La Bourse / Volume V / Nº V.05 / Workbook — the student

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

WORKBOOK — THE STUDENT

Chapter V.05 · Skill, Mastery, and Time

For the person learning something hard, in a term or in a life. This workbook treats your own skill as the capital asset it is: acquired at a cost, yielding a return, depreciating at a rate you can estimate and slow. The arithmetic is the same arithmetic a Swiss firm runs on an apprentice. You are simply on the other side of the bench, and you own the asset.

WHY THIS WORKBOOK IS DIFFERENT

Most study advice is about effort. This one is about schedule — where in time your learning pays, and what that implies about what you do next.

Three numbers carry it.

The return. About nine per cent a year in earnings per year of schooling, across 1,120 estimates in 139 countries. That is the headline number of the entire economics of education, and it is stable across decades.
The depreciation rate, δ. Between 1.35 and 10.41 per cent a year depending on what the skill is. Half-lives of fifty-one years and of six and a half years, from the same literature.
The payback month, P. The month at which what you produce overtakes what you cost. A Swiss apprentice reaches it at month 27.7 of thirty-six, and almost never knows.

You are going to compute all three for yourself this term.

PART ONE — DISCOVERY

Weeks 1–4: find the asset you already hold

Exercise 1.1 — The inventory (90 minutes)

List every skill you can currently perform at a standard somebody would pay for. Not what you have studied — what you can do. Aim for twelve to twenty lines, including things that feel too ordinary to write down. Driving. Reading a balance sheet. Calming a distressed person. Writing a sentence that lands.

Beside each one, write three things:

How you got it. Course, job, family, accident, obsession.
Who paid. You, an employer, the state, nobody.
How long since you last used it seriously.

The third column is the one that will surprise you.

Exercise 1.2 — Estimate your own δ (two hours)

For your three most valuable skills, place each on this scale and say why.

  delta        half-life    the kind of skill
  ---------------------------------------------------------------
   1.35 %/yr    51.3 yr     general capability — judgement, writing,
                            numeracy, the ability to learn a thing
   3.04 %/yr    22.8 yr     occupational skill — a trade, a craft,
                            a professional practice with a standard
  10.41 %/yr     6.7 yr     tool- and technology-specific skill —
                            a platform, a framework, a stack

The test that decides it: would somebody who stopped five years ago still be useful today? If yes, you are near the top of the scale. If they would need three months to catch up, you are near the bottom.

Now compute. For each skill, what proportion is left after five years without practice?

  remaining  =  exp(-delta x years)

  at 1.35%:  exp(-0.0675) = 0.935    93.5% left
  at 3.04%:  exp(-0.1520) = 0.859    85.9% left
  at 10.41%: exp(-0.5205) = 0.594    59.4% left

Write the number down. Most people's portfolio is a mix, and the mix is the finding: a fast-depreciating skill paying well today and a slow-depreciating one paying nothing yet is a completely different position from the reverse.

Exercise 1.3 — Ask three people (one week)

Ask three people who are ten to twenty years ahead of you, in fields you respect: what did you know at my stage that is now worthless, and what did you know that is worth more than ever? Take notes on the second answer. It is almost always more general than the first.

PART TWO — THE ARITHMETIC

Weeks 5–8: price the thing you are doing

Exercise 2.1 — Your own Mincer calculation (90 minutes)

Take the course, degree or training you are currently in.

  1. annual earnings you are forgoing            ________
  2. direct cost per year (fees, materials)      ________
  3. years of the programme                      ________
  4. expected proportional wage gain             ________
  5. years of working life remaining             ________

Then:

  total cost        =  (1 + 2) x 3
  annual gain       =  4 x your expected post-programme wage
  annuity factor    =  (1 - (1 + r)^-n) / r      with r = 0.05
  present value     =  annual gain x annuity factor
  net present value =  present value - total cost

Worked, from the chapter: nine per cent on €40,000 is €3,600 a year; over forty years at five per cent the annuity factor is 17.159, so the present value is €61,773 against €40,000 of forgone earnings — a net present value of €21,773 and an internal rate of return of 8.68 per cent.

Then do the honest version. Redo it with your δ from Exercise 1.2 applied to the gain:

  present value with decay  =  annual gain x sum over t of exp(-delta t) / (1 + r)^t

At δ = 1.35 per cent the answer barely moves. At δ = 10.41 per cent it collapses. That collapse is the single most useful thing this workbook will show you, and it does not mean do not study. It means: if you are studying a fast-depreciating skill, the value has to arrive early, so the question becomes how soon can I be doing this for real.

Exercise 2.2 — Your payback month (two hours)

If you have any placement, internship, apprenticeship or paid work attached to your study, compute your own P.

  month   what you cost the       what you produced      cumulative
          organisation (pay +     (your honest estimate,
          supervision time)       at what they'd pay
                                  someone to do it)

Estimate supervision honestly: an hour of a senior person's time is expensive. Swiss apprentices reach a productivity of 40 per cent of a qualified worker in year one and 80 per cent by year three — use those as anchors if you have nothing better.

The question is not whether you are ahead. In the first year you will not be. The question is which month you cross, and whether anything you could change would move it earlier. Usually something can: more real work sooner, on a narrower slice, with a clearer standard.

PART THREE — DREAM AND DESIGN

Weeks 9–14: build the schedule

Exercise 3.1 — The two-track portfolio (one afternoon)

Every durable career in a changing field is two portfolios held at once.

The fast track. The tool, the platform, the current method. High return now, δ near ten per cent, half-life under seven years. It gets you hired.
The slow track. Judgement, writing, the mathematics under the tool, the ability to learn the next one. δ near one per cent. It keeps you employed at fifty.

Deming and Noray's finding is the reason this is not a platitude: the applied STEM premium is 44 per cent at twenty-four and 14 per cent at thirty-five, and 64.7 per cent of it is gone within a decade. The people who do best are not the ones who avoided the fast track. They are the ones who were on both.

Write down, in one line each: what is your fast track this year, and what is the slow-track investment you are making alongside it that will not pay for a decade.

If the second line is empty, that is the finding, and filling it is the term project.

Exercise 3.2 — Move your own payback earlier (one week)

Three levers, in order of how much they move P.

Do the real thing sooner, on a smaller slice. The single largest driver of the Swiss payback is that apprentices spend roughly four days a week in the firm, most of that on productive work, from the beginning.
Narrow the standard. It is far easier to reach 80 per cent of a professional's productivity on one defined task than 30 per cent across ten.
Make the output visible. A contribution nobody can see is not counted, and uncounted contribution does not move anybody's P — including yours.

Pick one and apply it this month. Write down what you changed and what happened.

Exercise 3.3 — The compression conversation (45 minutes)

Read Brief 4 again. You are going to spend part of your working life on the short side of wage compression — paid less than you produce, because the outside market cannot see what you can do while your employer can.

This is not a grievance; it is how firm-financed training gets paid for, and you will be a beneficiary of it before you are a victim of it. What it means practically:

Portable proof compresses the gap. A certification, a public piece of work, a reference from someone outside the firm — each makes your productivity legible to the market and moves your pay toward it.
The gap is largest just after training and narrows with visible tenure. That is the moment to be deliberate rather than aggrieved.

Write down one piece of portable proof you could produce this term, and the date.

PART FOUR — DESTINY AND DELIGHT

Weeks 15–20: make it hold

Exercise 4.1 — The maintenance schedule (one hour)

Depreciation is continuous and maintenance is not. Build a schedule.

  skill              delta     hours of deliberate maintenance per quarter
  ---------------------------------------------------------------------
  fast track        ~10%/yr    a real project, not reading — 20-40 hrs
  occupational       ~3%/yr    one hard case per month
  general            ~1%/yr    continuous; it maintains itself through use

Put the fast-track maintenance in a calendar. Everything else will happen by itself; that one will not.

Exercise 4.2 — Notice the month (ongoing)

Somewhere in any serious apprenticeship there is a week when you stop checking and simply know. It arrives in the middle of something ordinary and the person teaching you usually sees it first.

Write the date down when it happens. Not for anyone else. It is the only moment in this entire arithmetic that belongs to you rather than to a ledger, and it is worth being able to find again.

THE TERM PROJECT

One piece of work, carried the whole way

Build your own skill balance sheet, and defend it.

A single document, six to ten pages, containing:

The inventory from Exercise 1.1, with δ estimated and justified for each line.
The valuation. Your Mincer calculation with and without decay, showing the internal rate of return both ways.
Your payback month, computed, with the assumptions named — including the ones you are least sure of.
The two-track portfolio, with this year's fast-track investment and the slow-track investment named and dated.
The maintenance schedule.
One honest negative. Name the skill in your inventory you are quietly over-valuing, and say what the evidence for its depreciation actually is.

Then present it to one person who will argue with you — a supervisor, a tutor, a mentor, someone in the field ten years ahead. The presentation is the assessment, because a balance sheet nobody has challenged is a wish list with column headings.

SELF-ASSESSMENT

Rate yourself honestly, once at the start of the term and once at the end.

	Start	End
I can name my three most valuable skills without hesitating
I can estimate δ for each of them and say why
I know, roughly, what my current programme returns and over what horizon
I have computed a payback month for at least one real placement
I have a slow-track investment running that will not pay for a decade
I have produced one piece of portable proof this term
I have a maintenance schedule for my fastest-depreciating skill
I can explain wage compression to someone who has never heard of it

Six or more at the end, and the arithmetic has become a habit rather than an exercise.

CARRYING IT FORWARD

Three things to keep after the term.

Re-run the inventory once a year, on a fixed date. Depreciation is invisible month to month and obvious year to year. A date in the calendar is the only instrument that catches it.

Never confuse a wage gain with a rate of return again. Over a forty-year career the Mincer coefficient and the internal rate of return differ by a third of a point. Over eighteen months they have nothing to do with each other, and most course marketing relies on you not knowing the difference.

Remember which sentence is true. Not skills change too fast to invest in. The true one is: rapid obsolescence destroys long paybacks, not training. It tells you to get to the real work sooner, not to stop.

THE ONE HONEST NEGATIVE, FOR YOU

The chapter's uncomfortable finding is about people who did exactly what they were told to do. Across eleven countries, men with a vocational education are 6.9 percentage points more likely to be employed at the start of their working lives than men with a general education — and that advantage is exhausted by age forty-nine and inverted by eleven and a half points by sixty-five. In the German data the turn comes at forty-three.

Read it precisely, because it is easy to read it wrongly. It is not an argument for a general degree over a trade. The early advantage is real, it is large, and it arrives at the moment in life when being employed matters most. It is an argument that a training that ends at twenty-two is a training with a known expiry, and that the expiry is roughly twenty-five years out.

What it asks of you is one decision, taken early and cheaply: keep a slow-depreciating track running the whole time. Not instead of the fast one — alongside it. The mathematics under the tool. The writing. The diagnosis. The ability to sit with a problem you have not seen before. Those carry a δ near one per cent a year, they cost very little to maintain because they maintain themselves through use, and they are what is still there at fifty.

The people this finding catches are not the ones who chose the trade. They are the ones who chose the trade and then stopped.

APPRECIATIVE QUESTIONS FOR YOUR SEMINAR

When has someone here learned something fastest? What were the conditions, and could they be arranged deliberately?
What is the most durable skill anyone in this room has, and how did they get it?
If everyone here knew their payback month, what would change about how we spend the first year of anything?
Who in this room is teaching someone else right now, and what has that taught them?