La Bourse / Volume V / Nº V.05 / Quiz, reflection, essays

A woman reading on a daybed, the shadows of palm leaves falling across the wall behind her in late sun. — Plate V.05 · Quiz, reflection, essaysThe 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.

ASSESSMENT · Chapter V.05 — Skill, Mastery, and Time

Three instruments: a ten-point quiz, eight reflection questions, five essay prompts. The quiz checks comprehension rather than recall. The reflections are private and first-person. The essays are arguable from more than one side.

THE QUIZ — ten points

Four on recall.

1. State Becker's distinction between general and specific skills, and what he predicted about who pays for each.

Specific skills raise productivity only at the current firm, so the firm will finance them. General skills are portable, so in a competitive market the trained worker can be bid away and the firm will not finance them — the worker pays, by accepting lower wages while training. One mark for the distinction, one for identifying the load-bearing assumption: that the wage rises one-for-one with productivity.

2. What is wage compression, and name three things that produce it.

A wage structure in which pay rises less than one-for-one with productivity, so the firm retains part of the gain from any skill it builds. Sources include search frictions, collective agreements and wage floors, efficiency wages, and — the strongest — asymmetric information, where the training firm knows how good the worker is and the outside market does not.

3. Give the three depreciation estimates in the chapter with their sources, and say what each one measures.

Arrazola and de Hevia (2004), 1.35 per cent a year, general human capital from earnings profiles. Hanushek and colleagues (2017), 3.04 per cent a year, the vocational employment advantage over the life-cycle. Deming and Noray (2020), 10.41 per cent a year, the applied-STEM earnings premium. Full marks require the point that these are not competing estimates of one quantity — they are measurements of different skills.

4. What are P and T, and what decision do they make?

P is the number of months until cumulative productive contribution overtakes cumulative cost. T is expected retained tenure in months, measured rather than assumed. Train on your own book when P is less than T; pool or shorten P when it is not.

Four on application.

5. A colleague says: "Our field moves too fast for training to pay." Take the claim seriously and then answer it.

The claim is a real observation about δ, and it should be granted: in fast fields δ is near ten per cent a year, so a skill has a half-life under seven years and no design recovering its cost over eight years of retention will work. What the claim does not license is stopping. Rapid obsolescence invalidates long paybacks, not training. The correct response is to shorten P — to move the productive contribution earlier in the programme — or to pool the cost. Credit any answer that separates the two sentences.

6. A Swiss firm and a German firm both train a three-year apprentice. The German firm is puzzled that the Swiss firm is relaxed about losing people. Explain.

The Swiss firm's payback lands at month 27.7 of a thirty-six-month contract, so it recovers its investment while the apprentice is still contractually present. Retention is not a variable in its case. The German firm carries net costs through the whole apprenticeship and recovers them only afterwards, from people who stay, so retention is the entire case. Same activity, different position of the payback in time.

7. Your firm wants to bond a €30,000 training programme with a five-year repayment clause. What happens, and what should be done instead?

It is very likely unenforceable. German doctrine scales the lock-in to the length of training, with roughly two years the practical ceiling, tapering monthly; English courts after Cavendish Square v Makdessi ask whether the sum is proportionate to a legitimate interest and strike figures not grounded in evidenced cost; US regulators treat aggressive versions as employer-driven debt. Instead: shorten the payback by restructuring what the trainee does in the first year, or share the cost through a consortium. Credit any answer naming the general rule — a bond big enough to matter is unenforceable.

8. Why does the Danish fund charge firms that do not train?

Because the externality is the whole problem. A firm that hires trained people without training anyone captures the benefit and pays none of the cost. A flat per-head contribution paid by everyone, with reimbursement only to trainers, prices the externality instead of appealing to it. The free-rider and the trainer pay the same; only the trainer is paid back.

Two that require the arithmetic to be done.

9. A three-year apprenticeship produces CHF 93,720 of total output, distributed across the years in the ratio 0.26 : 0.41 : 0.54, against a flat cost of CHF 28,070 a year. In which month does the firm turn net-positive? Show your working.

The shares sum to 1.21. Year one output is 93,720 × 0.26/1.21 = 20,138; year two 93,720 × 0.41/1.21 = 31,756; year three 93,720 × 0.54/1.21 = 41,825. Net by year: −7,932, +3,686, +13,755. Cumulative: −7,932, −4,245, +9,510. The crossing falls inside year three at 4,245 / 13,755 = 0.309 of the year, which is 3.7 months in — month 27.7 of thirty-six. Credit any method landing in the twenty-sixth to twenty-eighth month. The point of the question is that the answer is a date, and it falls before the apprentice is free to leave.

10. A firm carries €3,596 a year of net cost for three years. It retains 53 per cent of its apprentices and can hold back €4,000 a year against a retained worker's productivity. Over five years, does it recover? What retention rate would it need?

Investment is 3,596 × 3 = 10,788. Expected recovery is 0.53 × 4,000 × 5 = 10,600, which is €188 short. Break-even retention is 10,788 / (4,000 × 5) = 53.9 per cent. The stronger answer states the conclusion in the right register: the German model is not comfortably profitable, it is solvent by under a point of retention, and it is solvent only because German institutions hold mobility down. At Swiss mobility of 35 per cent the required rent rises to €6,165 a year, or 13.7 per cent of skilled pay, and the model fails.

REFLECTION — eight questions, for one person and a pen

These are not for a room. Write the answers by hand if you can; the slowness is the point.

What is the most valuable thing you know how to do that nobody taught you deliberately? Who was in the room while you learned it, and did they know what they were doing?

Estimate the depreciation rate of your own most marketable skill. Be honest about which end of the range it sits at, and then ask what you have been doing about it.

Think of a month when you stopped checking whether you were doing it right and simply knew. What was happening around you that week? Could you have arranged it deliberately for somebody else?

Who has invested in you without a contract that guaranteed them anything? What did it cost them, and have you ever said so to them?

Where are you currently being paid less than you are worth because the outside market cannot see what you can do? What would it take to make it visible — and is making it visible what you actually want?

What have you stopped being able to do that you were once excellent at? Sit with that for a moment before deciding whether it was a loss.

If you knew the payback month of every hour someone spends teaching you, would you work differently in the first year of anything? Answer honestly rather than admirably.

Who are you currently teaching, whether or not it is in anyone's job description? What would change if you treated that as the most productive thing you do?

ESSAY PROMPTS — five

Each is arguable from more than one side. Each requires at least one source the chapter cites and at least one it does not.

1. Who should pay for general skills? Acemoglu and Pischke show that firms finance portable training when the wage structure is compressed — which means, in part, that workers finance it by being paid less than they produce. Argue either that this is an efficient solution to a genuine market failure, or that it is a transfer from workers dressed as employer generosity and should be replaced by public or collective funding. Use Acemoglu and Pischke directly, and one source on wage-setting institutions or monopsony that the chapter does not cite.

2. The life-cycle trade-off. Hanushek and colleagues find that the vocational employment advantage of 6.9 points at entry is exhausted by age forty-nine and inverted by eleven and a half points by sixty-five. Argue either that this is a decisive case against early occupational specialisation, or that it is an artefact of systems that train the eighteen-year-old and abandon the forty-five-year-old, and is therefore a solvable design fault. Engage the paper directly, and one source on adult retraining or active labour-market policy that the chapter does not cite.

3. Is the Swiss model exportable? The chapter computes a Swiss payback at month 27.7 and shows the German model failing at Swiss mobility. Argue whether the Swiss design can be transplanted to a country without national training ordinances and strong employer associations — or whether the payback month is itself a product of institutions that cannot be copied quickly. Use Muehlemann and Wolter, and one evaluation of an apprenticeship transplant (the United States, England, India or Italy) that the chapter does not cite.

4. Did the levy work? National apprenticeship starts fell 24.1 per cent in the year the UK levy took effect, and the matched evaluation found training intensity rose at levy payers. Take a position on whether the Apprenticeship Levy should be judged a success, being explicit about which counterfactual you are using and why. Use Patrignani and colleagues, and one source on the concurrent reforms — standards, the twelve-month minimum, the twenty per cent off-the-job rule — that the chapter does not cite.

5. The measure that changes the thing. This chapter proposes putting a payback month on every training investment and telling the trainee what it is. Argue the counter-case: that scheduling a human being's productive contribution by month converts an apprenticeship into a production quota, degrades the teaching relationship, and pushes firms toward training that pays back fast rather than training that matters. Use the chapter's Swiss cost-benefit material, and one source on measurement effects, Goodhart's law or the quantification of care work that it does not cite.