Chapter 23 Waiting lists and medical treatment: Analysis and policies

Chapter 23

WAITING LISTS AND MEDICAL TREATMENT: ANALYSIS AND POLICIES* JOHN G. CULLIS, PHILIP R. JONES, University of Bath CAROL PROPPER University of Bristol

Contents Abstract Keywords 1. Introduction 1.1. An example of waiting lists: the UK

2. Waiting: theoretical issues 2.1. Demand and consumer surplus dissipation 2.2. Demand side: Lindsay's approach 2.3. Supply side: Iverson's approach 2.4. Supply side: other considerations 2.4.1. Medically "interesting" cases 2.4.2. Maintaining your empire 2.4.3. Fostering private practice 2.4.4. Waiting as part of least cost supply

3. Waiting: empirical matters 3.1. Demand side: estimating the "costs" of physical waiting 3.2. Demand side: estimating the "costs" of administered waiting 3.2.1. Costs of waiting from market data 3.2.2. Estimates of costs using contingent valuation methods 3.3. Supply side: estimating the impact of supply variables 3.4. Supply side: inter-sectoral effects

4. Waiting: policy issues 4.1. A taxonomy of policy options 4.1.1. Demand rationing and reduced waiting

1202 1202 1203 1205 1205 1212 1214 1215 1218 1218 1218 1220 1221 1221 1221 1222 1222 1225 1228 1230 1231 1232 1233

*We are grateful for comments made on this Chapter by Tony Culyer, Pat Danzon, Ulf Gerdtham, Joe Newhouse and Alan Williams. Thanks are due to Katherine Green for excellent research assistance. Remaining errors are our own. Handbook of Health Economics, Volume I, Edited by A.J. Culyer and J.P.Newhouse © 2000 Elsevier Science B. V All rights reserved

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J.G. Cullis, P.R. Jones and C. Propper

4.1.2. Supply expansion and reduced waiting 4.1.3. Subsidies to reduce waiting 4.1.4. Encouraging private provision 4.2. Efficient waiting 4.2.1. Indices for prioritisation 4.2.2. Quasi (internal) markets 4.2.3. Reducing uncertainty

5. Conclusions References

1234 1235 1238 1239

1240 1242 1242 1243 1245

Abstract A number of health care systems use waiting time as a rationing device for access to inpatient care. However, a considerable amount of research has focussed in particular on the UK's National Health Service and its perceived problem of waiting "lists". In this chapter a theoretical discussion addresses the issue of the optimum wait in the context of Paretian welfare economics. However, reference is also made to public choice analysis and to queuing theory. Empirical literature that explores the various dimensions of waiting costs is reviewed and evaluated. Different methods of estimation are illustrated and these include contingent valuation, implied valuation and econometric modelling. The policy section assesses various "solutions" to the waiting list "problem". Options are classified in terms of their impact on excess demand and the issue of waiting list management is addressed. In the absence of an over-arching welfare analysis both empirical work and policy recommendations are inevitably piece-meal and open to debate. Given the inherent weaknesses of applied welfare economics the challenge is to find a framework which would attract a broader consensus.

Keywords waiting lists, waiting times, waiting costs, NHS inpatient queues JEL classification:H11, I111, 1118

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1. Introduction Demanders of health care frequently wait in person to see a physician or to receive treatment. Such waits are common in all health care systems. However, in some health care systems, demanders of hospital care are allocated to explicit waiting lists. Typically, demanders of care will not allocate themselves to a list, but will be placed on the list by a physician acting as the patient's agent. This chapter examines the economics of these lists. These explicit waiting lists are predominantly found in health care systems where there is tax-financed insurance and where there is a global budget on expenditure. In tax-financed systems consumers do not pay the full price of their health care at the point of demand, so unless capacity exceeds demand when price is approximately zero, demand must be limited by means other than price. Explicit waiting lists are the most commonly used means of limiting demand in these systems. This is not to imply that tax finance is a sufficient condition for the existence of lists: publicly funded systems that reimburse providers by fee for service do not have explicit lists. There is also a potential waiting list problem in all insurance-funded systems where the supply side is constrained (for example, by managed care measures) not to meet all demand. However, measures adopted to limit the impact of moral hazard in private insurance do not make use of persistent, involuntary waiting lists. So lists occur where there is a combination of tax finance and global budgets. Countries in which lists are used include the UK, the Nordic countries, Canada, Australia and New Zealand. This chapter examines the theoretical, empirical and policy issues in the use of waiting lists. What economic theories explain the use and persistence of lists and what are the efficiency and equity consequences of allocation of medical care by lists? To what extent does the evidence on lists support these theories? What policies will ameliorate, if not resolve, efficiency and equity problems that arise from use of waiting lists? The central question addressed in this chapter is what is lost and what gained by opting for non-market resource allocation and not adopting explicit money prices. If prices are "wrong" or absent then introductory texts predict problems of signalling, incentives and rationing. The questions addressed here relate to the role of waiting lists with respect to these functions. What economic signals should and do they emit? What economic incentives should and do they provide? How should and do they ration medical care? From a consumer perspective, the existence of waiting lists raises the issue of time as a price of health care. The chapter examines when time on a waiting list is a price and the nature of that price. The notion of time as a price raises the interrelated issues of optimal waits, input stocks, queuing theory and their associated welfare effects. However, the fact that waiting lists are a feature of health care systems where the state is the financial mediator means that the political economy of waiting lists is important. There is a "public choice" dimension to allocation of care by lists. The political economy of waiting lists means that they cannot be understood simply as an exercise in applied neoclassical welfare economics or statistical queuing theory. Waiting time is not simply the outcome of unrelated demand and supply: to understand waiting lists and to put for-

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J.G. Cullis, P.R. Jones and C. Propper

ward policy proposals requires understanding the links between demand and supply in a tax-financed health care system. So any comprehensive economic treatment must take into account not only the demanders of care, but the place played by waiting lists in the allocation of funds into health care, the suppliers of care, and the interaction of demander and supplier of care with the elected representative and the agents of government. Other commentators would go further. The approach that underlies almost all the analyses to date of waiting lists is that of neo-classical welfare economics. As such, Paretian value judgements are either explicitly or implicitly invoked. There are arguments for an alternative approach. In a health care system where the funding is from the state, an explicit decision has generally been made to reject the market place. To adopt conventional welfare economics may look like re-introducing a rejected perspective by the back door. One line of argument would suggest that the government is elected partly to be responsible and accountable for a state health care system, so government rather than consumer sovereignty should be the criteria by which such a health care system is evaluated. This would be consistent with a rationale for state intervention rooted in "merit wants" where individual preferences are over-ridden because it is argued individuals act irrationality and/or on sub-optimal information. In addition it could be argued that individuals via the voting mechanism have made their choice "government choice". Whilst such arguments have some currency in health economics a government sovereignty framework seems insufficiently articulated to form a basis of sustained evaluation. In addition, the public choice perspective argues that government behaviour must be seen as the outcome of self-interested decision making by individual voters, consumers and producers. Another line of argument that follows from the observation that funding is public is that the efficiency of the system should be judged in terms of whether those in greatest need are served soonest. Waiting lists should be evaluated in terms of how they meet "need" for health care. So the yardstick against which waiting lists would be judged is do they, or do they not, ensure that this criteria is met. This perspective highlights the role of the producer and as we shall see below, producers play a key role in the allocation of patients to lists. A list is actually individual inpatient health care "investments" that physicians have accepted, in their professional judgement, as offering a positive net present value from hospital treatment. However, complete deference to medical expert views only makes sense in a world where medical care is viewed as a purely technical matter closed to interference from lay opinion. This view is not easy to accept uncritically in a system financed by the general taxpayer. In a collectively financed system the evaluation of waiting lists and waiting list policy might be expected to have some collective input. Further, adopting a perspective which gives large weight to professional judgements of physicians could be seen as giving an already powerful producer group even more power. The remainder of this chapter employs the conventional welfare economics approach. This is for two reasons. First, while there may be alternatives in principle, articulated government or producer sovereignty models do not currently appear in economics. Sec-

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ond, almost all of the existing literature adopts the conventional welfare approach: to adopt another framework would rule out most of the existing analysis from this survey. The organisation of this chapter is as follows. It begins with an example of how waiting lists operate in a health care system in which waiting lists play a key role. We present data on the length and nature of lists in the UK National Health Service. In Section 2 we examine the factors that have to be taken into account in determining the optimal waits in an NHS type health care system. Sections 3 and 4 focus on empirical matters and policy issues, respectively. Within each section the material, where possible, is organised in the sequence "demand", "supply" and "demand-supply interactions". 1.1. An example of waiting lists: the UK In the UK NHS allocation to a waiting list operates as follows. The patient will consult their primary care physician who, if he or she deems it necessary, will refer the patient to see a hospital-based physician as an outpatient. For those cases which are not emergencies but which require treatment, the patient may be put on a list for admission as an inpatient. These hospital based physicians are employed by the NHS, but, whilst in the employ of the NHS, may also work in the private sector, which specialises in the treatment of non-urgent conditions (mainly elective surgery) for which there are long waiting lists. Chart 1 presents the total number of patients on inpatient waiting lists for England and Wales from 1951 to 1998. These data exclude any wait to see a primary care physician and any wait between seeing the primary care doctor and the hospital doctor to whom the patient has been referred. The chart shows that total number of patients on a list was around 0.5 million for the first half of this period. The numbers then rose, and were around 0.7 million for most of the 1980s. In the early 1990s, numbers on lists fell sharply, but began again to rise in the mid 1990s. Numbers on lists in relation to total cases treated fell in the early part of the period, remained flat during the 1960s, then rose again from the mid 1970s to early 80s, since when they have basically fallen. From 1976 a separate count was made of numbers waiting less than and more than a year. The chart shows that the number waiting under a year grew up to 1994 then fell thereafter. The numbers waiting over a year (a significant minority of whom waited over 2 years) remained relatively constant until 1992. The picture has changed since then, with an elimination first of the number waiting over 2 years and then a major reduction in those waiting over 1 year. These changes are not random and the reasons for them will be explored further below. Chart 2 breaks down waiting lists by speciality. The chart shows clearly that lists are more important in some specialities than others. This is not chance and we examine reasons for this below. 2. Waiting: theoretical issues Whilst Samuelson's (1964, p. 56) parrot cum learned political economist had to learn the two words "Supply" and "Demand", his or her public sector counterpart must learn

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J.G. Cullis, PR. Jones and C. Propper

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Ch. 23:

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Waiting Lists and Medical Treatment

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"Costs" and "Benefits". At its simplest, given the public funding of health care, the waiting list issue can be seen as one of the optimal timing of medical treatment. The optimal inpatient treatment wait (which is unlikely to be zero for non-urgent cases) is one that equates marginal (social) cost and marginal (social) benefit so that the net benefit of inpatient treatment is maximised. 1 In Figure 1 total costs and benefits are illustrated for three waiting scenarios. The essential question being addressed is the optimal capacity size of the health care system (HCS). The shorter the wait, other things equal, the larger the capacity of the HCS will need to be. The total cost curves (TC) represent the present value of resources required to advance the treatment date of a particular case type2 (or speciality "representative" patient) and they have a negative slope. The negative slope reflects the fact that discounted cost declines with the deferral of treatment, as less real resources need to be allocated to the HCS at present date. (The precise shape of TC will of course reflect the nature of the production function and the prices of factor inputs.) Many different capacity structures are possible and as well as the associated short run marginal cost curves, capital costs of different sizes of HCS need to be incorporated. It is a case of locating the constant annuity, say k, which over

I The argument could be presented in terms of expected values but the main analysis would be unaffected in any significant way. 2 These costs can be thought of as being calculated on the basis that the remainder of the specialties in the health service are optimally adjusted.

J.G. Cullis, PR. Jones and C. Propper

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PV(TC) PV(TB)

TC1 to (a)

Waiting time (t) NB 1

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-TC 2 tm

to

Waiting time (t) NB2

(b) PV(TC) PV(TB)

to (C)

,'

tl

- . Waiting time (t) NB3

Figure 1. Determining optimal waits.

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the planning period constitutes a time stream of outlays whose present value is the base year capital cost (K). This is found by the familiar discounting formula: k=

Kr 1- [1/(1 + r)n]

'

(1)

where r is the rate of interest and n is the number of years of the planning period [see Millward (1971)]. TC then indicates the minimum cost of various capacity levels and involves summing annual equivalent capital costs with annual running or operating costs. When capacity is optimally adjusted, SRMC = LRMC and LRAC = SRAC. As indicated above, the underlying assumption is that the longer the wait for inpatient treatment the lower TC will be. The interpretation of the costs is that these are for cases of a given type or cases "representative" of a given speciality. If incurred, such costs would, in a "certain" world (i.e. one in which the number of cases per period is deterministic), offer the wait indicated on the x-axis. The total benefit curve (TB) represents the discounted benefits of treatment, which falls as the treatment day is delayed. Total benefit can be thought of as a "QALY" score converted into money terms [but there is some debate about the relevance of discounting in this context, e.g. see Cairns (1992) and Parsonage and Neuberger (1992)]. The final optimal capacity requires a measure of marginal benefit (typically price in market discussions). Who is to define benefits (and costs) in a non-market setting is debatable (in a collective institution some type of democratic mechanism may well seem appropriate) but here it is sufficient to note the optimal volume of output to provide is given by MB = SRMC = LRMC (with the latter equality indicating optimal capacity adjustment for that level of output has taken place). Equivalently it is a matter of choosing for each case type a waiting time that maximises net benefit. Depending on the empirical location of TC and TB, clearly differential optimal waits are dictated. Case type 1, depicted in Figure 1 panel (a), is the case where treatment yields benefit now (to) or not at all. Case type 1 individuals (treatment now) need not be urgent. It is just that, with treatment delay, the benefit of treatment falls and disappears quickly (perhaps the body self-corrects the health status disequilibrium itself). Case type 2, illustrated in panel (b), indicates a "medium" wait (tin), whereas in case type 3 the total benefit is not much affected by delay and a long wait (tl) appears optimal. In such circumstances it would be optimal when initially assessed if people were given a certain date when they are to become an inpatient. That is, there would be a record of "supply of patient input" dates for the inpatient health production process. In the case where TB < TC everywhere no offer of inpatient admission would be optimal and the implied inpatient wait would be infinite. In this simple world it is a question of providing the public health care inpatient capacity that maximises the net benefit from treatment. Cases for which TB < TC everywhere set the limit to the inpatient episodes of treatment to be provided in an optimal capacity HCS. Assume there are M possible case types and hence optimal waiting times with their associated discounted benefits. If there were N patients of each type the total benefit of

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J.G. Cullis, P.R. Jones and C. Propper

the HCS would be given by EN I CY_ I TBij . Similarly the total costs involved would be EN=I yM TCij. The net benefit secured would be EN1I EMI(TBij - TCij). In this abstract world there would be no waiting list problem as such but simply a record of the stock of case types (patients' names) that will be delivered at the end of a wait that maximises the net benefit that health service inpatient resources generate. To draw an analogy with the unemployment literature, the pool of unemployed (waiting list) is a stock where for each occupation (speciality) there is a stationary register (constant list) when inflows into unemployment (additions to the list) equals outflows to employment (discharges) in any period. In the present analysis the duration of waiting time (unemployment) as measured by the difference between entry date (name put on list) and exit date (discharge) would be optimal in that it serves to maximise the net benefit of the HCS. As with the unemployment stock the waiting list comprises an inflow (additions) and a duration (wait) component that in principle can be disaggregated. Note that for each speciality the flow and duration will be given but different, so that optimal list length varies by speciality but nevertheless would add to an aggregate waiting list that would be optimal. This implies that without undertaking detailed (and difficult) empirical work to determine what is the optimal list length for each speciality, observers looking at the data on waiting lists cannot say for any period that the waiting list is sub-, supra-, or actually optimal. In some ways this stock/flow inventory approach has the same structure as a queuing one. If the HCS underestimates the demand for inpatient care it will not provide valued inpatient treatments. If it overestimates demand it will either have idle capacity or be treating on an inpatient basis cases for which MC > MB. Can the waiting list be viewed as an optimal queue in this sense? A simple model of a queue [see, for example, Cox and Smith (1961), Wagner (1969) and Cooper (1981)] can be adapted to offer some insight into this question, especially if the certainty assumption underlying the discussion so far is relaxed. Elements in a very simple queuing model of the HCS inpatient treatment process would be: = mean number of individuals demanding inpatient treatment (reflecting, say, a Poisson distribution); S = mean number of individuals being treated per period; = the total number of individuals being treated or waiting; d 1 = the total number of individuals waiting on the list; Pd = probability of d individuals being treated or waiting per period; po = probability of zero individuals being treated or waiting per period; t = time a new joiner must wait before being treated; E (d) = expected number of individuals in the queue or being treated; E(1) = expected number of individuals waiting; E(t) = expected waiting time for each joiner to the list. D

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Key relationships are3: E(d) = (S

D

D)'

(2)

D2

S(S - D)' E(t) =

)

(4)

If reality could be adequately captured in this way (subsequent sections cast doubt on this conjecture) then values for E(d), E(l), and E(t) could easily be obtained. Such a model would readily provide valuable types of information. For example, if the period is a week, then total time lost (TTL) in the queue per year = E(l) E(t) 52 = TTL total cost of queuing (TCQ) = E(1) E(t) 52 - w = TCQ,

where w is the opportunity cost of time waiting. Two inferences that arise from these, albeit simple, theoretical considerations are summarised in a static way by Figure 2. In what is described above as an optimal capacity/waiting system, the occurrence of a type of ill health (j) will involve an optimal wait for treatment of t, . The effect of this on the utility of a risk averse individual can be captured in the downward shift and flattening of the utility function. Utility is assumed to depend on both full income (Yf) and health status (hs) [so that U = U(Yf, hs)], with U(Yf, w) > U(Yf, i), where w = well or healthy and i = ill. In addition, the flattening suggests U/ Yfl > U/ Yfli so that the marginal utility of income is lowered by illness. If Yfo is the individual's income level and t is guaranteed then there is a utility cost of waiting equal to Uw - Ui, which in terms of full income is the distance Yfo - Yfi. If this argument is accepted, such a cost is part of a Pareto efficient resource allocation (as it arises when t obtains). If, however, the waiting list is not run on a "guaranteed booked case" system and the uncertainty raised by queuing theory comes into play then E(t J ) = t. That is, the expected value of the optimal wait, E(tJ), equals the optimal wait, tJ , only on average. For risk averse individuals this imposes an additional cost equal to Ue - Ui in utility terms and Yfe - Yfi in income terms. Given that demand for inpatient treatment is inherently uncertain, this cost is also part of the Pareto efficient configuration. In this perspective the waiting list problem is one of non-optimal cost levels associated with two issues and their combination: viz. sub- or supra- optimal int, or an administrative system that does not minimise patient capacity that dictates t the variance of E(t), or both. 3 Other include: PO = 1-(D/S),

(In)

Pd = (D/S)dpo = (D/S)pdl

(2n)

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J.G. Cullis, P.R. Jones and C. Propper Total (expected) utility . . : .11,

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(,Yf,w)

Uw

U=U(Yfi)

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Whilst the questions directed at the waiting list issue are neatly encapsulated by the optimal capacity/waiting and associated queuing theory implications, there are limitations to this approach. For example, with respect to queuing theory, the waiting list context differs in a number of important ways. The queue is not a physical one and waiting may impose no direct opportunity cost of time; D is not a stochastic process but is much influenced by the behaviour of hospital and primary care physicians' decisions whose interaction create the waiting list stock (in contrast the recorded stock of unemployed is largely the result of an impersonal labour market profitability test); S is influenced by the number of direct admissions to hospitals; the queue is not organised on a first come first served basis - an everyday "equity" rule - but rather certain patients are selected from the list depending on their personal characteristics. For the moment, however, it is worth considering the physical queue analogy as it helps identify the cost of waiting, which has to be compared with the benefit. 2.1. Demand and consumer surplus dissipation Both optimal wait and queuing theory imply waiting costs for some types of potential inpatient. In the queuing discussion w was designated the opportunity cost of time spent waiting. Such costs have been viewed as prices and their ability to reduce consumer surplus analysed. Barzel (1974) describes a natural experiment in which a local bank had a one-off "sale" of money - selling notes at less than their nominal value on a "firstcome first-served" basis. To limit their financial commitment, only the first 35 persons get the maximum gain of £20, the next 50 each gain £10 and the next 75 each gain £4. The method of rationing was a physical queue. If the first person in the queue waited 17 hours and the thirty-fifth 9 hours, economic theory could be used to predict the wage

Ch. 23:

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Waiting Lists and Medical Treatment

Price

p

O

qg

qt Quantity of

Medical Care/t Figure 3. The demand and supply of inpatient care.

characteristics of these two individuals. Waiting in the queue involves costs to the extent of the waiting time (t) multiplied by the opportunity cost of time, say a wage rate (w). With £20 as the maximum possible gain, w times t should not exceed this figure except by accident, misinformation or economic irrationality. If an individual could earn £3 per hour, it would not pay him or her to wait in a queue for 9 hours in order to get a "free" £20, since they could have used the time to earn £27. For the first person waiting the limiting value for w is approximately £1.20 per hour, and for the thirty-fifth, w = about £2.20.

More generally, assume Dm in Figure 3 is an individual's demand curve for medical care. Zero money prices are charged so that the individual would demand Oqt per period. Suppose the government restricts quantity so that Oqg is the maximum amount of care an individual can obtain per time period. In these circumstances the maximum the individual would be prepared to pay for Oqg health care is 0 1 2 qg, which sets an upper bound on the value of the length of wait the individual will endure to secure Oqg. If the waiting costs [again the product of the opportunity cost of time (w) and length of waiting time (t)] exceed 01 2 qg the individual will not join the queue. Consumer surplus is dissipated completely by a cost of wait equivalent to 0 1 2 qg. In a market the consumer surplus gained would be the equivalent to triangle p1 2 , assuming for convenience the market clearing price is Op. Consumer surplus under the market system of allocation has to be greater than consumer surplus achieved under a time price system. Under the time price system the marginal receiver of care enjoys no consumer surplus. Under a price system the marginal consumer receives no consumer surplus only on the marginal unit of care they buy. (This assumes that individuals vary in the time prices that they are willing to

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J.G. Cullis, P.R. Jones and C. Propper

pay so that the market demand curve for a ration of 'Oqg' is standard downward sloping. If individuals do not differ then consumer surplus is dissipated for all individuals.) Unlike a market price, 012qg (= wt) is a deadweight cost and does not fulfill the incentive function of compensating factor input owners. The rationing function is, however, achieved. Is it possible to view waiting patients as "paying" for their care via a deadweight time price involving such intangible costs as pain, discomfort, uncertainty, etc., and tangible costs such as lost earnings? The answer is "yes" where patients wait in person (e.g. in a physician's surgery), as there is an opportunity cost involved in having to wait physically at the surgery. However, the answer is a qualified "no" for administered inpatient waiting where the alternative to waiting for care from the public health care system is to use the private sector (assuming a private sector alternative exists). The individual will take this decision if the expected consumer surplus gain from alternative care outweighs the additional costs associated with private care. Should this not be a relevant option the potential inpatient simply waits until they get to the top of the list, carrying on, in the meantime, as best they can. Not being on the list simply makes securing care from the HCS impossible: in other words, for a large number of waiting patients it is not economically rational to avoid the costs of waiting. Hence the marginal waiting individual is not the one whose value of waiting equals the valuation of the benefits of inpatient care but rather the individual who sees any benefit to care on the anticipated future date when it is received. (This abstracts from the time costs of getting on the waiting list and the pain and discomfort of treatment in itself which clearly are avoidable by not being on the list.) Culyer and Cullis (1976) explored the waiting time as a price argument in more detail. They found its main implications to be: a negative association between throughput capacity and waiting times; a positive association between capacity and waiting lists and a negative association between waiting lists and waiting times. These implications found little empirical support. The type of assumption needed to make this "naive" time price hypothesis hold up is that doctors, as patients' agents, act "as if" waiting times were a price and make decisions on behalf of patients on this basis. As long as the location of the demand curve for inpatient treatment is unaffected by waiting, the potential consumer surplus from inpatient treatment is not dissipated by the wait for treatment (which, however, imposes costs on the individual that arise because the delay of the benefits of inpatient treatment reduces the present value of the benefits) because the potential patient cannot undertake costly activities (unlike in the bank example above) that will qualify him or her for inpatient treatment. 2.2. Demand side: Lindsay's approach Lindsay (1980) [also see Lindsay and Feigenbaum (1984) and Spicer (1982)] builds a model of waiting lists that is equilibrated via waiting time on the list by attacking the assumption made in the theory above that the demand curve for inpatient care remains unaffected throughout the wait. In Lindsay's model waiting time matters because the

Ch. 23: Waiting Lists andMedical Treatment

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value of inpatient care decays the longer care is postponed after the diagnosis day. More specifically, in Lindsay's model waiting time equilibrates the queue by rising or falling until the numbers joining the queue equal the number of patients treated per time period. Marginal queue joiners satisfy the condition: C = Ve - t ,

(5)

where C is the lump sum costs of joining the queue, V is the valuation of inpatient treatment now that decays at a rate, d, until treatment occurs after a wait of t. Two main comparative static results are derived from this model. First, if the typical case of two different diseases with different decay rates, say di < d2, and C and V are assumed to be constants (C and V, respectively) then for = Ve -

d ltl

and

C= Ve -d 2t2

(6)

to hold simultaneously tl > t2 and waiting times for inpatient admission for each disease should be inversely related to the demand decay rate. Second, the responsiveness of waiting time to capacity changes should be negatively related to the decay rate. The logic behind this result is illustrated in Figure 4. In panel (a) the effect of increasing the supply capacity (rate of treatment) from SCI to SC 2 is to decrease waiting time from t to t2 and expand the number of joiners along J(t). Potential patient V 2e - d2t is not a joiner at waiting time t because such a long wait reduces the value of treatment to V2 < C, however, at waiting time t2, V 2 e- d2t = C and the individual becomes the marginal patient (as opposed to the di case initially). Equilibrium waiting time is depressed because with relatively low rates of decay (dl and d2) few potential demanders are discouraged (because of lack of possible substitutes) by the long waiting time and a relatively large reduction in it can be achieved by a capacity increase. Now consider panel (b) that illustrates the position of high decay rate diseases. Here treatment is needed quickly or not at all and if inpatient treatment is not available other sources of treatment (if any) must be sought. Given this, many potential patients are not in the queue and V3 e -d 3t can be viewed as a valuation curve typical of many patients. In these circumstances an increase in the treatment rate from SCI to SC2 induces very little change in waiting time (none in Figure 4) as there are large numbers attracted from the various substitutes to inpatient treatment by the addition of supply capacity. As long as the range of decay rates for given diseases is not too great then low decay rates will always be associated with longer waiting time and vice versa. 2.3. Supply side: Iverson 's approach Iverson (1993) outlines a supply side model in which "long waits" may result. In his model, observed waiting lists and waiting times for medical treatment are placed in the context of a political bargaining process over resources. The heart of his model is captured by Figure 5. He describes production possibilities between the number of expected treatments supplied E(s) and the expected wait E(t) before treatment. A key

1216

J.G. Cullis, P.R. Jones and C. Propper Waiting time (t) :h es

SC2

SC 1

Ie II

I

.

with ates

Joiners and throughput

SC 2

SC1

0

C

V

Cost and value

Figure 4. Lindsay's waiting list model.

assumption is that the number of expected treatments is affected adversely by increased waiting lists and times. As the waiting list lengthens, staff resources that could be used in providing treatment are absorbed into waiting list management tasks (keeping records, prioritising those listed, responding to enquiries, perhaps repeating diagnostic tests rendered invalid by the passage of time). For a given capacity constraint, SCo, increasing waits initially have a positive impact on expected treatments via improved capacity utilisation but after a critical wait E (to) the negative impacts described above dominate and the number of expected treatments falls (hence the shape of OSCo in Figure 5). To the left of E(to) waits are described as "short" to the right of E(to) as "long". A waiting time neutral decision taker would have a horizontal indifference curve map between

Ch. 23:

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Waiting Lists and Medical Treatment E(s)

;EPg

O

E(t o)

E(t)

Figure 5. Iverson's waiting list model.

E(s) and E(t) (not shown) and choose point 1 on SCo maximising expected treatment numbers for that and other levels of SC. As SC increases, e.g. SC 1, SC2 , the "shortlong" wait boundary is delineated as the "numbers maximising" equilibrium, point 2 for SC1 , point 3 for SC2 migrates to the right. Increases in supply capacity decrease the level of capacity utilisation for each level of E(t). Given this there is an increase in the number of expected treatments caused by a marginal increase in the expected wait as supply capacity increases. The slope of each production possibility arch reflects this being steeper at a given E(t) thereby generating the positive slope of the maximum treatments curve (M-T). Why might a long wait represent equilibrium? Intuition suggests that the expected wait is a "bad" and the expected number of treatments is a "good" so that indifference maps shaped like II, 12, 13 would be relevant and equilibrium (points 4, 5 and 6) found on a capacity expansion path like the curve labelled, CEPhg. Here the hospital doctors/administrators and the sponsoring agent (government at some level) both simultaneously act altruistically, or perhaps more accurately non-instrumentally indicated by the subscripts 'h', and 'g'. Given this "long" waits will not arise. Iverson then introduces the idea of bargaining for resources to highlight the circumstances in which long waits would result. If the budget decision is sequential [the government sets SC and the hospital actors set E(s) and E(t)] then the result turns on the shape of the government's capacity expansion path (CEPg) and the bargaining solution concept invoked. If the CEPg is positively sloped to the right of M-T then a Stackelberg equilibrium with the hospital as leader can be found at point 7. CEPg is the "follower" reaction function and I h is the highest utility level the hospital actors can achieve subject to that "reaction". Point 7 is associated with long waits as it is to the right of M-T and must be Pareto inefficient (like all Stackelberg equilibria) in that point 1 compared to point 7 (both on SCo) involves a larger E(s) and a lower E(t). For this solution to arise the government must base its supply capacity decision on the expected wait. In particu-

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J.G. Cullis, PR. Jones and C. Propper

lar, the valuation of the (negative) effect of an increase in E (t) on a patient's health must be larger than the (negative) effect on the cost of treating a patient as E(t) increases. Hence the slope of the government indifference curve I g at point 7 (the marginal benefit of treating a patient as waiting time increases is larger (smaller in absolute value) than the marginal cost of treating a patient when the waiting time increases). 2.4. Supply side: other considerations Iverson (1993) deliberately assumes altruistic agents but recognises there may well be deviations from this assumption. The public choice perspective in economics raises the question of the economics of processes and the argument that all economic actors are maximising their utility subject to constraints. In this context it means attention has to be directed towards the narrower incentives of producers (hospital physicians, managers and the like), those in the government (politicians) and central government bureaucracy (civil servants). What does such a perspective imply for waiting lists and times? 2.4.1. Medically "interesting" cases Feldstein (1970) suggested that physicians may get utility from maintaining a queue for their services because it enables them to increase their utility by selecting more interesting or urgent cases. Pauly (1990) also puts "interesting" cases in the physician's utility function. The context is a market one. Physicians are assumed to have a utility function of the form: U = U(Y, a),

(7)

where Y is money income and a the proportion of interesting cases in the workload. Given this, physicians "trade-off" income against more interest by charging less than market clearing prices and having a "list" to choose from. (A parallel might be an employer paying above market clearing wages to induce a queue of potential employees.) The desire for more interesting cases seems particularly plausible in a teaching hospital context where trainee doctors need to have some familiarity with a wide variety of cases. In such circumstances, where there are joint output benefits of treating certain cases, a shorter optimal waiting time may be consistent with net benefit maximisation. In a less attractive light Frankel (1989) also takes up the theme of interesting cases. He sees the problem of waiting in terms of the lack of interest by the medical profession in the treatment of the "day to day" complaints that await treatment; research interests being more active in other fields. This leads to lists building up in the routine uninteresting fields (and as evidence cites patterns such as those of Chart 2). 2.4.2. Maintainingyour empire Being on the waiting list is usually the result of a primary care referral to a hospital outpatient clinic. Within a limit set by the number of referrals and the bounds set by

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hospital managers, the hospital doctor can (at least in an "agency" model 4) have any length of waiting list he or she wants. In practice the situation is more complex than this and certain factors can be isolated that will help explain the decision to place a potential patient on a waiting list. It is well known that waiting lists predominantly arise in surgical specialities, largely because of the point at the heart of Lindsay's analysis that for some illnesses inpatient treatment is needed now, in the near future or not at all. Hence, for medical specialities if inpatient treatment is indicated but a bed is not available then an alternative treatment regime must be adopted. So waiting lists tend to build up for delayable "cold" surgical cases rather than for other treatments. Therefore lists are argued to be beneficial to the extent they represent a stock of available work ensuring that the scarce and skilled resources of surgeons and other theatre staff can be fully utilised (accounting for the positively sloped sections of the SC curves in Figure 5). Additionally as noted above a waiting list allows for a balance of cases of differing nature and complexity to be chosen facilitating the teaching function of many hospitals. Frost (1980) pointed out that on average in the 1970s each senior NHS hospital doctor had 160 individuals on his waiting list representing approximately two months' work. It was argued above that there was an optimal waiting time from the point of view of optimum resource allocation. However, unless hospital doctors fully internalise the costs of delay for potential patients, they may choose waiting lists that are too long. Lindsay (1980) questions the notion of a largely doctor determined waiting list. He argues that a direct test of an "agency" effect in the NHS can be made. Using Figure 6, which has a similar interpretation to Figure 4, suppose to is the initial equilibrium wait and that additional hospital doctors are appointed. Via the "agency" relationship, these new doctors increase the demand for inpatient care shifting the V-function to the right and the joining function to the left J(t) to J (t). The effect is to raise the equilibrium wait of the marginal joiner to tl as long as throughput capacity does not change. By contrast, if increasing the number of hospital doctors is viewed simply as increasing the supply capacity SCo to SCI, other things equal, the equilibrium wait should fall to t2 associated with point 3 on J(t). Lindsay's empirical evidence lends support to the latter proposition. But this test is not robust. As Frost and Frances (1979, p. 195) point out, consultants are not only the gatekeepers determining the length of the waiting list but also inputs in the hospital sector's production function. Once this dual perspective is recognised the unaffected throughput assumption made by Lindsay is too strong. Indeed, if hospital doctors are both "agents" and inputs, changes in their number can simultaneously shift the V-curve to the left, the J(t) to the right and increase supply capacity, thereby making a fall in waiting time conceivable under both scenarios (e.g. t3 in Figure 6 consistent with point 4). Hence it seems empirically testing for the "agency" aspect of waiting list construction in the way suggested by Lindsay is not decisive.

4 Agency effects raise the question of supplier induced demand. Here no assumption is made about the welfare consequences of the agency effect.

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J.G. Culis, PR. Jones and C. Propper

Waiting time (t)

Vle-dt 2' -

4

-to --------

--------------

J1 (t) J(t)

_- - - -- -

-ti -------

t3 t2

3 SC1

0

SCO

Joiners and throughput

C

V1 V2 Cost and value

Figure 6.Lindsay's "test" of the agency effect.

2.4.3. Fosteringprivate practice

It is commonly alleged that long waiting lists where physicians are also allowed private patients encourages the growth of private practice and results in increases in physicians' income. McAvinchey and Yannopoulos (1993) use a cost shares model to investigate the impact of hospital doctors on the shares of NHS acute care and insurance financed private acute care. Their econometric results are consistent with a direct effect of an increase in doctors employed in the NHS on costs (and so activity) in both sectors, as opposed to an increase only in public sector health care. However, there is also an indirect effect of waiting time on the public-private mix of care in their model. They derive a price index (P) for public sector care that is based on the cost of being on a waiting list: P = E(I + i) t ,

(8)

where E = a measure of average labour earnings, i = the short-term interest rate; t = the time wait on an NHS waiting list. Given that hospital doctors can control the waiting lists, and hence t, they can also affect the public-private mix indirectly via this admittedly "subjective index" (p. 179) of the price of public sector care.

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2.4.4. Waiting as part of least cost supply There are possible avenues via which gains from waiting can arise. Medical care contexts are generally uncertain ones and waiting may afford an opportunity to obtain more information about a patient and improve diagnosis and treatment. On seeing a patient in a hospital clinic the hospital doctors can refer the patient back to his or her GP, suggest an alternative hospital speciality, treat them more or less immediately or, assign them to a waiting list. In considering the last two options the hospital doctor may in uncertain circumstances be weighing up two costs, the cost of choosing the wrong treatment now as against the cost of waiting for new information which raises the probability of a correct choice of treatment at a later date. If the latter delay cost is small, waiting list assignment offers a potential net benefit over treatment now. However, given that waiting lists are predominately composed of cases involving a small number of conditions not associated with difficult surgery (see, for example, Chart 2) this argument cannot be used to explain much of the waiting list. In fact, it appears that supply increases designed to reduce waiting lists and/or waiting times seem to induce behavioural changes that results in fairly stable numbers on lists. In the UK case for example, waiting lists seem to remain at around half a million (Chart 1). Given that the stock of illness amongst patients does not change rapidly over time, this fact suggests that referral practices by primary care physicians and the willingness of hospital doctors to assign outpatient clinic attendees to the waiting list is not independent of supply. This has been referred to as Say's Law of Hospital Beds or "feedback" [Worthington (1987)]. The motivations that underlie such behaviour have been explored above, and do not seem consistent with making patients wait in case new information is revealed. In addition, this feedback mechanism highlights the problem of reducing recorded waiting lists: funds spent to decrease the list may simply result in higher referrals. It may or may not be efficient to treat the increased number of cases.

3. Waiting: empirical matters This section discusses empirical tests of the issues raised in Section 2. The empirical research can be grouped into tests of the impact of lists on demand, some of which attempt to estimate the cost of waiting lists for demanders of care or for society; tests of the association between public sector supply and waiting lists, and tests of the association between the rest of the medical care system and waiting lists. These empirical tests are often based on limited data and as a consequence, often provide only partial or rather indirect tests of the hypotheses discussed above. 3.1. Demand side: estimating the "costs" ofphysical waiting First, we briefly look at analyses of waiting in person. The costs of waiting in person are not the focus of this review, but recognition of the cost of such waiting is widespread,

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J.G. Cullis, P.R. Jones and C. Propper

and it has generated a large literature. One of the earliest analyses of the economic costs of waiting in person was Acton (1975) who proposed a model of the demand for medical care that incorporated time as an input. The consumer maximises utility, derived from the consumption of medical care and all other goods, subject to total income and total time constraints. Consumption of medical care in the Acton model has both a time and money cost. The comparative static results indicate that the elasticity of demand for medical care with respect to time depends on both the time and the money price; further, the absolute value of this elasticity is a positive function of the relative size of the time price. The implication is that time price will be more important in determining demand in health care systems in which care is allocated primarily by means of time, rather than money. This study and others that followed [e.g. Acton (1975), Phelps and Newhouse (1974), Coffey (1983), Gertler et al. (1987)] treated time as an input into the production of health care. However, although some of this research identified different types of time as having different cost, these studies did not estimate the cost of the allocation of care by waiting list. 3.2. Demand side: estimating the "costs" of administeredwaiting Waiting on a list has a cost because a good received later is worth less than one received now [the point made by Lindsay and Feigenbaum (LF)]. In addition, the individual on a list for treatment is generally in less good health than they would be after treatment [Propper (1995)]. The cost of waiting will generally be a function of both these components. The medical literature accepts that waiting lists are costly to users of medical care services. For example, in the UK, General Practitioners, as agents for patients, state that waiting times are one of the factors they take into consideration when making referrals [e.g. Kennedy and O'Connell (1993)]. There have been relatively few attempts to estimate the magnitude of these costs and the pattern of variation in cost across individuals. 5 Because consumers cannot buy shorter waiting time for public sector treatment, there are no direct measures of willingness to pay for shorter waits. When market data are missing there are basically only two alternative data sources. The first is to try to infer prices from observed behaviour in markets which interact with the public health care sector, i.e. to use revealed preference data. The second is to use direct inquiry via questionnaires (contingent valuation) or some form of utility experiment, i.e. to use stated preference data. 3.2.1. Costs of waitingfrom market data In the UK potential NHS patients can buy private care. Can the behaviour of individuals who choose private care be used to infer the costs of waiting? The answer is a qualified yes if total costs are sought, but no if the variation in costs across individuals is required. 5 Gribben (1992) measured the impact of waiting times on utilisation of GP services in New Zealand and found that long waiting times reduced utilisation. Regidor et al. (1996) who found that time spent waiting for doctor consultations in Spain varies by socio-economic status.

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Cullis and Jones (1986) used the LF framework to estimate the costs of waiting using data on length of lists and the price of alternative actions the demander of care may take. Like LF, they assumed the only cost to waiting arises because medical care is worth less if received later than sooner. Let P be the price of medical care in the private sector, V be the value of health care if received now, and V(t) be the value if received at time t(V(t) < V for all t > 0). The "submarginal waiter" is the individual for whom V - V(t) < P. She will not buy private care but will wait. The cost of waiting is less than P. The "marginal waiter" is the individual for whom V - V(t) = P, and the cost of waiting = P. Finally, the individual for whom V - V(t) > P will not wait, but will purchase immediate medical care on the private market and experience no cost of waiting. Given this taxonomy, Cullis and Jones concluded that the upper bound of the cost of waiting was equal to the average price of private medical care. The lower bound was zero: for some individuals the decay rate is 0. Using data on the prices of private medical care, and making the assumption of a uniform distribution of the costs of waiting, they multiplied the annual number of patients waiting for hospital admissions in the NHS by P/2 to derive an estimated cost between £1,205 to £2,155 million (the range depending on low and high estimates of P). This was equal to a cost per month of £110-220: equivalent to 9 to 16 percent of the NHS budget (0.5 and 0.8 percent of GDP) in the year of their analysis. If there is a positive cost to waiting per se, then the lower bound may be an underestimate. If the list is artificially inflated by people who no longer need treatment, or if individuals are subsidised to wait for treatment (for example, if time off work is covered by disability insurance individuals may overvalue V(t), and so wait in line when they would pay), the number on lists is too high, and the costs are an overestimate. If the value of time in bad health waiting is similar to the value of time in good health and treatment imposes costs, then bringing treatment forward will not necessarily increase welfare for all patients. In this case, the estimates will also be too high. To estimate the productivity cost (lost output) of waiting lists in two Canadian provinces, Globerman (1991) used the numbers on waiting lists in two provinces multiplied by the average wait to derive the total time waited in one year. He then deflated this by a factor reflecting the fact that only a proportion of those on waiting lists are incapacitated by the wait. This was then multiplied by the average wage rate to derive an estimate of productivity loss of between 0.1 and 0.2 percent of the total wage and salary bill in the two provinces. The sum was comparable to the income lost from strikes and lockouts during the same period. Feldman (1994) adopted a similar framework to Cullis and Jones to estimate the costs of waiting that would arise if the US health care system was replaced by a "US NHS" in which care was funded by taxation and excess demand rationed by waiting list. He used estimates of the elasticity of demand from the Rand Health Insurance Experiment to estimate the efficient level of health care expenditure (after adjustment for the impact

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J.G. Cullis, P.R. Jones and C. Propper

on prices of both provider monopoly and employer subsidisation of health insurance). 6 He made the assumption that this estimate was the level of care that would be funded by the "US NHS'. At this level of funding, there would be individuals waiting for care since the price is zero at point of demand. To derive the costs of waiting for all medical expenditures 7 Feldman estimated the percentage of total medical expenditure accounted for by those who would wait. By definition, the marginal waiter is the individual for whom the cost of waiting is the market price of treatment. As more expenses fall into the marginal category, so will the cost of waiting rise. Feldman made the following assumptions. First, the percentage of US NHS expenditure that was marginal could be 25, 50 or 75 percent. Second, the cost of waiting for the marginal waiters had a uniform distribution with mean p/2. Third, the cost of waiting for sub-marginal users had a uniform distribution with mean p/4 (to allow for the fact that the cost of waiting for a sub-marginal waiter, by definition, is less than the market price). Under these assumptions he calculated the cost of waiting per family ranged from around $720-1000 per year (1984 dollars), where the largest figure assumes that 75 percent of the waiters are marginal and the smallest figure that 25 percent are marginal. Offsetting this cost of rationing by lists is the consumer benefit from the reduction in risk from full insurance under the "US NHS". Using estimates of the risk premium (derived from the price elasticity estimates for health care under insurance), Feldman estimated the social cost per family of rationing by waiting were an NHS system to be introduced in the US to be in the order of $540-830 per annum (or 1-1.5 percent of 1984 GPD). 8 While this appears low, this figure may underestimate the cost of waiting. First, it ignores the cost of uncertainty that is associated with use of waiting lists. Second, it ignores the costs of other forms of rationing that arise whenever price is below marginal costs. 9 These papers have all estimated costs at a system level. Is it possible to use data on individuals who are covered by public insurance who then subsequently buy private care to infer their costs of waiting and so make estimates of variation across individuals in costs? The answer is generally not. First, the price which individuals pay for private care is not just the price of avoiding a wait. The consumer who chooses private care is also buying choice of location, choice of time for treatment, better hotel facilities, and

6 Adjustment for employer subsidisation of health insurance may be inappropriate since in the long run these costs are largely borne by employees in the form of lower wages. 7 The Feldman estimate is of all care, not just the hospital care costed by Cullis and Jones and Globerman. 8 Feldman argues that this is between 45-69 percent of the social cost from the over-utilisation of medical care by the 6/7th of the US population who have close to full insurance. 9 In systems where there are no waiting lists, but price is below marginal costs for the demander of care, other forms of price or non-price rationing do occur. Other non-price forms of rationing entail direct administrative costs, which may be lower or higher than the costs of waiting lists. Danzon (1992) made a rough estimate of the costs of non-price rationing by waiting in Canada and the administrative procedures used to limit demand in US private insurance, and concluded that in fact the US system was less costly.

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possibly better information. Second, even if the price were adjusted for this higher quality, typically the analyst does not observe how long those who chose private treatment would have had to wait. Third, any individual covered by private insurance will only pay the copayment. If copayments are zero, the demander may choose private sector treatment for any length of wait. l°0 One method of deriving valuations of non-directly marketed public or private goods is to estimate hedonic prices. This assumes that observed prices reflect variation in the characteristics that are not marketed. Estimates of the value of goods such as noise, air pollution and climate have been made by assuming that spatial variation in housing prices reflect spatial variation in these goods across different communities. In theory, as waiting times tend to vary considerably across communities, observations on house prices could be used to infer the value of shorter lists. However, use of such a method would require that correction could be made for differences in house prices due to factors other than the length of waiting lists, for factors which might drive both lists and house prices but did not link them causally, or for endogeneity of waiting times. The second possibility would arise if lower income individuals both lived in cheaper areas and had higher demand for health care services. There would be a negative association between prices and lists that was not due to the valuation of waiting time, but the fact that housing is a normal good and poorer individuals are sicker. The third case would arise if an influx of poorer people into a cheap housing area caused lists in that area to rise. In practice, this method has not been used to value costs of time spent on waiting lists. 3.2.2. Estimates of costs using contingent valuation methods The contingent valuation method uses sample surveys to elicit the willingness of respondent's to pay for projects or programs. The method has been widely used in resource and environmental economics, where it is used to elicit preferences for public goods, such as national parks, clean air, or to value the "existence value" of goods which individuals may not use but may value (such as the preservation of species). Outside resource economics, it has been used to value a large number of non-environmental policies or programs, including health related ones such as reduced risk of death from heart attack [Acton (1973)], reduced risk of respiratory disease [Krupnick and Cropper (1992)], highway safety [Jones-Lee, Hammerton and Phillips (1985)]. Contingent valuation can also be used as a means of eliciting preferences for private goods. It has, for example, been used extensively to value time savings in travel [e.g. Bates (1988)] and in health care has been used to value time spent on waiting lists and the value of other goods which are non-marketed but are mainly private [Ryan (1996)]. While there is no standard approach to the design of a contingent valuation survey, the elements of an application are the following [Pourtney (1994)]. First, the survey 10 Clearly the price of insurance is not zero. But once insured the demander of private care faces zero marginal cost if co-payments are zero.

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J.G. Cullis, P.R. Jones and C. Propper

must contain a description of the good that the respondent is being asked to value. Second, the survey must contain a mechanism for eliciting the values or choice from the respondent. These mechanisms may take a number of forms, which may be either open ended (e.g. "how much would you be willing to pay for x") or closed ended forms where individuals make discrete choices between fixed alternatives. Using the close-ended form of the survey instrument, individuals are asked to make discrete choices between goods that contain different amounts of each attribute. Assuming a random utility model for individual preferences, standard techniques for binary choice can be used to estimate a willingness to pay distribution function [Hanemann (1994)]. Third, the survey usually elicits socio-economic information on respondents, so that willingness to pay functions can be estimated which includes these characteristics as explanatory variables. Contingent valuation is currently the subject of controversy, particularly where used to elicit preferences for public goods where there are no close marketed substitutes and contingent values cannot be compared to observed market transactions. l In the case of waiting times, the good is private, but as for public goods it is not generally possible to observe trade-offs individuals would make between time and money. Propper (1990, 1995) adopted an economic framework used to study the value of the utility of time in transit economics to estimate the value of waiting time in the UK NHS. The framework assumes utility is derived from a vector of commodities, plus a vector of time spent in various activities [e.g. de Serpa (1971), Truong and Hensher (1985)]. Where the consumer chooses between discrete uses of her time, her problem is: max U(G, q, t), s.t. pG + Ejdjcj q +Ejdjtj

tj > t

Y

[],

T

[],

forall j

[y],

(9

where G is the quantity of a generalised consumption good, q is the time spent in a generalised activity, tj and cj are the time and costs, respectively, associated with alternative choices, dj, j = 1, ... , J are dummies such that dj = 1 if choice j is made and 0 otherwise, t is the technologically determined amount of time for activity j, and /I, and are the shadow prices of the income, total time and time spent in activity j constraints, respectively. Taking a first order approximation to the direct utility function (9) and substituting in the first order conditions, the total time and the money budget constraints, the conditional indirect utility function for choice j can be derived as a function of income, costs and time of each alternative. Given an indirect utility function, a probabilistic choice model can be used to allow estimation of the parameters of interest. Using a random utility model, terms common to both alternatives drop out of the specification of the

l See, for example, the Journal of Economic Perspectives (Fall 1994), Hausman (1993), National Oceanic and Atmospheric Administration (1993).

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deterministic component of (indirect) utility, and the deterministic element of indirect utility can be specified as Vj = -- c -

jtj.

(11)

The coefficients . and 9j can be interpreted as scale transformations of the marginal utility of cost and time respectively, and the ratio 99j/)X interpreted as the value of saving time in health care choice j. The indirect utility function (10) contains only linear terms in income, and so (11) contains no terms in income. Therefore income does not enter directly into the estimation. In estimation of this model, Propper allowed the constraints A and 99 to be functions of income and other socio-economic attributes. (For example, the marginal utility of income, X.may be expected to fall as income increases.) Data to estimate (11) were collected using a contingent valuation exercise, in which individuals were asked to trade-off waiting time against money for a non-urgent medical treatment (one with a low decay rate in the LF terminology). The hypothetical situation was designed to be as close as possible to the existing market. 12 The estimates indicated that the value of waiting time was of the order of £35 per month (1987 prices).13 In addition, there was systematic and significant variation by income: those with higher incomes had higher values of time. The total costs of waiting for treatments with zero decay rates was estimated to be around 0.1 percent of GDP. These estimates were below those of Cullis and Jones, who estimated the GDP cost of waiting to range between 0.5 and 0.85 percent of GDP. However, the difference was in the expected direction. The contingent valuation exercise explicitly considered only zero decay conditions while the Cullis and Jones analysis valued waiting lists for all conditions. In addition, given that the purchase of private care depends on ability to pay and so income, and that income has a log normal rather than a normal distribution, the Cullis and Jones assumption of a uniform distribution of waiting values may be an overestimate. The estimates from the contingent valuation exercise were also lower than those of the value of transit time [M.V.A. Consultancy et al. (1988)]. Again, the difference was in the expected direction: time spent in transit is closer to an exclusive use of time, whereas those on waiting lists can perform some of their normal activities. Johannesson et al. (1998) used contingent valuation exercise to derive willingness to pay for reductions in waits in Sweden. With a waiting time guarantee of 3 months given by the public health care system in Sweden taken as the benchmark, individuals in a survey in 1995 were asked how much they would pay for each of two different insurance plans that would reduce waiting to one week and to six weeks, respectively. In estimation, the authors allowed the probability that individuals would pay zero to

12 The contingent valuation design conformed to the practices listed as desirable in the National Oceanic and Atmospheric Report (1993). 13 Rebasing to 1991 prices gave an estimate of approximately £50 per month.

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avoid a wait to be strictly positive. The results suggested that on average individuals were willing to pay about SEK 2,000 per annum for an insurance plan which reduced waiting from three months in the state health care system to six weeks. In comparison to other estimates presented here, the results suggest individuals were willing to pay in the order of £95 to £100 per month (in 1991 prices) for a reduction of a month's waiting time. 3.3. Supply side: estimating the impact of supply variables More research effort has been directed to assessing the relationship between waiting lists and the supply of public sector care (primarily again in the UK NHS). In general, most studies that examine the association between list length and some measure of the level of supply (such as number of consultants, number of beds, hospital expenditure) find no clear pattern. Much of this literature simply examines bivariate relationships between some measure of supply (often at a geographically aggregate level) and numbers on waiting lists. Such an approach does not take into account the possible endogeneity of either demand or supply, and perhaps not surprisingly therefore, few clear results have emerged. Investigating the impact of changes in supply on changes in numbers on lists, Frost and Francis (1979) and Frost (1980) tested Frost's (1980) assertion that consultants (hospital doctors) adjust their waiting list/admissions thresholds in order to maintain a constant waiting list. The hypothesis implies that the elasticity of numbers on the waiting list with respect to supply of consultant numbers is unity. Using time series data on total numbers on the list and the number of consultants Frost (1980) found that a 1% increase in the supply of consultants led to approximately 1% increase in the size of lists. Using cross section data [Frost and Francis (1979)] found similar results. Findings such as these that are used either to support the hypothesis that "nothing can be done about lists", or to support "supplier induced demand": an increase in resources will simply lead to greater demand [Pope (1992), Roland and Morris (1988)]. The Frost (1980) evidence has been subject to critical comment. McPherson (1981), whilst conceding that some unknown element in waiting lists will be "consultant induced", pointed out that on average Districts in any Region with greater population will, in a centralised health care system, have greater numbers of both consultants and waiting patients. In short, waiting lists adjusted for population are likely to be very similar between districts. McPherson (1981, p. 194), having made a crude adjustment for population size (and ignoring two data points), commented ". . . to argue that in aggregate the numbers of consultants determines waiting list size would be foolhardy in the extreme". Buttery and Snaith (1979) used cross sectional data for 1977 and found no clear association between lists and surgical provision. Yates (1987) found no linear relationship between shortage of beds and long waiting times using data from the 1970s and early 1980s. Goldacre et al. (1987) used time series data for 1974 to 1983 and found no relationship between admissions and length of list. Newton et al. (1995) used time series

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data for 1987-1994 to examine the relationship between changes in the number of admissions to hospital and changes in list size. They found that changes in the number of admissions were inversely correlated with changes in list size, so an increase in admissions did not reduce list length because additions to the list tended to increase at the same rate (presumably because as lists fell more patients were referred onto the lists). But waiting times (as distinct from numbers on a list) appeared to fall as a result of increased admissions. So much of this research is inconclusive. Many have examined numbers on lists rather than average time (or the distribution of time) spent on lists. But it is the latter factor which affects the behaviour of demander or their agents (the family doctors who make referral decisions). Failure to model the demand-side response to a change in waiting times reduces the relevance of the research. Martin and Smith (1999) attempted to estimate a simultaneous model of demand and supply in which waiting times are the price of elective surgery. They argued on the demand side, an increase in waiting deters the marginal joiner of the queue, and on the supply side, an increase in waiting times leads either to additional resources and so supply of care, or on pressure to improve efficiency and so to more care. From this they argued that correct estimation requires estimation of a model in which demand, supply and waiting times are endogenous. They do not directly estimate the possible models of Section 2, but argued that demand and supply of elective surgery will be affected by the following variables: demand = f(waiting time (-), medical need (+), GP supply (?), provision of private sector supply (-)); and supply = g(waiting time (+), provision of NHS beds (+), length of stay in hospital (-), share of elective surgery done as day cases (+), proportion of admissions that are elective (?)). where their priors as to the direction of the associations were as given in parentheses. They estimated these demand and supply functions using small area level data for two years (1991 and 1992). The unit of observation was 4985 "synthetic wards", (small areas) with an average population of 10,000 people in each, for which they had over 2 million records on elective episodes of treatment in routine surgery or gynaecology. (Elective episodes are those for which waiting lists are used to allocated care.) They allowed for endogeneity of utilisation, waiting lists, the proportion of surgical cases that are elective, the proportion of admissions that are day cases and the average length of stay in elective surgery. The results for the demand equation indicated that the direct impact of waiting time on demand for elective surgery is small. The long run elasticity estimates suggest that a 1% decrease in waiting times will be associated with a 0.09% increase in demand. From

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this the authors conclude that the induced demand effect of a reduction in waiting lists is very small. In the supply equation, there is a larger association between waiting times and the supply of elective surgery: a 1% increase in elective surgery is associated with a 0.35% increase in waiting times. Solving for the equilibrium relationship between waiting times and supply, Martin and Smith found the net effect (i.e. after taking into account both supply and demand responses) of an increase in NHS resources on waiting times to be negative but not large. In recognising endogeneity of demand, supply and waiting times, the paper is a direct attempt to estimate the impact of the behaviour of demanders and suppliers of care. It therefore addresses the issues raised by the theoretical models of waiting lists. However, the results of the study cannot be used to distinguish between the different hypotheses advanced above. For example, the authors cannot test whether increases in lists lead to more resources with no change in efficiency (an Iverson type effect) or whether longer waiting lists lead to higher effort and greater efficiency. 3.4. Supply side: inter-sectoraleffects In a study that allowed for interaction between the public and private sector, McAvinchey and Yannopolous (1993) estimated a dynamic cost shares model with three goods: public sector medical care (the NHS), private sector medical care and all other consumption (see Section 2.4.3). The price of NHS care was the waiting time cost (see Section 2.4.3) and the price of private care was the price of private insurance. From their estimates from aggregate annual data for England, Scotland and Wales for 1955-1987 they derived both short and long run own-price and cross-price elasticities for NHS and private care. The own-price short run elasticities were small, and were smaller for the NHS than for private care (for NHS care they ranged from -0.29 to -0.68 and for private care from -0.79 to -0.85). The computed long run elasticities were, as is usual, much higher than the short run elasticities. The long run own-price elasticities in the two sectors are similar and highly elastic, being around -4.5 for the two sectors. These are perhaps rather high in comparison to price elasticities estimated for other health care markets. The movement of patients into the private sector following a rise in the costs of waiting (elasticity estimate = 0.6%) is estimated to be slightly less than that into the NHS following a rise in insurance premia (elasticity estimate = 0.82%). The results indicate both that waiting lists appear to act as a price, but also that the demand for care will depend on changes in both the public and private sectors. If, for example, a 1% rise in waiting lists is followed by a 1% increase in premia the net demand for NHS care will change very little. So if increases in NHS lists are offset by rises in private sector costs, then NHS demand may be little affected by waiting list changes. Further, the authors note a positive correlation between the number of consultants and the waiting time on a waiting list which is consistent with a "supplier induced" effect on the share of private health care. Besley et al. (1999) examined the impact of the quality of NHS care, as measured by the length of waiting lists, on the demand for private care. They advanced a simple

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model of the demand for private insurance in a market in which individuals have automatic entitlement to public sector care. They argued that the consumer's decision to buy private health insurance is a function of the quality of care in the two sectors. Under the assumption that the quality of NHS care is always lower than quality of private care (since any private supplier who had lower quality than a public provider would have zero demand since the public sector is free at point of use) they derive analytical results for the impact of income and quality of NHS care on demand for insurance. The analytical results show that selection into private insurance, and that a lower level of relative quality in the public sector increases demand for private insurance. Empirically, this model suggests investigating the determinants of demand for private health insurance as a function of the relative quality of public sector provision and other individual characteristics, particularly income. The model was estimated using 5 years of micro data from a cross sectional survey, the British Social Attitudes Survey (BSAS). These data cover the period 1983-1991 (i.e. prior to the NHS health service reforms). The quality of the NHS was measured in a number of ways: the total numbers on waiting lists, the total number of staff, spending on headquarters, spending on support staff, spending on treatment and the numbers waiting over a year. NHS quality is measured only at a regional level, so regional measures were matched to individual data using location data of individual respondents. The effect of the regional quality indicators is identified from deviations from regional and time means, which constitutes a stiff test of the NHS quality measures. Strictly speaking, the quality measures ought to have been entered as the differences between the private and public sector quality measures. As waiting lists are zero in the private sector, the measures of waiting time are de facto in differences, but the other measures of quality are not. The results indicate that only one of the NHS quality measures appears to determine private insurance purchase (conditional on individual level covariates, time and regional dummies): the proportion of individuals waiting longer than a year. This gives qualitative support to the hypothesis that private demand is affected by waiting lists.

4. Waiting: policy issues Section 2 addressed the question "what waiting time is appropriate?". Waiting is necessary when resources are insufficient to furnish immediate medical treatment; "optimum" waiting time occurs when a socially optimal allocation of resources has been provided in the NHS and when patients are ordered optimally in the list. However, even if an efficient waiting time is not achieved, it remains possible to be cost effective in the management of those who wait. In this case the aim is essentially X-efficiency; maximising physical output from inputs employed and choosing least cost input combinations. Optimum waiting time is unlikely to be zero (for if the optimum were zero this would imply that sufficient resources had been made available to ensure immediate treatment for all case types). If the analysis of Section 2 is accepted the application of much of

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the empirical work to policy is not direct. For example, the demand studies effectively measure, in the view of potential patients, the fall in the total benefit curves from to to the actual or anticipated treatment date in parts (b) and (c) of Figure 1. Some waiting costs (loss of total benefits) are optimal for illustrated case types 2 and 3. However, without knowing these amounts for each case type, empirical estimates of actual costs sit in a welfare vacuum. In the absence of further assumptions and/or empirical work it is impossible to look at waiting costs of, say, £x and draw strong normative conclusions. In the absence of an over-arching primary efficiency calculus, policy has been directed at a secondary level: at reducing the waiting numbers and their associated waits on the assumption that this is welfare improving. In practice, governments focus on ill-defined, almost ad hoc, target waiting lists and/or "guaranteed" waiting times. In the UK for example, waiting lists have assumed the same importance as other indicators of government performance, such as public sector borrowing [Cullis and Jones (1983, 1985)]. In recent years promises to "guarantee" waiting times have emerged in general election campaigns [Yates (1991)]. But the targets implicit in a reduction of waiting lists and waiting times are not rationalised in terms of welfare maximisation and, as explained in Section 2, the relationship between waiting lists and welfare is far from obvious.' 4 In just the same way as governments pursue public sector borrowing targets, waiting list targets are established without a strong welfare foundation. Yet from an economic perspective, the key consideration is how a reduction in waiting lists or times enhances welfare. 1 5 In this section a taxonomy of alternative policy options is presented and in each case efficiency and equity aspects are considered. Efficiency, defined in Paretian terms, is achieved when it is impossible to reallocate resources to make one individual better off without making another worse off. 4.1. A taxonomy of policy options As policy has been premised on the assumption that waiting list reduction is desirable, the following policy options have been considered. 14 Analysis of waiting lists [e.g. see Lee et al. (1987), Yates (1991)] show that they comprise: patients who have already died; patients who would refuse treatment if offered it immediately and patients who benefit clinically from waiting. For example, Hemingway and Jacobson (1995, p. 819) note that, while one third of patients continue to face operations, "the natural course of recurrent throat infection, the main indication for tonsillectomy, may be one of improvement". They note that, " ... a prospective study to determine the morbidity caused by a delay in tonsil surgery found that a fifth of patients grew out of their condition and were spared surgery". Though views on tonsil surgery differ [Yates (1995)]. 15 In the UK, 52% of those on inpatient waiting lists wait for General Surgery, Trauma and Orthopaedics and Ophthalmology (see Chart 2) and suffer from a variety of complaints, e.g. hernias, varicose veins, joint complaints. As patients also vary according to personal and social characteristics, it is unlikely that common targets for waiting lists and/or waiting time will be easily reconciled with maximisation of welfare. Pope (1992, p. 577) comments: "The length of time people wait to be admitted is undoubtedly important, but factors like severity, urgency and social and physical circumstances of the person waiting may be equally important in assessing the situation".

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4.1.1. Demand rationingand reduced waiting Waiting has been perceived as a reflection of excess demand at zero user cost. One response is to introduce mechanisms to ration demand.16 Seldon's (1967) answer would be to introduce a price, so that supply is rationed to those with the highest valuation. 17 Private (market-based) insurance often relies on utilisation reviews, protocols and provider-financial systems (e.g. capitation fees for physicians) to restrain demand pressures. Buchanan (1965) interprets the problem of excess demand with reference to an inconsistency inherent in non-market decision making. When individuals vote for a tax contribution that pays for the care of others they attach less weight to others than they do to themselves. The supply of health care resources is less than would emerge when individuals demand private medical insurance in a market scenario (when each individual is conscious of the benefits to be personally experienced). Hence waiting lists are endemic in the absence of institutional reform. Buchanan's policy solution is that health services be rationed and distributed in a manner that would ape the outcome of a competitive market. The policy of aping competitive markets is difficult to implement. To set a price, or to ration efficiently, would require that the point at which marginal benefit of medical treatment equals marginal cost be identified. It would be necessary to assess individuals' preferences accurately to know marginal benefit. It is far from obvious that the allocation of a ration and the removing of waiting would enhance welfare. Some patients may prefer waiting to the prospect of no further treatment. 18 Also, on efficiency criteria there is a case for considering "option demand" [Weisbrod (1964)]. Even if individuals make no use at all of hospital services, they still feel better off to know that such services are at hand if required. An allowance for option demand would be necessary when determining the appropriate ration. Turning to equity considerations, constructing a competitive market solution in the public sector is likely to be less attractive than instituting "fair" procedures. Frankel and West (1993, p. 129) argue: "... at the limit we probably all accept that there are conditions which are not recognised as diseases and as a consequence which do not deserve to be treated by the NHS". It may not be fair to offer all treatments via the public sector but, if equity arguments carry force, who should determine priorities? Frankel and West (1993) note that one of the implications of waiting lists is that it permits policy makers to blur such rationing issues.

16 As Globerman (1991) notes, non-price rationing in other markets (e.g. rent control) has been criticised when price is set "too low". 17 The Telegraph, Wednesday, 8 October 1997, reported that the British Medical Association favoured a small fee to consult general practitioners in order to ration demand. 18 Cullis (1993) notes individuals in the UK may be better off waiting than the non-insured in the USA who do not get a chance to join a list.

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4.1.2. Supply expansion and reduced waiting If waiting arises from excess demand, an alternative to rationing demand is to increase supply. Whether under-provision is the problem is a moot point. For example, while Yates (1987) argues that there is under-provision in the UK by comparison with other European countries, he also notes that there are countries, which spend less than the UK but which do not have a waiting list. Within the NHS he reports that waiting lists appear in both efficient and inefficient health districts. It is always possible to respond to a waiting list problem by commending better use of existing resources [e.g. Yeates (1980), Ingram (1980), Cottrell (1980), Yates (1987), Mills and Heaton (1991)]. To be more specific, Frankel and West (1993) call for better use of operating theatres and clinical staff. Also, in the UK context, they call for greater incentives for hospital consultants to spend more time treating NHS patients (rather than private patients). However, there can be dangers if better use of resources is interpreted as more intensive use of resources. Globerman (1991) warns that measures to speed up treatment to reduce waiting can have adverse consequences on quality of treatment. Moreover, if increasing throughput of patients leads to an increase in re-admissions the impact on waiting lists is not obvious. Even if the quality of care is not affected there remains the question of whether more productive use of resources will reduce waiting time; reduction of waiting time may simply stimulate demand from new patients. Demand for medical care is affected by the availability of new treatments and (as argued in Sections 2.4.2 and 3.3) by additional suppliers of medical care who have an incentive to foster waiting lists. Empirical studies do not show a clear association between increases in admissions and length of lists. For example, in the UK Goldacre et al. (1987) did not find a significant negative correlation between the number of admissions in one period and the length of waiting list in the next period, while Martin and Smith (1999) (Section 3.3) reported that an increase in supply would reduce waiting time. If additional funds are made available, it matters how they are used. Increased funding per se is less likely to reduce waiting than using funds to create direct incentives to reduce waiting. For example: (a) In the Australian State of Victoria three sets of changes were introduced in 1991 [Duckett and Street (1996)]. These were: (i) directives for surgeons to better categorise patient need for treatment; (ii) hospital funding linked to activity rather than unmet demand (lists); (iii) funding linked specifically to treatment of patients on the list. The intention of the last measure was to ensure that, as hospitals increased their throughput in response to payment based on activity, they did not allow lists for routine operations to grow. The impact of the policy was a fall in both waiting times and numbers on lists.l 9 However, while the results appear encouraging, the follow-up period (analysed by Duckett and Street) was only a year and the longer run policy impact has yet to be evaluated.

19 These changes were not simply due to re-categorising of patients.

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(b) In Sweden sponsors of health care services set a 3-month maximum waiting time guarantee for the year 1992. Waiting lists dropped substantially between 1991 and 1992. Providers undertook actions to bring down lists when paid to do so, but once funding stopped they no longer took these actions [Hanning 1996]. (c) In the UK a "Waiting Times Initiative" ran from 1987/88 to 1993/94 inclusive. Over this period a total of £252 million was allocated to reduce long waits. The InterAuthority Comparisons and Consultancy (1990) reported that mainstream funding had limited success and recommended that money be paid to health authorities who succeeded in reducing waiting time [see Iverson 1993]. Between 1991 and 1994 the percentage waiting over 12 months was established as a performance measure and there was a reduction of long waits. However, after March 1996 there was an upturn in patients waiting over 12 months and Edwards (1997) questions the longterm success of the initiative. While there is some support for the proposition that funding must be linked explicitly to reducing waiting there are problems. Once hospitals are (even partly) penalised for having long lists, list composition is likely to be managed more effectively [Hanning (1996), Druckett and Smith (1996)]. This may have some benefits, for example, removing patients who no longer need treatment. However, shortening of lists does not necessarily signal an equal increase in productivity if there is an incentive to admit fewer patients to waiting lists. The equity implications of increased funding also require consideration. Critics have argued that individuals from the middle class are better able to manipulate systems such as the NHS [Le Grand 1982]. The impact of additional funding may be to reduce waiting for those most able to secure treatment and the policy may not be progressive in terms of income distributional impact. However, more recent UK evidence [e.g. O'Donnell and Propper (1991)] suggests that the middle class bias is no longer evident. 4.1.3. Subsidies to reduce waiting Rather than increase funding for public sector treatment, waiting for public sector treatment may be reduced by using additional public expenditure to finance a subsidy to those who will leave the waiting list to purchase treatment in the private sector [Cullis and Jones (1983, 1985)]. In Figure 7, Do represents the demand for treatment of a medical condition. At OP1 the private sector deals with 0ql. The public sector, at zero price, reduces the remaining demand of ql q3 by ql q2, leaving a waiting list of q2q3. Whether this constitutes an "optimum" wait is a moot point. However, assume that a reduction to q4-q3 is desired and that a budget q212q4 has been allocated. A first response to this situation (described in Section 4.1.2) would be to increase public expenditure to increase output in the public sector by q2q4 cases. The cost of this expansion is q212q4 (assuming that private and public sector provision are equally cost effective at MC = AC). The same result might be achieved with a lower budget if demand for treatment is price elastic. If a subsidy were offered to those willing to pay something for private treatment, the cost of the subsidy will be P134P 2 when the private

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sector expands by ql -q5. Assuming supply is infinitely price elastic in the private sector, this switch to the private sector releases resources in the public sector, so that the waiting list is reduced to q4-q3 20 The cost of the subsidy is less than the increase in expenditure on the NHS of q212q4. (It should be noted that as ql53q5 equals q212q4, the resource cost of expanding capacity are identical so that the previous comparison is only in terms of "exchequer" budget costs.2 1) While the subsidy scheme ensures that those with the highest individual marginal valuations are treated, no such guarantee applies to the alternative strategy. However, the case for choosing a subsidy requires, in part, that demand for treatment is price elastic. To ascertain price elasticity, Cullis and Jones show that elasticity (e.g. at point 5 in Figure 7) is approximated for a linear demand function by the ratio: 1=

cases treated in the NHS + waiting list cases treated privately

(12)

When this ratio exceeds one, the option of providing a selective subsidy to private consumers of this type of medical treatment proves attractive but there are problems. First, there is the effect of "supplier-induced demand" (SID). With increased availability of resources, doctors (with asymmetric information) can respond by simply stimulating demand. As noted in Section 3.3, Frost and Francis (1979) and Frost (1980) found that the size of the waiting list responded positively to an increase in the number of consultants (a 1% increase in the number of consultants resulted in a 1% increase in the size of the waiting list). It follows that a growth in the number of surgeons may simply be reflected in a growth in the waiting list. The implications for the choice of private sector subsidy, rather than additional public sector funding, depend on the way in which SID operates. One possibility (Case A) is that the availability of additional resources may simply shift the demand curve in Figure 7 to the right, i.e. to D 1. Alternatively (Case B), the availability of additional resources specifically increases demand in the public sector, so that there would now be a kink in the demand curve (which becomes Do59q6).2 2 In Case A, if the government increases public expenditure there is an increase in demand (Do to D 1) but there is an increase in treatment in the private sector and the waiting list reduction is achieved (i.e. the waiting list is qg-q6 which is equal to the target q4-q3). In Case B, demand increases only in the public sector and even if there is an increase in public expenditure the waiting list will remain q4-q6. Now consider the effect of using a subsidy (Case C). If a subsidy is used, when Do increases to D 1 the waiting list will remain on target q4-q3 q8-q6 but the financial costs increase 20 As is evident in Figure 7 there are assumptions, e.g. concerning costs of treatment in the private sector. It is assumed, for example, that the costs of treatment do not rise in the private sector as a result of increased demand and that quality of treatment is not lower in the private sector (and conversely in the public sector). 21 Other costs (e.g. the dead-weight loss of taxation) are assumed constant in raising the same exchequer funds. 22 This second impact appears consistent with some empirical evidence [e.g. Frost (1980)].

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Price

D1

2 2

1

P1

1

P2

I

I

,I , I

O

I

q,

q5

II

I

I

I I I

I ,I

_I~_I~~

Private Psectore

I

I

II

,I

I,

MC=AC

q9

q7

Public sector

q2

.I~I

q4

q3

q8

Waiting list

Cases treated/t I

I

Waiting list

sector

'

q6

sector ubic d Private P sector

Public sector

.

I

iseictore:

Waiting list ' '-' C;CaseA I

I

I

Public sector

, ' '

Waiting list -

Case B b' Case

Figure 7. Effects of subsidies and expansion af the NIHS on waiting lists.

(P1 78P2 rather than P1 34P7). It follows that, if there is a need to allow for SID, the subsidy only operates with the risk that a budget constraint will be breached. Of course, this risk can be monitored. As the demand curve shifts to the right, demand becomes Price by reference to Equation (12) there is a signal that the subsidy is no inelastic and longer as attractive.

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J.G. Cullis, P.R. Jones and C. Propper

The assumption that there is an infinitely elastic supply of resources for the private sector is important. A second potential problem arises if the expansion of the private sector is only possible because resources are taken from the public sector. If resources were diverted from the public sector the subsidy would have two effects. The first is a positive impact on waiting by removing demand. The second is a negative effect by switching resources away from the public sector to the expanding private sector. If both effects operate, the net effect of private provision on waiting in the public sector is indeterminate. Iverson (1997) examines a situation in which the more price elastic the demand for public treatment the more that waiting time is likely to increase (if the private sector option is pursued). A third potential problem of using a price subsidy concerns the quality of output in the public sector. Expansion of the private sector is likely to remove those patients best able to exert pressure for improvements in the delivery of public sector medical care. Besley and Gouveia (1994) note that private sector expansion may reduce the size of the political coalition supporting the current level of public provision. The "exit" of some patients will affect the potency of "voice" in the public sector [Hirschman (1970)], if, as Besley et al. (1999) confirm, it is the wealthier and better educated who express dissatisfaction with public sector provision. Equity considerations are also important. The scheme will appear regressive if higher income "waiters" (more able to purchase private sector treatment) qualify for a subsidy. 23 However, there is no presumption in the above analysis that they will get a refund for their contribution to the NHS and those remaining in the public sector may have shorter waits. Income-related subsidies could be used to alter the distribution of benefits. However, the transactions costs of administering such schemes will also need to be considered. 4.1.4. Encouragingprivateprovision Offering subsidies to patients to purchase private sector treatment encourages demand in the private sector. An alternative policy response is to encourage private sector supply. While not looking explicitly at medical care, Shmanske (1996) considers a policy option to reduce waiting by encouraging private sector supply. In Figure 8 the demand curve is DD'. If the public sector supplies the good at a price of Pg (below average cost ACg) there is a loss of Oqg(ACg - Pg) and to mitigate this loss, public sector output is reduced to Oq'. Average cost is now AC' and the loss is Oq'(AC' - Pg). However, with a shortfall of q'-qg individuals must queue. The value of the good to the consumer at the margin is Pv, and a waiting cost of Pv - Pg is incurred to equilibrate the market. If a private sector firm were to offer units at a price of Pp intermediate to Pv and AC' (and therefore above Pg), the firm cannot supply the whole market. No one will

23 Iverson (1986) shows that private practice can reduce waiting time for patients but with an increase in inequality (as the demand for private health care depends on income).

Ch. 23: Waiting Lists and Medical Treatment

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Price

AC

ACg Pv AC' Pg

0

q'

qg

QX/t

Figure 8. Waiting in a non-contestable market.

patronise the private firm for those waiting know that, if other demanders switched to the private supplier, costs of waiting in the public sector will be reduced. With this free rider problem the market is non-contestable (i.e. the private firm is unable to supply the whole of the market). If the market were contestable an entrant could obtain the whole market by setting a price just below Pv. However, if the full price of Pv is composed of a "rigid" price Pg and a "flexible" price of Pv - Pg, the residual demand curve facing the private firm entrant (allowing for the existence of the public sector supply and the waiting problem) is Pv 12D'. The segment Pv1 is parallel to the original demand curve because, for any price P between Pv and Pg, the public sector supplier sells the first q' units. When a queue of waiters causes marginal waiting cost of Pv - Pg, the segment Pv 1 of the residual demand is below average cost. If there were no subsidy for losses (i.e. AC' - Pg per unit) incurred by the public sector supplier, then this supplier would compete like any private business (as far as covering costs is concerned). The public sector supplier would have to charge a price at least equal to the height at the minimum point on the average cost curve. In this case, entry of a second firm would not be precluded. Shmanske (1996) argues that, if queuing is created by the subsidy, the policy option is to "privatise" public sector provision (i.e. remove the public sector subsidy) and thereby encourage competition from the private sector. However, if government policy also addresses under- consumption of the good (as in the case of medical care) there is a case to retain a subsidy in some form. 4.2. Efficient waiting In this sub-section we address policy options that aim to manage existing lists. The objective is to reduce costs for existing patients and the focus of attention is on measures to prioritise patients. Of course, different rules of prioritisation may stimulate or deter demand from new patients [e.g. Bowles (1982), Worthington (1987,

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J.G. Cullis, P.R. Jones and C. Propper

1991)]. For example, Goddard and Tavakoli (1994) use a queuing model to assess the impact of: (i) treating complaints in the order that they join the queue; (ii) affording priority to achieve equality between the total level of "suffering" experienced by all complainants; (iii) offering rapid rationing to as many seriously ill complainants as the system can cope with. The method of prioritising affects demand (e.g. in the third case considered, many with minor complaints would not bother to join the queue as there would be no hope of treatment). While the focus of attention in this section is on cost-effective management of existing lists the impact on overall demand cannot be ignored. Nor can equity considerations be dismissed. Prioritisation of patients based on explicit and consistent criteria is commendable for waiting list management but, for equity, this also applies to decisions to refer patients to waiting lists. 24 4.2.1. Indicesforprioritisation A number of different criteria can be employed to prioritise waiting list patients. A "first come first served" approach or "a common guaranteed waiting time" approach may seem "fair" ways of proceeding [Higgins and Ruddle (1991)],25 but both these approaches imply that individuals who have minor ailments but come earlier will be treated while others who come later with more substantive ailments (or social need) would continue to wait. Naylor et al. (1990) use clinical guidelines to determine the urgency of patients with angiographically proven coronary disease and in need of revascularisation procedures. 2 6 One comment on British experience is that, implicitly, doctors have adopted a forgone present value of patient earnings criterion [Aaron and Schwartz (1984)].27 Of course, a broader set of criteria than either clinical guidelines or present value of patient earnings is likely to prove more acceptable. Culyer and Cullis (1976) suggested that selection of patients who are waiting should depend on: (i) time already spent on the waiting list; (ii) urgency based on the expected deterioration of the patient's condition; (iii) urgency based on the patient's health status; (iv) urgency based on the social productivity of the patient and the number of economic dependants; (v) urgency based upon other social factors. An attempt to apply these broader criteria (by allocating points for each element on a range between 0 and 4) was adopted by a consultant anaesthetist at Salisbury District Hospital in the UK [Edwards (1994)]. Edwards (1997) argues that waiting list and waiting time information should be published not only by clinical speciality but also by medical condition so that, if national 24 Hicks (1972), Forsyth and Logan (1968) reported evidence of wide variation in referral rates. 25 "In many ways, a system of rationing by queuing is a fairer more open way of restricting access to scarce resources than some of the alternatives used in other countries" [Higgins and Ruddle (1991, p. 18)]. 26 Factors considered were severity and stability of symptoms of angina, coronary anatomy from angiographic diagnostic studies and the results of non-invasive tests for the risk of ischaemia. 27 The implication is that the narrow objective of maximising national output applies.

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maximum waiting times are to be stated, there should be a gradient of "clinically appropriate times". More difficult is to ascertain how social considerations are to be integrated and, on this, Edwards calls for greater information about the views of relevant interested parties (patients, members of the general public, general practitioners, purchasers and politicians). Decisions will be sensitive to the precise formula adopted and the question arises as to who should determine and implement criteria. In New Zealand in the late 1990s one of the tasks of the National Health Committee is to generate criteria for the prioritisation of elective waiting lists. Both clinicians and members of the public are involved in determining criteria [Dixon and New (1997)].28 When considering who will implement selection criteria, the study by Brattberg (1988) of an experiment at a Department of Anaesthesia at Sandvikken Hospital in Sweden is relevant. Rankings of patients made by the secretary and nurse (based on a questionnaire completed by the patients) were compared with assessments by the doctor (based on consultation with the patient). The general result was that the secretary and nurse were inclined to overestimate urgency of treatment. One selection criterion employs Quality Adjusted Life Years (QALYs). Williams (1988) suggests that, for each medical speciality, patients should be ranked periodically by a predicted QALY score. Selection should then be carried out to maximise total predicted QALYs secured. Assume that there are two specialities, A and B, and that currently the same level of resources are allocated to both specialities. If in A the QALY per pound spent for the last patient treated exceeds that of the last patient treated in B, the implication is that resources should be moved away from speciality B to speciality A until QALY per pound is equalised. 2 9 Attempts have been made to operationalise this procedure. Gudex et al. (1990) calculated the QALY gain from treatment versus no treatment and the QALY gain from treatment now versus treatment one year later for 22 common medical conditions on Guy's Hospital's general surgical waiting list [see also Edwards and Barlow (1994), James et al. (1996)]. Some prioritisation processes concentrate simply on costs (e.g. the Duthrie Report for the UK recommended that points be allocated to waiting patients according to the resources required, so that estimates could be used to assess the number of operating theatres required to meet pressure from different the waiting lists3 0). By comparison, Williams' measure has the advantage that it also incorporates an estimate of the productivity of treatment time. Williams' suggestion also means that the doctor no longer has the same incentive to foster long waiting lists (as length of waiting list is no longer the

28 The criteria included both clinical and social considerations but not length of time waited.

29 As Williams (1988, p. 240) notes, a speciality with a small list of people waiting a short time for very beneficial treatment may still have priority over a speciality with a long list of patients who have waited a long time. Yet, as Edwards (1994) comments, patients have the same opportunity of being treated (given their expected total health gain per pound of treatment) regardless of which clinical speciality they required. 30 For the Duthrie Report see Department of Health and Social Security (1981). Note that Donaldson and Stoyle (1987) argue that using the waiting list to assess theatre time is more informative.

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sole criterion for resource allocation). Moreover, patients who can expect little benefit from treatment soon realise that the only course is to move to the private sector (i.e. patients form correct expectations of what might be possible if they join waiting lists). The approach is not based on Paretian efficiency; the objective is the maximisation of health not of welfare per se. However, it is questionable that the measure is sufficiently robust for waiting list prioritisation [Coast et al. (1996)]. With respect to equity, Broome (1987) notes that individuals have "claims" to the publicly funded health care system, and that claims should be met in proportion to their strength but never be completely over-ridden. It would follow that people should always be entitled to treatment as long as they are prepared to wait an appropriate length of time. 3 1 4.2.2. Quasi (internal)markets In 1990 NHS reforms created an "internal" or quasi-market. While there were broad policy objectives, Frankel and West (1993, p. 130) assert that "... the reforms can ... be best understood as the definitive waiting list initiative". The emphasis again is on cost efficiency [Jones and Cullis (1996)]. Quasi-markets make a distinction between purchasers and providers. A health authority or a GP (as "purchaser") acts as the agent of the patient to secure the best quality of hospital treatment (from the "provider"). The greater knowledge of agents about the availability of treatment at different hospitals is expected to assist the principal (i.e. taxpayer/patient). For example, agents may allocate funds to purchase treatment for their patients from hospitals and, when choosing hospitals, waiting time will be an important consideration. Health authorities and GPs are not tied to local hospitals; they are able to negotiate contracts with hospitals located further afield but with lower waiting times. In Working for Patients [Department of Health (1989)] and associated documents it is asserted that increased efficiency from competition would decrease waiting lists [Mullen (1993)]. While hospitals compete for patients and respond to incentives to reduce waiting times, the transactions costs associated with operating the internal markets cannot be ignored [Bartlett (1991), Jones and Cullis (1996)]. Also, critics suggest that, if the incentives are to reduce waiting lists, this may be achieved in part by refusing patients access to lists. Mullen (1993) argues that, if hospitals are judged by waiting times or length of waiting list then, provided hospitals have dealt with the contract numbers agreed with the purchasers, they have an incentive to decline admissions to their waiting lists. 4.2.3. Reducing uncertainty Propper (1990, 1995) valued a reduction of one month on a UK waiting list for nonurgent treatment at £50 (in 1991 prices). The average value of the disutility of uncer31 Stronger normative criteria may give weight to the numbers treated. Culyer and Cullis (1976, p. 262) note that "... a greater reduction in total need is possible if, say, two persons with relatively short expected lengths of inpatient stay and low index scores are admitted instead of one person with a long expected stay and a high index score".

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tainty of admission date was, additionally, around £30 (in 1991 prices). One objective of stipulating priorities is to reduce uncertainty for patients. For example, in the UK, the "Patient's Charter" launched in April 1991 stated an entitlement: there was to be guaranteed admission for treatment no later than two years from the date when the consultant places the patient on a waiting list [Mullen (1993)].32 However, such guarantees can prove inefficient. Using theoretical queuing models, Goddard and Tavakoli (1994) comment that the Patient's Charter performs poorly in terms of efficiency because those who are treated are not those who will receive the greatest benefit, as some with minor ailments will have to be treated before others in order to guarantee the maximum waiting time for all. Mullen's criticism also applies. If health authorities or GP fundholders try to secure treatment with another provider to meet their guaranteed target, the other provider may not have an incentive to add to their list in the absence of additional resources. It has already been noted that in Sweden after 1991 waiting time (for patients for any of 12 different procedures) was to be limited to 3 months from the physician's decision to treat/operate. 3 3 However, only in the first year of the scheme was the guarantee associated with extra resources. Waiting time was reduced and this was a result of increased production, of improved administration of the waiting list and of a change in attitudes toward waiting lists [Hanning (1996)]. Increased funding and a change in incentives achieved a more intensive use of medical resources as well as a reduction of uncertainty. Booking appointments can mitigate patient uncertainty. Some classes of patients in the USA may wait longer than patients in the UK [Light (1990)], but patients in the US who have definite appointments do not see themselves as "waiting" [Frankel and West (1993)]. Of course, the administration of a booking system requires a relatively predictable length of stay and, when booking systems have been used, emergency admissions will fall if facilities for dealing with emergencies have already been assigned [Devlin (1980) and Southam and Talbot (1980)].

5. Conclusions Following an essentially Paretian perspective, theoretical considerations relating to waiting lists and waiting times involve a number of deceptively simple arguments. In a normative context it was suggested that optimal waiting times should be computed for

32 In 1995 the Patient's Charter promised that the waiting time guarantee of 18 months that covered hip, knee replacements and cataract operations was to be extended to all admissions to hospital [Department of Health (1995)]. Moreover, it guaranteed that 9 out of 10 patients can expect to receive an outpatient consultation within 13 weeks of referral by the general practitioner. 33 It was understood that, if the hospital with primary responsibility for the patient cannot offer treatment within such a waiting time, the patient would have the right to be treated in another hospital, or by a private clinic, at the expense of the home hospital.

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each case type and a booked inpatient date be offered. Given the stochastic nature of inpatient demands, a further requirement was that the variance of the actual inpatient date about the booked date be minimised. This normative perspective takes the goal of suppliers and demanders as maximising welfare. But in practice, the actions of suppliers, demander and governments are not necessarily to maximise social welfare, and theory on waiting lists reflects this. It has developed in a more positive context in which central contributions have focused on the role of waiting times in the decay of the benefit of inpatient care, bargaining over budgets to be allocated to medical care and arguments consistent with consultants seeking their self-interest. Many of these theories have not been rigorously tested: in part the result of poor data. However, in a more positive light, the relatively few estimates of the costs on consumers imposed by waiting lists that have been made indicate magnitudes that may not be all that great at the individual level. Econometric investigations of the relationship between waiting lists and resource allocation to the public health care system have provided few definitive results. Early work on the UK NHS suggested an increase in resources had no impact on lists; later work has suggested an increase in supply may decrease lists. Empirical work also indicates connections between the public sector in which there are waiting lists and the private sector that operates alongside large publicly funded systems on both the demand and the supply side. But given the absence of work related to the normative theoretical considerations, it is difficult to assess the welfare significance of these empirical findings. A review of policy issues for dealing with waiting lists reveals that none is obvious in terms of practical simplicity. Each option poses difficulties. However, the way in which the policy issue is approached is of critical importance. Policy discussion should be conducted using an explicit set of criteria against which options can be assessed. The issue of the optimum waiting time for different medical procedures also needs to be addressed. When addressing the issue of the optimum wait, questions of efficiency and equity stand in sharp relief. The optimum wait is unlikely to be the same for every medical condition and for every patient. Much policy analysis has ignored this. But these attempts to "treat" the "symptoms" of waiting lists by relying on ad hoc methods of waiting list reduction do not result in changes which are necessarily welfare improving. More broadly, it was noted at the outset of this chapter that there is not necessarily a consensus over the evaluative framework to be used to assess the significance of, and costs and benefits of waiting lists. Whilst economics offers individual valuations as the natural benchmark, this, as discussed above, does not always command wide assent in the health care arena. However, without a resolution of the question of the yardstick by which the costs and benefits of the delay of inpatient treatment is to be measured and the construction of that yardstick, the further question of what is the optimal waiting list or time for a state health care system to aim for is left in limbo. Suggestions for waiting list policy that make sense by reference to one set of criteria do not necessarily make sense by reference to another and almost certainly are not commensurate. Hence the onus is on advocates for policy changes to make clear their underlying assumptions

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and subsequent analysis. To date the implicit framework adopted by most researchers in economics has been a Paretian one. In summary, despite the considerable range of work that has been carried out on waiting lists and related issues, the interpretation of data on waiting lists is difficult. Lord Kelvin (1889) is often quoted as saying "When you cannot express it in numbers your knowledge is of a meagre and unsatisfactory kind". The general conclusion here is that even when the event can be expressed in numbers (for example, the NHS waiting list) knowledge is of a meagre and unsatisfactory kind. The challenge is to root policy discussion in productive, theoretical and empirical soil. References Aaron, H.J., and W.B. Schwartz (1984), The Painful Prescription: Rationing Hospital Care (Brookings Institution, Washington, DC). Acton, J. (1973), "Evaluating public progress to save lives: The case of heart attacks", RAND Research Report R-73-02 (RAND, Santa Monica). Acton, J. (1975), "Nonmonetary factors in the demand for medical services: Some empirical evidence", Journal of Political Economy 83:595-614. Alderman, H. (1987), "Allocation of goods through non-price rationing mechanisms, evidence on distribution by willingness to wait", Journal of Development Economics 25:105-124. Babes, M., and G.V. Sarma (1991), "Out-patient queues at the Ibn-Rochd Health Centre", Journal of the Operational Research Society 42:845-855. Bartlett, W. (1991), "Quasi markets and contracts: A markets and hierarchies perspective on NHS reform", Public Money and Management 11:53-61. Barzel, Y. (1974), "A theory of rationing by waiting", Journal of Law and Economics 18:73-95. Bates, J. (1988), "Econometric issues in SP analysis", Journal of Transport Economics and Policy 22:59-70. Besley, T., and M. Gouveia (1994), "Alternative systems of health care provision", Economic Policy 19:199258. Besley, T., J. Hall and I. Preston (1999), "The demand for private health insurance: Do waiting lists matter?" Journal of Public Economies 72:155-181. Bowles, R.A. (1982), "Delay as a rationing device", International Journal of Social Economics 19:90-104. Brattberg, G. (1988), "Priority setting with regard to placement on waiting lists to a pain clinic: The feasibility of a delegated ranking procedure", Scandinavian Journal of Social Medicine 16:173-179. Brookshire, D.S., M.A. Thayer, W.D. Schulze and R.C. D'Arge (1982), "Valuing public goods: A comparison of survey and hedonic approaches", American Economic Review 72:165-177. Broome, J. (1987), "Good, fairness and QALYs", in: M. Bell and S. Medus, eds., The Proceedings of the Royal Institute of Philosophy Conference on Philosophy and Medical Care (Cambridge University Press, Cambridge). Buchanan, J.M. (1965), "The inconsistencies of the NHS", Occasional Paper No. 7 (Institute of Economic Affairs, London). Buttery, R.B., and A.H. Snaith (1979), "Waiting for surgery", British Medical Journal, Supplement (2):403404. Buxton, M. (1992), "Are we satisfied with QALYs?", in: A. Hopkins, ed., Measures of the Quality of Life and the Uses to which Measures may be Put (Royal College of Physicians, London). Cairns, J. (1992), "Discounting and health benefits: Another perspective", Health Economics 1:76-80. Coast, J., J. Donovan, J. Frankel and S. Frankel (1996), Priority Setting: The Health Care Debate (John Wiley and Sons, Chichester). Coffey, R. (1983), "The effect of time price on the demand for medical care", Journal of Human Resources 18:406-424.

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