1Demonstration 1 of 4
Heads rise and capability does not
If the target rises, which rule changes what the people can do?
The target rule closes the headcount gap under every rule, so heads end close together. Capability reads the experience stock, which a shorter ramp fills faster.
Headcount is thousand persons on payroll. Effective capability is thousand effective persons, where a new hire counts as 0.4 of a seasoned one and the rest is made up over a ramp. The step is the target raised above its trend at month 0.
Predict first. Which of the four rules ends month 24 with the most capability per head?
Choose an example
Constructed example on the committed public record: the model is fitted to it, the rules are the chapter's constructed rules, and the five percent step is a constructed variant.
Calculated values
- Rule
- Baseline
- Target step
- 10 percent
- Headcount, month 24 (thousand)
- 159,721
- Effective capability, month 24 (thousand)
- 129,864
- Capability per head
- 0.813
- Hires over 24 months (thousand)
- 154,441
- Capability above baseline (thousand)
- 0
- Record, no push: employment, January 2017 (thousand)
- 145,628
Capability per head = 129,864 / 159,721 = 0.813. Against the baseline under the same step, capability differs by 129,864 - 129,864 = 0 thousand, while headcount differs by 159,721 - 159,721 = 0 thousand. A hiring target acts on the first stock and the rules differ mostly in the second. Capability is a construct of the model, inferred from a fit to a national aggregate, and the record has no column for it.
Use the idea
Put a capability column beside the headcount column before choosing a hiring rule.
Where the conclusion applies
Fitted knobs are inferred from the record. The initial capability of 0.4 and the other rule settings are assumed. The conclusion fails if early leavers carry less than the average.
Check your understanding: If capability is 130,000 and headcount is 160,000, what is capability per head?
Chapter 37 source: section "A headcount target buys heads and not capability". Demonstration C37-D01.
2Demonstration 2 of 4
Two surveys, one identity
Do hires less separations match the change in employment?
In the model headcount has exactly the hire, quit and layoff flows, so the identity holds to floating point. In the record two samples count different things, so a small gap remains.
Hires and separations are thousand persons a month from JOLTS. Employment is thousand persons from CES. The gap is cumulative net hires minus the employment change.
Predict first. Over 2015 to 2019, is the gap between the two surveys under one percent of the change?
Choose an example
Constructed example on the committed public record: the window ends are constructed choices on the committed data.
Calculated values
- Window
- January 2015 to December 2019
- Hires less separations (thousand)
- 11,253
- Employment change (thousand)
- 11,226
- Gap (thousand)
- 27
- Gap share of the change (percent)
- 0.24
- Model identity residual (thousand persons)
- 0.000
Hires less separations come to 11,253 thousand and employment rises 11,226 thousand, so the gap is 11,253 - 11,226 = 27 thousand, and 27 / 11,226 = 0.24 percent of the change. Two surveys count different samples, so the identity holds in the record only approximately. In the model headcount has exactly those flows, and the residual over 59 months is 0.000.
Use the idea
Run the identity on a record before trusting one series as a check on the other.
Where the conclusion applies
The window starts in January 2015 and counts flows from February. The gap is noise only if the surveys share a definition of a job.
Check your understanding: If cumulative net hires are 11,000 and employment rises 10,900, what share of the change is the gap?
Chapter 37 source: section "The identity the critic checks". Demonstration C37-D02.
3Demonstration 3 of 4
A fit within tolerance, a holdout outside it
Where does the fitted model sit against the record before, during and after the fit window?
The model carries a trend and two loops through 2020 and 2021 with nothing in it that knows the pandemic happened, so it meets the holdout on the wrong side of the record.
Hires and quits are JOLTS thousand persons a month. The error at a month is model / record - 1. The fit window is the first 60 months, the holdout is the last 36.
Predict first. In January 2022, is the model's quit count above or below the record, and by about how much?
Choose an example
Constructed example on the committed public record: the fitted path is inferred from it, and the months shown are constructed picks.
Calculated values
- Series
- quits
- Month
- January 2022
- Model (thousand)
- 3,507
- Record (thousand)
- 4,413
- Model against record (percent)
- (-20.5)
- Fit window error (percent)
- 3.15
- Holdout error (percent)
- 10.72
At January 2022 the model reads 3,507 against a record of 4,413: 3,507 / 4,413 - 1 = (-0.205), which is (-20.5) percent. The mean absolute percentage error is 3.15 percent over the 60 fit months and 10.72 percent over the 36 holdout months. The fitted values are inferred from the fit window, and the model runs through 2020 with nothing in it that knows what happened.
Use the idea
Quote the holdout error beside the fit error, and the sign of the miss.
Where the conclusion applies
Fitted values are inferred from 2015 to 2019. The holdout fails when the world breaks the structure, which is a judgment for people who run the system.
Check your understanding: If the model reads 3,500 and the record 4,400, what is the error as a percentage?
Chapter 37 source: section "The holdout, reported as it came out". Demonstration C37-D03.
4Demonstration 4 of 4
Which parameter decides capability
Which assumption moves month 24 capability most, and does that depend on where the others sit?
The ramp sets how fast hires become seasoned, which the capability stock reads directly. Gap-closing time changes how fast requisitions open, which the headcount rule largely offsets.
Each parameter is swung across a range somebody would defend. Capability is thousand effective persons at month 24 under a ten percent target step.
Predict first. With the others at their midpoints, does ramp time or gap-closing time move capability more?
Choose an example
Constructed example on the committed public record: ranges are the chapter's chosen ranges, and the fitted-values hold is a constructed variant of the midpoint hold.
Calculated values
- Parameter swung
- ramp_time
- Range swung
- 2.00 to 12.00
- Others held at
- midpoints of their ranges
- Capability at month 24, low end (thousand)
- 153,668
- Capability at month 24, high end (thousand)
- 131,257
- Swing (thousand)
- 22,410
Swing = |high end - low end| = |131,257 - 153,668| = 22,410 thousand effective persons at month 24. This is one parameter at a time with the others held where stated, over a range somebody would defend, not a confidence interval. The ramp is a fitted value that the record barely constrains, so a ranking that puts it first is a pointer to what to measure.
Use the idea
Measure the parameter at the top of the ranking before choosing a rule.
Where the conclusion applies
One parameter at a time, chosen ranges, and a structure that failed its holdout. The ranking changes with the hold setting.
Check your understanding: If the high end reads 143,000 and the low end 120,000, what is the swing?
Chapter 37 source: section "Which parameter decides it". Demonstration C37-D04.