Chapter 6

Question 1

Who uses projected mortality rates?

Answer 1

Life companies and pensions companies - need to set correct premiums to make money and remain competitive.
Governments - need to know future trend to fund state pensions and healthcare social care etc

Question 2

How has the view on mortality projection changed?

Answer 2

In the past view was that past trends in mortality improvements would continue. Also there was a high element of judgement and consultation with experts. These methods generally underestimated mortality - Interest now is more in extrapolation of past trends by fitting models - less reliance on judgement

Question 3

Explain extrapolation

Answer 3

Extension of a graph, curve or range of values by inferring unknown values from trends in the known data

Question 4

Whats a key point about mortality trends

Answer 4

A positive rate of improvement in mortality rates is always evident! Also our projections will always be wrong even our best estimates.

Question 5

describe the two deterministic models we will study

Answer 5

CSO method projecting mortality rates in Ireland: two factor model incorporating age and period. Its extrapolative, deterministic and targeting
UK ONS method to forecast UK population mortality: three factor model incorporating age, cohort and period. Its extrapolative, deterministic and targeting

Question 6

Explain in the context of mortality what a deterministic model tells us

Answer 6

Means for each age x I have one mortality rate

Question 7

Name the two stochastic models for projecting mortality

Answer 7

Lee- Carter Stochastic model for mortality projections
Coherent (Bayesian) forecasting - the UN stochastic model

Question 8

What are three possible methods to forecast mortality - which si most commonly used

Answer 8

Mathematical model of ageing process
From a projection of factors known to significantly impact mortality
From an atheoretical extrapolation of historical patterns

Question 9

Why do we not use method of mathematical model or projection of factors influencing mortality to project mortality rates

Answer 9

Mathematical model - No reliable model is available
Factors method - Such variables are nearly as difficult to forecast as the mortality rates. We often don’t have enough data to understand these factors association with mortality also.

Question 10

Explain the method of extrapolation of historical patterns to project mortality rates

Answer 10

Can be stochastic or deterministic
Aggregate trend or pattern based on past data then use targetting methods
Assume a target mortality table in some future year and interpolate values between current and targeted values
Then use the parametric method to fit a curve and project trends in best-fitting parameters over time.

Question 11

Why do we not use methods based on froecasting by underlying cause very often?

Answer 11

Its difficult to achieve success in decomposition of mortality by cause of death:
Cause of death reporting is unreliable, especially at older ages
Causes of death often act synergistically - not realistic to limit to one caus of death
Time series of data are often rather short - only been collecting data since the 1950s so for older ages there’s not much to draw on

Question 12

What common features does evolution of mortality rates share across different countries

Answer 12

Near log linear decline of mortality rates at any age with time and the rate of decline of the mortality rate with age diminished with increasing age (it goes flat)

Question 13

Wht does the extrapolative technique of projecting future rates do?

Answer 13

Finds and fits a relationship to past data and projects mortality assuming the relationships hold into the future with the knowledge that rates of improvement tend to increase

Question 14

What is the interpretation of q x,t

Answer 14

The rate of mortality at age x at future time t

Question 15

What two factors if q x,t usually defined on

Answer 15

Age and period (future year)

Question 16

What is a third g=factor that can also be combiend (even though there are other variations)

Answer 16

Cohort - (year of birth) combination of age and period so the three factors are not independent

Question 17

Summarise a one two and three factor model example

Answer 17

1. Age
2. Age and period or less commonly age and cohort
3. Age period and cohort - or in actuarial applications might replace cohort with size of pension

Question 18

Why is using the cohort factor tricky

Answer 18

Makes heavy data demands - for recent cohorts we do not have alot fo records of deaths
Cohort effects on mortality are much smaller than period effect in majority of cases, though the factor is not negligible

Question 19

What was the smoking cohort?

Answer 19

Males born 1890 to 1910

Question 20

What disadvantages does age, period, cohort model have?

Answer 20

Any one factor is linearly dependent on other two
Cohort effects in a model have heavy data demands - requires nearly 100 years of data to observe mortality of a cohort over all ages

Question 21

Describe the Method used by the CSO to forecast irish population mortality

Answer 21

Targeting method - identifies the short term trends and forecasts these over the short term future. The short term trend is bended over future 25 years into an assumed long term rate of improvement. Method for projecting rates - multiply the mortality rate form the base table by a cumulative reduction factor CFR(x,t)

Question 22

Give the numbers assumed in CSO 2018 projection basis

Answer 22

Short-term rates of improvement: Male 2.5% and female 2.0% for 0-90 years. From 91-99 years the rate of improvement is estimated by linear interpolation between the assumed rate and 0%pa at 100 years. Stays like this for 100+ years

Long-term rates of improvement (2041 onwards) male are 1.5% and female is 1.5%. From 91-99 years the rate of improvement is estimated by linear interpolation between the assumed rate and 0%pa at 100 years. Stays like this for 100+ years

Question 23

Describe how the ONS in UK method works for forecasting UK population mortality

Answer 23

Also, a targeting approach blending current short-term rates of improvement by age and gender to long-term uniform rates over the next 25 years - Projections are done overall in the UK and by each constituent country also

Question 24

What are the key projections of the model?

Answer 24

Long-term rate of improvement after 25 years: 1.2% for those 92 and under, for 92<x<110 the rate declines from 1.2% to 0.1% linearly and remains here for age over 110.
Currently observed short term rates are estimated separately by age and sex. They are used for first eyar of projection and converge to long term rates over 25 eyar period
Convergence of current to long term is at the same pace for male and female and for those born between 1940 and 1960 convergence is by cohort

Question 25

Why does the UK include an allowance for the cohort effect - where did this originate?

Answer 25

Golden cohort (born 1923-1938) had higher rates of improvement than other generations which ensued a debate about incorporating year of birth along side age and calendar year. Golden cohort no longer appear to experience highr ates of improvement so cohort is no longer considered for them but ti is for group 1940-1960

Question 26

What makes the lee carter model stochastic?

Answer 26

The point projections of mortality rates are accompanied by confidence intervals that give a measure of their reliability based on the underlying probability model - confidence intervals widen further into the future

Question 27

What is the interpretation of ax in the lee carter original model for mortality rates

Answer 27

Original mortality rate?

Question 28

What is the interpretation of Betax in the lee carter original model for mortality rates

Answer 28

Sensitivity measurement at each x to changes in overall mortality index

Question 29

What is the interpretation of Kx in the lee carter original model for mortality rates

Answer 29

Describes trend in mortality rate over time - mortality index

Question 30

What is the interpretation of epilson x,t in the lee carter original model for mortality rates

Answer 30

IID normal random variables error terms with zero mean and variance depending on x,t

Question 31

What is the importance of the constraints places on the lee carter stochastic model

Answer 31

Ensures a unique solution

Question 32

How do we extrapolate from this method - how do we find parameters

Answer 32

Requires only extrapolation of mortality index Kt . Ax and Beta x are estimated from past data and held constant for duration of the projection

Question 33

What are two ways to predict future mortality rates trends commonly used for Kt

Answer 33

Random walk or linear regression

Question 34

What does the Lee Carter model rely on

Answer 34

A near log-linear decline of mortality rates at any age with time - this is evident in most countries so this is why this method became popular

Question 35

What are the advantages of the Lee-Carter model

Answer 35

After parameter estimation forecasting is straightforward done with standard time series method so uncertainty in parameter estimates and mortality forecasts can be assessed
Model can be adapted to suit context

Question 36

What are the disadvantages of the Lee-Carter Model

Answer 36

Heavily dependent on estimates of parameters ax and Bx which may be influenced by past events
Tendency for forecasts to become increasingly rough with time
The model assumes underlying rates of mortality are constant over time - not always true however later ages only recently saw improvements
The model has no cohort term
Unless the observed rates are used for forecasting it can produce a jump-off effect for first future period and most recent data

Question 37

What are the disadvantages of the Lee-Carter Model

Answer 37

Heavily dependent on estimates of parameters ax and Bx which may be influenced by past events
Tendency for forecasts to become increasingly rough with time
The model assumes underlying rates of mortality are constant over time - not always true however later ages only recently saw improvements
The model has no cohort term
Unless the observed rates are used for forecasting it can produce a jump-off effect for first future period and most recent data

Question 38

What was the reaosn for coherent projection method to differentiate it from other methods

Answer 38

One issue with methods that treat single populations separately is that forecasts of mortality for either sub groups within the population or with other populations can produce inconsistencies long term. Coherent projection has projections for related populations that remain related!

Question 39

What are two ways to incorporate prior information into a projection?

Answer 39

Judgement and bayesian techniques

Question 40

Where is the coherent multipopulatuon approach used

Answer 40

The Netherlands
Also UN population division used it for all countries in the world in 2014

Question 41

Explain coherent forecasting within a bayesian model

Answer 41

For an unknown quantity theta and sample information y the likelihood function L(y|theta) provides empirical information of theta. The prior distribution represents initial uncertainty on theta. And the bayesian inference on theta is made using posterior distribution proportional to likelihood by prior. Knowledge and opinion are expressed in prior, transformed into a posterior distribution by incorporating empirical evidence (likelihood)

Question 42

How did the UN population division issue stochastic population projections for the world in 2014

Answer 42

Used bayesian hierarchial model, parameters were drawn from a common world population and then male life expectancies were derived form female life expenctancies, projecting the gap between them
Done this for 159 countries - 90% of population

Question 43

What countries were excluded from the population projections by the UN?

Answer 43

Those with under 100,000 population and those with AIDS epidemics

Question 44

Which stochastic model tends to underestimate

Answer 44

Lee Carter

Question 45

What are the main sources of error in mortality forecasts

Answer 45

Model mis specification big one!!!
Uncertainty in parameter estimates
Random variability - not so much errors often have zero mean
Error in data - age misstatement example

Question 46

What do positively correlated forecast error vs negative correlated forecast errors do?

Answer 46

Positive - tend to reinforce one another and widen the prediction interval
Negative - tend to cancel out

Question 47

What is more prominent in mortality forecasts positive or negatively correlated forecast errors

Answer 47

Positively - we believe age patterns of mortality to be smooth so the mortality rate at any age contains information about the mortality at adjacent ages.

Question 48

What does ONS stand for

Answer 48

Office of national statistics

Question 49

What does ONS stand for

Answer 49

Office of national statistics

Question 50

Indicate why and how you might allow for future mortality improvements in mortality rates

Answer 50

It is important to allow for future improvements in mortality, as there is a strong secular
trend. [1]
The LO has an exposure to future mortality rates being lower than expected. [1]
There are several approaches that can be used. Maybe copy what ONS or CSO use in
population projections. [2]
I would not use a stochastic model.
I would not incorporate cohort effects.