Intergenerational Equity: An Exploration of the ‘Fair Innings’ Argument

EQUITY

INTERGENERATIONAL EQUITY: ANEXPLORATION OF THE ‘FAIR INNINGS’

ARGUMENT

ALAN WILLIAMS*Centre for Health Economics, University of York, UK

SUMMARY

Many different equity principles may need to be traded off against efficiency when prioritizing health care. Thispaper explores one of them: the concept of a ‘fair innings’. It reflects the feeling that everyone is entitled to some‘normal’ span of health (usually expressed in life years, e.g. ‘three score years and ten’) and anyone failing toachieve this has been cheated, whilst anyone getting more than this is ‘living on borrowed time’. Four importantcharacteristics of the ‘fair innings’ notion are worth noting: firstly, it is outcome based, not process-based orresource-based; secondly, it is about a person’s whole life-time experience, not about their state at any particularpoint in time; thirdly, it reflects an aversion to inequality; and fourthly, it is quantifiable. Even in common parlanceit is usually expressed in numerical terms: death at 25 is viewed very differently from death at 85. But age at deathshould be no more than a first approximation, because the quality of a person’s life is important as well as itslength. The analysis suggests that this notion of intergenerational equity requires greater discrimination against theelderly than would be dictated simply by efficiency objectives. © 1997 by John Wiley & Sons, Ltd.

Health Econ. 6: 117–132 (1997)

No. of Figures: 10. No. of Tables: 4. No. of References: 28.

KEY WORDS — equity; priority-setting; QALYS

BACKGROUND

Priority-setting and the efficiency–equity trade-off

The inescapable imbalance between the technicalcapabilities of the health care system and theresources available to exploit them make priority-setting in health inevitable. Such priority settingcan be conducted in a variety of ways, each ofwhich reflects a particular ideology.1 Here I shallconcentrate on priority-setting which is informed,in part at least, by some kind of egalitarianideology.

When analysing the problem of priority-setting,economists routinely accept that there is a conflict

between equity and efficiency objectives, butrarely go on to estimate the actual trade-offbetween them.2 This reluctance may be partlyexplained by the fact that before attempting to doso it would be necessary to define both equity andefficiency in terms that were policy-relevant andunambiguous and in a manner that made meas-urement possible. The purpose of this paper is toexplore what is entailed in that quest, concentrat-ing on one particular equity principle and itsimplications for intergenerational equity.

The general concept of efficiency used here

I shall here take efficiency to mean maximizinghealth gain as measured in some standardized

*Correspondence to: Professor Alan Williams, Centre for Health Economics, University of York, York YO1 5DD, UK.

HEALTH ECONOMICS, VOL. 6: 117–132 (1997)

CCC 1057–9230/97/020117–16 $17.50 Received 4 April 1996© 1997 by John Wiley & Sons, Ltd. Accepted 10 January 1997

way [e.g. in life-years or in quality-adjusted life-years (QALYs)]. I am therefore following theapproach used by Wagstaff3 in 1991 rather thanthat used by Culyer4 in 1995. For Culyer, healthmaximization simply means getting to the fron-tier. As Culyer shows, several different pointsmight be chosen on this frontier, each of whichcould be justified by a specific equity argument.But because they lie on the frontier, they mustalso be efficient, so there is no equity–efficiencytrade-off in that situation. With the type ofproduction possibility frontier that is normallyassumed, the maximization of uniformly valuedhealth gains will define a single point on such afrontier, where it is tangential to a particularformulation of the Social Welfare Function, inwhich all units of health are equally valued nomatter who gets them.5 So the key differencebetween the two approaches is whether ‘healthmaximization’ generates a whole frontier, ormerely one point on it. In the latter case theequity–efficiency trade-off involves the estimationof the number of (uniformly-valued) units ofhealth that are sacrificed by moving from thatpoint to any other on the frontier. This is theapproach adopted here.6

The general concept of equity used here

The kind of equity issue in which I aminterested is one that adduces some personalcharacteristic of the beneficiary as a relevantconsideration in the estimating the social value ofa particular health gain.7 But a careful distinctionneeds to be drawn here between personal charac-teristics of the beneficiary which affect the quan-tum of benefit to be expected from a treatmentand personal characteristics which affect the valueattached to any given quantum of benefit. Forinstance, being old may reduce the number ofextra life years gained from an intervention (aquantum effect related to age), but being old mayalso affect the value that is given to each life yeargained (a valuation effect related to age). Thequantum effect will influence the shape andposition of the production possibility frontier. Thevaluation effect will influence the shape of thesocial welfare function. I regard the former as anefficiency issue and the latter as an equity issue.Those who do not like the implication that in theefficiency calculus the quantum effect may dis-criminate against some group whom they regard

as particularly deserving (e.g. the old, or the poor,or smokers or those with serious concurrentmedical conditions) are, of course, free to pursuesome countervailing argument as an equity argu-ment (which is what typically already happens inthe literature).

Some relevant equity principles

It is impossible within the short span of thispaper to provide a comprehensive account of allthe equity principles that have been, or might be,put forward as relevant for priority-setting inhealth care. I will not even consider in detail allthose reviewed by Culyer.4 My particular selec-tion is guided partly by the results of some surveysof popular opinion and partly by a personaljudgement that ultimately it is going to be equityconcepts related to outcome (i.e. health) which willbe decisive, not concepts which focus on processor resources.8 In various surveys9 that have beenconducted to elicit people’s views as to whoshould be given priority over others, there aresome recurring themes. One is that the youngshould in general be given priority over the old(though not infants over slightly older children).Another is that those looking after young childrenshould have priority over those without thatresponsibility. Many people also believe thatpriority should be given to those who have caredfor their own health over those who have not (e.g.by smoking, drug abuse or heavy drinking).

I have also noted another recurring theme,namely that those who have had a hard life (eitherspecifically to do with health, or more broadly todo with life in general) should not be furtherpenalised in health-care priority-setting by apply-ing to them the full rigours of the efficiencycalculus. Rawls’s advocacy of the rule that policyshould be guided solely by its effects on the worst-off member(s) of a community is the mostextreme manifestation of this kind of argument.10

It also manifests itself in a slightly less extremeform as a ‘double jeopardy’ argument,11 where itis said that those who have already experiencedsignificant misfortune should not have furthertribulations imposed upon them because they arenot good candidates (within the efficiency calcu-lus) for the receipt of health care.

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Health Econ. 6: 117–132 (1997) © 1997 by John Wiley & Sons, Ltd.

THE ‘FAIR INNINGS’ ARGUMENT

The argument stated in general terms

One version of this general approach centres onpeople’s supposed entitlement to a ‘fair innings’.This reflects the feeling that everyone is entitledto some ‘normal’ span of health (usuallyexpressed in terms of life years, e.g. ‘three scoreyears and ten’). The implication is that anyonefailing to achieve this has in some sense beencheated, whilst anyone getting more than this is‘living on borrowed time’. Thus whereas the‘double jeopardy’ argument directs attention onlyto those on the down-side, the ‘fair innings’argument considers both those on the down-sideand those on the up-side.

The fair innings argument12 is expounded inJohn Harris’s book The Value of Life, (Routledgeand Kegan Paul, London, 1985), where it appearson pages 91–94. He seems to have some difficultyin accepting it, however, as may be gained fromthe following passage:

‘What the fair innings argument needs to do is tocapture and express in a workable form the truth thatwhile it is always a misfortune to die when one wants togo on living, it is not a tragedy to die in old age; but itis on the other hand both a tragedy and a misfortune tobe cut off prematurely.’

Without telling us what are the key distinctionsbetween a ‘misfortune’ (a person’s judgementabout themselves?) and a ‘tragedy’ (a socialjudgement that separates one misfortune fromanother?), he ends up accepting

‘a reasonable form of the fair innings argument’

as being one in which

‘people who had achieved old age or who were closelyapproaching it would not have their lives furtherprolonged when this could only be achieved at the costof the lives of those who were not nearing old age’.

It is worth noting four important characteristicsof the ‘fair innings’. First of all, it is a notion ofequity that is outcome based, not process-based orresource-based. Secondly, it is about a person’swhole life-time experience, not about their state atany particular point in time. Thirdly, it reflects anaversion to inequality. And fourthly, it is quantifi-able and even in common parlance it has strong

numerical connotations. Death at 25 is viewedvery differently from death at 85 and age at deathis the key variable which is most often focusedupon. In my view, age at death should be no morethan a first approximation, however, because thequality of a person’s life is important as well as itslength, as I will indicate shortly.

Specific requirements in practice

It is the specific implications of this generalargument that I shall explore in the remainder ofthis paper. It requires us to address three keyquestions:

(a) what is a relevant personal characteristic bywhich to classify people for such policypurposes?

(b) how are we going to measure health?(c) how are we going to measure a health

inequality?

With this information before us, we then haveto decide just how averse we are to any inequalityso described, i.e. what sacrifices in the originalefficiency maximand we would be prepared toaccept to achieve a specified reduction in thepolicy-relevant inequality.

Policy relevant categorizations

Unfortunately, almost every conceivable cate-gorization of personal characteristics is likely tobe relevant for some policy decision or otherwhich might adduce the ‘fair innings’ argument as(at least partial) justification. Political priority-setting, where equity is a strong element, isundertaken at levels ranging from the WorldHealth Organization and the World Bank,through public bodies at national, regional andlocal levels, to hospitals, clinics and individualclinicians. Some of these policy-makers specialiseonly in health or health care matters, but somehave to weigh the claims of health and health careagainst the claims made for other ways ofimproving the length and quality of people’s lives,such as social care, education and the relief ofpoverty. Out of this welter of material I haveselected one characteristic which seems to beimportant in most communities at a fairly aggre-gate level, namely differences in health by social

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© 1997 by John Wiley & Sons, Ltd. Health Econ. 6: 117–132 (1997)

class (or by one of its close associates, such aseducation level, occupation, or income). This isnot the only relevant or important differentiatingcharacteristic that might be considered, of course,but it will serve as an example of how policyanalysis of health inequalities might proceed. Ileave it to the imagination of the reader toidentify ways in which these ideas might beapplied more widely, with such modifications asmay be necessary to make them relevant in othercontexts.

BASIC DIAGRAMMATICS

Culyer and Wagstaff13 approach these matterswith commendable clarity and Fig. 1 is a modifiedversion of the NE Quadrant of their diagram-matics, in which the production possibility curverepresents what health services can do to affectthe health of two (groups of) individuals A and B.It concentrates on the segment where the action islikely to be and identifies three key points. Theone labelled ‘equal’ is where the health of A andthe health of B are identical (lying as it does onthe 45° line from the origin). It is the preferredposition for a pure egalitarian. The point labelled‘maximum’ is where the aggregate health of thetwo individuals is as great as possible and thiswould be the preferred position of a pure effi-ciency maximizer (in the meaning of efficiencythat I am using).14 For those wishing to pursueboth efficiency and equity, some ‘intermediate’position will be preferred, depending on theprecise shape of their social welfare function. It isthis ‘intermediate’ position that is the focus ofinterest in this paper.

QUANTIFICATION

Reasons for pursuing a quantitative approach

On the whole, debates about equity are not cast inquantitative terms. Much more typical is philo-sophical argument designed to persuade thereader in principle to adopt or abandon a partic-ular position, such arguments often being con-ducted around illustrative case studies, whichpresent problems to be resolved, but which areusually inconclusive. This is because ethical princi-

ples are ‘essentially contestable’, by which ismeant that ‘there are competing conceptions ofjustice, all of which have respectable arguments intheir favour’.15 Most commentators observe thatsuch principles inevitably conflict with each otherand none ‘trumps’ the others, so that no principleis absolute. In the presence of such unanimityabout the relativity of ethical values, it is the moresurprising that there has been almost no attemptto establish empirical trade-offs (or even to asserta personal opinion as to what they should be).

If the nature and implications of particularpositions are to be clarified in a policy-relevantway, this discussion has to move on to seekquantification of what are otherwise merelyvaguely appealing but ambiguous slogans (e.g.that access should be determined by need, with-out ‘access’ or ‘need’ being defined in an opera-tionally meaningful manner and without anyattempt to estimate the costs, in terms of otherbenefits foregone). Only with some quantificationwill it be possible to devise rules that can beapplied in a consistent manner with a reasonablechance of checking on performance (i.e. holdingpeople accountable). At present, although reas-surance is frequently offered that equity con-siderations have been taken into account, there isno way of establishing what bearing, if any, thoseprinciples actually had upon the outcomes. Judg-ing by the persistence of health inequalities andthe almost universal agreement that they aredeplorable, it is tempting to conclude that therhetoric is not matched by any real commitmentto do anything effective. Quantification thus haspotential for clarification, for performance meas-urement, for accountability and for policy analysisand reappraisal. The quest for greater quantifica-tion of equity considerations seems worth pursu-ing on those grounds alone, despite the hostility itis likely to engender from those who mistakenlyequate precision with lack of humanity.16

The ‘fair innings’ argument applied to lifeexpectancy

A powerful part of the rhetoric about equity inhealth care employs the notion of equality appliedto people’s whole lifetime experiences and not justto their current situation. Adopting that broadperspective and looking first at life expectancy, wefind considerable variation both between coun-tries and within countries. If we take life expec-

A. WILLIAMS120


tancy at birth as defining a ‘fair innings’ within anysociety, then in the UK the differences in malesurvival rates between the professional and mana-gerial groups (social classes 1 and 2) on the onehand and the semi-skilled and unskilled manualworkers (social classes 4 and 5) on the other, hasbeen estimated to differ by about 5 years (72.5compared with 67.7).17 The differences in survivalrates at each year of age are shown in Fig. 2. Theequalization of life chances in terms of lifeexpectancy seems to require some changes inpublic policy, though not wholly confined tohealth care. But limited though the contributionof health care may be, it could be exploited morefully by weighting additional life years gainedfrom the various health care activities accordingto the social class of the potential recipient. Thesesame weights might also be applied to otherrelevant social programmes, so that their com-bined effect might be coordinated.

The ‘fair innings’ argument applied toquality-adjusted life expectancy

But if it is to capture the full flavour of this kindof thinking, the concept of a ‘fair innings’ needs tobe extended beyond simple life expectancy toembrace quality-adjusted life expectancy. Other-wise it will not be possible to reflect the view thata lifetime of poor quality health entitles people tospecial consideration in the current allocation ofhealth care, even if their life expectancy isnormal.

The measurement of health-related quality-of-

life is now under way in several countries18 andalthough I shall here draw only on UK material,the data from these other countries tells a similarstory about the unequal distribution of healthwithin them, by population characteristics that arerelevant to their own health care policies. Butthey are all fairly rich countries and it is possiblethat comparable data from much poorer countrieswill tell a very different story, though I doubt it.

The actual UK data on health-related quality-of-life that I shall use are from a survey repre-sentative of the adult population living in theirown homes, conducted by the Research Group onthe Measurement and Valuation of Health at theUniversity of York, in collaboration with Socialand Community Planning and Research in Lon-don.19 They are based on self-reported healthstates at each age, using the EuroQol EQ-5Ddescriptive system (see Table 1), valued by a set ofweights derived from the whole population bytime-trade-methods.20 It is clear from these data(shown in Fig. 3) that surviving members of socialclasses IV and V have noticeably worse healththan their contemporaries in social classes I andII, especially once they are past the age of 40years. When these data are combined with thedifferences in survival rates we find that thequality-adjusted life expectancy at birth of some-one in social classes 1 and 2 is nearly 66 QALYs,but for someone in social classes 4 and 5 it is onlyabout 57 QALYs.21 To achieve the mean value ofabout 61.5 QALYs (a ‘fair innings’ for a pureegalitarian) they would need to live to be 65 and71 years old, respectively, a feat achieved by about76% of social classes 1 and 2, but by only 46% ofsocial classes 4 and 5.

Figure 1. Health production possibilities: with social welfarefunction.

Figure 2. Survival rates from initial cohort males: by socialclass groupings.



Table 1. Health-related quality-of-life descriptors as presented in EUROQOLEQ-5D

By placing a tick (thus ) in one box in each group below, please indicatewhich statements best describe your own health today.

MobilityI have no problems in walking aboutI have some problems in walking aboutI am confined to bed

Self-CareI have no problems with self-careI have some problems washing or dressing myselfI am unable to wash or dress myself

Usual Activities (e.g. work, study, housework, family or leisure activities)I have no problems with performing my usual activitiesI have some problems with performing my usual activitiesI am unable to perform my usual activities

Pain/DiscomfortI have no pain or discomfortI have moderate pain or discomfortI have extreme pain or discomfort

Anxiety/DepressionI am not anxious or depressedI am moderately anxious or depressedI am extremely anxious or depressed

✓

Aversion to inequality

How should we respond to such data, assumingthat it is approximately true? Clearly thatdepends on (i) how convinced you are that the‘fair innings’ argument is a good basis for making

equity adjustments in the allocation of healthcare, (ii) how convinced you are that QALE atbirth is a good indicator in any country of whatconstitutes a ‘fair innings’ (and of departures fromit) and (iii) on how far you are willing to have theoverall level of health of the community reduced

Figure 3. Health-related quality-of-life: males by social class.

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in order to reduce inequalities in the distributionof health. So far I have not considered the lastpoint in detail and this is the time to do so.

In Fig. 1 I presented a close-up of the segmentof the health production possibility frontier that isrelevant to policy-making about health, indicatingthree points on it which might be objectives ofpolicy. These were the pure efficiency point(‘maximum’), the pure equity point (‘equal’) andone in between (‘intermediate’), the last being thepoint of tangency with a social welfare function.In Fig. 4 these abstractions are given substance. Init, health is measured as life expectancy at birthand ‘A’ and ‘B’ have become UK social classes 4and 5 and 1 and 2, respectively. The point labelled‘intermediate’ is the actual current distribution oflife expectancy at birth between the two, namely67 for SC4 and 5 and 72 for SC1 and 2. Theproduction possibility frontier and the socialwelfare function are hypothetical and as drawncharitably represent the current situation as beingthe best we can do on efficiency grounds andwhere we would choose to be on equity grounds,given the circumstances in which we find our-selves. Neither of these propositions may betrue.

Henceforth I am going to ignore the productionpossibility frontier, because my argument doesnot need it. Even if (as seems likely) we wereinside the frontier rather than on it, but off thelocus of points of perfect equality, our equityobjectives would lead us to prefer to movetowards that locus even if we cannot get to thefrontier. It would not be a wise strategy to say ‘let

us first of all get to the frontier and then we willworry about equity’. Firstly, we are unlikely everto get to the frontier and secondly, even if we did,we might find ourselves in such an extremelyinequitable situation that there would be no wayof remedying it. It is better to accept thatinefficiency and inequity are both endemic in allsystems and both have to be worked onsimultaneously.

Whether or not it is true in fact, I would askpeople to assume that moves towards greaterequality can only be achieved by reducing thelevel of overall health. The equity-efficiencytrade-off then consists in discovering the answerto the question, ‘how big a sacrifice in the overallhealth of the population would you be preparedto accept in order to eliminate the disparities inhealth between A and B?’. Different As and Bscould then be specified and the current disparitiesbetween them would be the actual comparator inthe above question.

Returning to social class differentials betweenmales in the UK, suppose people were preparedto sacrifice 6 months of life expectancy at birth, inorder to eliminate the disparity of 5 years. This isthe situation represented in Fig. 5, which startsfrom the same ‘current UK situation’ (previouslycalled ‘intermediate’), but which also shows themean life expectancy (69.5 years) and the equallife expectancy that people would settle for if the5 year disparity could be eliminated (‘equal at69’). This last point and the current situation andthe obverse of the current situation (where therespective situations of A and B are reversed), are

Figure 4. Life expectancy at birth: males by social class



all on the same social welfare contour. So, byfitting a suitable function to them (i.e. one that issymmetrical about the 45° line from the origin),we can draw the relevant social welfare contour.22

This is in fact the one that has been there from thebeginning and from it we can compute thegradient at the current situation. It is approx-imately –2, meaning that we should attach twicethe weight to improving the life expectancy atbirth of people in SC4 and 5 as we do to doing sofor SC1 and 2.

As and when the disparity reduces, theserelative weights will decline as we move along thesocial welfare contour towards the locus of pointsof perfect equality. Obviously, the smaller theefficiency sacrifice that people are willing to make,the less will be the curvature of the contour andthe smaller the differential weight at any point inthis space. The curvature of the contour resultingfrom various combinations of discrepancy sizeand sacrifice size is shown in Table 2. The caseshown in Fig. 5 was for a discrepancy size of 5 anda sacrifice size of 0.5 (half a year), giving a valueof r equal to 10.4. Table 3 shows what the equityweight (social welfare contour gradient) would befor any r and any discrepancy size, when thereference point is equality at 70. The referencepoint is important, because it sets the absolutelevel of social welfare at which inequality aversionis being evaluated.

It is, of course, quite likely that people willregard different discrepancies with differingdegrees of concern according to their size, nature

(e.g. whether it is a difference in life expectancy orin quality-adjusted life expectancy) and likelycauses (e.g. whether due to inherited factors orfreely chosen lifestyle).

Fine-tuning the ‘fair innings’ argument

There are two respects in which it might bedesirable to ‘fine tune’ the crude version of the‘fair innings’ argument that I have presented sofar. One would be to make it more dynamic andthe other would be to individualize it. I will sketchout each possibility in turn.

In the Culyer diagrammatics, the situation inwhich A and B find themselves is not ‘at birth’, butsome way into their respective lives.23 In thepresent context this raises the issue as to whetherit is right that the fair innings is defined as at birth,or whether it should be recalculated for survivorsaccording to where they are at present. Forinstance, for those surviving to the age of 20, 40,60 and 80 the expected age of death and theexpected lifetime QALY totals, increase as shownin Table 4. The changes are not dramatic until thelater ages, when survival is a more distinctiveachievement and survival with good HRQOLeven more so (especially for SC4 and 5). Theargument against ‘renegotiating’ the notion of afair innings in that way is that, in raising it forsurvivors we would delay the point at whichanyone gets penalised for having more than theirfair share, which means redistributing resourcesaway from those less likely to survive. Theargument in favour is that as general livingstandards rise, it is only right that the higher lifeexpectancy now enjoyed by subsequent ‘cohorts’should be shared with the earlier ones and oneway of doing this would be to raise the level of the‘fair innings’ somewhat.24

But that leaves open the question of having theweights change over a person’s lifetime as theyapproach and perhaps eventually exceed, thepredetermined ‘fair innings’. The situation formales by social class is set out in Fig. 6, whichshows the expected lifetime QALYs for the twosocial classes. At the vertical axis is shown quality-adjusted life expectancy at birth (approximately66 and 57, as reported earlier). But for those menin each social class who survive to the various agesshown, the expected lifetime QALY totalincreases, being made up of the QALYs they havealready enjoyed, plus the relevant age-specific

Figure 5. Inequalities in life expectancy: males by socialclass.

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Table 2. Implied value of r (which indicates the strength of aversion to inequality) accordingto size of sacrifice and size of inequality (both measured in the same unit, e.g. years)

Size Size of sacrificeof

difference 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1 56.5 * * * * * * * * *2 13.1 27.7 43.7 61.8 84.0 * * * * *3 5.2 11.6 18.1 25.1 32.6 40.8 50.2 61.3 75.0 92.84 2.5 6.0 9.6 13.3 17.2 21.3 25.6 30.3 35.5 41.35 1.2 3.5 5.8 8.1 10.4 12.9 15.5 18.2 21.0 24.06 0.6 2.1 3.7 5.3 6.9 8.5 10.2 12.0 13.8 15.77 0.1 1.3 2.4 3.6 4.8 6.0 7.2 8.4 9.7 11.08 # 0.7 1.6 2.5 3.4 4.3 5.2 6.1 7.1 8.19 # # 1.1 1.8 2.5 3.3 3.9 4.6 5.3 6.1

10 # # 0.7 1.2 1.8 2.4 2.9 3.5 4.1 4.7

Table 3. General table of resulting gradients or equity weights (when equality point = 70)

Size Value of index of inequality aversion (r)of

difference 1 2 3 4 5 6 7 8 9 10

1 1.03 1.04 1.06 1.08 1.09 1.11 1.12 1.14 1.16 1.182 1.06 1.09 1.12 1.16 1.20 1.23 1.28 1.32 1.36 1.413 1.09 1.14 1.20 1.25 1.32 1.39 1.46 1.54 1.63 1.724 1.12 1.20 1.28 1.36 1.46 1.57 1.69 1.82 1.98 2.165 1.16 1.25 1.36 1.48 1.62 1.79 1.98 2.21 2.48 2.826 1.20 1.32 1.46 1.62 1.82 2.06 2.36 2.74 3.23 3.897 1.23 1.38 1.56 1.79 2.06 2.41 2.88 3.52 4.46 5.968 1.27 1.46 1.68 1.97 2.35 2.87 3.62 4.78 6.82 11.299 1.32 1.54 1.82 2.19 2.72 3.49 4.74 7.09 12.94 48.9210 1.36 1.62 1.97 2.46 3.19 4.38 6.65 12.56 56.44 >100

Table 4. UK health expectancy at different ages: males by social class. Source: Bloomfield and Haberman,and MVH HRQOL data

Expected age at death Expected lifetime QALYAge total

SC 1 and 2 SC 4 and 5 Difference SC 1 and 2 SC 4 and 5 Difference

At birth 72.0 67.2 4.8 65.8 57.1 8.7At 20 72.3 67.7 4.6 66.0 57.5 8.5At 40 72.8 68.5 4.3 66.5 58.2 8.3At 60 74.1 71.0 3.1 67.6 60.3 7.3At 80 81.7 81.0 0.7 73.9 66.9 7.0



quality-adjusted life expectancy. Even a man inSC4 and 5 will eventually achieve the ‘fairinnings’, here supposed to be 61 QALYs,25 by thetime he is 64 years old. The equity weights usedshould reflect this fact and if recalculated year byyear to reflect the divergence of actual prospectsfrom the ‘fair innings’, would take on the valuesshown in Fig. 7, which obviously manifests theobverse of the pattern in Fig. 6. Thus there wouldbe generated a set of age weights to apply withineach relevant subgroup of the population.

It would be possible to go a step further andidentify other groups whose health is of specialpolicy relevance, for instance the permanentlydisabled. This is rather complex territory but, toindicate the possibilities, in Fig. 8 I have sketched

out four simple cases, where from birth to deaththe disabled person is in a stable state, which inhealth-related quality-of-life terms is rated at 0.5or 0.6 or 0.7 or 0.8. No deterioration with age hasbeen assumed and survival rates are taken to bethose for males in the UK. The social welfarefunction used is the one that has r = 1.9 and a fairinnings is taken to be 61 QALYs, making this casecomparable to that depicted in Fig. 7. It will beseen that for the most severe disability con-sidered, the equity weights would be extremelyhigh if we took the view that the permanentlydisabled are entitled to the same ‘fair innings’ aseveryone else. In the most severe case this is justnot deliverable and even at levels 0.6 and 0.7 it israther unlikely and would be even more unlikelyif deterioration with age were taken intoaccount.

Age-weights as well?

What is the relationship between the age-weights considered in the preceding section andthe age-weights promulgated by the World Bank?Do we need both, or are they substitutes for eachother? The World Bank has published26 the set of‘age-weights’ reproduced here as Fig. 9 and hasused these weights when measuring the ‘burden ofdisease’ in different countries. The authors of theWorld Development Report 1993 observe that

‘Most societies attach more importance to a year of lifelived by a young or middle-aged adult than to a year oflife lived by a child or an elderly person’.Figure 6. Survivors’ expected lifetime QALYs: males by social

class.

Figure 7. Equity weights over lifetime: males by social class.Figure 8. Equity weights over lifetime: males with permanent

disabilities.

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So in their table of age-weights a weight of zerois attached to newborns, the weights peak in thelate 20s and then decline to fall below 1 in theearly 50s. These age-weights are important socialjudgements, which may well be appropriate to theconditions in the countries with which the WorldBank mainly deals in the field of health. Thus toohigh a birth rate may justify the low weight givento infants; the peak productivity of manualworkers in countries living near subsistence mayjustify the high weights in the range 15–40; andthe low level of real income in such countries mayjustify the weight less than 1 given after the age ofabout 50. In richer countries things may bedifferent. For example, with a low birth-rate thestarting values will be higher. If the productivityof a largely non-manual workforce peaks later,the peak will be later. And with greater realincome an ageing population is more supportableso the age at which the age-weights fall below 1will come later.

Thus one simple route into the equity–effi-ciency trade-off might be to use weights such asthese in the maximization process, so that insteadof maximizing life years or QALYs, it would beage-weighted life-years or age-weighted QALYsthat are maximized.27 It would only be bycoincidence that the maximization of age-weighted health gains also maximized unweightedhealth gains and the ‘efficiency loss’ should becalculable from the difference between them.

But the age-weights emerging from the ‘fairinnings’ argument and those emerging from theWorld Bank’s argument, are picking up differentthings. The World Bank’s age-weights aredesigned to reflect the view that people ofdifferent ages have a different (social) value

(which in turn reflects their likely life stage). Theyears between 20 and 50 are particularly valuableto society because those are the years of procrea-tion and child-rearing and the years in which therest of society gets the maximum economic returnfrom earlier investments in an individual’s educa-tion and training, etc. Even at individual level thisperiod is frequently referred to as ‘the best yearsof my life’ or the ‘prime of life’ and the markedlack of enthusiasm with which my younger col-leagues celebrate their 40th and 50th birthdaysseems to reinforce the view that these achieve-ments are seen as ‘millstones’ rather than‘milestones’.

The age-weights relating to the ‘fair innings’argument have a different rationale. They arelinked to the likelihood that over your lifetimeyou will achieve a certain target number of lifeyears or QALYs. So what ought to be happeningis that the World Bank age-weights are appliedbefore a ‘fair innings’ is calculated, though I havenot done so here because of my wish to highlightone thing at a time and not take on boardeverything at once. I have however done somecalculations to see where World Bank-type age-weights would lead and Fig. 10 shows the effect ofage-weighting upon male life expectancies atdifferent ages. It will be noted that using theseweights sharply increases quality-adjusted lifeexpectancy in the early years, with a crossover atabout age 35. The use of such age-weightsincreases the ‘fair innings’ (QALE at birth, as canbe seen from its starting point on the verticalaxis). It does this because of the high weight givento the middle years. But this also makes it easierto attain a ‘fair innings’ within the average lifeexpectancy, which in turn would mean that the‘fair innings’ age-weights would fall below 1.0 atan earlier age.

CONCLUSIONS FOR POLICY AND FORRESEARCH

Motivation

This exploration of certain equity issues, along-side the pursuit of efficiency, was motivated bytwo different desires. The first was to relatediscussions of social justice, as typically conductedby non-economists, more closely to ways ofthinking that are natural to economists, so as to

Figure 9. Relative value of a year of life (World DevelopmentReport 1993).



encourage other economists to pick them up andrun with them. The second was to impose somequantitative rigour upon the assertions made bynon-economists about what is equitable, so thatwhenever it is argued that more weight should begiven to one class of persons, it has to beacknowledged that this means that some specifiedother class of person is going to suffer. There is aregrettable tendency for equity arguments to beconducted within a rhetorical framework in whichit appears possible to ‘do good’ at no opportunitycost whatever. It generates a great deal ofrighteous self-satisfaction for the romantic escap-ists and it puts economists back in the role of thedismal scientists always stressing the sacrifices, butit does not help the hard-pressed decision-makerswho grapple with the issues in real-life everyday.

This is a first attempt to take one such equityprinciple, the ‘fair innings’ argument and subject itto empirical manipulation. The term ‘manipula-tion’ is used advisably, because the empirical datathat are employed are stretched to their limits(some would doubtless say beyond their limits) inorder to stimulate thought and to indicate whatcould be done if we chose to go down that route.Such manipulation is essential if we are to bringhome the fact that giving priority to one groupinevitably disadvantages others, a consequencewhich many advocates of particular equity princi-ples fail to make clear (and they rarely state whowill be called upon to make what sort of sacrificeeven when they do acknowledge this implication).I have not attempted a philosophical critique ofthe ‘fair innings’ argument itself, which I mustconfess I find intuitively appealing. But consider-ing what an apparently simple idea it is, it seems

to lead us into deep water rather quickly. But itdoes seem to capture a great deal of the concernsthat people express when resisting the single-minded pursuit of efficiency notions in healthcare.

Subject to what might emerge from furtherexploration of these ideas, however, I would liketo end with some observations which rest on thetentative conclusion that I have got the broadpicture right, even though the detail may besuspect.

Equity weights?

One of the few issues in the equity field aboutwhich there seems to be an overwhelming con-sensus, is that the young should have somepriority over the old (a view held by the old aswell as by the young). Unfortunately, this remark-able consensus is likely to evaporate when thequantitative issue is addressed as to how muchpriority the young should have, since I doubtwhether many people would interpret this priorityranking to mean that everyone over a certain ageshould be denied all health care.

For a long time I have been of the view that thebest way to integrate efficiency and equity con-siderations in the provision of health care wouldbe to attach equity-weights to QALYs. QALYsmeasure benefits of health care in standard unitsand equity-weights allow benefit valuation tobecome person-specific to the extent that that ispolicy-relevant.28 But there is a danger that suchweights become arbitrary and capricious andcome to be used to fudge outcomes in ways thatwould not be acceptable if their basis wereexposed. One safeguard against this is to havesome underlying (or ‘over-arching’?) general prin-ciple enunciated, which can be confronted withevidence, so that its various implications can beexplored in a quantitative way. The fact that it ispossible to move from a general notion of a ‘fairinnings’, to specific numerical weights reflectingthe marginal social value of health gains todifferent people, seems to me to be an importantbreakthrough.

It also sparks off an interesting research agendaof both a theoretical and an empirical kind. Mostof the theoretical work will be interdisciplinary,requiring (some) economists to get to grips withboth the philosophical concepts and the socialcategorizations that would be relevant to definingFigure 10. Different life expectancies: males at various ages.

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a ‘fair innings’. Should there be just one ‘fairinnings’ for everyone served by a particular healthservice, or is there one for men, another forwomen and variants within each of these forsocial class and race and location and smokingbehaviour and life style and so on? This is notsomething that economists can decide, but it issomething we can force out into the open andseek to have clarified.

At an empirical level, this enterprise will bequite data hungry. I have been surprised at thepaucity of life expectancy data for differentsubgroups within the community. I already knewthat there was a dearth of data on health-relatedquality-of-life, which I and my colleagues havebeen busy remedying over the past few years. Butwe know little or nothing about the willingness ofpeople to sacrifice life expectancy (especially theirown?) in order to reduce health inequalities intheir own communities.

Finally, I think that the focus on outcomes-with-equity-weights-attached has great advantagesover other approaches to the reduction of healthinequalities, because it rules out the giving ofpriority to things that do no good, which is thedanger with equalization policies that concentrateon process (including access) or on resources. Italso sets clear limits on how far we are willing togo in helping the disadvantaged. For instance, aweight of 2 indicates that we are willing to spendtwice as much as the norm to provide 1 extraQALY for such a disadvantaged person, but thatis the limit. This is far preferable to the vaguenotion of ‘priority groups’ whose champions areleft to compete on unclear terms with morepowerful competitors in the annual scramble forresources.

Intergenerational equity

But these ‘fair innings’ equity weights haveparticular salience for the issue of intergenera-tional equity. If what we wish to equalize islifetime experience of health, then it indicates thatthose who have had a ‘fair innings’ (like me)should not expect to have as much spent on ahealth improvement for them as would be spentto generate the same benefit for someone who isunlikely ever to attain what we have alreadyenjoyed. It calls for self-restraint by us elderly andespecially by those of us who have flourished inhealth terms throughout our lives. Otherwise we

may find that demands are being made on thehealth care system which will deny healthimprovements to the less fortunate. Unfortu-nately, that restraint will be called for at a timewhen our current health is declining and when itwould be perfectly possible to spend vastresources on us in the vain pursuit of healthyimmortality. The advantage of these ‘fair innings’generated equity weights is that they will not ruleout the offering of very efficient procedures thathelp improve the QALE of the elderly, but theywill establish a variable cut-off point dependingon the previous history of the potential benefici-ary. This is what a ‘fair innings’ is all about and thisis what we need to explore more carefully.

ACKNOWLEDGEMENTS

The general stimulus for this paper has come from themany non-economists with whom I have argued aboutthe rival moral claims of equity and efficiency over theyears. In preparing the paper itself I owe a considerabledebt to Paul Dolan, who not only helped me byextracting the relevant data on HRQOL by social classfrom the survey work undertaken by the MVH Group,but in his characteristically argumentative way helpedme to focus more sharply on the measurement issuesinvolved. Without the HRQOL data generated by theMVH Group in York, in collaboration with SCPR inLondon, I could not have done this work and the long-term support of the UK Department of Health inLondon in financing it is gratefully acknowledged. Atkey moments when I was stumbling over the mathemat-ical and computing demands made by my approach, Idrew on the crucial expertise of Arnold Arthurs andMinoru Kunizaki. Finally, many colleagues kindly madeuseful comments on an earlier draft, amongst whom Imust mention Angela Boland, John Broome, MartinBuxton, Marie-Odile Carrere, Tony Culyer, DianeDawson, Rhiannon Edwards, John Harris, JulianLeGrand, Erik Nord, Jeff Richardson, and, last but notleast, Aki Tsuchiya. Whether any of these people willactually approve of what I have done as a result is quiteanother matter! They should remain blameless.

REFERENCES

1. Williams, A. Priority-setting in public and privatehealth care systems: a guide through the ideologicaljungle. Journal of Health Economics 1988; 7:173–183.



2. Two recently published exceptions are Lindblom, L.,Rosen, M. and Emmelin, M. An epidemiologicalapproach towards measuring the trade-off betweenequity and efficiency in health policy. Health Policy1996, 35: 205–216 and Johanneson, M. and Gerd-tham, U.-G. A note on the estimation of the equity–efficiency trade-off for QALYs. Journal of HealthEconomics 1996; 15: 359–368. In the former piece‘cases treated’ rather than health outcomes are thefocus of attention and one discrete binary choice wasoffered which leaves the trade-off implicationsrather imprecise except where the equality case isinvolved. The latter piece focuses on healthy lifeexpectancy, but also offers discrete binary choices,each of which has a trade-off implication, these thenbeing weighted by the number of votes they get. Onesurprising conclusion is that the mean trade-offbetween additional years of healthy life expectancyfor the better and worse off people is unaffected bythe size of the initial discrepancy between them.

3. Wagstaff, A. QALYs and the equity–efficiency trade-off. Journal of Health Economics 1991; 10: 21–41.The arguments in favour of such a definition are laidout on pp. 22–27. However, it is possible to take theview that this uniform valuation itself reflects aparticular equity view, so even the efficiency notionused here has an equity element hidden away in it.

4. Culyer, A. J. Equality of what in health policy?Conflicts between the contenders. Discussion PaperNo. 142, p. 18. York: Centre for Health Economics,University of York, November 1995.

5. In Culyer’s diagrammatics, such a Social WelfareFunction generates iso-welfare contours which arestraight lines at 45° to each axis.

6. In common with others active in this genre, I workon the (possibly naive) assumption that the healthcare system is primarily concerned with health,rather than with some more general concept ofwellbeing, welfare, or utility. To the extent that anyhealth care system is pursuing objectives not relatedto health, the conclusions reached here will need tobe modified.

7. Here I shall ignore the efficiency and equity issuesthat attend the method of financing health careprovision. Van Doorslaer and colleagues have dem-onstrated that that is also important to any overalljudgement about the equitability of any health caresystem (especially between rich and poor). VanDoorslaer, E., Wagstaff, A. and Rutten, F. (eds)Equity in the Finance and Delivery of Health Care:an International Perspective. Oxford: Oxford Uni-versity Press, 1993.

8. There are plenty of commentators who favour aprominent role for process measures alongsideoutcome measures, e.g. Mooney, G. Key Issues inHealth Economics, especially pp. 15–20. HarvesterWheatsheaf, 1994. Much of the practical work onequity has been concerned with bringing about a

more equitable distribution of resources, in the hopethat this will lead to a more equitable distribution ofoutcomes. In the UK the most recent manifestationof this approach was Carr-Hill, R. A. et al. A Formulafor Distributing NHS Revenues Based on Small AreaUse of Hospital Beds. York: Centre for HealthEconomics, University of York, 1994, which was onlypartially implemented by the UK Government (seePeacock, S. and Smith, P. The resource allocationconsequences of the new NHS needs formula.Discussion Paper No. 134. York: Centre for HealthEconomics, University of York, 1995). I will com-ment later on why I think a more direct focus onoutcomes may be a better long-term strategy thanthese indirect approaches.

9. See, for instance, Charny, M. C. et al. Choosing whoshall not be treated in the NHS. Social Science andMedicine 1989; 28: 1331–1338. Brakenhielm, C. R.Vard pa lika villkor. In: Calltorp, J. and Brake-nhielm, C. R. (eds) Vardens Pris. Stockholm: Ver-bum, 1990. Bjork, S. and Rosen, P. Prioritizing inhealth care: an empirical study of the views of healthcare politicians on resource allocation. WorkingPaper 1993:1. Lund: Swedish Institute of HealthEconomics, 1993. van Busschbach, J. J., Hessing, D. J.and de Charro, F. T. The utility of health at differentstages in life: a quantitative approach. Social Scienceand Medicine 1993; 37. Australians and Norwegiansseem to be different, however; see Nord, E.,Richardson, J., Street, A., Kuhse, H. and Singer, P.Maximizing health benefits vs egalitarianism: anAustralian survey of health issues. Social Science andMedicine 1995; 41: 1429–1437.

10. Rawls, J. A Theory of Justice. Oxford: OxfordUniversity Press, 1972.

11. As promoted, for instance, by Harris, J. QALYfyingthe value of life. Journal of Medical Ethics 1987; 13:119–120, and challenged by Singer, P., McKie, J.,Kuhse, H. and Richardson, J. Double jeopardy andthe use of QALYs in health care allocation. Journalof Medical Ethics 1995; 21: 144–157.

12. An essentially similar argument has been expressedby Nord et al., which they call egalitarian ageism. Itruns as follows: all else equal, an individual has agreater right to enjoy additional life years the fewerlife years he or she has already had. In other words,people may have a preference for equity betweenpatients with respect to total life outcome. Nord, E.,Street, A., Richardson, J., Kuhse, H. and Singer, P.The significance of age and duration of effect insocial evaluation of health care. Health CareAnalysis 1996.

13. Culyer, A. J. and Wagstaff, A. Equity and equalityin health and health care. Journal of HealthEconomics 1993; 12: 431–457; Culyer, A. J. Equalityof what in health policy? Conflicts between thecontenders. Discussion Paper No. 142. York: Centre

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for Health Economics, University of York, Novem-ber 1995.

14. The fact that the point labelled maximum lies to thenorthwest of the point labelled equal indicates thatthe production possibilities have here beenassumed to be such that it is possible to do more forthe health of B than for the health of A.

15. For a more detailed account of this notion, seeChadwick, R. Justice in priority-setting. In: Ration-ing in Action. London: BMJ Publishing Group,1993, who cites Gallie, W. B. Essentially contestedconcepts. Proceedings of the Aristotelian Society1955–56; 56: 169–198.

16. Two very important, easily quantifiable, variablesare going to be totally ignored in what follows,however: (a) people’s attitudes towards risk and (b)their feeling about time preference. It is possiblethat aversion to inequality is as much motivated byrisk aversion as by any sense of justice or solidarity,and if views about time preference are verydifferent between the different groups whosehealth prospects I consider later, this will greatlycomplicate the rather simple welfare implications Iam trying to draw. But things are complicatedenough as it is and it seems a better strategy not totackle everything at once!

17. Bloomfield, D. S. F. and Haberman, M. A. Malesocial class mortality differences around 1981: anextension to include childhood ages. Journal of theInstitute of Actuaries 1992; 119: 545–559.

18. Those I know of are Bone, M. R., Bebbington, A.C., Jagger, C., Morgan, K. and Nicolaas, G. HealthExpectancy and Its Uses. London: HMSO, 1995;Mathers, C. D. Health Expectancies in Australia1981 and 1988. Canberra: Australian Institute ofHealth, AGPS, 1991; Robine, J. M. and Mormiche,P. L’esperance de Vie sans Incapacite Augmente,INSEE PREMIERE No 281, 1993; Wilkins, R. andAdams, O. B. Health expectancy in Canada, late1970s. American Journal of Public Health 1983; 73:1073–1080; Eriksson, P., Wilson, R. and Shannon, I.Years of healthy life. Statistical Notes No. 7, pp1–14. Washington, DC: National Center for HealthStatistics, US Department of Health and HumanServices, April 1995.

19. Not all of these results have yet been published, buta general account of the research programme isgiven in Williams, A. The measurement and valua-tion of health: a chronicle. Discussion Paper No.136. York: Centre for Health Economics, Uni-versity of York, June 1995. For some of the keydata, see Kind, P., Gudex, C., Dolan, P. andWilliams, A. Variations in population health status:results from the MVH National Survey. CHESeminar Paper: 14th March 1996, Centre for HealthEconomics, University of York, York, England. Wehave no data from our study relating to the qualityadjustments for those under the age of 18, so they

have been assumed to be equal to those of the 18year olds. We also have only very limited data forover-80s, so for them the trends already evident inthe data have been extrapolated.

20. See Discussion Paper No. 136, cited in Ref. 19, fordetails of this tariff of weights and its derivation.

21. Obviously this assumes that a person remains in thesame social class throughout their lives. Movementbetween social classes will make these differencesless clear cut at individual level.

22. The function used was of the CES type, whichallows for considerable flexibility in the key param-eters. The basic equation is W = q[bHa∧–r + (1–b)Hb∧–r]∧–(1/r). W is an index of the overalllevel of welfare, here assigned the value it takes atits intersection with the perfect equality locus. Thusin Fig. 5 it is 69. The coefficient q translates units ofhealth into units of welfare and is here assumed forsimplicity’s sake to be 1. The coefficient b deter-mines the weight given to the health of each party,which is here assumed to be equal, so the coeffi-cient takes the value .5. Ha and Hb are the levels ofhealth of the two parties (measured in identicalunits, in this case years of life expectancy at birth).The coefficient r is the parameter determining thedegree of curvature of the contours, which hererepresents the extent of social aversion to inequal-ity. It is this parameter that is estimated from thedata.

23. This later starting point for the analysis is identifiedin Culyer’s diagrams as the situation PS (presentsituation), in which A and B have already enjoyedsome life years or QALYs and the problem is whatto do from here on.

24. This is not unlike the argument that has raged inthe field of state retirement pensions, as to whetherpensioners are entitled only to the real level ofpension that could be afforded for them when theyretired, or whether they should be allowed to sharein the improved general living standards enjoyedsubsequently by the working population, by havingtheir pensions linked to real wages.

25. For equality at 61 to be on the same social welfarecontour as the initial situation, the inequalityaversion coefficient, r, would have to take the valueof 1.9. This is therefore also the value of thatparameter used in calculating the associated equityweights in Fig. 5.

26. World Development Report 1973. Box Fig. 1.3 on p.26 and further discussion on p. 213.

27. Many people appear to believe that QALYs canonly be used in a simple QALY-maximizing con-text. I challenged this assumption in Economics,QALYs and medical ethics Discussion Paper No.121. York: Centre for Health Economics, Uni-versity of York, 1994, and have dealt with it morefully in QALYs and ethics: a health economist’s



perspective, Social Science and Medicine, 1996; 43:1795–1804.

28. Following John Broome, these weights may be seenas measuring the relative strength of differentpeople’s equity-based claims on health care

resources. Broome argues that what fairness thenrequires is that such claims actually be satisfied inproportion to their strengths (emphasis in theoriginal). Broome, J. Weighing Goods, p. 195.Oxford: Blackwell, 1991.

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Documents

Intergenerational Equity: An Exploration of the ‘Fair Innings’ Argument