Calculating compensation for loss of future earnings: estimating and using work life expectancy


Richard Verrall, Faculty of Actuarial Science and Insurance, Sir John Cass Business School, City University, 106 Bunhill Row, London, EC1Y 8TZ, UK.


Summary.  Where personal injury results in displacement and/or continuing disability (or death), damages include an element of compensation for loss of future earnings. This is calculated with reference to the loss of future expected time in gainful employment. We estimate employment risks in the form of reductions to work life expectancies for the UK workforce by using data from the Labour Force Survey with the purpose of improving the accuracy of the calculation of future lifetime earnings. Work life expectancies and reduction factors are modelled within the framework of a multiple-state Markov process, conditional on age, sex, starting employment state, educational attainment and disability.

1. Introduction

In the English law of tort, any person who is injured through the fault of another can claim monetary compensation for the impact of injuries sustained. The main impacts of injury in relation to loss of earnings are displacement from employment and continuing disablement. The purpose and measure of compensation is to provide financial restoration to the pre-injury position. Compensation for a future stream of losses is awarded as a lump sum which is capitalized to the date of settlement. The calculation of the lump sum is based on assumptions about life expectancy (future care expenses) and work life expectancy (WLE) (loss of future earnings). In this paper we present an interdisciplinary approach, using methods from actuarial science and economics, for the estimation of the WLE. Actuarial science has been concerned with lifetime risks (but not particularly in relation to labour market behaviour) and labour economics has been concerned with labour market outcomes (but rarely over individual lifetimes). Our primary interest is in the practical application of the WLE in the calculation of loss of future earnings.

In the opening part of this paper (Section 2) we give a short overview of the current UK tort system of valuing compensation for loss of future earnings. For reasons of practical application within the existing law on damages, we are constrained to work within the multiplier–multiplicand method of calculation. We describe this calculation in the context of the courts’ valuation of damages for loss of future earnings. Loss of earnings is measured over a future working lifetime. We review some US studies that seek to model employment outcomes over individual lifetimes, including applications to future loss of earnings that were found in the US forensic economics literature. Research on employment in the UK is used to inform our estimation of WLEs by using labour market data for the UK. The statistical concept of the WLE is central to the calculation of loss of future earnings and we introduce the statistical theory which underpins our estimates of WLEs and their associated employment risks reduction factors (RFs).

Section 3 includes a description of the labour market data that we use and our approach to the estimation of WLEs. Mindful of the need to strike a balance between the competing objectives of rigour and accessibility, we develop two models. The first is a simple empirical model based on observed transition probabilities in a two-state model (employed and non-employed) which is disaggregated by disability status. In this model, the WLE is calculated as a function of age, sex and disability by using a spreadsheet in a way which is meaningful to lawyers. The second is a more complex empirical model based on hazard rates (or transition intensities) that are estimated from labour force movements, again in a two-state setting. Baseline transition rates are estimated as a function of age and sex and the analysis is extended to allow for stratification on a number of additional variables, including industry, region, level of educational achievement and disability (unless otherwise stated, disability refers to that which results from the injury for which compensation is being determined). We find that, in the context of the impact of injury, education and disability are the best determinants of the WLE and we conclude our analysis by estimating their joint effects. In Section 4, we present our results in the form of a set of age-specific WLEs and RFs disaggregated by sex, initial employment status, disability and level of education.

In the belief that the general principle, in terms of both methodology and consequences, can be usefully illustrated with reference to a specific example, in Section 2.2 we provide an example of the existing approach to the calculation of loss of future earnings. Later in Section 4.1 this example is reworked by using the alternative method that is developed in this paper. We note that the Labour Force Survey (LFS) is not designed with the intention of estimating WLEs (or the impact of disability or educational achievement on WLEs). Hence, in Section 5 we discuss some potential sources of bias which might arise from the use of these data in the particular context of education- and disability-adjusted WLEs. Having made some suggestions for further research concerning the estimation of compensation for loss of earnings in Section 5, we present our conclusions in Section 6.

2. The multiplier–multiplicand valuation of a future loss

2.1. Background

Historically, the English legal system has adopted a ‘broadbrush’ approach to the calculation of individual future losses with the objective of providing simplicity, certainty and consistency across cases. The intention is that lawyers should be able to undertake the calculation themselves without recourse to expert advice in each case. To this end, the application of science was often rejected in favour of judicial intuition and the precedent of decisions in past cases. The judiciary has justified this position on the basis that

‘the exercise upon which the court has to embark is one which is inherently unscientific … average life expectancy can be actuarially ascertained but to assess the probability of future political, economic and fiscal policies requires not the services of an actuary or an accountant but those of a prophet’

(Lord Oliver, 1989, in Hodgeson versus Trapp (1989), 1 A.C. 833). However, the rejection of actuarial and statistical evidence as a means of guidance increases the potential for both inaccuracy and inconsistency and the courts’ decisions were regularly criticized on precisely these grounds (Kemp, 1997, 1999). When compared with actuarial calculations, the judiciary was found to be overly prudent in terms of applying reductions for mortality and employment risks (Haberman, 1996; Luckett and Craner, 1994).

Judicial discretion over compensation for future losses was curtailed in a House of Lords’ decision in 1999 (Wells versus Wells (1999), 1 A.C. 345). This specified a particular formula for the calculation of all future losses and endorsed actuarial estimates concerning life expectancy and employment risks for inclusion in this formula. The formula is known as the multiplier–multiplicand calculation and it is the foundation of the calculation of loss of future earnings. As a method for calculating future loss, it remains broadbrush in character and it continues to be amenable to application by lawyers.

The formula comprises the product of the multiplicand, an annual loss (annual care cost or annual lost earnings), and the multiplier, the discounted number of years over which the annual loss is payable (life expectancy or WLE). The multipliers are prepared by the Government Actuary's Department in consultation with a multidisciplinary (actuaries, accountants and lawyers) working party and are published every 2 years together with explanatory notes. The baseline loss of earnings multipliers represent the discounted life expectancy until final separation from the labour market (due to retirement at the statutory age or death). They are published in a set of tables that are disaggregated by age, sex, discount rate and year of retirement. These multipliers are referred to as Ogden multipliers and the tables as the Ogden tables (after the Chair of the original working party, Sir Michael Ogden, QC). The Ogden tables were in the fifth edition at the time of this study. The baseline multipliers are adjusted downwards to take account of non-mortality risks by using a set of broadly defined discounted employment risks, expressed as RFs. The RF is simply the WLE expressed as a proportion of the remaining years until retirement (see Section 2.5). The RFs are reported in the supplementary tables A, B and C of the Ogden tables (fifth edition) and are based on Haberman and Bloomfield (1990). They range from 0.98 at age 20 years to 0.90 at age 60 years, calculated at a 2.5% discount rate, for a man retiring at age 65 years. It is worth noting that the RF falls as the WLE falls (ceteris paribus), and hence a high RF corresponds to a low employment risk. Employment risks are differentiated according to age group, occupational group, geographical location and level of economic activity. They are not distinguished on the basis of disability; nor are they distinguished on the basis of current employment status.

2.2. Illustration of the multiplier–multiplicand method on a case example

In the following example, we illustrate the valuation of the loss of future earnings following personal injury which makes use of the traditional multiplier–multiplicand calculation method and the risks for contingencies other than mortality that are contained within the Ogden tables (fifth edition). Later on, we return to this case example to compare this award with that calculated on the basis of a new approach that is proposed in this study.

2.2.1. Case example

The claimant is female and aged 35 years at the date of the trial. She has three A levels, but not a degree, and was employed as a personal assistant in a private sector company at the date of injury at a salary of £25000 net of tax. She had no pre-injury disability. As a result of her injuries, she now has a continuing disability and is employed at the time of the trial as a secretary in local government at an annual salary of £17000 net of tax.

2.2.2. Valuation based on the fifth edition Ogden tables recommendations

The baseline multiplier from the fifth edition Ogden tables (Table 8) is 18.39 on the basis of a 2inline image discount rate. The reduction for employment risks is 0.97 (Ogden tables, Table C).

Table 8.   Average differences in employment risks RF (2.5% discount rate) based on model 2 classified by sex, age, initial employment status, disability and education level†
DisabilityHighest qualificationResults for employedResults for non-employed
<30 years3050 years>50 years<30 years3050 years>50 years
  1. †Source: model 2 (quarterly longitudinal LFS 1998–2003).

Non-disabledDegree or higher0.011−0.001−0.0260.0080.0170.009
Higher education (below degree)0.004−0.004−0.0140.0030.0000.001
A level or equivalent0.0120.0140.0060.0110.0220.007
General Certificate of Secondary Education grade A–C or equivalent−0.005−0.0130.003−0.008−0.017−0.029
Other or no qualifications−0.036−0.0100.035−0.049−0.036−0.014
DisabledDegree or higher0.1470.1550.1780.1130.1590.103
Higher education (below degree)0.1420.0900.0400.1780.0800.028
A level or equivalent0.1100.010−0.0090.145−0.0100.002
General Certificate of Secondary Education grade A–C or equivalent0.0660.0700.0950.0640.0770.048
Other or no qualifications−0.080−0.055−0.019−0.100−0.051−0.021
Non-disabledDegree or higher0.0740.044−0.0040.0890.0860.107
Higher education (below degree)0.0750.0520.0220.0870.0920.072
A level or equivalent0.0170.0140.0320.0230.0270.045
General Certificate of Secondary Education grade A–C or equivalent0.0120.0190.0140.0030.024−0.001
Other or no qualifications−0.124−0.0490.004−0.146−0.093−0.038
DisabledDegree or higher0.2920.2230.0700.3190.2510.118
Higher education (below degree)0.1930.114−0.0320.2080.1050.025
A level or equivalent0.1140.1090.0530.0900.0600.020
General Certificate of Secondary Education grade A–C or equivalent−0.0030.0150.0430.0040.0400.008
Other or no qualifications−0.142−0.075−0.016−0.116−0.063−0.011

The pre-injury expected future earnings are £25 000×18.39×0.97=£445958.
The post-injury expected future earnings are £17 000×18.39×0.97=£303251.
A typical Smith versus Manchester Corporation lump sum award is set to 12 months post-injuryearnings (see Section 2.3) =£17 000.
The award for loss of future earnings is £445 958−£303 251+£17 000=£159 707.

2.3. Shortcomings of the current approach

Although the use of the multiplier–multiplicand formula, and the use of the Ogden tables, undoubtedly provides greater transparency and objectivity in comparison with legal practice before Wells versus Wells (see Judicial Studies Board (2004)), several shortcomings remain in the method of calculation. This paper addresses those that relate to the calculation of RFs for employment risks, both before and after injury. A lack of precision in individual cases is the unavoidable cost of a broadbrush approach. However, finding the appropriate compromise between accuracy and simplicity requires some thought about the level of error in individual cases and bias across cases. When Lewis et al. (2003) used a US style method to recalculate loss of future earnings damages awarded in 100 personal injury trials in the UK between 1990 and 1999, they found a wide error distribution, generalized undercompensation of claimants and particular undercompensation of certain groups of claimants, e.g. young men with post-injury earning capacity. They also found that almost a quarter of the cases could be overcompensated when applying these adjustments to some groups of claimants. This is attributed to the RFs that are used in the Ogden tables being generally too high and particularly so for women (see Section 3 and Fig. 2 in Section 4).

Figure 2.

 Age-specific RFs by starting economic state and disability based on models 1 and 2 in comparison with the Ogden tables RF for (a) males and (b) females (all RFs are discounted at 2.5%): —×—, non-disabled and employed, model 1; inline image, disabled and employed, model 1; inline image, non-disabled and non-employed, model 1; inline image, disabled and non-employed, model 1; inline image, non-disabled and employed, model 2; inline image, disabled and employed, model 2; inline image, non-disabled and non-employed, model 2; inline image, disabled and non-employed, model 2; inline image, Ogden tables

The majority of claimants are employed and without a disability at the time of injury and the consequences of ignoring these conditions are likely to be an overstatement of the employment risks (i.e. RFs will be too low) in the pre-injury component of the loss-of-earnings calculation. Conversely, since any claim for loss of future earnings has as its foundation a long lasting work affecting disability, employment risks which account for neither disability nor displacement from employment will tend to be too low (i.e. the RFs will be too high). This additional employment risk is recognized by the courts and an attempt is made to compensate for the resulting loss through an additional lump sum payment. This lump sum is assessed separately from the multiplier–multiplicand calculation and has come to be called a Smith versus Manchester Corporation lump sum. The award is named after the case in which the principle for such an award was established (by Lord Scarman in Smith versus Manchester Corporation (1974), K.I.R. 1). The extensive use of Smith versus Manchester Corporation lump sum awards is discussed in Randolf (2005). The determination of the value of this lump sum is particularly arbitrary. When applied to a claimant who is employed at the time of trial, it is usually in the range of 6–24 months of post-injury earnings (Ritchie, 1994).

Whereas the tables for the baseline multipliers are updated every 2 years as life expectancy and interest rates change, the RFs have remained unchanged since their original publication in 1994. These RFs are ‘unconditional’ employment risks and they ignore the importance of past employment status as a determinant of current employment status. It is now possible, and indeed is common practice, to incorporate the transitions between different employment states which characterize the typical employment history into the estimation of the WLE. Using information on individual transitions between employment states, we use a Markov chain model to ‘condition’ future employment patterns on current employment states. This is particularly relevant to the present context because most claimants are in employment at the time of injury and suffer interruptions in employment as a result of injury. This is clearly illustrated in the Lewis et al. (2003) study where, out of 100 claimants, 96 were over the school leaving age and were employed at the time of injury, 63 of these were judged to have post-injury earning capacity but only 28 were in employment after their injury.

Currently, the Ogden tables contain some recommendations (based on the estimates that were reported in the Haberman and Bloomfield (1990) study) which attempt to account for the potential effect of occupational group, regional location and level of economic activity on employment risks. We re-examine the influence of each of these, and also the effect of educational attainment, and review the benefits of making adjustments for each. Some recent US studies indicate that following the onset of disability immediate losses are greater and longer-term recovery is lower, in terms of both income and employment, for those with low levels of education (see for example Charles (2003)). Disability and displacement will also impact negatively on earnings (see Gregory and Jukes (1997) for the UK and Kuhn (2002) for the USA). This latter effect is accounted for in the reduced post-injury multiplicand which the court determines on the basis of evidence from employment consultants (see Martin and Vavoulis (1999) for forensic economics approaches to the estimation of post-injury baseline earnings).

Importantly, the Ogden tables offer no recommendations on how to account for the impact of disability on employment risks and we have seen that the courts deal with the issue in a peculiarly imprecise and ad hoc manner, which has neither empirical nor theoretical foundation. From 1998, sufficient information is available in LFS data to calculate WLEs and RFs according to disability status and thus to incorporate the employment effects of disability within the multiplier–multiplicand calculation. We propose that employment risks RFs be calculated separately for individuals who are disabled and that these be applied to the baseline multiplier to produce a ‘disability-adjusted multiplier’ in the calculation of post-injury future earnings. We apply this method of calculation for the worked example in Section 2.2 again in Section 4.1 and we suggest that this alternative method of calculation should replace the Smith versus Manchester Corporation approach in the majority of cases.

2.4. Estimating working lifetimes

Whereas intense socio-economic research has been conducted into the causes and effects of unemployment and non-participation in the UK (see Verrall et al. (2005)), there has been very little interest in estimating labour market risks for the purposes of legal compensation. Although most of the applied modelling approaches are relevant in their own right, and indeed some could be extended to the problem of estimating employment risks over individual lifetimes, such work has yet to be completed in the UK. The dynamic modelling of employment decisions was developed in the USA from the early 1980s (see for example MaCurdy (1981, 1983) and Smith (1983)). These ‘life cycle’ models of labour supply sought to provide a theoretical context to explain the consistent inverted ‘u’-shaped participation and hours profiles with respect to age that are found in empirical studies. The focus at both the theoretical and the empirical levels has been the behaviour of hours of work, although the work life tables of Smith (1982) for the US Bureau of Labor Statistics provide age-related estimates of lifetime employment.

The first attempt to estimate lifetime employment risks for the UK was undertaken by the actuarial profession in the context of the valuation of loss of earnings in England and Wales (see Section 2.1). The study was undertaken by Haberman and Bloomfield (1990) and their results were presented as a set of actuarial RFs which capture the effect of contingencies other than mortality on the discounted number of years to retirement or death. At the time of this study, the modelling of employment outcomes in the UK was limited to static approaches which were based on age-specific prevalence rates. They made use of a traditional actuarial tool to construct a working life table based on adjusted labour force participation rates from the 1970s and 1980s, allowing for sickness and unemployment. They were well aware of the limitations of the data and the static methodology that was used. They considered that, compared with the multiple-state approach that was advocated by Hoem (1977), their employment risks were understated by as much as 8%. To date, no other estimates of lifetime employment risks have been produced in the UK to replace these early recommendations.

Since the Haberman and Bloomfield (1990) study, there have been some significant advances in the quality of the labour market data in the UK which allow for the dynamic modelling of labour force movements between economic states. Longitudinal labour market surveys for the UK have been available from the early 1990s in the form of the British Household Panel Survey, which was started during 1991, and the first LFS matched panel data, which were available from the beginning of 1992. There have been a few short-lived cohort-based studies available before the 1990s (e.g. the Department of Health and Social Security unemployment registry of men followed up from 1978 to 1980), but these targeted specific segments of the population and were insufficient for broader applications. Longitudinal data, combined with a Markov-type increment–decrement model, allow for the conditioning of future employment risks both on age and on starting economic state.

In contrast with the UK, the study of dynamic statistical modelling towards the measurement of WLEs for valuing damages is well established in the North American (US and Canadian) forensic economics literature. The Bureau of Labor Statistics has published work life tables of the US population since the 1950s and regularly publishes reviews of the methodologies and results. These tables generate a large amount of socio-economic research, including research on applied methodology. The first set of work life tables that was published by the Bureau of Labor Statistics, which used a Markov chain increment–decrement model, was based on the research of Smith (1982). This early methodology has been revisited in Alter and Becker (1985), who developed a clear mathematical framework for the estimation of WLEs. Further work that was undertaken by Smith (1986) extends this later model to allow for the effect of some individual characteristics, including race and education. Additional aspects of the multiple-state Markov chain estimation have been explored, for example, in Ciecka et al. (1995, 1997, 2000). Richards (2000) has provided an alternative view and pointed out empirical inconsistencies in comparison with the ‘conventional’ approach of WLE estimates. Krueger (2004) presented a detailed description of the modelling structure and estimation of the multiple-state Markov model from US data and reported on particular issues that are related to the application of WLE in the area of compensation for loss of earnings. More recently, the logit (and probit) parametric formulation of the odds ratios of the decrements has been the most commonly used approach for modelling the transition probabilities (see Millimet et al. (2003)).

The multiplier–multiplicand method of calculation that is used in the UK is crude by comparison with a US style approach. Its weaknesses as a method for the valuation of damages were addressed by Lewis et al. (2003), who estimated lifetime employment probabilities, and subsequently the actuarial value of a stream of future earnings, from a three-state Markov model (employed–unemployed–inactive) by using 1997 LFS data. The comparison of 100 adjudicated awards with those calculated by using this alternative approach makes a compelling case for the use of dynamic methods in valuing labour market risks in the UK tort system. The value of re-estimated awards was on average 21% higher than the awards that were actually made by the courts. For those claimants who were considered to have future employment prospects, the difference was 37%. The primary purpose of the Lewis et al. (2003) study was to propose a new methodology for the estimation of work life earnings rather than to document WLEs. The new methodology was proposed as an alternative to, and a replacement for, the multiplier–multiplicand method of calculation. In this study, we take the multiplier–multiplicand method of calculation as the given framework and seek to provide lawyers with an adaptation to this, their chosen method. This adaptation is based on an improved estimation of disaggregated RFs for the UK.

2.5. Work life expectancy and employment risks reduction factor

The statistical concept of WLE is central to the calculation of future loss of earnings in both the UK and the USA. The WLE represents the number of years that a person of age x is likely to spend working (and earning) until his or her final separation from the labour market, through either death or retirement. This can be formulated mathematically in the framework of a two-state Markov model, where the states at age x are denoted by Sx={1,2}, representing the state of being employed and non-employed respectively. Then, the WLE is calculated as the integral of the expected proportion of people who in t years time will be alive and in the employed state, conditional on being alive at the age x and in a given starting state Sx=i. Thus, in a multistate model, the WLE is expressed as the integral of the product between the transition probabilities from state i to j, inline image, and the corresponding survival probabilities, px(t), in t years from age x:


where we make use of the actuarial notation inline image to represent the total expected time spent in state j from age x over the remaining active time up to retirement age (tpx), when starting in state i. From the point of view of compensation for loss of earnings, only the future expected time in the employed state (i.e. j=1) is relevant and we can drop the j-notation in expression (1). Further, since we consider only discrete future times (tgeqslant R: gt-or-equal, slanted0), equation (1) can be approximated by making use of the trapezium rule, leading to the summation


where the boundary conditions are given by inline image, inline image and px(0)=1. The way in which the age-specific transition probabilities inline image are estimated depends on the type of data and on the complexity of the modelling method (see Section 3). In addition, in this study, we assume that the survival rates px(t) are the same for both economic states and depend only on age. This simplification is prompted by the shortcomings of the LFS with respect to the individual mortality experience of the participants. Although other longitudinal studies record the mortality of the participants together with socio-economic variables (most notably the British Household Panel Survey), it can be problematic to match these mortality rates against the economic states and covariates that are used in our study. Thus, we make use of the age-specific survival probabilities that are reported or contained in the UK interim life table for 1999–2001. Although we acknowledge that employment status affects mortality (along with educational attainment and disability status), we do not expect that the effect of these simplifications on the RFs will be significant given that the mortality rates over the working age range are relatively small. In addition, we note that it would be open to the court to select a case-specific life expectancy (term certain) based on medical evidence.

In the legal context, the WLE is the statistical estimate of the future number of years over which the annual loss of earnings occurs. This estimate needs to be discounted to account for early receipt of payments. The resulting measure is better known in the UK as the loss of earnings multiplier, which is computed by adjusting equation (2) by a real rate of interest r:


where ν=1/(1+r). In the computations, we have made use of r=2.5% (i.e. 0.025) in accordance with the latest recommendations of the Lord Chancellor that were set in June 2001.

In the USA, population WLE tables are published at the Federal level by the Bureau of Labor Statistics and the courts make extensive use of these and other sources of labour market data which are presented and interpreted in expert evidence from forensic economists. There is no ‘official’ equivalent of the WLE for the UK and there is a long standing reluctance on the part of the courts to hear evidence from experts in any discipline which might contribute to the assessment of future losses.

The empirical work that we present here is based on estimating age-specific WLEs for the UK. However, since we are working within the constraints of the multiplier–multiplicand formula (see Section 2.1), we convert these into an employment risks RF, which represents the ratio of the WLE to the expected number of years remaining alive up to pension age. To be consistent with the treatment of the WLE measure, we also need to express this as conditional on the starting state Sx=i at age x and to allow for survival and discounting:


where inline image is the discounted value of an annuity of £1 per annum paid up to retirement age tp. This is equivalent to the total of the discounted expected times in the two (alive) economic states.

The use of RFs has some clear practical advantages to the courts. First, the RF is a standardized measure that provides a simple, intuitive and self-explanatory index for users which can be readily applied to the baseline multipliers (discounted life expectancies) with which the courts are already familiar. Secondly, accounting separately for the effects of various factors (such as employment status, disability and education) in the form of adjusted RFs (see Section 3) aids transparency. The RFs are used by the courts as guidelines from which to depart depending on the individual circumstances of the case. Once the total discount for future employment risks has been disaggregated into its component parts, the courts would be able to make any discretionary adjustments.

3. Data and methodology

Our empirical analyses are based on recent LFS data. The LFS continuously collects information on an extensive set of socio-economic and labour force characteristics from a rotating sample of around 60 000 households. The survey was originally designed to provide periodic cross-sections of the working population and has been collected on a regular quarterly basis since 1992–1993. Each household is interviewed in five waves over a 1-year observation period. Consequently, each quarterly cross-sectional sample is formed by five separate waves (cohorts) of an approximately equal number of respondents. Making use of a matched files approach, this survey design allows the LFS to reconstruct the panel (cohort) segments from the corresponding fractions of the consecutive cross-sectional data sets.

We make use of two multiple-state models to estimate the WLE, inline image, utilizing equation (2), and we compare the results of each in terms of the corresponding RF, inline image, as given in equation (4). The models differ in terms of the underlying data and the complexity of the method that is used to estimate age-specific transition probabilities inline image. However, each is based on the basic increment–decrement model of labour force movements, as depicted in Fig. 1, and leads ultimately to the empirical estimation of age-specific transition probabilities of individuals between different economic states, conditional on surviving to a given age and on the previous economic state.

Figure 1.

 Two-state Markov model of labour force transitions (the non-employed state includes those who are unemployed and those who are inactive: (i) methodology 1, based on estimates of transition probabilities inline image, disaggregated by disability; (ii) methodology 2, based on estimates of hazard rates inline image, disaggregated by disability and education

Both models recognize the dynamic nature of the labour market and explicitly model multiple entries into, and exits from, employment as opposed to relying on a static distribution of the labour force across different economic states. Observations on the timing and the number (or intensity) of the transitions from one state to another make it possible to estimate the likelihood of the time that is spent in a particular state, conditional on age and on the starting economic state. The theoretical aspects of the application of multiple-state Markov chain models to econometric problems are well developed in the literature and the general consensus is that they provide a technically superior mathematical framework for the analysis of labour market behaviour, albeit with more demanding requirements on the data.

3.1. Methodology 1

The first approach applies a simple empirical methodology to three spring quarters of the LFS cross-section data (2002–2004). The purpose is to offer a transparent and accessible (at least intuitively) approach for users without specialist statistical training, particularly the legal profession. The method follows Alter and Becker (1985) and estimates age-specific employment probabilities based on year-by-year observed transitions between two labour market states, employment and non-employment:


where inline image are the total number of participants of age x who 1 year earlier were in economic state i and inline image are those moving from i to j over the age year (x−1,x). Thus, these rates are based on the observations of current employment status at age x and employment status 12 months previously. The economic states in Fig. 1, alternative (i), are further disaggregated by disability. Finally, the age-specific transition probabilities over any number of years t are estimated as a function of the yearly transition probabilities from equation (5) making use of a recursive formula. (This is equivalent to the matrix approach that is given by equation (8) and applied in the second methodology, as described in Section 3.2.)

Current employment status in the LFS is based on International Labour Office definitions of employment and different types of non-employment. The variable which measures employment status 12 months previously is recalled by respondents (i.e. retrospective in nature) and, in its aggregated form, can be mapped onto the aggregated form of current employment status. Both employment status variables include multiple categories of employment and non-employment. Owing to small sample sizes, when disaggregated by age, sex, disability and employment status 12 months previously, these multiple-category variables indicating various alternative forms of economic activity (i.e. categories 1–5) and inactivity (i.e. categories 6–29) are aggregated into two main transient states ‘employed’ (categories 1–3 and categories 1 and 3) and ‘non-employed’ (categories 4–29 and categories 2 and 4–10). Table 1 reports the full distribution of the LFS variable (INECACA), on which our classification of current employment status is based, and which contains four categories of employment. We are interested only in employment which attracts earnings, and hence our definition of employment excludes unpaid work (i.e. category 4). Non-employment includes unemployment and the many different forms of inactivity. Aggregation across the multiple categories of non-employment is required because of small subsample sizes when disaggregated by sex, age, disability and labour market status. The unemployed account for around 4% (males) and 3% (females) of the working population, which are insufficient to allow for separate categorization.

Table 1.   Employment categories by sex and disability based on LFS longitudinal data over the period of 1998–2003
CategoryDescriptionResults (%) for menResults (%) for women
3Government employment and training programmes0.430.320.450.270.200.28
4Unpaid family worker0.
5International Labour Organisation unemployed3.984.033.982.842.782.86
6Inactive—seeking, unavailable, student0.
7Inactive—seeking, unavailable, looking after family, home0.
8Inactive—seeking, unavailable, temporarily sick or injured0.
9Inactive—seeking, unavailable, long term sick or disabled0.
10Inactive—seeking, unavailable, other reason0.
11Inactive—seeking, unavailable, no reason given0.
12Inactive—not seeking, would like work, waiting results of job application0.
13Inactive—not seeking, would like work, student0.560.270.610.580.300.62
14Inactive—not seeking, would like work, looking after family, home0.370.600.343.043.113.04
15Inactive—not seeking, would like work, temporarily sick or injured0.230.890.140.250.970.15
16Inactive—not seeking, would like work, long term sick or disabled2.6819.510.181.7913.850.11
17Inactive—not seeking, would like work, believes no job available0.180.320.
18Inactive—not seeking, would like work, not started looking0.
19Inactive—not seeking, would like work, not looked0.360.460.340.470.520.47
20Inactive—not seeking, would like work, no reason0.
21Inactive—not seeking, not like work, waiting results of job application0.
22Inactive—not seeking, not like work, student2.140.912.332.390.962.60
23Inactive—not seeking, not like work, looking after family, home0.581.000.519.219.009.24
24Inactive—not seeking, not like work, temporarily sick or injured0.120.530.
25Inactive—not seeking, not like work, long term sick or disabled4.6333.480.334.1931.730.32
26Inactive—not seeking, not like work, not need or want job0.350.330.350.950.790.96
27Inactive—not seeking, not like work, retired3.234.392.831.692.001.49
28Inactive—not seeking, not like work, other reason0.
29Inactive—not seeking, not like work, no reason given0.

There is an inevitable loss of precision. The different subcategories within the non-employed category will have different levels of attachment to the labour market (see for example Jones and Riddell (1999)) and therefore also different WLEs. In particular, those whose status is ‘unemployed’ rather than ‘inactive’ are likely to be characterized by greater labour market attachment, greater WLEs and greater RFs (see again Jones and Riddell (1999)). The decision to include the unemployed with the inactive, as opposed to the employed, is justified with reference to their predicted lifetime employment outcomes. When disaggregated by disability, the employment outcomes of the unemployed are closer to those of the inactive than of the employed (see Butt et al. (2006)). Kreider (1999) grouped the unemployed with the employed but noted that this has ‘virtually no effect on the results of the analysis’ (see Kreider (1999), footnote 16). The potential for bias which results from our classification is considered to be small and is discussed in Section 5.

The LFS has collected full information on health indicators from 1998 and provides two compound measures of disability. The first refers to the adverse effect of impairment on either the amount or the type of work that the respondent can undertake. The second is defined in terms of the Disability Discrimination Act 1995 as ‘having a substantial adverse effect on a respondent's ability to carry out day-to-day activities’ (in Appendix B we present the LFS classification methodology of this disability variable). Disability is defined here as meeting three criteria:

  • (a) having lasted for over 1 year,
  • (b) meeting the Disability Discrimination Act condition and
  • (c) limiting the amount or the type of work that the respondent can undertake.

In the context of the current investigation, disability refers to the disablement that results from the injury which is the subject of the claim for compensation. We make use of this measure of disability to capture the impact of injury on the claimant's future employment prospects. Respondents who fall outside this definition of disability are not necessarily healthy. The non-disabled category includes individuals who may have some impairment which either does not meet the Disability Discrimination Act criteria or which does not affect their work.

The pooled LFS cross-section sample (2002–2004) comprises 191 508 individuals of working age (16–65 years for men and 16–60 years for women). Table 2 summarizes the data in terms of unconditional aggregate employment rates that were observed in the cross-sectional (and panel; see Section 3.2) data sets. We note that each sex is equally represented in the LFS samples, and that both contain a similar proportion of disabled, of about 12%. It is interesting that the rates of employment among the disabled are roughly equal for men and women (around 30%), whereas there are significant differences among the non-disabled (about 10% higher for men than for women). The sharp reduction in employment rates for those who are disabled is a first indication of the inadequacy of the Smith versus Manchester lump sum.

Table 2.   Population prevalence rates by sex, disability and employment status†
  1. †Source: cross-sectional LFS 2002–2004 (panel LFS 1998–2003 results are in parentheses).

Men 50% (49.8%)Women 50% (50.2%)

There is a considerable literature on the measurement error that is associated with self-reported disability (see Kreider (1999)) and the various attempts to estimate the resulting bias in relation to employment outcomes (see Kreider and Pepper (2007)). The financial and social incentives for non-workers to overreport disability mean that self-reported disability is not exogenous in the context of labour market outcomes. Berthoud (2006) discussed these deficiencies in relation to the LFS measure of disability. These deficiencies include the subjectivity that is inherent in self-reported disability, particularly when disability is reported alongside the collection of information on employment (see also Bound (1991)). In addition, the LFS definition of disability imposes a binary classification on a heterogeneous set of conditions and impairments at different levels of severity. These deficiencies are not new to this survey, or to this study (see Burchardt (2000)), and the consequences in terms of potential for bias in our estimated RFs are discussed in Section 5.

The definition of disability is important in the context of measuring its effect on employment, as rates of employment decrease according to the strictness of the definition (see Kruse and Schur (2002) for the USA and Berthoud (2006) for the UK). This is illustrated in Table 3 where rates of employment increase as the prevalence of disability increases. This study defines disability as strictly as is possible within the confines of the data to reflect the type of impairments in which claims are made for loss of future earnings. On this ‘strict’ definition of disability, the percentage of the labour force that is classified as disabled is consistent with that reported by the Berthoud (2006) study using the Health and Disability Survey in 1996–1997. Following the methodology that was developed by the Office of Population Censuses and Surveys in their disability survey in 1985–1988, respondents do not classify themselves in terms of disability. Rather, respondents report conditions and impairments and are classified, on the basis of these data, by the research team. According to Kreider (1999),

Table 3.   Disability prevalence rates and employment rates†
StudyDisability prevalence (%)Employment rate among (%)Employment rate among (%)Employment rate in population (%)
  1. †Source: cross-sectional LFS 2002–2004, panel LFS 1998–2003 and Berthoud (2006).

LFS cross-section 2002–2004
Disability Discrimination Act and work affecting12.231.579.874.0
Work affecting15.639.280.474.0
All disabled19.847.980.474.0
LFS longitudinal 1998–2003
Disability Discrimination Act and work affecting12.631.381.475.1
Work affecting16.239.482.075.1
All disabled20.347.882.075.1
Health and Disability Survey 1996–199712.630.076.071.0
Office of Population Censuses and Surveys disability survey 19857.831.0  

‘questions about specific conditions are often considered more concrete and less subjective than questions about work capacity’.

Consistency in disability prevalence rates between our study and Berthoud (2006) provides some level of confirmation that the strict version of the LFS disability variable does not exaggerate the population prevalence of disability nor the effect of disability on employment. The reported incidence of work-related illness also correlates well with the Office of Population Censuses and Surveys disability survey in 1985–1988 and the incidence of illness that is reported in visits by the adult population to general practitioner physicians (see Hodgson et al. (1993)).

In this simple methodology, we estimate RFs conditional on sex, age, starting employment status and disability status case by case by using cross-section data. The calculation is undertaken by using a spreadsheet for each sex, age and disability status. Although this methodology meets the objective of simplicity and transparency, and indeed has proved invaluable in enabling specialist injury lawyers to follow and to understand the calculation at each stage, it suffers from three obvious deficiencies:

  • (a) information on employment status 12 months previously is collected retrospectively and is therefore subject to a potential for recall and/or misclassification error;
  • (b) interim transitions during the 12-month period are ignored;
  • (c) the small sample size when disaggregated by sex, age, disability status and employment status precludes further analysis of any occupational, regional or educational effects.

These deficiencies provide the motivation for the more sophisticated approach that is described next.

3.2. Methodology 2

In our second approach, we make use of a total of 20 longitudinal five-quarter LFS data sets (i.e. cohorts of respondents) covering the period of spring 1998–winter 2003. There are a total of 203966 working age respondents in the pooled sample, made up by approximately 11000 participants per data set (Table 2 presents the aggregate employment rates by sex and disability).

This methodology is based on the empirical estimation of age-specific transition intensities between economic state i and j (see Fig. 1, alternative (ii)), given by the ratio


where inline image represents the expected total time (or exposure to risk) that is spent in the initial state i across all individuals of age x. The inline image are estimated from the observed quarterly flow of the labour force between the two economic states over individual ages. As in the first approach, it is possible to calculate the transition rates conditionally on additional factors (other than age), by disaggregating the original two-state model by additional variables. However, the estimation procedure is improved because the transitions between the layers of the additional covariate (e.g. shifts in the type of disability occurring in a year) contribute to the estimate of the total exposure to risk and hence no information is lost. Nevertheless it is a constraint of both approaches that the initial conditions at age x, as defined by the additional factors (e.g. disability and education), are fixed over the individual's lifetime. For a detailed description of the methodology that is applied, the reader is referred to Butt et al. (2006). It should be noted that there are potential deficiencies in the data, owing to factors such as attrition of the sample, non-response among panel members and the presence of third-party proxy responses. The effect of sample attrition has been investigated but was found to have no significant effect on the results.

We form a transition intensity matrix


that facilitates mathematical tractability and also simplifies the calculations, given that all the remaining computations are implemented by means of matrix operations that can be readily extended to any number of states. The crude estimates of transition intensities have been further smoothed by using cubic splines (see Appendix A). Although smoothing is appropriate for ameliorating the effect of either zero or undetermined transition intensities (i.e. either inline image or inline image), resulting from extensive subgrouping of the original data set, we note that our analysis shows that it does not strongly influence the WLE estimates.

The transition probabilities, conditional on starting economic state and age, are derived from the empirical estimates of the transition intensities by using a matrix approach. The 1-year transition probability matrix is calculated from the age-specific transition intensity matrix, as follows:


where diag(dx) is a diagonal matrix with entries formed by the eigenvalues of Mx (dx={d1,d2}x) and Ax is a matrix that is made up by the corresponding eigenvectors.

Then the transition matrix over any number of years t, conditional on being alive at age x, is given by the product of yearly transition matrices for each consecutive age–year up to age x+t:


Making use of the first column entries of the transition matrix in expression (8), we can proceed to estimate the discounted age-specific WLEs and the corresponding RFs based on equations (3) and (4), as described in Section 2.5. Alternatively, we provide matrix versions of the above expressions, which yield the age-specific WLEs and RFs for all of inline image and inline image respectively for any possible combinations of i and j economic states (for full details see Butt et al. (2006)).

As a means of estimating standard errors on the RFs we make use of the variance of the smoothing regression, as in equations (10) and (11) in Appendix A, to simulate random samples of (n=1000) independent age-specific transition intensities that are applied, in turn, to obtain samples of age-specific RFs. These random samples are used to estimate the standard errors of the reported RF figures.

4. Results

In this section, we present the age-specific RFs (and their corresponding WLEs) for the UK, conditional on sex, initial employment status, educational attainment and disability status. The advantage of reporting the RFs over the WLEs is that they provide a scaled measure for the lifetime employment risks, allowing a systematic and efficient comparison of the results. Fig. 2 illustrates the age-specific RFs resulting from methods 1 and 2 for males and females, conditional on disability and starting economic states. The RFs are compared with the current recommendations in the Ogden tables (using the average economic conditions scenario and ignoring the effects of industry and region). These results demonstrate clearly that the current Ogden tables recommendations are

  • (a) overoptimistic in terms of the RFs corresponding to the pre-injury conditions of those claimants who are employed at the time of the injury,
  • (b) not suited for those who are non-employed at the time of the injury and
  • (c) inadequate to assess the employment risks that are faced by an injured claimant with post-injury earning potential because they do not account for the negative impact of disability on future employment prospects, irrespective of the employment state of the claimant at the time of the trial.

It can be observed in Fig. 2 that the results are broadly similar by using each model, although neither the levels nor the profiles are identical. This may seem unsurprising given that the data cover different time periods and different methods were used for estimating age-specific transition probabilities. On further investigation, we find the source of the difference to be the frequency of observations on transitions between employment states. The effect of the frequency of observation depends on the starting economic state and on the disability status. Thus, for the employed starting state, the quarterly data yield systematically less time in employment than annual data, over a working lifetime, most especially for those who are disabled (see the curves for disabled and employed for models 1 and 2). The lower employment risks (i.e. higher RFs) for those in employment, when measured annually, suggest that short spells of non-employment exceed short spells of employment and particularly so for those who are disabled. Alternatively, for the non-disabled population when initially in non-employment, the quarterly data lead to systematically more time in employment than the annual data (see the curves for non-disabled and employed for models 1 and 2). The difference is negligible for the disabled whose employment prospects are poor (when already in non-employment) and who are unlikely to experience short-term employment spells. The differences are slightly greater for females, suggesting that women experience more frequent short-term transitions between the employed and non-employed economic states over a working lifetime.

As the frequency of measurement of labour force activity yields systematic differences in transition probabilities over a working lifetime so, in turn, the differences in transition probabilities generate differences in RFs. Short spells in employment or non-employment which are not captured in the annual data are sufficiently important to affect the total time that is spent in employment over a working lifetime. Since substantial bias due to attrition seems unlikely, we conclude that transition probabilities that are based on quarterly observations are the more accurate guide to lifetime employment prospects and we use the results of model 2. The numerical outcomes for the employment risks RFs and WLEs, corresponding to model 2, are reported in detail (together with their simulated standard errors) in Tables 4 and 5 respectively.

Table 4.   Employment risks RFs (with standard errors in parentheses) by sex, age, initial employment status and disability 1998–2003 (2.5% discount rate)
Age (years)Results for malesResults for females
Non-disabled and employedDisabled and employedNon-disabled and non-employedDisabled and non-employedNon-disabled and employedDisabled and employedNon-disabled and non-employedDisabled and non-employed
Table 5.   WLE (with standard errors in parentheses) by sex, age, initial employment status and disability 1998–2003 (discount rate 2.5%)
Age (years)Results for malesResults for females
Non-disabled and employedDisabled and employedNon-disabled and non-employedDisabled and non-employedNon-disabled and employedDisabled and employedNon-disabled and non-employedDisabled and non-employed

Focusing on model 2, Fig. 2 (and Table 4) shows that for men between the ages of 20 and 40 years who are not disabled, and whose starting state is employed, the proportion of their remaining working life that they can expect to be in employment is around 90%. The risk of non-employment increases steadily between the ages of 40 (0.11) and 60 (0.26) years. The shallow dip, at around 55 years, may reflect the difficulties that are faced by jobseekers in middle age and the effect of early retirement (which is stronger for men). The percentage of their remaining working life that non-disabled men can expect to spend in employment increases from the age of 60 years. This is not unexpected and it is most likely a product of selection effects in the labour market. The individuals who remain in employment until their 60s are likely to be those who are more motivated towards employment and/or who have achieved a good match in terms of skills and job requirements compared with those who have already left the labour market. The lower RFs for non-disabled women reflect the effect of child care. In contrast with men, the RFs for women increase with age so the gap between RFs for males and females narrows and achieves parity at the age of 52 years.

The most striking feature of Fig. 2 (and Table 4) is the negative impact of disability on lifetime employment prospects, even for those whose starting state is employed. There is an average difference in the RFs between a disabled and a non-disabled man (whose starting state is employed) of about 40 percentage points until the age of 55 years, after which the differences begin to diminish. Disability appears to become less of a disadvantage in the labour market with increasing age for those starting in employment. The pattern is much the same for disabled women whose starting economic state is employed, although the difference between RFs for males and females is lower than for the non-disabled at all ages and the parity year is earlier at 41 years. We note that a similar effect can be observed in Table 2, which shows an approximate 10% difference between the overall rate of employment of non-disabled men and women which reduces to only about 1% for those who are disabled.

Fig. 2 (and Table 4) also indicates that a starting state of non-employed is not a major disadvantage to the young who are not disabled. This is partly because, at this age, the non-employed include many whose inactivity is purposeful (e.g. higher education) and also because

unemployment is less ‘scarring’ for the young in terms of future unemployment (see Mroz and Savage (2006) for the USA and Burgess et al. (2003) for the UK). However, a starting employment state of non-employed for the non-disabled has a progressively increasing effect on future employment risks with age. On the basis of model 2, the increase in the employment risks for males from starting as non-employed (as opposed to employed) is around 7 percentage points at the age of 40 years after which it increases rapidly to 23% at age 55 years. Employment risks for women whose starting economic state is non-employed are around 10–15 percentage points greater than for equivalent men until the age of 45 years, again reflecting women's greater role in child care. After the age of 45 years, this gap increases steadily until retirement age, reflecting the diminishing employment prospects of unemployed women after their child-bearing age.

In addition to the impact of disability on employment risks, we also consider the level of economic activity and the effects of region, type of industry and educational attainment. Although we find some evidence for an industry and region effect (for further details see Butt et al. (2006)), it seems that, once the level of education and disability have been taken into account, these effects become largely insignificant. Educational attainment captures a large amount of the variability of the future working experience and has a strong effect on lifetime employment risks, both when estimated individually and when estimated jointly with disability. Tables 6 and 7 show the categories of the LFS variable HIQUAL (highest qualification) and the observed prevalence rates by education, sex, disability and employment status.

Table 6.   Groupings of the highest educational attainment categories
Highest qualificationLFS variable HIQUAL categoriesHighest qualificationLFS variable HIQUAL categories
Degree or higherHigher degreeA level or equivalentScottish Certificate of Education higher or equivalent
National Vocational Qualification level 5  
First degree AS level or equivalent
Other degree Trade apprenticeship
 General Certificate of Secondary Education grade A–C or equivalentNational Vocational Qualification level 2 or equivalent
Higher education (below degree)National Vocational Qualification level 4 General National Vocational Qualification intermediate
Diploma in higher education  
  Royal Society of Arts diploma
Higher National Certificate or Higher National Diploma, Business and Technician Education Council higher etc.  
  City and Guilds craft
  Business and Technician Education Council or Scottish Vocational Education Council first or general diploma
Teaching—further education  
Teaching—secondary O level, General Certificate of Secondary Education grade A–C or equivalent
Teaching level not stated  
Nursing etc.  
Royal Society of Arts higher diplomaOther or no qualificationsNational Vocational Qualification level 1 or equivalent
Other higher education below degree level  
  General National Vocational Qualification or General Scottish Vocational Qualification foundation level
  Certificate of Secondary Education below grade 1, General Certificate of Secondary Education below grade C
A level or equivalentNational Vocational Qualification level 3 Business and Technician Education Council first or general certificate
General National Vocational Qualification advanced  
  Scottish Vocational Education Council modules or equivalent
A level or equivalent  
Royal Society of Arts advanced diploma or certificate  
  Royal Society of Arts other
  City and Guilds other
Ordinary National Diploma or Ordinary National Certificate Youth Training or Youth Training Programme certificate
Business and Technician Education Council or Scottish Vocational Education Council national Other qualification
  No qualifications
  ‘Don't know’
City and Guilds advanced craft  
Scottish 6th-year certificate  
Table 7.   Prevalence rates by education (grouped highest qualifications), sex, employment status and disability over the period 1998–2003
Highest qualificationResults for males (%)Results for females (%)
Employed (79.5%)Non-employed (20.5%)Employed (70.3%)Non-employed (29.7%)
Degree or higher17.8410.6418.238.184.4011.0915.1411.4315.346.243.187.48
Higher education (below degree)8.826.928.925.183.856.1912.1112.2812.105.735.815.70
A level or equivalent32.5933.5332.5425.6926.1125.3717.2915.8817.3713.619.5015.28
General Certificate of Secondary Education grade A–C or equivalent17.3615.4917.4617.089.3623.0329.1025.4429.3125.7318.2228.77
Other or no qualifications23.3933.4222.8443.8856.2834.3326.3634.9825.8748.6963.2942.78

Figs 3–5 illustrate the joint effect of education and disability on the RFs, conditional on age, sex and starting economic state. Table 8 reports the average differences in the disability-adjusted RFs for broad age ranges. Educational attainment has the least effect on the employment risks for able-bodied employed men (see Fig. 3). The difference between the RFs of those with the highest and with the lowest qualifications is less than 5 percentage points over the first half of the working age range (see Table 8). This initial difference gradually reduces over the years and eventually the RF profiles cross over at the age of 45 years. Thereafter, those with the lowest level of qualifications spend more time in employment until retirement than those with any other level of qualifications.

Figure 3.

 Age-specific employment risks RF (2.5% discount rate) of the non-disabled population by educational attainment when initially employed for (a) males and (b) females (LFS 1998–2003): inline image, degree or higher; inline image, higher education (below degree); inline image, A level or equivalent; inline image, General Certificate of Secondary Education grade A–C or equivalent; inline image, other or no qualifications; inline image, overall non-disabled

Figure 4.

 Age-specific employment risks RF (2.5% discount rate) of the disabled population by educational attainment when initially employed for (a) males and (b) females (LFS 1998–2003): inline image, degree or higher; inline image, higher education (below degree); inline image, A level or equivalent; inline image, General Certificate of Secondary Education grade A–C or equivalent; inline image, other or no qualifications; inline image, overall, disabled and employed

Figure 5.

 Age-specific employment risks RF (2.5% discount rate) of the disabled population by educational attainment when initially non-employed for (a) males and (b) females (LFS 1998–2003): inline image, degree or higher; inline image, higher education (below degree); inline image, A level or equivalent; inline image, General Certificate of Secondary Education grade A–C or equivalent; inline image, other or no qualifications; inline image, overall, disabled and non-employed

Educational achievement has a much greater influence on the lifetime employment prospects of non-disabled employed women than men (see Fig. 3), so a 20-year-old woman with a higher education qualification or above (higher education (below degree) or degree or higher) can expect to spend 22% more time in employment until retirement than an unqualified woman. The difference between highly qualified and unqualified non-disabled women gradually reduces with age and achieves parity at the age of 54 years. It is worth noting that the results suggest that young women with higher degrees can expect to spend just as much time in future employment as their male counterparts (nearly 90%) and that, after the age of 40 years, they are likely to experience more time in employment than males.

However, it is among the disabled that educational achievement has the strongest effect on employment risks. The average difference between the RFs of disabled workers with high and low education levels, who are already in employment (Fig. 4), and below the age of 30 years, is 23 and 43 percentage points for males and females respectively (see Table 8). This difference between the employment risks profiles at the two ends of the education spectrum stays relatively constant until the age of 50 years, estimated at 20 and 30 percentage points on average for males and females respectively. Thereafter, the difference gradually reduces up to retirement age.

A particularly striking feature that can be observed in Table 8 (and Figs 4 and 5) is the positive effect of a degree on the employment prospects of the disabled. Thus, a highly educated disabled woman under the age of 30 years can expect to spend as much as 29% (when employed) and 32% (when non-employed) more time in future employment than the average disabled woman.

Higher education appears to compensate for many of the employment disadvantages that are brought about by disability.

However, the disabled are less likely to be more highly qualified than the non-disabled and particularly so if they are not in employment (see Table 7). For the non-employed and disabled participants in the survey 56% and 63% for males and females have only a low level of qualifications. This compares with about 23% and 26% for males and females, who are employed and not disabled. Low prevalence rates for those with higher education qualifications (around 8%)explain the more randomly progressing RF profiles that are observed in Fig. 5. Clearly, both

educational achievement and disability have major effects on individual lifetime employment prospects and it is therefore important to account for both in valuing damages following personal injury. There are also important wider policy implications here in favour of increasing participation in higher education for those who are disabled.

Previous recommendations in the Ogden tables included adjustments to RFs to reflect the effect of economic climate (high, medium and low). In practice, the middle range figures are almost always used. When we examine the effect of level of economic activity on RFs by comparing aggregate RFs for the periods 1993–1997 and 1998–2003 we find no significant differences (see Butt et al. (2006)). Although average employment rates are lower in the first period than in the second, both periods are periods of economic growth. A less propitious economic climate would potentially result in lower RFs, but it is beyond the scope of the LFS data to explore such effects. Moreover, it is not possible to predict economic conditions over the period for which any award of compensation is designed to cover.

4.1. Application to case example: valuation based on the education- and disability-adjusted multipliers

We revisit the worked example at Section 2.2 earlier and apply the revised RFs to the pre- and post-injury earnings calculations.

The baseline multiplier discounted at a rate of 2inline image% remains the same as above (18.39). The discounted reduction for employment risks for a non-disabled women employed at the age of 35 years is 0.84 (Table 4). This RF is adjusted upwards on account of the claimant's educational achievement by 0.01 (Table 5).

The disability-adjusted reduction for employment risks for this woman, on the basis that she is employed at the age of 35 years, is 0.41 (Table 4). This reduction factor is adjusted upwards on account of the claimant's educational achievement by 0.11 (Table 5).

The pre-injury loss of future earnings is £25000 ×18.39×(0.84+0.01)=£390788.
The post-injury earnings are £17 000×18.39×(0.41+0.11)=£162568.
The award for loss of future earnings is £390 788−£162 568=£228 220.

The damages award for loss of future earnings would be almost 43% higher (£68513) by using the education- and disability-adjusted multipliers method of calculation. This is consistent with the findings of Lewis et al. (2003) who reported that their method of calculation produces an average uplift of 38% on loss of future earnings for women who have post-injury earning capacity.

Alternatively, if the claimant had not been employed at the time of trial (or settlement) but earnings in part-time employment at £17000 per annum were expected, then the post-injury calculation would be as follows: £17 000×18.39×(0.23+0.06)=£90663. Hence, post-injury employment risks are higher and RFs are lower for the non-employed. Compensation is then higher (£300125) to reflect the higher expected loss.

5. Discussion

Although the approach to the compensation for loss of future earnings which is based on these revised employment risks RFs, and which uses education- and disability-adjusted multipliers to calculate post-injury earnings, represents a major improvement, there still remains the potential for bias. We discuss some of the main sources of bias in this section.

Disability and level of education are assumed to remain unchanged from the date of measurement. This ignores the possibilities that a non-disabled or an unqualified individual will become disabled or gain some qualifications during the course of their working lifetime. Although it is fairly straightforward using the panel data to extend the multiple-state model to allow for changes in the levels of disability or education, further disaggregation to this level (e.g. age-specific changes of health and level of education) would produce statistically unreliable subsamples. However, further disaggregation could be accommodated by using age ranges (e.g. over 5-year age intervals) instead of individual ages.

Disability is self-classified and there can be a tendency for people to exaggerate the limitations of their disability. This is particularly true when information on disability is collected in the context of employment outcomes since there is less stigma attached to non-employment where the cause is ill health or disability. This overreporting of health problems generates downward bias in the estimation of the post-injury employment risks. The simultaneous determination of employment status and disability generates upward bias (see Charles (2003) and Hotchkiss (2004)). There is also a financial incentive to non-employment by reason of disability (in the UK) in the form of payment of incapacity benefit.

The definition of disability is broad and does not distinguish different levels of severity. Disability is a heterogeneous variable and severity has an important effect on employment (see Charles (2003) and Berthoud (2006)). Similarly, we cannot distinguish in the LFS data between individuals who are disabled from their early years and those who become disabled after completing their education. The timing of disablement is likely to influence an individual's future employment prospects (see Charles (2003)) and to create a selection effect over time. Those who are disabled from birth, but whose disability does not preclude them from future employment, may be better able to adapt their education and training to suit the restrictions that disability places on their employment and thus to minimize the impact of disability on their employment prospects. For the older injured claimant, the potential mismatch between the abilities that are required for the pre-injury job and the post-disablement capacity for employment may be greater. For example, the skills and abilities of a middle-aged man who was employed in manual work before injury will be ill suited to the clerical work for which he is physically restricted to following injury (see Charles (2003) for explanation). For a given level of severity of disability, employment prospects diminish with age and with the mismatch between pre- and post-injury skill requirements. Since most personal injury claims involve injury or disease following the completion of education and training, LFS-based employment estimates will tend to understate the impact of disability on future employment.

Currently, the health variable in the LFS distinguishes different disability conditions but does not distinguish by impairment or by severity (see Appendix B). Without information on the nature of the condition which is the cause of disability, the effects of impairment and severity, which may differ in important ways, are conflated. Nevertheless, additional information in relation to disability, number of years since onset and cause of disability were collected in the LFS spring quarter of 2002. These provide scope to control for two aspects of heterogeneity on labour market outcomes: that of cause and timing of disability.

The use of a two-state (employed–non-employed) model in which the non-employed category includes the inactive and the unemployed is likely to bias the RFs in an upward direction for the inactive non-employed and in a downward direction for the active non-employed. Given the low incidence of unemployment within non-employment, the magnitude of any upward bias is likely to be very small. The incidence of unemployment among claimants is likely to be less than for the population generally, both pre injury (the most common form of tortious injury occurs at work) and post injury (the basis for any claim for loss of earnings is a significant and long lasting disability which suggests non-employment due to inactivity), so the downward bias will impact on very few cases. Again, the only way to accommodate a three-employment-state model is to combine different ages.

6. Conclusions

This paper uses dynamic labour market modelling to predict future expected time in employment for the purpose of valuing future earnings. The purpose is to provide greater accuracy in fulfilling the objective of the damages principle, i.e. financial restoration for the claimant. The results of this study have been substantiated by two different methodologies applied to different types of labour market data. We use the results to propose improvements to the multiplier–multiplicand method of calculation of loss of future earnings.

Through the use of a multiple-state Markov chain for the modelling of lifetime employment patterns, we estimate RFs which are conditioned on starting employment status (employed or not employed). The model allows for disaggregation by disability and thus for the separate calculation of post-injury future earnings. This provides a more accurate and reliable measure than does the Smith versus Manchester Corporation lump sum. Disaggregating by educational attainment accounts for the effect on employment of different levels of educational qualification. The results indicate that RFs vary substantially according to starting economic state, disability status and level of educational attainment.

We demonstrate, in an example, the application of both the traditional and the adapted methods of calculation and the consequences for the claimant in terms of level of compensation. We recognize that the long-term future employment risks of a heterogeneous workforce cannot be fully described by the means of a few variables (i.e. age, sex, starting economic state, education and disability) that are measured at a single point in time. In this regard, we have some sympathy for Lord Oliver's view (see Section 2.1). Our purpose, however, is to provide a more accurate starting point within the established broadbrush framework that is used by the courts. The intention is that the courts may deviate from this starting point subject to the particular characteristics and circumstances of individual cases.


Principal financial support from Economic and Social Research Council grant RES-000-22-0883 and a further contribution by an Institute and Faculty of Actuaries research grant for this research study are gratefully acknowledged.


Discussion on the paper by Butt, Haberman, Verrall and Wass

Robin de Wilde (London Chambers)

When all of us were at school, there was a clear division between the scientists, in whom I include the mathematicians, and the rest of us. That division continues into the real world and faces us today.

Lawyers are, for the most part, innumerate, save for Lord Denning who took a double first in mathematics at Oxford before he strayed into the law.

My own view is that most lawyers (Lord Denning excepted) have difficulty in doing anything more than counting and that solely for the purpose of examining their bank accounts. They do not understand money, but then most of us do not do that either. One Court of Appeal Judge summed up that phobia about figures, when asking me what I did for recreation. When I mentioned that I was concerned with the Ogden tables, he shuddered and said: ‘Those damned Tables, pages of them!’.

The late Sir Michael Ogden, QC, understood his own profession only too well. When he wrote his autobiography, he stated that he wrote to the Government Actuary of the day (before Chris Daykin) what the explanatory notes should do. His remarks have been included as the epigraph to the last two editions of the tables (circa Chris Daykin). It reads as follows (Ogden, 2002):

‘When it comes to the explanatory notes we must make sure that they are readily comprehensible. We must assume the most stupid circuit judge in the country and before him are the two most stupid advocates. All three of them must be able to understand what we are saying.’

So what happened to the mathematicians who were once at school? They became accountants, actuaries and statisticians. I accept that you have to be clever to become either an actuary or a statistician.

That is what happened to Zoltan Butt, Steven Haberman and Richard Verrall. They would be recognized today by their school contemporaries. Together with Victoria Wass, an economist (the dismal science), they have provided a solution to that most intractable of problems measuring partial loss of earnings, a problem that is not easily understood or translatable into monetary sums. It has been a great problem. How do you measure future partial loss of earnings?

It is all relatively simple, when the injured claimant who was working at the time of his injury and it is clear that he will never work again. It is a much more difficult, a more subtle and complex operation, when he is left with some partial earning capacity and the balance has to be calculated.

Is it what Jonathan Swift called ‘turning cucumbers into moonshine'? Not quite, but there is an element of that about it, when you are estimating and attempting to predict what an injured person's future loss of earnings is.

The legal test was first set out by that great Victorian judge, Lord Blackburn, 128 years ago, when he stated that the principle was

‘to attempt to put back the injured party in the same financial position as he would have been in before the accident, caused by the tort of another’

(Livingstone versus Rawyards Coal Company (1880) 5 App. Cas. 25 at 39).

As with most things in life, it is easier to state what you have to do rather than actually working out a method to achieve it. The process has led to the Ogden tables and the principle was restated again in the House of Lords 9 years ago in the famous case of Wells versus Wells ((1999) 1 A.C. 345 at 362).

To satisfy Lord Blackburn's dictum, you must look into the future and calculate that future loss of earnings in a way that provides a sufficient and adequate sum, which is fair and reasonable compensation.

That is why this paper is a great piece of academic work by all four authors, all from slightly different disciplines. There may be an element of ‘cucumbers and moonshine’ about it, but it does provide a better way of calculating future partial loss of earnings than that which existed previously.

The authors are honest and state the problems more clearly than has been done before. They recognize and face up to the difficulties. There may even be better ways of meeting the problems than they set out. By any standards, they have done something that no one else has done before. The process has already been followed by one judge in a reported case (Conner versus Bradman and Company Limited (2007), EWHC 2789 (QB), HH Judge Coulson, QC; November 30th, 2007). Since he gave that judgement he has been made a High Court Judge.

They, all four of them, deserve our appreciation and congratulations, particularly from the non-mathematicians, who have been attempting to cope with a practical problem.

There will be many injured people who will now achieve proper compensation for their future losses. The names of Butt, Haberman, Verrall and Wass should be on their lips, last thing at night and first thing in the morning. They will not be, but they should be.

That is why they should receive our thanks and congratulations on their achievement.

Chris Daykin (Government Actuary's Department, London)

I have great pleasure in seconding the vote of thanks for the paper, which is not only interesting from a methodological point of view but also of considerable practical importance as a backdrop for the sixth edition of the Ogden tables. I am not a disinterested observer, since as Government Actuary I was responsible for encouraging this research to take place.

The UK courts have struggled to know how best to fulfil the agreed intention, which is to put the injured person in the same financial position as if the accident had not happened, as articulated by Lord Blackburn in his classic 1880 judgement (Livingstone versus Rawyards Coal Company (1880) 5 App. Cas. 25 at 39).

For many years the courts were resistant to statistical and actuarial evidence, on grounds that they were dealing with individuals and that methodologies that were based on averages were not appropriate.

The first edition of the Ogden tables was published in 1984 and gradually gained acceptance for actuarially sound multipliers. The appropriateness of using recognized actuarial tables was settled with the Civil Evidence Act 1995, which refers explicitly to the admissibility and proof of the Ogden tables.

In the second edition, factors were introduced to allow for contingencies other than mortality, principally absences resulting from unemployment and sickness. The factors were based on a study by Haberman and Bloomfield (1990), which relied on 1973–1985 Labour Force Survey data.

The unavoidable limitations of this study, and hence the dubious validity of the adjustments for contingencies other than mortality in the subsequent editions of the Ogden tables, were widely recognized, but it proved difficult to initiate research to produce something better. We now have that research, the fruit of co-operation between the team at City University, who had experience in calibrating multiple-state Markov models, and the work of Victoria Wass at Cardiff Business School, who had experience of the practical outworking of the law of damages. I congratulate the authors of this paper for the combination of rigorous statistical methodology and practical explanation of the application of the work.

It represents an important advance in methodology, despite there still being limitations in what the data will support. Ideally we would like information to enable cohorts of disabled and non-disabled people to be tracked through successive periods of employment and non-employment, including information about the severity of impairment.

The methodology utilizes transition intensities between labour market participation levels at five successive quarterly measurement points to build the Markov multistate model. This is still clearly a somewhat blunt tool, when employment status can change frequently for those for whom employment opportunities are difficult. It also involves putting together information from a limited time period relating to different cohorts of individuals. Although this is a standard technique it can be problematical if the underlying data are heterogeneous and do not enable cohort and period influences to be distinguished.

I have another concern over the Markov assumption. The transitions between employment states are almost certainly not independent of the path that is taken to the current status. They will also depend, in principle, on the duration in the previous state, and particularly perhaps the accumulated duration in the employed and the unemployed state. However, taking these factors into account would require a more complicated model and much better data, which at present are not available for the UK.

The authors have worked hard to ensure that the definition of disability is as appropriate as possible for the expected application to the assessment of compensation, but it is still quite broadbrush. The alignment of the level of disability with that emerging from the Berthoud study (Berthoud, 2006) is helpful in establilishing credibility. Personal injury practitioners will clearly be concerned about whether the experience that is reflected here is relevant to particular disabled claimants. Sadly there are some cases of severely disabled claimants where post-injury employment prospects are very limited indeed, where the Courts will place a zero value on mitigation of loss. The new adjustment factors should be suitable for application to a wide range of other disabled claimants who are not in the category of no possible future earnings potential.

The analysis of factors which influence the necessary adjustments for time that is spent out of the labour market is also very important. The evidence from the authors’ work seems to be that the factors that are used for the previous adjustments, which are based on economic activity levels, occupation and region, do not show a significant effect especially when the data are controlled for education. What is now seen to be of greatest importance is educational achievement level, since that has an important influence on whether someone can rise above their injury-induced disability and take up employment opportunities.

This is a very important statement. However, it will probably take the courts some time to get to grips with thinking in this way and to use the new adjustments appropriately.

I congratulate the four authors on an excellent piece of work.

The vote of thanks was passed by acclamation.

James E. Ciecka (DePaul University, Chicago)

The US usage of the term ‘work life expectancy’ may be viewed as a misnomer because it refers to time in the labour force, whether working or looking for work (Krueger, 2004). Zoltan Butt, Steven Haberman, Richard Verrall and Victoria Wass use the term more restrictively to denote time spent working. Their usage seems appropriate in personal injury and wrongful death matters since earnings and fringe benefits flow from work time. However, the US usage has merit as well when an individual's work history, especially when it encompasses several years, automatically incorporates the effects of unemployment into that person's base earnings (multiplicand); and no additional adjustment for unemployment would be required or desirable. When including only employed time in work life expectancy, we must avoid double counting the effects of unemployment: once in a plaintiff's base earnings and a second time embedded into work life expectancy.

Formula (3) of the paper computes all the present value pieces comprising work life; the sum of which is the multiplier. This is not commonly done in the USA where work life consists of undiscounted labour force time. The US convention potentially creates a ‘front loading’ problem and overestimates of lost earnings (Skoog and Ciecka, 2006). This problem is avoided in the authors’ construct of work life, which focuses on present value, the ultimate object of interest for compensation purposes.

Recent work in the USA takes a different approach to finding work life expectancy from formula (3). The US approach defines a years-of-activity discrete random variable YAx and computes its probability mass function with recursive formulae (Skoog and Ciecka, 2002). With the probability mass function in hand, YAx’s characteristics can be computed such as its expected value E(YAx), or work life expectancy as the term in use in the USA, and standard deviation. Standard errors in this paper and the standard deviation of YAx are both important but different: the authors’ standard errors relate work life itself whereas the standard deviation of YAx places a bound of error on years of labour force activity—the former standard errors being much smaller than the latter. Standard errors for work life have been bootstrapped by Skoog and Ciecka (2004) using the US version of the work life concept; their standard errors are comparable with the authors’ standard errors but somewhat larger, perhaps related to different work life measures.

Finally, I have read and agree, in all respects, with my colleague Gary Skoog's following comments on this paper.

Gary R. Skoog (DePaul University, Chicago, and Legal Econometrics, Glenview)

I echo my colleague Jim Ciecka's comments on this paper. It is an important contribution to the literature and rightfully focuses on a Markov process model. Our recent work has produced Ogden-type tables, in which the multiplier incorporates the forces of interest, mortality, and non-participation in the labour force due to all causes, notably morbidity, health and election not to participate.

In the US tort system, experts, who are more often economists than actuaries, present damages evidence. This is in keeping with the US rules of ‘best evidence’ and the rights to a ‘trial by jury’. For these reasons, another class of testimony—from vocational experts—is also present and would be replaced in the authors’ tables by average employment experience of ‘disabled’ people in the Labour Force Survey database. However useful this might be if only a ‘rough-and-ready’ multiplier is deemed sufficient, the use of such averages generally is avoided in the USA where better evidence is desired or required. Vocational experts assess the plaintiff for type of work and ability to hold competitive employment, post accident. They take into account the unique qualities of the injured party—the effects of his education, training, occupation and transferable skills. Rather than determine that a large statistical group might retain 32% of its former capacity when disabled, a more careful analysis is undertaken. In considering transferable skills, and acknowledging that the vast heterogeneity in the disabled population gives little guidance for ‘disabled’ individuals, it is concluded that, if the injured plaintiff can hold a job post accident, and absent specific medical evidence to the contrary, economic losses are likely to be reflected in lower wages (the multiplicand) in the post-accident job rather than in lowered work life expectancy. For example, the employment experience of ‘disabled’ coal-miners from a particular musculoskeletal injury has virtually nothing to say about what the prospective employment experience would be for an injured plaintiff school-teacher suffering an adult onset brachial plexus injury, who further has a duty to mitigate damages by working if possible. The illusion of precision in using disability data often adds noise rather than signal and can in fact create damages where none exist—e.g. by declaring a person disabled who is earning the same amount in the same job post accident, a statistically irrelevant lowered work life spuriously assigns damages where none may exist. We therefore urge caution in the use of disability multipliers.

Grahame Codd (Irwin Mitchell Solicitors, Manchester)

Deficiencies in the historical approach

A claimant who suffers compensatable injuries, cannot return to pre-accident employment owing to disability but retains some residual earning capacity would be undercompensated under the historical multiplier–multiplicand approach. This is because the multiplicand representing the mitigation of loss on returning to work is effectively being subject to the same multiplier as the full loss of future earnings. The court would, in some cases, make a separate award under the principle in the Smith versus Manchester Corporation case, representing ‘handicap on the labour market’: this arbitrary sum would normally lie in the range of 6–24 months of post-injury earnings and fail to provide adequate compensation.

The problems faced by claimants who have some residual earning capacity

With the benefits of rehabilitation some claimants can resume employment, albeit at a lower level than before their accident. Their incomes will often be at a reduced level owing to a combination of lower grade work and also a reduction in working hours. For several reasons it is very unlikely that this group of disabled claimants will be able to enjoy a working life expectancy at a level approaching that enjoyed before their accident.

The disability-affected multiplier approach

The new disability-affected multiplier approach provides a more accurate starting point for the assessment of the capital figure representing mitigation of loss by reference to the claimant's residual earning capacity over residual working life expectancy.

The new methodology avoids the need to contemplate any Smith versus Manchester Corporation award in the vast majority of cases.

There remains flexibility in the system affording the opportunity for either side to argue for an increase or reduction in the disability-affected multiplier, taking into account the subjective facts and in particular the educational status of the claimant in any particular case.

The variables which apply in any particular case (i.e. age, sex, economic status, education and disability) and their interpretation will inevitably provide opportunities for the parties that are involved in litigation to adopt different positions so far as the calculation of future losses is concerned: however, beginning negotiations from a safer starting point should result in sensible settlements of claims in the vast majority of cases.


The excellent academic work that has been undertaken by the authors has been distilled into a simplified table of adjustment factors to be applied to working life multipliers, which has now been incorporated into the sixth edition of the Ogden tables, thus eliminating the pre-existing deficiency in methodology.

The authors are to be congratulated on facilitating a significant improvement in the ability of legal representatives more accurately to calculate future loss of earnings, particularly in cases where disabled claimants retain some residual earning capacity.

The following contribution was received in writing after the meeting.

Anthony Carus (Carus Consulting Actuaries, Stratford-upon-Avon)

I welcome this paper as a much-needed development of the work that was initially undertaken by Haberman and Bloomfield (1990). It is a fine example of a rigorous study of a very practical issue affecting the assessment of damages in court for some of the most disadvantaged members of society.

The authors quite rightly stress the need for the results of this research to be accessible by non-statisticians, and in particular by lawyers. The research has been incorporated into the sixth edition of the Ogden tables (Government Actuary's Department, 2007), and there is therefore a need to assess both its usefulness and its shortcomings within the context in which it will be used. Its ultimate output, in the form of reduction factors (RFs), meets the need for a simple, practical and accessible application but creates a requirement for the court to make choices in employment, disability and educational attainment statuses that are stark and, in the first two of the three categories, bipolar. The third requires a choice from three categories. The effects of the choices that are made are significant.

By way of example, if a disabled female claimant, aged 40 years, with a degree, is considered to be employed her RF will be 0.60 (Table D of the Ogden tables), leading to an adjusted multiplier of 9.32. If considered to be non-employed the factor will be 0.38, giving rise to a multiplier of 5.91. This substantial variation invites a difference of opinion on the loss of earnings claim and lends itself to argument on the meaning of the term ‘non-employed’ and the subsequent potential for court compromise. One such case has already been heard: Conner versus Bradman (2007) EWHC 2789 (QB). In that case the judge was faced with two divergent views from counsel and in his judgement exercised discretion in his choice of RF, averaging the separate claimant and defendant positions. Although this research, via the Ogden tables, illuminated the judgement, the fact that such divergence existed and required compromise suggests that further work might be required.

I believe that the authors’ intention, which is expressed in Section 6, to provide a more accurate starting point from which the Court may deviate, has been fulfilled. I would nonetheless encourage them to move on to the next stage of research to derive a further development of RFs that will assist and inform the court to an even greater extent.

The authors replied later, in writing, as follows.

We begin by thanking all the discussants for their contributions. We believe that this is an important policy area, and it is one to which statistical analysis has much to offer in the interests of justice and fairness. Robin de Wilde summarizes this extremely well and emphasizes the advantages that the statistical approach that is taken in the Ogden tables has over a more ad hoc approach. This is now clearly recognized through the various Acts and judgements which deal with many of the contentious areas of compensation awards. But we believe that current practices are working less well for the case of people who are injured but nevertheless left with some post-injury working capacity. We are grateful for the recognition of the importance of our work in this regard, e.g. in the comments of Grahame Codd, but we also acknowledge that there is more work to be done. Some of the work that, in an ideal world, we would have liked to have been able to do was not possible owing to its inherent complexity or because of lack of data. For example, Chris Daykin lists some shortcomings of the assumptions that we have made, in particular the Markov assumption. We have always realized that the assumption that the transition intensities depend only on the current state and not on the previous work history might be questionable in some cases. This is one of the reasons for stating that the Ogden tables provide guidance and should not be seen as prescriptive in every individual case. Notwithstanding this, we would welcome further research to throw light on the likely effect of the Markov and other assumptions, on the estimates of work life expectancy. Although we admit that some adjustment away from the figures in the tables may be appropriate in individual cases, we recommend great caution about how much discretion should be applied. This recognition should not be taken as a licence to move back to the way that things were done before the first Ogden tables were produced! An example of excessive discretion, about which we have some very real concerns, is the recent case of Conner versus Bradman and Company (2007) EWHC 2789, where the judge moved a considerable way from the figures in the tables, without a proper statistical justification. Anthony Carus points this out and we agree with him that this is clearly an area where the statistical approach needs to be developed further, to give guidance about how much discretion is appropriate, and how this discretion should be used. We were particularly interested, therefore, in the comments by Jim Ciecka and Gary Skoog. We also have been investigating how we can move forwards in this area and will certainly be reading with interest what Ciecka and Skoog have produced, e.g. through bootstrapping approaches. Gary Skoog urges caution in the use of disability multipliers on the grounds that they give an ‘illusion of precision’. We do not agree with this argument. In fact, we would argue the other way that, if you take everyone as an individual, you give a false impression that you can assess the work life expectancy with some precision for each such individual. We believe that it is better to start with verifiable ‘average’ figures and to depart from these as individual circumstances dictate.

References in the discussion


Appendix A: Cubic B smoothing spline regression

Let us consider n distinct realizations of a response variable y=(y1,y2,…,yn)T, corresponding to a given

predictor x=(x1,x2,…,xn)T. Then a cubic B smoothing splines regression model of y is defined as


where θ=(θ1,θ2,…,θp)T is an underlying p parameter vector of the model and f(x)=(f1(x),f2(x),…,fp(x))T is a vector of cubic B splines of the same length.

It is possible to show that the maximum likelihood estimate of θ is given by the matrix product


where F is often referred to as the smoother matrix, which is formed by the vector f(x) at the observation points x, i.e.


It can be shown that the estimator of the cubic B splines model (9) is asymptotically normally distributed with a variance that is given by the equation


where inline image is the overall variance of the error term and f(x)T(FTF)−1f(x) is a quadratic form representing the leverage (levx) of the response variable at point x.

In the current paper we have applied the findings of Rice (1984), which show that the overall variance, under the normal distribution assumption, can be estimated on the basis of the following sum of squares:


Appendix B: Disability algorithm (DISCURR)

Fig. 6 illustrates the LFS algorithm that is used to derive a four-category health variable, representing a long lasting disability status of the participants (DDA and work limiting, DDA only, work limiting only

Figure 6.

 LFS classification algorithm to determine the current disability status of the participants (DISCURR): source, Labour Force Survey User Guide, volume 4, LFS Standard Derived Variables 2004

or not disabled). The applied classification algorithm is based on a series of questions that are related to health status and work limiting conditions. Thus, only those participants are classified as disabled who experience health problems for more than a year (LNGLIM). However, those who report a long lasting disability, but this does not limit their day-to-day activity (HEALIM), and it is not a progressive illness (HEAL=16), and also does not have any work limiting effects, e.g. limits neither the type nor the amount of paid works (LIMITK and LIMITA), are also classified as non-disabled. In any other cases, the participants will be classified as disabled at one of the three predefined levels. In the current investigation, we have considered as severely disabled only those participants who have been known to suffer both by Disability Discrimination Act and by work limiting conditions. This level of disability corresponds to people with conditions that either limit their day-to-day activities or where it is a progressive illness, and in addition it is also perceived by the participants as disadvantaging them in the labour market both in terms of type of work and amount of earnings.