## Sunday, January 8, 2017

### The Internship/Residency crisis - is it overhyped?

Much publicity has been circulated regarding the internship/residency crisis facing New South Wales.
But what actually is the crisis? And where did it originate?
And is it really a crisis?
I argue it's not that big of a deal in the long term

The problem can be simply characterised by looking at key policy changes in the late 20th century in combination with supply-and-demand.

## Policy overview

• 2009 - Universities start increasing the number of medical students
• 2012 - Official government policy to deregulate medical student admissions
• 81% increase in domestic graduates from Aussie med schools, from 1348 in 2005 to 2442 in 2012.
• No real provision of increased training resources at the other end of the spectrum.
Charts from MJA (reference below):

## Economic model

Let's define a "block" as a segment of a training pathway between two selection bottlenecks (e.g. block #1 = between HSC and internship, block#2 = between internship and registrar year 1, etc).
An simplified  might be something like

#trainees in block = ∑_i X_i
:= T

where:
a block is years ranging from j to k
∑_i is the sum over all i (j≤i≤k)
X_i is the intake in year i

A step-wise policy update in year P1 that isn't replaced until year P2  changes the X_i for P1≤i≤P2. It will take k-j years for P1 to entirely affect T.
Of course if the policy at P1 is a time-dependent function the previous statement makes no sense. Which is basically the current situation: policy_P1 = f(t) = Ae^kt (some exponential).
The number reaching the next selection bottleneck B (outgoing cohort) is clearly X_k, with those "missing out" being X_k - B.
The potential size of X_k - B is the source of fear: what happens to these 'lost commodities', who will be left to compete with the overflowing X_(k-1) the following year?
If B is fixed, we end up with a logjam in the system over Y years of
Logjam = ∑[X_(k-y) - B]
= ∑[X_(k-y)] - BY

where ∑ is from y=0 to y=Y

We could also subtract some attrition constant for the people who give up each year, but you get the point.
When a policy directive causes the term ∑[X_(k-y)] to be exponential rather than linear, this incites fear due to concern that the constant B is limited by consultants available to train new people.
However the assumption that B is constant is flawed. B is also a function of time. Each newly trained consultant is available to train the next person.
Assuming 1<-->1 training:

With training time M,  we get an additional boss pool of size B_[k-1-M]
B_k = B_[k-1] + B_[k-1-M]
= B_[k-2] + B_[k-2-M] + B_[k-1-M] by recursion
= B_[k-3] + B_[k-3-M] + B_[k-2-M] + B_[k-1-M]
etc.
= ∑B_[k-l-M]
where the sum is on l for 0≤l≤k
Peoples' concern is when

Logjam formula becomes:
Logjam = ∑_y [X_(k-y)] - ∑_y* ∑_l B_[k-l-M]
But if we wait l=k years (k usually no more than 6 years in reality), we find that the inner ∑l sum is stuck at B_[-M] (ie M years before the selection date), and we have that the right hand term reduces to:
Logjam = ∑_y [X_(k-y)] - ∑_y B_[-M] + ∑_y * constant
= ∑_y [X_(k-y)] - B_(-M) + constant ]
So over time y, we look at the logjam and eventually, once y=k, the only variable term ∑_y X_(k-y) also becomes a sum of a constant.
So we have
Logjam = ∑_y[some other constant]
Then ∑_y = Y/2*(Y+1) by adding the ends of the sum together.
I.e. independent of changes in intake at X_k, after k years you always just get a logjam proportional to a quadratic in Y (the total years you let the model progress). This quadratic can be multiplied by zero by balancing the constants:
• bosses available at time zero
• intake at time zero

## Summary (or TLDR)

• The training system is adaptive
• Things balance out in the long run.
• Things will balance out more quickly the higher the trainee:trainer ratio
•  Government funding is essential to allow this adaptation, but this cannot be judged until the current system has been running for k years (allowing the intake to block 1 to move to block 2). It is a matter of personal opinion as to whether it is at this 'judgement' stage yet or not. I think it is not.

## References

• https://www.theguardian.com/higher-education-network/2014/aug/07/lifting-the-cap-on-student-numbers-five-lessons-learned-from-australia

Please leave your thoughts in the comments. I wrote this article to provide a (hopefully) refreshing counterpoint to the typical "doom and gloom" story espoused by media outlets.

## Error somewhere?

Entirely possible, comment below.

1. 1. 2. 