Chapter 6 Flashcards
Who uses projected mortality rates?
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
How has the view on mortality projection changed?
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
Explain extrapolation
Extension of a graph, curve or range of values by inferring unknown values from trends in the known data
Whats a key point about mortality trends
A positive rate of improvement in mortality rates is always evident! Also our projections will always be wrong even our best estimates.
describe the two deterministic models we will study
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
Explain in the context of mortality what a deterministic model tells us
Means for each age x I have one mortality rate
Name the two stochastic models for projecting mortality
Lee- Carter Stochastic model for mortality projections
Coherent (Bayesian) forecasting - the UN stochastic model
What are three possible methods to forecast mortality - which si most commonly used
Mathematical model of ageing process
From a projection of factors known to significantly impact mortality
From an atheoretical extrapolation of historical patterns
Why do we not use method of mathematical model or projection of factors influencing mortality to project mortality rates
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.
Explain the method of extrapolation of historical patterns to project mortality rates
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.
Why do we not use methods based on froecasting by underlying cause very often?
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
What common features does evolution of mortality rates share across different countries
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)
Wht does the extrapolative technique of projecting future rates do?
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
What is the interpretation of q x,t
The rate of mortality at age x at future time t
What two factors if q x,t usually defined on
Age and period (future year)
What is a third g=factor that can also be combiend (even though there are other variations)
Cohort - (year of birth) combination of age and period so the three factors are not independent
Summarise a one two and three factor model example
- Age
- Age and period or less commonly age and cohort
- Age period and cohort - or in actuarial applications might replace cohort with size of pension
Why is using the cohort factor tricky
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
What was the smoking cohort?
Males born 1890 to 1910
What disadvantages does age, period, cohort model have?
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
Describe the Method used by the CSO to forecast irish population mortality
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)
Give the numbers assumed in CSO 2018 projection basis
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
Describe how the ONS in UK method works for forecasting UK population mortality
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
What are the key projections of the model?
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
Why does the UK include an allowance for the cohort effect - where did this originate?
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
What makes the lee carter model stochastic?
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
What is the interpretation of ax in the lee carter original model for mortality rates
Original mortality rate?
What is the interpretation of Betax in the lee carter original model for mortality rates
Sensitivity measurement at each x to changes in overall mortality index
What is the interpretation of Kx in the lee carter original model for mortality rates
Describes trend in mortality rate over time - mortality index
What is the interpretation of epilson x,t in the lee carter original model for mortality rates
IID normal random variables error terms with zero mean and variance depending on x,t
What is the importance of the constraints places on the lee carter stochastic model
Ensures a unique solution
How do we extrapolate from this method - how do we find parameters
Requires only extrapolation of mortality index Kt . Ax and Beta x are estimated from past data and held constant for duration of the projection
What are two ways to predict future mortality rates trends commonly used for Kt
Random walk or linear regression
What does the Lee Carter model rely on
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
What are the advantages of the Lee-Carter model
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
What are the disadvantages of the Lee-Carter Model
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
What are the disadvantages of the Lee-Carter Model
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
What was the reaosn for coherent projection method to differentiate it from other methods
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!
What are two ways to incorporate prior information into a projection?
Judgement and bayesian techniques
Where is the coherent multipopulatuon approach used
The Netherlands
Also UN population division used it for all countries in the world in 2014
Explain coherent forecasting within a bayesian model
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)
How did the UN population division issue stochastic population projections for the world in 2014
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
What countries were excluded from the population projections by the UN?
Those with under 100,000 population and those with AIDS epidemics
Which stochastic model tends to underestimate
Lee Carter
What are the main sources of error in mortality forecasts
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
What do positively correlated forecast error vs negative correlated forecast errors do?
Positive - tend to reinforce one another and widen the prediction interval
Negative - tend to cancel out
What is more prominent in mortality forecasts positive or negatively correlated forecast errors
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.
What does ONS stand for
Office of national statistics
What does ONS stand for
Office of national statistics
Indicate why and how you might allow for future mortality improvements in mortality rates
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.
