The Ogden Tables and Contingencies Other than Mortality Zoltan Butt Steven Haberman Richard Verrall Ogden Committee Meeting 21 July 2005

Acknowledgement Research support from Institute and Faculty of Actuaries’ Research Grant and from ESRC.

Outline Aims of Project The Multipliers and the role of the Ogden Tables Related Research Multiple State Model Labour Force Survey (LFS) Methodology Interim Results Conclusions and Further Work

Aims of project To assess the past and current methodology of estimating contingencies other than mortality in England and Wales. To measure labour force (LF) dynamics based on Markov chain methodology and longitudinal LFS data sets. To assess the suitability of the current Ogden Tables multipliers in the light of current population worklife expectancy.

Related Research Haberman and Bloomfield (1990) Forms the basis of the reduction factors for contingencies other than mortality in the last 4 editions of the Ogden Tables. The methodology is primarily based on measuring static labour force participation rates and making adjustments with respect to days lost due to illness and industrial disputes. It makes use of a large spectrum of data sources from the 1970s and 1980s. It emphasizes the disadvantages of the static methodology when applied to the LF and predicted that their estimates overstate the worklife expectancy on average by 5%.

Related Research Lewis, McNabb, Robinson and Wass ( ) Produces empirical evidence towards an improved methodology of estimating pecuniary losses based on a dynamic multi state approach (as applied in the USA). Highlights the disadvantages of the multiplicand-multiplier approach materialized by the Ogden Tables. It applies a Markov chain approach of estimating future loss of earnings, but also allowing for future economic and productivity growth. The authors argue that the alternative methodology could yield an average increase of 36% in compensations (for plaintiffs without post- injury earnings potential) compared to the Ogden Tables approach. The growth factors account for about 25% out of the above average increase.

It captures the true dynamic nature of the underlying process, characterized by continuous flows in and out of the labour force. The expected time spent in a given economic state strongly depends on the starting conditions. The timing of the movements between states is a significant factor in the valuation of contingencies. It avoids the problem of making stationary assumptions about the labour market composition. The Importance of Multiple State Modelling of Labour Force

Current Methodology Construct a 3 state Markov model of LF transitions (Employed, Unemployed and Out of LF) : Estimate age-specific transition intensities from the observed waiting times (i.e. central exposures) based on longitudinal LFS data sets. Estimate yearly transition probabilities from observed and smoothed transition intensities and calculate the age-specific worklife expectancy conditional on the starting state. Calculate discounted age-specific reduction factors based on the worklife expectancy and current life expectancy to the pension age 65 (60).

Transition intensity (TI) for lives in economic state i to move into state j, at exact age x. - Assumed continuously varying with age x. - No dependence on duration in current state. - Out of LF includes Inactive (i.e not seeking work) and Temporarily or Long Term Sick/Disabled - Force of mortality the same for all three economic states. Multiple State Model of LF Dynamics EMPLOYED (1) UNEMPLOYED (2) OUT of LF (3)

Maximum likelihood estimates of age-specific transition intensity matrix: Corresponding age-specific yearly transition probability matrix for age (x, x+1) result from: where A is the eigenvector matrix corresponding to eigenvalues d of. Multiple State Model

The age-specific worklife expectancy (in state S = j ) conditional on the starting state at age x (S x = i) : is given by the [i, j] th entry of the following matrix function: where p x+t is the age-specific survival probability, P x+t is the transition matrix and I is the identity matrix t p is the pension age (65 and 60 for males and females respectively) EW x needs to be discounted for the the future real rate of interest: Worklife Expectancy (EW)

The reduction factor represents the ratio of the average number of years in a given economic state and the number of years remaining alive to pension age t p. or Life expectancy is based on 3 year UK interim life tables matched to the grouped LFS data sets: Reduction Factor (RF) Period 5 years 10 years LFS 1993 – – UK Interim LT 1994 – –

Labour Force Survey (LFS) The UK LFS collects information on LF characteristics based on a rotating sample of around 60,000 households. Interviews are carried out in waves and at each census point about a 1/5 of the sample is replaced. Since 1992 information is collected on a quarterly basis, each household normally is re-interviewed exactly 5 times in a year. This design allows the ONS to create linked (longitudinal) data sets, making sure that the appropriate weightings are being applied to compensate for any bias introduced by the linking procedure.

Five-Quarter (LFS) Longitudinal Data Sets for 1993 – 2003 There are published five-quarter data sets resulted from linking the observations on a sample of individuals that are followed over the same one year intervals, from winter 92/93 onward. Each five-quarter data will contain (quarterly) LF characteristics on approximately 10,000 working age individuals (i.e. 16 – 65 and 16 – 60 for males and females respectively; with each gender being fairly equally represented). We have made use of all the available five-quarter data from Jun 1993–Aug 1994 to Jun 2002–Aug The INECACA variable has been used to define the economic states represented in the multi-state Markov model.

Restricted to the longitudinal LFS for 1998 – Prevalence Rates (PR) in states gives us an overview of the current labour market make up by age: Observed and smoothed transition intensities (TI); Raw and smoothed Worklife Expectancy (EW); Reduction Factors (RF); Interim Results

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Multiple state modelling of the LF is the way forward. Data requirements for multiple state modelling are met, but single years are likely to be insufficient. There are significant differences between the static and dynamic methods of valuing future contingencies. In general, the multiple state method yields lower reduction factors than the traditional approach. The value of the multiplier should be conditioned on the starting conditions. Conclusions

Allowing for covariates – area of residence, type of industry/employment. Extension of the multiple state model to include a ‘Dead’ state with the force of mortality specific to economic state. Disaggregating the ‘Out of LF’ economic state into ‘Economically Inactive’ and ‘Sick’ Detailed comparison with the Ogden Tables recommendations. Further Work