1. Unemployment models The probability of unemployment
The event of someone becoming unemployed is a significant event, in other words a risk, especially in financial terms
That’s where we actuaries come in. Financial protection is one way to protect: although it appears that many policyholders when the situation arise stop paying the mortgage protection policy fee (and loss protection) before stop paying mortgage... That’s a different problem I guess...
The GFC has uncovered the risk of unemployment and various loanbooks were significantly impaired.
So, wouldn’t it be great if we would know the:...
Klaas Stijnen
New Zealand Society of Actuaries Conference 2010
© 2010 Deloitte Actuarial Services

2. P [unemployment | employment] = ?
Introduction
P [unemployment | employment] = ?
P [employment | unemployment] = ?
Unchartered water?
Introducing these formulaic statements and promise it will be the only one in the rest of the presentation!
Like with many things in life, as far as I know, these weren’t available publicly... Is this unchartered water?
Data directly historical transferred is not directly available (as far as I know).
Related, but not necessarily strongly correlated measures are historically available
The data model behind these publicly available measures implicitly represents a multi-state model implicitly, but not explicitly capturing the percentage of people that historically transferred from being employed to being unemployed and vice versa.
What I will explain is that with using logic and other publicly available data providing information on the transfers in the multi state model allows us to estimate the historically observed transfers and therefore historically observed probabilities of a person being employed to become unemployed and vice versa (‘unemployment probabilities’). 2
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3. Unemployment data
Statistics New Zealand: Labour Force Household Survey Unemployment data (Quarterly – 20 yrs history. Segmented for region, age, qualification and gender)
Working
Age
Population
Active
Labour
Force
Non
Employed
Unemployed
Unemployment rate =
Unemployed
Labour Force
Participartion Rate =
Labour Force
Working Age Population
What is the data source I used?
Explain slide:
Great data source: long history, probably quite reliable and segmented – if ever we could extract the movements between
Explain what we see on the picture: what are these different groups
So this data gives us snapshots of headcounts at points in time, but it doesn’t tell us directly how many people have transferred from employment to unemployment and vice versa, which is what we are interested in. 3
© 2009 Deloitte Actuarial Services

4. Unemployment multi state model – Example 1
Working
Age
Population
Non
Labour Force
Employed
Unemployed
Unemployment rate
t = 0: 5%
t = 1: 7% +5 +3
P[empl | unempl] = 0%
P[unempl | empl]=60%
To give you a feel for the multi state model
Explain the different transfers (The labour force is the sum of the unemployed and employed – left out) - CLICK
Explain example t=0 t=1 – CLICK
Explain examples of transfers and how unrelated these potentially can be with the unemployment rate - CLICK +5
t = 0: 35
t = 1: 35
t = 0: 5
t = 1: 7 4
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5. Unemployment multi state model – Example 2+6
Working
Age
Population
Employed
Unemployment rate
t = 0: 5%
t = 1: 7%
P[unempl | empl] = 5%
P[unempl | empl]=40% +1 +2 +5
Quite easy to see that the relation between change in unemployment and probability of (un)employment is obvious
Non
Labour Force
Unemployed
t = 0: 35
t = 1: 35
t = 0: 5
t = 1: 7 5
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6. Unemployment multi state model - Assumptions
8 interlinked equations and 16 variables (of which 4 are known) form the multi state model to estimate historical probabilities.
5 assumptions to solve the model:
Number of people leaving the working age population = estimated mortality + net migration
t = 0: 140
t = 1: 145
+10
Working
Age
Population
Won’t bother you with the equations
We will need some assumption and or extra data to solve this equations
Explain assumption 1 – CLICK
Explain transfers +5 6
© 2009 Deloitte Actuarial Services

7. Unemployment multi state model - Assumptions
Net Working age population inflow or outflow spreads proportionally
- EXAMPLE -
Working
Age
Population
Non
Labour Force
Employed
Unemployed
t = 0: 100
t = 1: 110 (+10%)
t = 0: 60
t = 1: 66 (+10%)
t = 0: 30
t = 1: 33 (+10%)
t = 0: 10
t = 1: 11 (+10%)
Explain assumption 2
In some ways this is also reflecting the data. Well, I think it will be alright as these proportions are very stable over time. If these proportion would change massively between periods than this assumption would not make much sense probability. 7 7
© 2009 Deloitte Actuarial Services

8. Unemployment multi state model - Assumptions
If the size of non labour force decreases / increases during the period then there are no / only people moving from the employment and unemployment state to the non labour force during the same period.
EXAMPLE
Working
Age
Population
Non
Labour Force
Employed
Unemployed
t = 0: 30
t = 1: 33 X
Explain assumption
This assumption is probably not too bad as the labour force / (employed + unemployed) is very steady linear trend. 8 8
© 2009 Deloitte Actuarial Services

9. Unemployment multi state model - Assumptions
The number of people that move from being unemployed to employed is equal to the relative amount of people that have an observed duration of unemployment less than a quarter.
Example Data:
Duration of unemployment
Period X
Less than Perc
1 Month 25%
1 Quarter 50%
Half year 75%
Year 90%
Working
Age
Population
Non
Labour Force
Employed
Unemployed
50%
Explain assumption:
That is enough information to solve the puzzle
Almost like a sudoku puzzle: recursive
This data is available 9 9
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10. Results – historical probability of unemployment
Explain graph
Discuss mean, slope and R^2 10 10
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11. Results – historical probability of employment
Explain graph
Discuss mean (remember people from employment coming in means with people leaving the unemployment rate can stay the same),
Discuss slope and R^2.
The curves is these graphs can be a very useful instrument in modelling 11 11
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12. Results – Segmented unemployment probabilities
Given the change in unemployment rate and the fitted curve the (un)employment probabilities can be estimated.
Is that relationship stable for different segments? Some sample testing:
Prob of employed to unemployed
Prob of unemployed to employed
Mean*
Slope**
Mean
Slope
Total population 3% 9%
50%
93%
Qualification – No Qual 8%
64%
Sample Age – 40 to 44 2% 5%
71%
Gender – Female
81%
Remember we had the household survey unemployment data for various segments,
So, how convenient would it be if this formula is stable for different segments. It seems like it! But the additional data is not always available...
That means that the only variable you’d have to change for different segments in your models is the behaviour of the unemployment rate
*The probability of (un)employment with no change in unemployment rates
** The slope (if assumed to be linear) of the fitted curve with increasing unemployment rates 12 12
© 2009 Deloitte Actuarial Services

13. Results – Segmented unemployment probabilities
The estimated (un)employment probabilities are dependent on the change in unemployment.
Correlation over the last 20 years between the change in unemployment rate for New Zealand total and:
Gender: 90%
Between regions, age and qualification: 40% – 70%
The volatility of changes in unemployment rate differ considerably across segments.
Estimated unemployment probabitlities can be significantly different for various segments. 13 13
© 2009 Deloitte Actuarial Services

14. How can these results be used
Financial protection products (pricing and risk modelling):
Estimated probability of (un)employment
Estimated duration of unemployment
Probability distribution of duration of unemployment
Retail loans credit models
Probability of default
Loss given default
Macroeconomic forecasting models
More granular information than unemployment rate 14 14
© 2009 Deloitte Actuarial Services