La Bourse / Volume V / Nº V.05 / Ten concept briefs

A woman reading on a daybed, the shadows of palm leaves falling across the wall behind her in late sun. — Plate V.05 · Ten concept briefsThe Twenty-Eighth Month.There is a month in every apprenticeship when the firm stops paying for the learning and starts being paid by it. In Switzerland it is month twenty-eight of thirty-six, and almost nobody — including the apprentice — knows the date.

TEN CONCEPT BRIEFS · Chapter V.05 — Skill, Mastery, and Time

One page each. A reader who reads only these ten pages has the chapter.

BRIEF 1 — Skill as a Capital Asset Nobody Capitalises

The idea. Skill has every property of a capital asset. It costs money to build, it raises output for years, it wears out at a measurable rate, and it can be lost. It has one unusual property: nobody puts it on a balance sheet.

The firm expenses training in the period it was incurred, so a three-year investment shows as three unrelated costs. The worker owns the asset and has no accounts. The tax authority allows the deduction and asks nothing further. The result is an asset class of enormous scale that is never scheduled, never depreciated on a measured rate, and never compared against the alternatives it was funded instead of.

Worked example. A Swiss firm spends CHF 28,070 a year on an apprentice and receives CHF 31,240 of productive output. Over three years that is CHF 84,210 of cost against CHF 93,720 of output — a net benefit of CHF 9,510 per apprentice. In the management accounts it appears as wage and supervision cost, and the output appears as ordinary production. No line anywhere says the firm made money by training somebody.

Why it matters. Anything unscheduled is invisible to capital allocation. Training does not lose the argument against a new machine; it never gets into the argument, because the machine arrives with a schedule and the training does not. Build the schedule and the argument becomes winnable.

You already know this because you have watched someone leave and heard the room say we have lost years there — which is an impairment charge, spoken aloud by people who would never have booked it.

BRIEF 2 — The Mincer Coefficient, and Why It Is a Rate of Return

The idea. Regress log earnings on years of schooling and the coefficient is the proportional wage gain per extra year. Psacharopoulos and Patrinos assembled 1,120 estimates across 139 countries: about nine per cent per year of schooling, stable over decades, higher for women and higher in low-income countries.

Worked example. Nine per cent on a €40,000 wage is €3,600 a year. Over forty years, discounted at five per cent real, the annuity factor is 17.159, giving a present value of €61,773 against one year of forgone earnings — a net present value of €21,773. Solve instead for the discount rate that sets cost equal to benefit and you get an internal rate of return of 8.68 per cent, which is 0.32 of a point below the coefficient itself.

  40,000  =  3,600 x (1 - (1+r)^-40) / r     ->     r = 8.68%

The catch worth carrying. That convergence holds because the career is long. For a six-week course with an eighteen-month useful life, a percentage gain in wages is not a rate of return and treating it as one will mislead you badly.

Why it matters. It is the one number that lets training be discussed in the same language as every other investment the firm makes — and the reason a finance director can be brought into the conversation at all.

You already know this because you have never once thought of your own education as an expense. You have always thought of it as a thing you have.

BRIEF 3 — Becker's Result, and Where It Breaks

The idea. Gary Becker (1964) drew a sharp line. Specific skills are useful only at this firm, so the firm will pay for them. General skills are useful anywhere, so a competitive market bids the trained worker away and no firm will pay — the worker must finance them by accepting low wages while learning.

It is a clean result and it is correct given its assumption: that the wage rises one-for-one with productivity.

The problem. Germany, Switzerland, Austria and Denmark all run large apprenticeship systems in which firms visibly pay for skills that are portable by design, certified nationally, and explicitly written to be recognised everywhere. That is not a small exception. It is the second-largest training system in Europe doing the opposite of the prediction.

Worked example. A German firm carries €3,596 a year of net cost per apprentice and roughly seventy per cent of German training firms do the same. None of that spending makes sense under strict Becker. All of it happens anyway, year after year, in firms with competent finance functions.

What survives. Becker's framework survives intact; only the competitive-market assumption fails. Relax it and everything observed falls out — which is Brief 4.

You already know this because you have paid for someone's certification knowing perfectly well the certificate was portable, and you did it because the alternative was worse.

BRIEF 4 — Wage Compression

The idea. Acemoglu and Pischke's resolution: firms pay for general training whenever the wage structure is compressed — whenever a worker who becomes twenty per cent more productive receives, say, ten per cent more pay. The untaken ten per cent is the firm's return on the training.

  firm trains iff   d(productivity)/d(skill)  >  d(wage)/d(skill)

Where compression comes from. Search frictions, so the worker cannot costlessly test the market. Collective agreements and wage floors. Efficiency wages. And above all asymmetric information: the training firm knows how good this particular person is and the outside market does not, so outside offers are priced at the average and the best trained workers are underbid.

Worked example. A German firm's three-year net investment is €10,788. At 53 per cent retention, recovering it over five years requires holding back €4,071 a year — about nine per cent of a skilled worker's pay. That nine per cent is the compression, quantified, and if the labour market ever prices these workers accurately it disappears and so does the training.

The uncomfortable corollary. Firm-financed general training is partly financed by workers being paid less than they are worth. That is a real distributional fact, not a slur, and it is the strongest argument for the alternative designs in Briefs 8 to 10.

You already know this because the person in your team everyone quietly relies on is almost certainly not the best paid, and everyone knows it including them.

BRIEF 5 — The Depreciation Rate of a Skill

The idea. Skills decay. The rate is called δ, and it is not one number.

  route                            delta       half-life   what it measures
  -------------------------------------------------------------------------
  Arrazola & de Hevia (2004)       1.35 %/yr    51.3 yr    general human capital
  Hanushek et al. (2017)           3.04 %/yr    22.8 yr    vocational advantage
  Deming & Noray (2020)           10.41 %/yr     6.7 yr    applied STEM skill

How the last is computed. The applied-STEM earnings premium is 44 per cent at age 24 and 14 per cent at age 35. So ln(0.44 / 0.14) / 11 = 0.1041. At that rate 64.7 per cent of the premium is gone within ten years — which matches the authors' own sentence, "declines by more than 50 per cent in the first decade."

How the middle one is computed. Men with general education are 6.9 percentage points less likely to be employed at entry than men with vocational education, and the gap closes by 2.1 points a decade. So it reaches zero at 16 + 6.9/0.21 = 48.9 — and the authors report the crossover at forty-nine.

Why it matters. A factor of eight between the slowest and the fastest means the same training design cannot be right for both. Everything downstream — the payback you can tolerate, the retention you need, the instrument you choose — is decided by which end of that range you are standing at.

You already know this because you can still ride a bicycle and you cannot remember a single thing about a software package you were expert in nine years ago.

BRIEF 6 — The Payback Month

The idea. For any training investment there is a month at which cumulative productive contribution overtakes cumulative cost. Call it P. It is a date, and a date can be compared to something.

Worked example — the Swiss three-year apprenticeship. Distribute the survey's CHF 93,720 of three-year output across the published productive-value shares of 0.26, 0.41 and 0.54, and hold cost at CHF 28,070 a year:

  year    output      cost        net     cumulative
  --------------------------------------------------
    1     20,138    28,070     -7,932        -7,932
    2     31,756    28,070     +3,686        -4,245
    3     41,825    28,070    +13,755        +9,510

The cumulative line crosses zero at month 27.7 of thirty-six. Let costs rise across the years instead and it crosses at month 26.2. Under either profile the firm is ahead before the apprentice is free to leave.

What P is for. It is compared to T, the expected months of retained tenure, measured from your own last three cohorts. P < T means train on your own book. P > T means either shorten P or pool.

Why it matters. It converts an argument about loyalty into a comparison of two numbers, and the two numbers are both things you can change.

You already know this because every lease, every loan and every machine you have bought came with a payback period, and you would not have signed one that did not.

BRIEF 7 — The Poaching Externality, Measured

The idea. A firm that trains and loses the worker has funded a competitor. This is a genuine externality and it is measurable rather than rhetorical.

The measurements. In Germany, slightly more than half of apprentices — 53 per cent — are still with the training firm a year after qualifying. In Switzerland it is about 35 per cent; more than sixty per cent leave within the first year. Swiss firms nonetheless train more willingly than almost anyone.

Worked example — when training is rational anyway. At a €4,000 annual rent over five years, the retention rate at which the German €10,788 investment breaks even is 10,788 / (4,000 x 5) = 53.9 per cent. Measured German retention is 53 per cent. The model clears by less than a point, and only because German institutions keep mobility low. Run the same firm at Swiss mobility and the required rent becomes €6,165 a year — 13.7 per cent of skilled pay, which no European wage structure delivers.

The condition under which training is rational for a single firm anyway. Either the payback lands inside the contract (Switzerland), or compression is strong enough and mobility low enough to support a post-training rent (Germany), or the cost is shared (Denmark). There is no fourth case.

Why it matters. "People leave" is true and is not an argument. It is an input, and it belongs on the same page as P.

You already know this because you have hired someone brilliant that another firm trained, and you did not feel you had stolen anything.

BRIEF 8 — The Levy-Grant Scheme

The idea. Tax every employer a fixed share of payroll, and refund it to those who train. Free-riders fund trainers by construction.

The real case. The UK Apprenticeship Levy, since April 2017: 0.5 per cent of the pay bill above £3 million, a £15,000 allowance, a ten per cent government top-up, funds held in a digital account and expiring after twenty-four months. A firm with a pay bill of eight million pounds pays £25,000 and holds £27,500.

The measured outcome, both halves. National starts fell from 494,900 in 2016/17 to 375,800 in 2017/18 — down 24.1 per cent. And the matched evaluation found training intensity rose at levy-payers relative to comparable non-payers, by 0.1 to 0.5 percentage points, with no displacement of other training. Both are true: the levy worked on the firms it touched, and three other reforms landed in the same year.

The unit cost. At 229 employees and a 0.5-point effect, £25,000 buys 1.14 additional starts — £21,875 per marginal start, and £109,375 at the low end. Most of the money funds training that was going to happen anyway.

Why it matters. A levy is a price, not a programme. Cost it per marginal start before adopting it, and expect the answer to be large.

You already know this because you have paid a mandatory insurance premium and then not claimed, and understood exactly why the scheme required you to pay.

BRIEF 9 — The Training Bond and Its Ceiling

The idea. Make the worker repay the training if they leave early. Every serious jurisdiction has capped it, and the caps are the interesting part.

Germany. Labour-court doctrine scales the permitted lock-in to the training: a month of training supports roughly six months bound, two months supports a year, three to four months supports two years, and repayment must taper month by month. Twenty-four months is the practical ceiling, so a €10,788 claim writes down €449.50 for each completed month.

And the case where it is removed entirely. §12(1) of the German Berufsbildungsgesetz voids any clause restricting an apprentice's occupational activity after training ends — the one exception being a commitment to employment agreed in the final six months. The largest training investment in this chapter cannot be bonded at all.

England. After Cavendish Square v Makdessi (2015) the question is whether the sum is proportionate to a legitimate interest. A figure not grounded in evidenced cost is a penalty and unenforceable.

United States. Training repayment agreements have drawn regulatory attention as employer-driven debt, and state restrictions on post-employment restraints narrow them further.

The rule. A bond big enough to matter is unenforceable; a bond the law will keep is too small to matter.

You already know this because you have signed something you did not read and assumed, correctly, that the unreasonable parts would not survive a court.

BRIEF 10 — Collective Provision

The idea. If the problem is that one firm cannot capture the return, let the group capture it. Everyone pays; only trainers are reimbursed.

The real case. Denmark's Employers' Reimbursement Fund, established 1977. Every employer, public and private, pays a flat per-head contribution — DKK 2,821 per full-time employee at the 2026 rate. A 200-person firm pays DKK 564,200 a year, about €75,600, whether it trains or not. Firms that host apprentices draw reimbursement for wages during school periods, and an annual quota carries a bonus for exceeding and a surcharge for missing.

The private version. A group training organisation — Lehrbetriebsverbund, Ausbildungsverbund, GTO — employs the apprentice and rotates them among member firms. Members pay a hosting fee per apprentice-month and a subscription per employee. It is the Danish design without the legislation, and it is available to any five firms that want it.

  subscription per member  =  aggregate shortfall (P - T months of cost)
                              ------------------------------------------
                                    total member headcount

Why it matters. It is the only one of the four instruments that works when mobility is high, compression is weak, and the payback cannot be shortened — the conditions most service and technology firms are actually in.

You already know this because you have been in a trade association, a mutual, or a shared apprenticeship arrangement and noticed it worked better than anyone expected.

All figures in these briefs are computed in lib/verify/V_05.py and sourced in the chapter's Works Cited. Run python3 lib/verify.py V.05 to see the inputs, the intermediate terms and the results.