies a world economy of US$122.2 trillion on a purchasing-power basis, which is what the world economy was. The estimate is internally consistent, and it uses an implied hourly rate of US$1.84. It is a floor, not a valuation.

And the distribution is not ambiguous. Women perform 76.2 percent of those hours: 265 minutes a day against 83 minutes for men, a ratio of 3.19 to one. In a year that is 1,612 hours for women against 505 — a gap of 1,107 hours, which is 0.81 of a full working year, unpaid, every year, for half the species.

The second thing that is working is that some institutions have already put a price on it and acted. In England and Wales, Valuing Carers 2021 priced unpaid adult care at £162 billion a year against an NHS England budget of £164 billion — a ratio of 0.99. There is a second health service in that country and it is staffed by relatives. Once that number existed, carer's leave legislation and identification duties on health services followed, because a figure that size is difficult to leave in a footnote.

The third thing that is working is the employer-side case, proven repeatedly by firms that were not trying to prove anything. Patagonia has run on-site child care since 1983 and reports retention of new mothers close to universal; its own published analysis of the programme finds that tax credits, retention savings and productivity recover the large majority of the cost. Goldman Sachs and a long list of hospital systems run back-up care because the finance function worked out what a missed theatre list costs. None of these organisations adopted care provision as a values exercise. They adopted it because somebody costed absence.

And the fourth thing that is working — the one this chapter is built on — is that Quebec ran the experiment. In 1997 the province introduced a universal low-fee childcare programme. It has been studied for a quarter of a century by economists who disagree with each other, with clean identification, and it is the closest thing labour economics has to a controlled trial of care as infrastructure. It produced a large, real, replicated increase in maternal employment. It also produced a result on child outcomes that its own authors did not want. Both halves are below, and the second half is why the first is credible.

THE ARITHMETIC

What works, what does not, and where the line sits

First: two methods, one hour, and a wedge you can measure.

There are exactly two defensible ways to value an unpaid hour, and they answer different questions.

Replacement cost asks: what would it cost to buy this on the market? Price the hour at what a substitute earns. In the United States in May 2023 the median wage for home health and personal care aides was US$16.12 an hour; for childcare workers, US$14.60.

Opportunity cost asks: what did it cost to supply this? Price the hour at what the carer gave up. Median usual weekly earnings for women in full-time work in 2023 were US$1,005 over a 40-hour week — US$25.12 an hour.

  opportunity / replacement    25.12 / 16.12  =  1.559 x
  opportunity / childcare wage 25.12 / 14.60  =  1.721 x
  the gap, per hour                              US$9.00

The same hour is worth 56 percent more under one method than the other, and neither method is wrong. They are asking different questions, and the size of the wedge is not a measurement nuisance — it is the thing being measured. The wedge is large precisely because the market wage for care sits at the bottom of the wage distribution, and it sits there partly because so much of the work is done unpaid. The valuation problem and the wage problem are the same problem seen from two sides.

Apply the wedge to a real account. US GDP in 2010 was US$14.99 trillion; household production at 26 percent is US$3.9 trillion; at the aide's wage that is 242 billion hours, which across a population of 309.3 million is 2.14 hours a day per head — infants and the retired included, so the order of magnitude survives inspection. Re-price the identical hours at the opportunity wage and the same account reads 40.5 percent of GDP instead of

The method choice moves a national account by 14.5 points of GDP.

There is a price attached to that wedge and it is paid by named people. The measured net wage penalty for care work, after controls for skill, sector and hours, is on the order of five to ten percent. At 7.5 percent on a US$38,000 salary that is US$2,850 a year; discounted at 3 percent real over a 30-year career — an annuity factor of 19.600 — the present value of choosing care work is US$55,900 surrendered.

Second: the employment multiplier, done from the input-output work.

De Henau and colleagues modelled investing 2 percent of GDP in the care industry across seven OECD economies. In the United States, on a 2014 GDP of US$17.4 trillion — a spend of US$348 billion — that creates about 13 million jobs. The same money in construction creates about 7.5 million.

  care          13.0m / US$348 billion  =  37.36 jobs per US$1m
  construction   7.5m / US$348 billion  =  21.55 jobs per US$1m
  ratio                                       1.73 x

The later UK work puts the ratio at 2.7 times for jobs overall and 6.3 times for women's jobs; the Turkish study of early childhood education and care against construction puts it at 2.5 times. Different countries, different years, different models, same direction.

Now decompose it, because a ratio you cannot explain is a ratio you cannot defend. Direct jobs per million is labour share, times one minus import leakage, divided by average compensation:

  sector          labour share   import leak   compensation   jobs/US$1m
  ---------------------------------------------------------------------
  care                   0.75          0.02        38,000         19.34
  construction           0.45          0.10        68,000          5.96
  manufacturing          0.20          0.28        82,000          1.76

On the direct term care beats construction 3.25 to one and manufacturing 11.01 to one. But the published total multiplier is only 1.73. That difference is the honest part: construction pulls a long and largely domestic supply chain behind it, and care pulls almost none. Care wins enormously on the direct term and gives a large share of it back on the indirect term. Anyone quoting the direct ratio as the answer is quoting the wrong number, and the people who model this properly say so.

Third: does provision actually move labour supply? Two routes, and they agree.

The Quebec programme gives the credible identification: a policy change in one province, the rest of Canada as the control, difference-in-differences. Baker, Gruber and Milligan found childcare use up 14.6 percentage points and the labour force participation of married mothers up 7.7 percentage points — a relative increase of 14.5 percent, which implies a baseline of 53.1 percent and is therefore internally consistent with what Canadian married-mother participation actually was.

Now the second route, sharing none of the same assumptions. The reviewed literature puts the elasticity of maternal employment with respect to the price of care near −0.20. A programme that cuts the out-of-pocket fee by 60 percent therefore raises maternal employment by 12.0 percent; on a baseline employment rate of 65 percent that is 7.80 percentage points.

  meta-analysed elasticity   ->  7.80 pp
  Quebec difference-in-diff  ->  7.70 pp
  they differ by                 0.10 pp

A tenth of a point. Two instruments that share no assumptions landing on the same answer is the only reason either is worth quoting.

Fourth: the fiscal return, built from the inputs up.

Specify a quality place. Staff ratio 1:6, degree-qualified, loaded cost US$52,000 a year, staff at 65 percent of total cost. That is US$8,667 of staff per child and US$13,333 all in.

Now find the payers. The employer's own saving is real and verifiable: on a US$70,000 salary, with the replacement cost of an employee at 21.4 percent of salary, a 6-point fall in the annual separation rate among parents of under-fives is worth US$899, and two avoided absence days at a US$269 day rate is US$538 — US$1,437 a year, defensible on the firm's own P&L with no appeal to anything. Cap the parent's fee at US$400 a month, or US$4,800. The public residual is US$7,096.

Does the public get it back? Per place, independent of any behavioural effect, the care worker's own pay returns US$2,080 in tax and US$593 in consumption tax — US$2,673 of fixed recovery. Then each induced maternal entrant, earning US$38,000 at an effective wedge of 28 percent including both payroll sides, plus US$2,600 of reduced transfers, multiplied by a 2.5× persistence factor for years of labour-force attachment against years of care use, plus consumption tax on her net pay at a 90 percent propensity and a 10 percent effective rate, returns US$35,562.

  break-even jobs per place  =  (7,096 − 2,673) / 35,562  =  0.1244

One induced entrant per 8.0 places and the public share pays for itself.

jobs per place	recovery
0.050	62.7%	part-funded
0.078	76.8%	part-funded
0.100	87.8%	part-funded
0.1244	100.0%	break-even
0.150	112.8%	self-funding
0.200	137.9%	self-funding
0.350	213.1%	self-funding

The elasticity model gives 0.078. Quebec realised 0.350 — 70,000 additional women employed against roughly 200,000 subsidised places. The truth straddles the break-even, which is why honest people disagree about this.

So calibrate against the one measured case. Fortin, Godbout and St-Cerny found Quebec's programme cost C$1.6 billion in 2008 and recovered 104 percent of that to the Quebec treasury and 43 percent to the federal one — 147 percent combined. This model, at Quebec's jobs-per-place, gives 213.1 percent. It runs rich by a factor of 1.449. Apply the calibration factor of 0.690 to the conservative case and the honest answer is:

  recovery of the public share:  53% (conservative)  to  147% (Quebec, measured)

And here is the cut. Look again at where Fortin's money landed. C$1.66 billion to Quebec, which paid. C$0.69 billion to Ottawa, which paid nothing — 29.3 percent of the entire return, collected by a treasury that did not write the cheque. The programme is self-funding. It is not self-funding for the payer. Whether childcare "pays for itself" is therefore not a fact about childcare at all; it is a fact about which desk is asking, and no amount of further evidence will settle it, because the disagreement is not empirical. It is a question of whose ledger. The remedy is not another study. It is a revenue-sharing clause, and it is drafted in the last movement of this chapter.

Fifth, and this is the honest negative: quality does not survive scaling at the budgets usually offered.

The famous returns come from small programmes. Perry Preschool: 123 children, US$17,759 per child per year in 2006 dollars, which with CPI-U moving from 201.6 to 313.7 — a factor of 1.5561 — is US$27,600 today. Rate of return 7 to 10 percent a year. ABC/CARE: 111 children, 13.7 percent a year. Over thirty years, seven percent compounds to 7.61×, ten percent to 17.45×, and 13.7 percent to 47.08× — which is itself a warning, because a claim whose headline multiplies by six depending on a rate you chose is a claim about the rate.

Now the scaled programmes. Head Start's appropriation of US$11.996 billion across 833,000 children is US$14,400 each — about 1.92× less than Perry. Average state pre-K spending is US$6,600, which is 4.19× less. And the randomised Head Start Impact Study found cognitive impacts of roughly 0.1 to 0.2 standard deviations at the end of the programme year, not distinguishable from zero by the end of third grade.

Tennessee's voluntary pre-K programme was evaluated by lottery — the strongest design available at scale. Children gained at the end of pre-K. By sixth grade the treated group scored lower in maths, science and reading than the control group, with higher rates of disciplinary infraction and special-education placement. Not a fade-out. A reversal.

And Quebec, the same programme that produced the labour-supply result, produced increases in child anxiety and aggression; the long-run follow-up found worse self-reported health and life satisfaction and higher criminal activity in the exposed cohorts. Quebec expanded fastest through the least-regulated, lowest-cost places it could find.

The mechanism is not mysterious. It is in the staffing line:

  1:6  with a degree-qualified teacher at US$52,000   ->  US$8,667 per child
  1:10 with a credentialled aide at US$38,000         ->  US$3,800 per child
  1:12 at US$34,000                                   ->  US$2,833 per child

A factor of 3.06 in the one input that the research says carries the effect — and it is the first input a scaling budget cuts. The label survives scaling. The ratio does not. Care investment is not reliably good. High-quality care investment is reliably good, and quality is a cost line, not an intention.

Any proposal that does not name its ratio, its staff qualification and its turnover target is not a care proposal. It is a subsidy with a nursery attached.

DREAM

What becomes ordinary

In the economy that has absorbed this, the care account is simply part of the accounts, and nobody finds that unusual.

The national statistician publishes the household satellite account on the same morning as GDP, in the same release, with the same seriousness. Both numbers are on the front page and both are revised quarterly. When output falls and unpaid hours rise, that shows, and the two movements are read together instead of one being read alone. A country can see itself substituting.

Inside firms, the people function carries a care capacity line beside headcount. It reports how many of the firm's people are carrying a dependent, what the firm's exposure is in turnover terms, and what it has done about it — and it reports this because the finance function asked for it, not because anybody campaigned. The number that made it standing was the one from the turnover schedule: it turns out the most expensive thing a firm loses is a competent person in their thirties, and the most common reason is care.

Procurement asks about it. When a hospital tenders for a facilities contract, the tender asks the bidder what its staff turnover is among parents of under-fives, because turnover predicts service quality and the hospital has learned to price it. Bidders who provide care win work, so care provision spreads through the supply chain without any regulator writing a rule.

Childcare places are commissioned the way road capacity is commissioned: against a published quality specification with money at risk on it. A provider is paid an availability payment per place, deducted against ratio, qualification and staff turnover. Nobody argues about whether quality matters, because quality has a price and the price is in the contract.

And the work itself is paid like the infrastructure it is. The wage penalty is gone — not because anybody legislated affection, but because when the employment multiplier became a standard column in fiscal analysis, the sector stopped being treated as a cost to be minimised and started being treated as capacity to be built. Care workers have career ladders, credentials that transfer, and a recognised occupation with a wage curve.

None of this requires anyone to think differently about families. It requires four reports that do not currently exist and one contract form that does.

DESIGN

The structure that gets there

Layer one: the account. Get care into a measured series before you try to finance anything. Inside a firm this is three fields on the HR system — is this person a primary carer, for whom, and what is their separation rate against the firm's baseline. Inside a public body it is the household satellite account, which in most OECD countries already exists and is simply not read.

Publish both valuations, always, side by side. Never publish one. A replacement-cost figure alone invites the reply that it is priced at a poverty wage; an opportunity-cost figure alone invites the reply that it is priced at a wage the carer was not in fact earning. Published together, with the 1.559× wedge named, the account is honest and the objection is pre-empted.

Layer two: the quality specification, written before the money. Ratio, staff qualification, staff turnover, and a named observational measure of process quality. Put the ratio in the contract as a number, not as a standard that a later budget round can reinterpret. This is the layer that the evidence says decides the outcome, and it is the layer that is normally decided last, by whoever is left holding the shortfall.

Layer three: the three payers. Each pays only what its own ledger already justifies, so no payer is being asked for charity:

Payer	Per place	Basis
Parent	US$4,800	A fee cap, set as policy
Employer	US$1,437	Its own verified turnover and absence saving
Public	US$7,096	The residual, against the tax recovery
Total	US$13,333	The quality place

The employer's share is the interesting one, because it is the only share that requires no political decision and can be underwritten by a single firm this quarter. It is also self-limiting: an employer will fund exactly its own measured saving and not a cent more, which is precisely the discipline you want, because it makes the employer contribution unarguable.

Layer four: the revenue-sharing clause. Where the cost sits with one level of government and a measured share of the return accrues to another — 29.3 percent of the total return, in the one case anybody has measured properly — write the transfer into the agreement in advance, indexed to the measured induced employment, verified by the statistical office rather than by either party. Without this clause, the lower tier funds and the upper tier collects, and the lower tier learns not to do it again.

Layer five: the sequence. Account, then specification, then employer share, then public share, then the revenue-sharing clause. In that order, because each layer produces the evidence the next one needs, and because the employer share is the only one that can start without anybody's permission.

DESTINY

How it holds when nobody is pushing

Three things make a care programme permanent, and they are not the three things programmes usually invest in.

It holds when the quality metric has money on it. A ratio in a policy document is an aspiration. A ratio with 8 percent of the availability payment deducted against it — US$1,067 per place per year — is a fact, because the provider's finance director is now the ratio's most reliable defender. Quality survives a budget round only when cutting it costs more than keeping it.

It holds when the return is split where it is earned. The Quebec arithmetic is the whole lesson: a programme that recovers 147 percent to the public sector and 104 percent to the government that paid is stable. Move either number below one hundred and the programme becomes a recurring argument, and recurring arguments are eventually lost. This is why the revenue-sharing clause is a durability mechanism and not an accounting nicety.

It holds when the employer share exists. A programme funded entirely by the state has one counterparty and one election. A programme with an employer contribution has a constituency with a P&L reason to defend it, and that constituency does not change every four years.

Now the failure modes, stated plainly.

It fails when the places expand faster than the workforce. There is no way to staff a rapid expansion at ratio and qualification, so the ratio is what gives, and when the ratio gives the effect goes with it — that is the Quebec and Tennessee result in one sentence. Expansion should be rate-limited by the training pipeline, explicitly, in the contract.

It fails when the induced-employment figure is assumed rather than measured. The whole fiscal case turns on jobs per place and the break-even is 0.1244. Measure it from the second year, by linking take-up to employment records, and publish it whether it is good or not — because a number nobody publishes is a number the next government assumes.

It fails when the account is built only to make the case. An account built as advocacy will be read as advocacy. Publish the wedge, publish the method, publish the year the estimate weakens.

And it fails, most quietly, when the programme is evaluated on enrolment. Places filled is an input. Ratio, staff turnover, maternal employment and child outcome at age nine are the outputs, and only one of them is easy to collect.

DELIGHT

What it feels like

There is a specific relief in the second week, and people who have lived it describe it the same way: the morning stops being a negotiation. The hour before work becomes an hour, rather than a series of contingencies held together by a phone call to somebody's mother. You arrive at work having already worked, but not having already lost.

Then there is what it does to a room. In an organisation that has funded this, the conversation about a person's dependent stops being a confession. Nobody lowers their voice. The question "can you make four o'clock" gets a plain answer instead of a calculation about how the answer will be read, and a whole layer of small performances disappears from the week.

And there is the pleasure that belongs to the people doing the care work, which this literature almost never mentions. Care work is one of the few occupations where the output is visible daily, in a face. What the wage penalty takes is not the satisfaction — it is the ability to stay. Paying it properly does not add meaning to the work. It lets the people who already find it meaningful remain in it, which is the same thing as quality, arriving from the other direction.

OPERATIONALIZE THIS

At the level of finance

The instrument: a quality-linked availability payment for care places, funded by a three-party consortium, with an intergovernmental revenue-sharing clause.

This is not a grant and it is not a benefit. It is the structure a treasurer already recognises from availability-based social infrastructure: the operator builds and runs the capacity, the consortium pays per available place, and the payment is deducted when the specification is not met. The only novelty is what is being made available, and what is being deducted against.

The structure.

The asset. Places, not buildings. The unit is one available, compliant place for one year at US$13,333, and the contract defines compliance as ratio, staff qualification and staff turnover — the three inputs the evidence says carry the effect.
The payment. An availability payment per place, paid monthly in arrears, with 8 percent — US$1,067 per place — at risk against the quality specification. Deductions are formulaic and published. There is no discretion in them, because discretion is where quality standards go to die.
The payers. Parent US$4,800 by fee cap; employer US$1,437, being its own verified turnover and absence saving; public US$7,096 residual. Each pays against its own ledger.
The term. Ten years, with the quality specification fixed for the full term and the fee cap indexed. A five-year term will not clear the measurement horizon on child outcomes and therefore cannot renew on evidence.
The revenue-sharing clause. Where a higher tier of government collects a measured share of the return, that share transfers annually, indexed to induced employment as measured by the statistical office. In the one properly measured case that share was 29.3 percent of the total return.
Security. The availability stream, with step-in rights on quality failure rather than on payment failure — because in this asset class the thing that fails first is the ratio, not the cash.

The balance-sheet treatment. For the employer, an availability payment for places it does not control is a service contract and sits in operating expense — it is not a lease, because the employer directs neither the asset nor the staff. Say this to your auditor early and in those words. Where the employer does build and control an on-site facility, it is a lease and a right-of-use asset, and the depreciation schedule should be written against the facility's regenerated life. For the public payer, treat the programme the way road capacity is treated: a maintenance line on a productive asset, not a transfer payment. The reclassification from transfer to infrastructure is the single most valuable thing in this whole chapter, and it costs nothing but an argument with a classifier.

The counterparty. Start with an anchor consortium — one hospital, one university, one local authority — because they share a labour market, they all lose the same people for the same reason, and between them they can fill a setting without a demand forecast. Add a specialist operator with an existing qualified workforce. Add a social-infrastructure lender only at the point where you have two years of availability data, because by then you are refinancing a performing asset rather than funding a hope.

The first ninety days.

Day	Action	Artifact
1–15	Count carers and their separation rate against baseline	The care exposure line
16–30	Cost turnover and absence at the firm's own figures	The verified employer saving
31–45	Draft the quality specification: ratio, qualification, turnover	The specification
46–60	Assemble the consortium; agree the three shares	Heads of terms
61–75	Agree the measurement of induced employment, and who verifies	The measurement protocol
76–90	Sign the availability agreement with deductions formulaic	The agreement

The number that decides it. One figure, and it belongs on the front page of the paper:

                 induced jobs per place
   ----------------------------------------------------  >  0.1244
    (public share per place − fixed recovery per place)
                  ÷ recovery per induced job

Above 0.1244 the public share returns itself and the programme is infrastructure financed out of its own yield. Below it, the residual is the honest price of the thing the account was for — the children, and the hours, and the 1,107 hours a year somebody was working for nothing. Both of those are defensible positions. Only one of them is a finance paper, and you should know which one you are writing before you walk into the room.

APPRECIATIVE QUESTIONS

Twelve, for a room

Discovery — what is already working

Think of someone here who stayed through a period when they could easily have left, because something we did made it possible to keep working. What was it, and who arranged it?
Where in our own numbers is care already showing up — in turnover, in absence, in the roles we find hardest to fill — and who first noticed?
Which of our people carry a dependent and have never had to hide it here? What did we get right for them that we have not deliberately extended?

Dream — what becomes possible

If our reporting pack carried a care capacity line beside headcount, what would be on it, and what would we do differently the first month we saw it?
Imagine the tender we issue three years from now asks every bidder for their turnover among parents of under-fives. What changes in our supply chain?
If the hour before work stopped being a negotiation for everybody here, what would that be worth — first in what people could do, then in what it saves?

Design — what we build

What ratio and what qualification would we be willing to put money at risk against, and who would write the deduction formula?
Which three institutions in our labour market lose the same people for the same reason, and what could we commission together that none of us could commission alone?
What is the smallest verified saving on our own P&L that would justify a contribution this year, without anybody having to believe anything?

Destiny — how it holds

What would have to be true for the ratio to survive a bad budget year — and who would be the first to defend it?
Who collects the return on this that did not pay for it, and what would a fair sharing clause look like in writing?
What is the first sign we would see if quality were slipping, who would notice it first, and does that person currently have anywhere to say so?

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Note on figures. Every figure above is computed in lib/verify/V_04.py and printed with its inputs, its units and its source; run python3 lib/verify.py V.04. The fiscal model is the chapter's own construction from published parameters, calibrated against the one measured case by a factor of 0.690, and every rounding that appears in the prose is declared in the module's final block.