Forecasting Apprentice Completions

What would be your forecast of this monthly time series?

Applying this logic to driving would be problematic

• … unless you live in Saskatchewan.

Would observing new apprentice registrations influence your forecast?

Would observing new apprentice registrations influence your forecast?

Main assumption:

• The arrival rate of new registrants is the constraint on the “production” of journey-persons.
• i.e. “production” scales up/down with the arrival rate of registrants, without changes in attrition or delay (no congestion effects).
• If true, we can use new registrants as a leading indicator of apprentice completions.

No real indication of (historic) congestion…

• But there is some policy uncertainty going forward.

A simple forecast based on registrations:

• Assume for the sake of argument that 50% of those who register complete their apprenticeship, and they all take exactly 48 months to complete.
• We would form our forecast by adding 48 months to the registration date, and divide the number of new registrants by 2.

A simple forecast:

Simple vs. slightly more realistic transistion probabilities.

Simple vs more realistic forecast:

Estimation:

• We use Kaplan-Meier and historical completion data to estimate, rather than assume, the transition probabilities.
• The transition probabilities are the joint probability of “survival thus far” (not yet a journey-person) and the instantaneous probability of “death” (graduation).

1. Survival Curve: the probability of “survival thus far”.
2. Hazard Rate: the instantaneous probability of “death”, conditional on survival thus far.

Are transition dynamics stable?

• Yes: we can be more confident in forecasts.
• No: are we doing better or worse over time?

The App: