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

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 © 2009 Deloitte Actuarial Services

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

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 © 2009 Deloitte Actuarial Services

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 © 2009 Deloitte Actuarial Services

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

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

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

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 © 2009 Deloitte Actuarial Services

Results – historical probability of unemployment Explain graph Discuss mean, slope and R^2 10 10 © 2009 Deloitte Actuarial Services

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 © 2009 Deloitte Actuarial Services

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

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

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