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Institute of Actuaries of Australia

Disability Claims - Does Anyone Recover?

David Service FIA, ASA, FIAA David Pitt BEc, BSc, FIAA

2002 The Institute of Actuaries of Australia

This paper has been prepared for issue to, and discussion by, Members of the Institute of Actuaries of Australia. The Council wishes it to be understood that opinions put forward herein are not necessarily those of the Institute and the

Council is not responsible for those opinions.

The Institute of Actuaries of Australia Level 7 Challis House 4 Martin Place

Sydney NSW Australia 2000

Telephone: +61 2 9233 3466 Facsimile: +61 2 9233 3446 Website: www.actuaries.asn.au

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Disability Claims – Does Anyone Recover?

Abstract

The common feature in all recent reports of disability experience has been the deterioration of claims termination rates. The adequate analysis of termination rates requires very material amounts of data. In this study the authors have had access to claims data submitted to the Institute of Actuaries of Australia Disability Committee over the period 1980 to 1998 covering 106,000 claims.

The authors have analysed this major dataset using conventional approaches –Actual/Expected – and using the latest Generalised Linear Modeling techniques. Also presented is a comparison of a stochastic approach to the setting of reserves for outstanding claims liabilities with the corresponding deterministic method.

Nineteen characteristics of the experience are reported using Actual/Expected techniques. Most show material differences between different values of the characteristic.

The analysis confirms the deterioration of experience but suggests that 1997 and 1998 showed significant improvement. The authors ask whether this is a real improvement or merely a pause before even worse experience.

David Service David Pitt

Centre for Actuarial Research Centre for Actuarial Research Australian National University Australian National University [email protected] [email protected]

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1. INTRODUCTION

The common feature in all recent reports of disability experience has been the deterioration of claims termination rates. The adequate analysis of termination rates requires very material amounts of data.

In this study we have had access to claims data submitted to the Institute of Actuaries of Australia Disability Committee over the period 1980 to 1998 covering 106,000 claims.

The authors have analysed this major dataset using conventional approaches –Actual/Expected – and using the latest Generalised Linear Modeling techniques. Also presented is a comparison of a stochastic approach to the setting of reserves for outstanding claims liabilities with the corresponding deterministic method.

This paper is set out in 6 sections and several Appendices, as follows Section 1 – Introduction

This introduction Section 2 – Data

A description of the data, its characteristics and the selection criteria used

Section 3 – Comparison of Actual vs Expected Claim Terminations

A comparison of actual terminations vs those expected on the basis of IAD89-93.

Section 4 – Generalised Linear Model of Claim Termination Rates

A description of the GLM fitted to claim termination rates on the basis of the data

Section 5 – Stochastic Claims Reserving

The results of calculating claims reserves with stochastic methods

Section 6 – Further Research

Some notes on further research opportunities in regard to the use of GLMs in connection with disability business

Appendix A – Some Data Specifications

Details of the data selection specifications Appendix B – Actual vs Expected

Detailed results of the actual vs expected analysis

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Appendix C – GLM

Full details of the GLM

Acknowledgements

This research could not have been carried out without significant support by the Institute of Actuaries of Australia,

• the authors received a research grant from the IAAust 2001 Research Grants Scheme, and

• the IAAust Disability Committee was prepared to supply the authors with their extensive claims database.

The authors gratefully acknowledge this support.

The original version of this paper was presented to the Horizon meetings in July 2002. The discussion at those meetings has informed this final version.

Health Warnings

In interpreting these results readers should note that the quality of data submitted to the Disability Committee has materially improved over the period covered by this analysis and we have, necessarily, taken the data supplied at face value. It has, of course, already been through the Committee’s own validation process. However, in some cases the interpretation used by companies in submitting data may have changed over the period.

In using these results for any particular company it should be borne in mind that the Disability Committee’s reports have consistently shown wide variation in experience by individual companies. As no company information was supplied it was not possible to investigate the possible intercompany variations for any of the characteristics analysed.

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2. DATA

The IAAust Disability Committee supplied the authors with their claims database for the period 1980 to 1998. This database had all identifiers relating to company or policy removed prior to its being provided to the authors. The database contained records relating to 106,000 individual claims and their various characteristics.

Each claim record contained the following data Country

Disability Definition Gender

Deferment – Accident Deferment – Sickness

Date of Policy Commencement Benefit Period – Accident Benefit Period – Sickness Occupation

Date of Birth Expiry Age Benefit Rate Benefit Type Medical Evidence Coverage Type Contract Type Cause of Claim Smoker Status Benefit Proportion

Date Disability Commenced Date Claim Ceased

Some of these characteristics were summarised to reduce the number of data points but without sacrificing data quality. The summarised characteristics were

• Deferment

• Claim cause

• Coterminus benefits

• Proportionate benefit

• Benefit rate

• Age at claim

The detailed specifications used to determine these summarised characteristics are set out in Appendix A.

Certain records were excluded from the analysis due to missing data or to match the primary data selection criteria used by IAAust Disability Committee. The exclusion criteria are set out in Appendix A.

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After these records were excluded 101,000 claims with 875,000 months of exposure remained for the analyses.

Not all claims remained in the original Disability Committee database from commencement to termination. Some claims commenced prior to 1980, some remained open at the end of 1998 and some companies only contributed data to some of the years between 1980 and 1998.

Nevertheless, each claim contributed to the exposure for the months for which data was available for it and contributed to actual terminations only if it terminated in the data available for it.

Claim cessation due to death, recovery or lump sum payment was defined as a claim termination. Claim cessations due to benefit expiry were not treated as a claim termination. Claims which terminated due to death comprised 1.1% of all claims terminated and lump sum terminations comprised 0.3% of all claims terminated.

Claim durations were taken at monthly intervals from the date disability commenced regardless of the deferment period. The first month was duration 0.

In the Actual/Expected analyses only benefits classified as “Full” were included except for the comparison of “Partial” and “Full” benefits.

Claims were classified as “Partial” if less than full benefits had been paid at any time in the claims payment history. 13% of all claims were so classified.

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3. COMPARISON of ACTUAL vs EXPECTED CLAIMS TERMINATIONS

The IAAust Disability Committee primarily reports claim termination experience by using average duration of claims for the first three years of claims. This makes sense given that each report concentrates on the four years covered. However, as noted in those reports, average claim duration needs to be interpreted with care as it can change due to changes in new claims volumes without any change in underlying termination rates.

For this paper we have concentrated on actual vs expected claim terminations (by claim numbers) as the measure of termination rate experience. For the calculation of expected terminations we have used IAD89-93.

The results are presented as an index which is the inverse of Actual/Expected in order that as results deteriorate the ratio increases. Fewer terminations than expected is bad news!

The base data includes only claims which satisfied the following criteria

• Individual coverage (excluding Business Overheads)

• Contract type not Cancellable

• Not a partial benefit at any point in the claim payment history Detailed Actual vs Expected results are set out in Appendix B. The more important conclusions are summarised in following paragraphs.

In this section only a one-dimensional view is taken of the experience.

There are simply too many possible cells to allow a reasonable analysis to be conducted using actual/expected techniques. However, the section dealing with the generalised linear model does, of course, take a multidimensional approach.

IT will be noted that the data for the period 1989 to 1993 does not have an index of 100%, i.e. the data does not agree with IAD89-93 for the same period. This is due to three sources of difference

• The data provided to the authors was of later origin than that used to derive IAD89-93 due to subsequent revisions and submission of additional data by contributors,

• The analysis in this paper has summarised some data, and

• IAD89-93 uses an “artificial” approach to setting termination rates at longer durations.

Since the comparisons used here are based on the relative values of the “index” the small difference between our 1989 to 1993 results and IAD89-93 is not significant in the interpretation of the results.

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3.1 Experience over Time

In this analysis the year is the year of exposure (and claim termination).

Table 1: Comparison of Actual and Expected Experience over Time

Year Expected Actual Index 1980 19 26 74%

1981 79 92 86%

1982 226 261 87%

1983 515 651 79%

1984 629 715 88%

1985 763 826 92%

1986 1202 1146 105%

1987 2090 2381 88%

1988 2142 2580 83%

1989 2352 2513 94%

1990 3261 2681 122%

1991 4895 4625 106%

1992 5148 5082 101%

1993 6447 5736 112%

1994 6960 6369 109%

1995 7737 5840 132%

1996 8166 5658 144%

1997 7490 5862 128%

1998 5477 4830 113%

65600 57874 113%

This analysis confirms the general deterioration of experience over time but interestingly suggests that in the last two years (1997 &

1998) some improvement may be evident. Is this a real improvement or, like the periods 1986 to 1988 and 1990 to 1992, a mere fluctuation before the deterioration resumes its course?

Because of this very material change in aggregate experience over time the results of the analyses by each of seventeen characteristics are presented in a two dimensional form to show the experience over time as well as by the values for each individual characteristic. The only exceptions to this presentation style were experience by benefit size, age at claim, duration and year of policy commencement where the number of individual values for each characteristic were too great to allow such an analysis.

3.2 Summary of Results

Table 2 shows the results for each characteristic presented as the Index for the total period ignoring differences by year. The experience by year for each characteristic is to be found in Appendix B. This table

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identifies which values for which characteristics are material in impacting the termination experience.

Table 2: Index of Termination Rates by Characteristic

Characteristic Value Index

Gender Male 112%

Female 125%

Occupation A 126%

B 111%

C 107%

D 111%

Deferment 7 days 66%

14 days 108%

30 days 125%

90 days 245%

Definition Own / Any 2 years 110%

Own 126%

Any 95%

Benefit Type Level 105%

Increasing 119%

Medical Evidence Medical 83%

Non Medical 101%

Other 126%

Coverage Individual 113%

Business Overheads 126%

Contract Type Level – Guaranteed 114%

Level 109%

Stepped Guaranteed 97%

Stepped 116%

Cancellable Level 85%

Cancellable Stepped 103%

No Claim Bonus No 114%

Yes 113%

Smoker Status No Differentiation 107%

Non Smoker – Checks 107%

Non Smoker 113%

Smoker 127%

Claim Cause Unknown 115%

W 69%

X 147%

Y 190%

Accident 101%

CoTerminus Yes 112%

No 117%

Benefit Period 2 years 102%

5 years 115%

Expiry 127%

Lifetime 123%

Benefit Proportion Full 113%

Partial 196%

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3.3 Some Initial Conclusions

These results suggest that the characteristics used in IAD89-93 to differentiate termination rates – deferment, gender and occupation – ado not capture significant differences in experience according to some other characteristics.

In addition, not only is the experience deteriorating to an extent where IAD89-93 is materially overstating the likely termination rates but also its shape for various characteristics may be materially different to that shown in the experience.

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4. GENERALISED LINEAR MODEL of CLAIM TERMINATION RATES 4.1 Background to Generalised Linear Models

Generalised linear models (GLMs) were first developed by Nelder and Wedderburn (1972). GLMs extend the basic linear regression model.

The linear regression model, when used for the prediction of a dependent variable, Y (for example claim termination rate), with a number of independent variables, X1, X2,..…,Xp, (for example occupation class, duration of claim, age, smoker status) can be described as follows:

1. The random component: each value of Y is normally distributed with expected value µ and constant variance σ2.

2. The systematic component: a set of independent variables X1, X2,

…,Xp which combine to produce a linear predictor η given by

1 p

j j

η=

x β where the βj are regression coefficients estimated by the least squares principle.

3. The link between the linear predictor and the mean of Y is µ = η The GLM extends this basic model in two significant ways:

1. The dependent variable, Y, may come from an exponential family distribution rather than just the Normal distribution. The exponential family encompasses most of the statistical distributions used by actuaries in general insurance and includes the Normal, Poisson, Binomial, Gamma and Inverse Gaussian distributions.

The advantage of using this broader class of distributions for the response variable is that it gives the user a wider range of possible relationships between the variance of the dependent variable and the mean of that variable.

2. The link function in (3) above can be any monotonic differentiable function. Common link functions are the identity link, the log link, the inverse link and the logit (or log-odds) link.

Having fitted a GLM the process of determining whether predictors are adding value to the model is also different to the process used in traditional linear modelling.

To assess the adequacy of the fit of a GLM we need to define the deviance statistic. The deviance is the discrepancy between the actual values of the dependent variable and the fitted values of that dependent variable.

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The formula for the deviance is

( )

ˆ, 2

( )

,

( )

ˆ,

D Y Y = φl Y φ −l Y φ

where φ is the dispersion parameter and l Y

(

ˆ,φ

)

is the log-likelihood function for the observed values.

The deviance is therefore the difference in log-likelihoods between a perfectly fitting (or saturated) model and the model for which the deviance is being calculated.

The addition of independent variables to a GLM therefore reduces the deviance. The amount of this reduction in deviance (in other words the size of the step taken towards the perfectly fitting model) is used as a measure of whether that particular independent variable is adding significant predictive power to the model.

4.2 Actuarial Use of Generalised Linear Models

Actuaries in both life and general insurance have both made use of generalised linear models. General insurance actuaries now routinely use GLMs for pricing a range of both long and short-tail lines of business.

Brockman (1992) describes the use of GLMs in motor vehicle insurance pricing and details some of the diagnostic procedures commonly employed to ensure a good model fit. Haberman (1996) summarises the actuarial use of GLMs in a very accessible paper.

The first use of GLMs by actuaries in the life insurance domain appears to be by Renshaw (1991). His paper, Generalised linear models and actuarial science, describes how models traditionally used by actuaries in the graduation of mortality rates can be viewed as special cases of GLMs. The traditional Gompertz and Makeham functions for describing the variation in the force of mortality by age and the Wilkie model for mortality are recast as GLMs. The Wilkie model for mortality is

( ) ( )

1 0

ˆ

exp ˆ

ˆ where ˆ

ˆ 1 exp

x s j

x x

x j

q η η β x

η

=

= =

+

j

It is clear that this is a GLM with a binomial error distribution and logit link function.

The first significant mathematical model of disability was that developed by Miller and Courant (1974). GLMs were first used in connection with disability income insurance by Renshaw. Renshaw

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(1995) describes the use of generalised linear modelling for graduating transition intensities in the well known multiple state model used to describe the dynamics of disability income insurance. This model is shown below.

ABLE

DEAD

ILL

Figure 1: Multi-state model used for Disability Income Insurance Modelling

This paper is concerned with the rate of termination of disability claims. That is, we endeavour to estimate the transition intensity from the ill state to the able state. This transition intensity is denoted ρ and can be thought of as the “force of recovery”.

The 1997 Report of the Disability Committee of the Institute of Actuaries of Australia (IAAust) highlights the significance of rating factors in describing the incidence rates of disability. We suspected that some or all of these rating factors might be significant in the explanation of termination rates. GLMs have been employed to quantify this relationship in a multiple simultaneous predictor setting.

4.3 Advantages of Using Generalised Linear Models for Claim Termination Rates

The advantages of using GLMs in describing termination rates are

• they enable the impact of changing the level of a rating factor to be quantified in a way that does not simultaneously consider the simultaneous change in other rating factors. For example the 1997 Disability Report considers the impact of occupation class on claim duration. The report states that claim duration for occupation class A is longer than that for occupation classes B to D. The GLM enables you to isolate out the impact of the change in occupation class from the changes in other variables which occur when you move from occupation class A to D. For example females are rarely in occupation class D and the fact that occupation class A lives are usually more severely disabled

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before they are unable to work than is the case for say occupation D lives;

• they provide a predicted value of the termination rate for a particular life with all rating factors specified to be determined along with a variance of this predicted value;

• they enable suitable modelling of the variance of the mean termination rate unlike conventional linear modelling; and

• the predicted termination rates will be smooth since they are the output of a mathematical function. This means that premiums and reserves calculated from the model will also be smooth.

• the results for termination rates are a result of a single model rather than a big range of different tables.

4.4 Analysis

The GLM fitted in this paper used data from the whole period 1980 to 1998 but with only a limited set of characteristics in order to facilitate the actual calculations by reducing the number of cells analysed.

Fitting a GLM to the full set of characteristics using only data from the latest data period – 1995 to 1998 – would be a valuable further step.

The authors are currently planning that project.

The fitting of a suitable GLM requires choices as regards the distribution of the errors, the link function, the predictors to use and whether any transformation of those predictors is useful. In addition it is worthwhile to investigate interactions which may exist between the predictor variables.

A number of different GLMs were fit to the termination rate data. After considerable analysis it was found that the Poisson error structure was the most appropriate for describing the mean variance relationship inherent in the data. It was comforting to note that this error family is the same one commonly used for claim inception rates in the modelling of many short-tail lines of general insurance business.

The data selection for the final GLM adopted used claims which had a deferment of 14 or 30 days, did not have an Unknown claim cause and had Individual coverage. There were 83,000 such claims with 675,000 months of exposure. The following characteristics were retained

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• Definition

• Gender

• Occupation

• Smoker Status

• Age at Claim

• Claim Cause

• Deferment

• Benefit Rate

• Year of Exposure

• Duration

There were 275,000 cells in the data.

It should be noted that unlike the Actual/Expected analysis the data used to fit the GLM included both “Partial” and “Full” benefit claims.

In order to give greater weight to those observations which we have more confidence in, the GLMs were fitted using the exposure for each rating factor combination as weights.

The results in Appendix C show that all of the following rating factors aid significantly in the prediction of termination rates: age at date of claim, cause of claim, duration of claim, gender, occupation class, smoker status, deferment period, benefit rate and the calendar year at the date of possible claim termination. The dataset includes all claim terminations so that at every possible duration only certain claims will actually be observed to terminate.

From the output in Appendix C one can calculate the fitted values for claim termination rates. The formula is

Claim Termination Rate = exp(32.3 - .008AgeClaim + 0.371(ClaimCauseW) + … -.00652(AgeClaim*Sqrt(Duration))) It is clear from Appendix C that the model has a significant residual deviance. This result is not surprising given that the nineteen years of data was included in the analysis and only a limited number of rating factors were included as explanatory variables. The interpretation of deviance residuals is explained in McCullagh (1989). A number of other variables and transformations of existing variables could also be explored and these are mentioned in Section 6 which is devoted to further research.

Graphs and other comparisons of modelled termination rates versus actual data will be included in a future paper which is currently being written by the authors. This paper will build a model for claim termination rates (and incidence rates) based only on the most recent five years of data. This reduced dataset will allow a considerably

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improved fit to the data to be achieved than was possible in this analysis.

Other interesting results of the analysis include:

• The benefit rate has a statistically significant negative impact on the rate of claim termination;

• there is a statistically significant interaction between duration and deferment period in determining the termination rate. At shorter durations the predicted termination rate is significantly higher for the shorter deferment period. After durations of approximately 8 months this difference becomes non- statistically significant;

• there has been a statistically significant decline, over time, in termination rates when aggregated across all levels of the rating factors. The decline in termination rates is still statistically significant even after the impact of all other rating factors has been allowed for.

An alternative to the second method of fitting an interaction term between deferment period and duration is to use “break-point predictor terms”. This has been employed successfully in the UK by Renshaw (1995). The idea is to include terms of the form (Duration – 3)+ which are only positive if the duration is greater than 3 and otherwise are zero. Such terms enable the rating factors to exhibit a non-constant linear relationship (after allowing for the link function) with the termination rate. They prove useful in modelling the lower termination rates that one observes at the very shortest durations.

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5. STOCHASTIC CLAIMS RESERVING

Given the GLM in Appendix C we aim to find the approximate distribution, using simulation, of the required reserves to ensure different probabilities of adequacy. The analysis is for the average of 100 claims that are new at the date of valuation with a monthly disability payment of $2600. The graph below was generated using a male aged 40, in occupation class A, with a deferred period of 2 weeks who became disabled because of an accident.

Percentage

Reserve($)

0 20 40 60 80 100

250003000035000400004500050000

Reserve Requirements for $2600 Monthly Claim at Duration Zero

Figure 2: Reserve Requirements for varying probabilities of adequacy In the above analysis allowance has been made for deteriorating claims termination rates and for interest at 6% per annum continuously compounding.

The calculation above is made using two probability distributions.

First the fitted value for the natural log of the termination rate from the GLM is normally distributed. This is the case because this fitted value is a linear combination of coefficient estimates and independent covariate values and the coefficient estimates are maximum likelihood estimates which are themselves (asymptotically) normally distributed.

The delta method was then used to find the variance of the actual fitted values for the termination rates. The number of terminating claims, given the termination rate, then comes from a binomial distribution.

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The table shows the reserves required to give a particular probability of the reserve being adequate using the stochastic techniques.

Table 3: Reserve Requirements by Probability of Adequacy Probability Claim Reserve

at Start of Claim

Increase Over 50%

50% 33,764

75% 36,749 9%

90% 39,692 18%

95% 41,180 22%

99% 45,357 34%

The reserve using a traditional deterministic approach would be that at the 50% probability level.

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6. FURTHER RESEARCH

There is considerable scope for further research into the description of claim termination rates in disability income insurance. For example,

• the use of generalised additive models which enable the use of a range of smoothers (for example, kernel smoothers and local linear loess estimates);

• use of the fact that the predicted termination rates are lognormally distributed to derive a numerical approximation to the distribution of outstanding claim reserves;

• further work on the use of interaction and break-point predictor terms in the fitting of the GLMs;

• use of economic variables for explaining termination rate experience in addition to the variables considered in this paper;

and

• build a further GLM using data from 1995 to 1998 and a larger set of independent variables to explain variation in claim termination rates over this period.

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References

Benjamin B. and Pollard J. H. (1993). The Analysis of Mortality and Other Actuarial Statistics. Published by the Institute and Faculty of Actuaries.

Brockman, M. J., and Wright, T. S. (1992). Statistical motor rating:

making effective use of your data. Journal of the Institute of Actuaries 119, pp. 457-543.

Haberman, S. and Pitacco, E. (1999). Actuarial Models for Disability Insurance. Published by Chapman and Hall/CRC.

Haberman, S., and Renshaw, A. E. (1996). Generalised linear models and actuarial science. The Statistician 45, pp. 41-65.

McCullagh P. and Nelder J. A. (1989) Generalised Linear Models.

Second Edition. Published by Chapman and Hall/CRC.

Miller, J.H. and Courant, S. (1974). A Mathematical Model of the Incidence of Disability. Transactions of the Society of Actuaries 25, pp 1-42.

Nelder, J. A. and W. Wedderburn, R. W. M. (1972). Generalised linear models. Journal of the Royal Statistical Society A 135, pp. 370-384.

Renshaw, A. E. (1991). Actuarial Graduation and Generalised Linear and Non-Linear Models. Journal of the Institute of Actuaries 118, II, pp.

295-312

Renshaw, A. E. and Haberman, S. (1995). On the graduation associated with a multiple state model for permanent health insurance. Insurance, Mathematics and Economics, 17, pp. 1-17.

The Institute of Actuaries of Australia Report of the Disability Committee (1997). Transactions of the Institute of Actuaries of Australia 489-576.

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APPENDIX A – Some Data Specifications A1. Claims Excluded

Country Not Australia

Deferment Sickness Not Equal Deferment Period Accident Sickness Only cover or Accident Only cover

A2. Summarised Characteristics Deferment

The original data has deferment period in days. These were summarized as follows.

0 – 10 7 days 11 – 24 14 days 25 – 31 30 days 32 – 61 60 days 62 – 92 90 days 93 – 183 180 days 184 - 365 days CoTerminus

If Benefit Period Accident = Benefit Period Sickness then CoTerminus.

Proportionate Benefit

If at any time a claim payment is not the full benefit then the claim is recorded as Partial

Age at Claim

This is recorded in quinquennial steps starting at 22.

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Benefit Rate

Recorded in the following bands ($ per month) 0 – 999 500

1000 – 1999 1,500 2000 – 2999 2,500 3000 – 3999 3,500 4000 – 4999 4,500 5000 – 5999 5,500 6000 – 6999 6,500 7000 – 9999 8,500 10000 – 14999 12,500 15000 – 19999 17,500 20000 - 25,000 Claim Cause

All claims had an alpha cause coded. These were summarized as follows in order to reduce the number of possible cells in the data matrix. The choice of combinations was deliberately made based on the average claim duration as shown in the Disability Committee Reports so as to give three broad groups – short, medium and long.

Summarised Cause Original Causes

V None recorded

W A, H, I, J, K, L

X C, D, F, G, M. N, P, R, S

Y B, E,

Z Accident

The original causes are the WHO International Classification of Diseases as follows.

A Infective and parasitic diseases

B Neoplasms (MN = Malignant and BN = Benign) C Endocrine, Nutritional and Metabolic diseases D Diseases of the blood and blood forming organs E Mental disorders

F Diseases of the Nervous system and sense organs G Diseases of the circulatory system

H Diseases of the respiratory system I Diseases of the digestive system J Diseases of the genito-urinary system

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K Diseases of Pregnancy and childbirth

L Diseases of the skin and subcutaneous tissue

M Diseases of the musculoskeletal system and connective tissue N Congenital anomalies

P Senility and ill defined conditions

Q Accidents, poisoning and violence (external causes) R 100 AIDS related complex and full blown AIDS S 101 HIV+ and Lymphadenopathy

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Appendix B – Detailed Actual / Experience Results B1. Experience by Calendar Year of Exposure

Year

Expected Actual Index 1980 19 26 74%

1981 79 92 86%

1982 226 261 87%

1983 515 651 79%

1984 629 715 88%

1985 763 826 92%

1986 1202 1146 105%

1987 2090 2381 88%

1988 2142 2580 83%

1989 2352 2513 94%

1990 3261 2681 122%

1991 4895 4625 106%

1992 5148 5082 101%

1993 6447 5736 112%

1994 6960 6369 109%

1995 7737 5840 132%

1996 8166 5658 144%

1997 7490 5862 128%

1998 5477 4830 113%

65600 57874 113%

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B2. Experience by Gender

Male Female

Year Expected Actual Index Expected Actual Index 1980 19 26 72% 0 0 0%

1981 75 79 95% 5 13 35%

1982 202 240 84% 24 21 115%

1983 453 599 76% 62 52 119%

1984 561 646 87% 67 69 98%

1985 685 757 91% 77 69 112%

1986 1094 1030 106% 108 116 93%

1987 1870 2151 87% 220 230 96%

1988 1864 2295 81% 278 285 98%

1989 2058 2220 93% 294 293 100%

1990 2847 2384 119% 415 297 140%

1991 4330 4104 106% 565 521 108%

1992 4442 4467 99% 707 615 115%

1993 5596 4983 112% 850 753 113%

1994 6056 5628 108% 904 741 122%

1995 6695 5143 130% 1043 697 150%

1996 7088 4972 143% 1078 686 157%

1997 6444 5117 126% 1046 745 140%

1998 4742 4270 111% 736 560 131%

57120 51111 112% 8480 6763 125%

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B3. Experience by Occupation

A B C D

Year Expected Actual Index Expected Actual Index Expected Actual Index Expected Actual Index

1980 15 17 86% 1 0 0% 4 9 42%

1981 30 27 111% 1 0 0% 13 19 68% 36 46 78%

1982 63 61 103% 6 6 108% 61 57 107% 96 137 70%

1983 138 215 64% 60 60 100% 201 248 81% 116 128 90%

1984 199 247 81% 70 53 131% 176 215 82% 184 200 92%

1985 242 260 93% 63 39 161% 185 193 96% 273 334 82%

1986 282 280 101% 178 70 254% 369 284 130% 373 512 73%

1987 445 457 97% 368 387 95% 868 1046 83% 409 491 83%

1988 462 471 98% 365 433 84% 913 1128 81% 402 548 73%

1989 547 549 100% 396 415 95% 957 1114 86% 452 435 104%

1990 792 488 162% 444 366 121% 1290 1143 113% 736 684 108%

1991 1277 1117 114% 521 437 119% 1692 1642 103% 1406 1429 98%

1992 1486 1320 113% 484 517 94% 1700 1835 93% 1479 1410 105%

1993 1900 1572 121% 565 562 101% 2078 1955 106% 1904 1647 116%

1994 2042 1753 116% 602 606 99% 2440 2290 107% 1876 1720 109%

1995 2252 1564 144% 549 391 140% 2758 2083 132% 2178 1802 121%

1996 2348 1452 162% 409 360 114% 2901 2242 129% 2508 1604 156%

1997 2248 1594 141% 465 349 133% 2802 2299 122% 1976 1620 122%

1998 1642 1210 136% 255 190 134% 1988 1978 101% 1593 1452 110%

18410 14654 126% 5800 5241 111% 23391 21771 107% 17999 16208 111%

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B4. Experience by Deferment

7 Days 14 Days 30 Days 90 Days

Year

Expected Actual Index Expected Actual Index Expected Actual Index Expected Actual Index 1980 0 0 0% 4 11 38% 7 14 50% 8 1 766%

1981 2 0 0% 53 61 87% 17 30 58% 7 1 690%

1982 4 0 0% 140 169 83% 74 92 81% 8 0 0%

1983 42 93 46% 311 403 77% 149 151 99% 12 4 291%

1984 51 105 49% 372 394 94% 192 209 92% 13 7 190%

1985 53 83 64% 469 499 94% 224 241 93% 16 3 541%

1986 51 70 72% 846 756 112% 280 306 92% 25 14 181%

1987 41 78 53% 1590 1901 84% 411 389 106% 47 13 364%

1988 44 66 66% 1606 2054 78% 454 445 102% 38 15 254%

1989 47 69 68% 1763 1897 93% 502 532 94% 41 15 273%

1990 39 48 80% 2351 2021 116% 835 606 138% 37 6 611%

1991 44 61 72% 3508 3510 100% 1298 1041 125% 45 13 346%

1992 34 36 95% 3542 3708 96% 1516 1316 115% 56 22 256%

1993 20 30 68% 4245 4002 106% 2120 1679 126% 61 25 245%

1994 35 32 109% 4497 4329 104% 2366 1969 120% 62 39 160%

1995 24 31 76% 4849 3771 129% 2804 2010 140% 61 28 216%

1996 2 4 52% 5195 3667 142% 2910 1955 149% 60 32 187%

1997 0% 4392 3556 124% 3014 2268 133% 84 38 222%

1998 2 4 43% 2959 2706 109% 2453 2092 117% 64 28 228%

535 810 66% 42693 39415 108% 21627 17345 125% 745 304 245%

(28)

B5. Experience by Disability Definition

Own / Any 2 Own Any

Year Expected Actual Index Expected Actual Index Expected Actual Index 1980 3 2 153% 15 22 66% 1 2 43%

1981 23 18 127% 50 73 68% 5 1 456%

1982 100 94 107% 101 130 78% 24 37 66%

1983 340 491 69% 147 116 127% 27 44 61%

1984 384 452 85% 207 211 98% 31 52 59%

1985 452 479 94% 224 239 94% 77 108 71%

1986 624 341 183% 303 345 88% 199 356 56%

1987 1281 1449 88% 494 483 102% 222 313 71%

1988 1320 1635 81% 544 540 101% 214 299 72%

1989 1431 1582 90% 550 488 113% 308 341 90%

1990 1953 1422 137% 956 774 124% 288 413 70%

1991 2891 2843 102% 1613 1317 122% 316 365 87%

1992 2908 3073 95% 1834 1604 114% 332 333 100%

1993 3587 3231 111% 2391 1965 122% 408 489 83%

1994 3649 3498 104% 2664 2266 118% 577 540 107%

1995 3454 2681 129% 3357 2426 138% 815 610 134%

1996 3751 2601 144% 3471 2409 144% 871 573 152%

1997 3108 2346 132% 3736 2826 132% 506 541 94%

1998 2139 2135 100% 2677 1890 142% 364 447 81%

33399 30373 110% 25332 20124 126% 5585 5864 95%

(29)

B6. Experience by Benefit Type Level

Increasing Level - Out of Working Hours Increasing - Out of Working Hours Year Expected Actual Index Expected Actual Index Expected Actual Index Expected Actual Index

1980 13 19 71% 6 7 81%

1981 61 71 85% 19 21 89%

1982 177 204 87% 50 57 88%

1983 404 544 74% 111 107 103% 0 0 0%

1984 482 572 84% 143 143 100% 4 0 0%

1985 595 661 90% 166 165 100% 2 0 0%

1986 951 918 104% 248 228 109% 3 0 0%

1987 1616 1860 87% 472 521 91% 2 0 0%

1988 1522 1924 79% 617 656 94% 3 0 0%

1989 1604 1697 94% 740 816 91% 1 0 0% 8 0 0%

1990 2119 1843 115% 1112 838 133% 16 0 0% 14 0 0%

1991 2849 2795 102% 1909 1700 112% 56 83 68% 81 47 171%

1992 2692 2844 95% 2297 2097 110% 69 86 80% 90 55 164%

1993 3006 2921 103% 3201 2659 120% 81 70 115% 159 86 185%

1994 3018 2884 105% 3691 3285 112% 91 100 91% 160 100 160%

1995 3092 2451 126% 4319 3251 133% 78 51 154% 248 87 285%

1996 3275 2369 138% 4567 3145 145% 61 70 87% 264 74 357%

1997 2563 2085 123% 4432 3621 122% 50 52 96% 445 104 428%

1998 1701 1627 105% 2760 2554 108% 23 22 106% 993 627 158%

31739 30289 105% 30859 25871 119% 527 534 99% 2476 1180 210%

(30)

B7. Experience by Medical Evidence

Medical Non Medical Other

Year Expected Actual Index Expected Actual Index Expected Actual Index

1980 7 7 93% 9 19 46% 4 0 0%

1981 15 10 154% 51 82 62% 13 0 0%

1982 49 53 93% 146 208 70% 32 0 0%

1983 190 281 68% 284 370 77% 41 0 0%

1984 233 345 67% 304 370 82% 92 0 0%

1985 328 411 80% 321 399 80% 113 16 706%

1986 377 590 64% 517 463 112% 285 72 395%

1987 432 560 77% 961 1088 88% 659 711 93%

1988 343 518 66% 959 1227 78% 790 787 100%

1989 329 488 67% 963 1096 88% 1010 886 114%

1990 281 283 99% 1413 1453 97% 1525 910 168%

1991 340 390 87% 2217 2387 93% 2309 1824 127%

1992 266 270 99% 1526 1465 104% 3338 3347 100%

1993 231 268 86% 1877 1713 110% 4311 3753 115%

1994 281 268 105% 2280 2273 100% 4358 3828 114%

1995 332 287 116% 2455 2185 112% 4900 3368 145%

1996 240 148 162% 2440 1908 128% 5396 3602 150%

1997 160 155 103% 2339 2300 102% 4855 3407 143%

1998 78 85 91% 1388 1238 112% 3759 3505 107%

4511 5417 83% 22449 22244 101% 37788 30016 126%

(31)

B8. Experience by Coverage Type

Individual Business Overheads Year Expected Actual Index Expected Actual Index

1980 19 26 74%

1981 79 92 86%

1982 226 261 87%

1983 515 651 79%

1984 629 715 88%

1985 763 826 92% 2 0 0%

1986 1202 1146 105% 6 0 0%

1987 2090 2381 88% 18 28 66%

1988 2142 2580 83% 29 21 138%

1989 2352 2513 94% 57 48 118%

1990 3261 2681 122% 86 49 175%

1991 4895 4625 106% 178 155 115%

1992 5148 5082 101% 216 200 108%

1993 6447 5736 112% 308 287 107%

1994 6960 6369 109% 226 94 241%

1995 7737 5840 132% 369 312 118%

1996 8166 5658 144% 328 265 124%

1997 7490 5862 128% 251 187 134%

1998 5477 4830 113% 195 158 123%

65600 57874 113% 2269 1804 126%

Figure

Table 1: Comparison of Actual and Expected Experience over Time
Table 2: Index of Termination Rates by Characteristic
Figure 1: Multi-state model used for Disability Income Insurance  Modelling
Figure 2: Reserve Requirements for varying probabilities of adequacy  In the above analysis allowance has been made for deteriorating  claims termination rates and for interest at 6% per annum  continuously compounding
+2

References

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