Discounting future health benefits: The poverty of consistency arguments.
Health Economics 2011, 20, 16-26.
Key words: time preference, discounting, health benefits, consistency argument, Keeler-Cretin paradox
Word count: 5195.
Author: Erik Nord.
Research institution: Norwegian Institute of Public Health.
Corresponding author: Erik Nord, Norwegian Institute of Public Health,
All work done on fixed salary.
No conflicts of interest.
In economic evaluation of health care, main stream practice is to discount benefits at the same rate as costs. But main papers in which this practice is advocated have missed a distinction between two quite different evaluation problems: (1) How much does the time of program occurrence matter for value and (2) how much do delays in health benefits from programs implemented at a given time matter? The papers have furthermore focused on logical and arithmetic arguments rather than on real value considerations. These ‘consistency arguments’ are at best trivial, at worst logically flawed. At the end of the day there is a sensible argument for equal discounting of costs and benefits rooted in microeconomic theory of rational, utility maximising consumers’ saving behaviour. But even this argument is problematic, first because the model is not clearly supported by empirical observations of individuals’ time preferences for health, second because it relates only to evaluation in terms of overall individual utility. It does not provide grounds for claiming that decision makers with a wider societal perspective, which may include concerns for fair distribution, need to discount health benefits and costs equally. This applies even if health benefits are measured in monetary terms.
The rate at which one should discount future health benefits in economic
evaluation of health care has been under debate for decades (Weinstein and Stason,
1977; Cropper and Portney, 1990; Cairns, 1992; Olsen, 1993; Jones-Lee and Loomes 1995; Gravelle
et al, 2007). The arguments underpinning
opposing views are many and varied. My ambition in this paper is not to
summarize them all, let alone suggest a specific answer as to what the discount
rate for health benefits ought to be. I
only take issue with a specific type
of argument that seems to play a quite undeserved role in guiding discounting practice in some jurisdictions, including the
The recommended practice in the two mentioned countries is to discount health benefits at the same rate as costs (Gold et al, 1996; Gravelle and Smith, 2001; Claxton, Sculpher and Culyer et al, 2006). The validity of this practice is not self-evident. The rationale for discounting costs lies in de facto returns to investments in the market place, while discounting of benefits has to do with strength of preferences for consumption now rather than later (Weinstein and Stason, 1977). One would think that a case for equal discounting would have to build on a demonstration of some tight empirical link between these two rationales. In fact, such a link is in theory possible, and I return to this in the last part of the paper. However, over the years equal discounting has primarily been advocated on grounds of ‘logical consistency’, with emphasis on numerical demonstrations of the logical ‘unavoidableness’ of equal discounting (Weinstein and Stason, 1977; Keeler and Cretin, 1983; Viscusi, 1995). These ‘consistency arguments’ for equal discounting have later been accepted and reinforced by a number of prominent health economists (Lipscomb, Torrance and Weinstein, 1996; Claxton, Sculpher and Culyer et al, 2006; Drummond et al 2007). It is this ‘consistency line of argument’, that I challenge in the following.
The paper is organised as follows: I first make a distinction between two different decision problems that seems to have received insufficient attention in the health benefits discounting literature. Based on this distinction I argue that the so called ‘Keeler-Cretin’ paradox (Keeler and Cretin, 1983) has been given undeserved weight in the discounting debate. I proceed to closely examine the logic in four other main papers in the field. I find that ‘consistency arguments’ for equal discounting consistently either skirt the issue of real interest to policy makers or are simply logically flawed. Lastly I spell out an argument which in a sensible, empirical way links time preferences for health at the margin to the market rate of interest on investments and thus to the discount rate for costs. This argument for equal discounting is internally consistent, but it is empirically questionable and it has limited relevance if priority setting in health care is guided by wider considerations than simple utility maximisation.
2. Two different aspects of time preference
Defense of discounting health benefits is often based on the so-called Keeler-Cretin paradox of ‘indefinite delay’ (Keeler-Cretin, 1983). In brief it goes as follows: Candidate programs X and Y are equal in all respects, including distribution of costs (C) and benefits (H) over time, except that X would take place now while Y would take place in ten years. To illustrate:
Year: 0 10
X: C, H
In the following I shall call this a program start time difference. Keeler and Cretin pointed out that if one discounts future costs at a rate r and future benefits at a lower rate d, program Y will obtain a better cost-benefit ratio than program X. So if one goes by present value cost-benefit ratios in priority setting, there will always be a case for giving a later program priority over an identical earlier one if d < r. This seems to be an unreasonable implication of economic evaluation (or a ‘paradox’, to use the term of Keeler and Cretin). To avoid the paradoxical result, one should arguably discount health benefits at a rate no smaller than that of costs (Lipscomb et al, 1996).
The policy relevance of the Keeler-Cretin paradox is in my view much exaggerated. I have two arguments for this claim.
First, for the purpose of averting a premium on postponement of programs, one can simply introduce the convention that equal programs occurring at different times should be compared in terms of their cost-benefit ratios at their respective start times. This leads to exactly the same result as equal discounting from start times to present time. Equal discounting to present value seems to be an unnecessarily complicated way of dealing with a very simple policy point.
Second, and more importantly, people who question discounting of future health benefits typically have in mind a decision problem that is quite different from ‘where in time to locate a given program’. The typical policy relevant issue is as follows: Consider program Z, which is like program X, but is directed at another group of people, in whom it yields the same benefits in ten years. To illustrate:
Year: 0 10
Z: C H
In the following I call this a benefit time difference between programs X and Z. It may for instance be due to X being a curative program while program Z is a preventive one. Many people do not find it obvious that the outcome in program Z is less valuable than the outcome in program X . They may thus not want to discount the benefits in program Z, or at least not discount them as much as one discounts future costs.
Note that the distinction I here make resembles the distinction Cropper and Portney (1990) made between inter- and intragenerational discounting issues. However, the distinction between start time and benefit time preferences applies whether or not beneficiaries of programs belong to the same generation.
I submit that the two decision problems above are largely independent of each other. The fact that decision makers do not want to place a premium on postponements of programs does not necessarily mean that they have a preference for benefits now rather than later in programs with given start times.
Some might object that separation of these two issues in time preference could lead to ‘inconsistency’ in cost-benefit assessments. A possible argument goes as follows. Let r be the discount rate for costs and d be the discount rate for benefits. Assume:
(1) X ~ Y (‘start time neutrality’, d = r)
(2) X ~ Z (‘benefit time neutrality’, d = 0)
For program Y there is an equivalent program W in which future costs C are replaced by equivalent present costs. So we have:
Year: 0 10
Z: C H
W: C / (1,0r)10 H
(3) W ~ Y
Combining (1) and (3) yields
(4) X ~ W
One thus gets the paradoxical result that X according to (2) and (4) is equivalent to both Z and W, even though W is clearly preferable to Z. Arguably, if (1) is true, then X is equivalent to W and thus preferable to Z . To achieve such consistency, it may be argued that the discount rate for health benefits needs to be the same in both decision problems.
But the inference that X is preferable to Z presupposes transitivity in preferences across decision contexts in which different considerations are invoked. As argued by many, such a transitivity assumption does not necessarily hold (Kahnman and Tversky, 1979; Nord, Richardson and Menzel, 2003; Nord, Daniels and Kamlet, 2009). As noted above, the consideration in X versus Y is a desire among societal decision makers not to place a premium on postponement of programs. The consideration of societal decision makers judging X versus Z may be that the beneficiaries in the two programs are equally much in need of intervention now, even if benefits occur at different times, and that priority should go by need rather than by when beneficiaries will have the capacity to benefit. I note in passing that this thinking would be analogous to and consistent with QALY-critical theory from the last two decades to the effect that need may outweigh capacity to benefit in priority setting (Nord, 1993; Nord, Pinto and Richardson et al, 1999; Menzel et al, 1999; Ubel et al, 2000). Given that the considerations in the two decision problems are different, the valuation of future health benefits relative to present health benefits in the comparator in question may also be different.
One may ask whether having different discount rates for health benefits in the two decision contexts above could lead to inconsistency and confusion in actual decisions. I do not think so. First, as noted above, prioritising in health care normally has to do with distributing current resources (the current budget) on current candidate programs. The question of whether one should implement a given program later rather than now is rarely an issue. The Keeler-Cretin paradox argument for discounting health benefits may thus be seen as a case of a small tail wagging a big dog. Second, consider decision makers facing programs X and Z. Assume that for once they in fact do consider the possibility of postponing each of them. Assume that they do not see any value in postponing either of them. So for that decision problem they implicitly discount health benefits at a rate no lower than the discount rate for costs. Now they compare the two programs as current candidates. In this decision problem, the consideration of need comes into play. The decision makers may feel that the two groups of beneficiaries are in equal need of action. So they value the two outcomes equally, i.e. they do not discount the future benefits in program Z. I fail to see that a practical inconsistency problem might arise.
To summarize, I submit (i) that in problem 1 - i.e. X versus Y – discounting from program start times to present time is not really necessary at all, (ii) that if one does discount in this problem, the rate will depend on start time preferences and (iii) that the discount rate for benefits in problem 2 – i.e. X versus Z - will depend on benefit time preferences and need not be consistent with the discount rate in problem 1. For instance, one may want to apply a 2 % annual rate for discounting delayed benefits in program Z to program start time (which in Z is year 0) and a 4 % annual rate (equal to the discount rate for costs) for discounting the start time values of the costs and benefits in program Y (i.e. at year 10) to present values (at year 0).
3. Weinstein’s and Stason’s chain of logic
In ‘Foundations of cost-effectiveness analysis’ Weinstein and Stason
(1977) applied a so-called ‘chain of logic’ in order to justify equal
discounting in a situation where a saved life year is expected to have the same
dollar value (value in relation to other goods) at different points in time
(inflation disregarded). They assumed a discount rate for costs of 5%. They took
as an example a program A that saves a life year (LY) in 40 years at a cost of
$ 10,000 now. They then described a
program A1 which saves a life year in 40 years at a cost of $
Year 1 40
Given a discount rate of 5 %, the present value of the cost in A1 is $ 10,000. So the costs and benefits of A1 and A are the same. Accordingly A1 is equivalent to A.
W&S then described a program A2, which saves one life year now at a cost of $70,000 now:
Year 1 40
According to W&S, ‘A2 simply translates the benefits and costs of A1 to the present’. Given the assumption of a constant dollar value of a life year, the cost-benefit-ratios of A1 and A2 are the same. So according to W&S, A2 is equivalent to A1 and thus also to A. Since the costs in A2 are seven times the costs in A, the value of the life year in A2 (occurring in year 1) must then be seven times the value of the life year in A (occurring in year 40). This is the same as saying that the life year in year 40 needs to be discounted by 5 % per year, i.e. at the same rate as costs are discounted.
There are two problems here.
First, W&S were incorrect in claiming that ‘A2 simply translates the
benefits and costs of A1 to the
present’. To ‘translate’ means to replace with an equivalent term. The move
from A1 to A2 is not translation, but transportation (in time). $ 70,000 now
(A2) is not equivalent to $
W&S were in effect imposing that it did. Without saying so, they were assuming start time neutrality in societal decision makers’ preferences for health programs. Given that value assumption, A2 is indeed a ‘translation of’ A1 – i.e. equivalent to A1. But then it also becomes trivial: A2 ~ A1 is simply another way of stating start time neutrality.
This leads to the second, larger problem. Like the Keeler-Cretin paradox, W&S’ assumption that A2 is equivalent to A1 relates to the ‘different-program-start-times’ decision problem. W&S only showed the mathematical fact that if one goes by present value cost-benefit ratios in priority setting, and if there is program start time neutrality, then there must be equal discounting of cost and benefits from start time to present time. As noted in the previous section it does not follow that there needs to be equal discounting in the ‘different-benefit-times’ decision problem. W&S did not make this distinction and thus implied that there is a need for equal discounting also in the latter politically much more relevant context. But this does not follow from their argument.
In the report from the Washington Panel (Gold et al, 1996), Lipscomb, Torrance and Weinstein (1996) reproduced W&S’ complete ‘chain of logic’ under the label of ‘the consistency argument’ and described this argument and the Keeler-Cretin paradox as the ‘two major substantive rationales (…) in support of setting the discount rate for health consequences equal to that of costs’. It follows from the analysis above that this was in effect reproduction of two unsound arguments.
Interestingly, Lipscomb et al presented the notion of ‘time neutrality’ (meaning program start time neutrality) as a separate argument that ‘added force’ to W&S’ argument (page 221). But as noted above, start time neutrality was the assumption underlying W&S claim of equivalence between programs A2 and A1, i.e. the implicit moral basis of the ‘consistency argument’ itself. Without this basis, there would have been nothing with which to be consistent, and W&S’ ‘consistency argument’ would not only have been limited in policy relevance, but completely empty.
I stress that the idea of ‘start time neutrality’ is understandable, not implausible and certainly worthy of consideration. Lipscomb et al embarked on a discussion of it, with reference to equity considerations across generations and cohorts, drawing also on the concept of preferences behind a veil of ignorance. In doing so, they moved into discussing some of the real moral issues related to discounting health benefits. In my view, these moral issues are what really deserves our attention. The mathematical demonstration that ‘if start time neutrality applies, then the two discount rates should be equal in comparisons of equal programs with different start times’ is trivial. Unfortunately, Lipscomb et al’s discussion of the justification of start time neutrality is too brief. That said, one should bear in mind the point made earlier that start time preferences are a much less policy relevant issue than benefit time preferences.
5. Viscusi’s equivalence argument
Unlike the authors noted above, Viscusi (1995, p. 133) explicitly addressed the more policy relevant aspect of the time preference issue, i.e. the one relating to delayed benefit time. Viscusi took as an example a program that at a cost now of $ 8 million will save two statistical lives in 10 years, the value of which is assumed to be 2V in year 10 (for instance in terms of future potential beneficiaries’ willingness to pay for risk reduction, my précis). The going interest rate on investments is assumed to be r. Benefits are discounted at annual rate d. Normally one would evaluate the program in present value terms and say that the value of the program exceeds the costs if
(1) 2V / (1+d)10 > 8
Since discounting of health benefits is controversial, Viscusi suggested that one could instead look at ‘terminal values’, according to which the value of the program will exceed the costs provided that
(2) 2V > 8 (1+r) 10
Viscusi then rearranged the terms of the inequality:
(3) 2V / (1+r) 10 > 8.
Viscusi pointed out that requirement (3) is mathematically equivalent to requirement (2). From this he concluded that ‘shifting the reference point in this manner does not alter the relative attactiveness of the policies. The real issue is not whether health effects will be discounted. The fundamental question is whether one will appropriately recognize that economic effects at various points in time should be weighted differently to reflect the opportunity cost of capital’.
Viscusi’s interpretation is not correct. He actually only made a trivial arithmetic point, namely that if one uses the same discount rate in both cases (which is what he did in (2) and (3)), it does not matter whether one looks at present values or terminal values. His example does not address the real issue, which is whether there should be equal discounting in (1) and (2). From his conclusion one gets the impression that he by way of (3) demonstrated equivalence between (1) and (2) and hence that d must equal r. But (1) and (3) are equivalent if and only if d = r, which is what is being questioned. In his example, Viscusi in effect assumed the answer d = r in his argument and thus skirted the real value issue at hand.
A general lesson from this example is that when the question is whether a future health benefit is less valuable than a present one, compounding costs is a blind alley for the investigator. Consider the following example, where C denotes costs, H denotes health benefits and subscripts denote year of occurrence.
Program A: C0, H0
Program B: C0, H10
The question is: What is the value of H10 compared to H0 ? One may try to answer this by compounding costs in program B as follows:
(10(1+r)10)10 , H10
But the same can of course be done with program A:
(10(1+r)10)10 , H0
The question remains the same: What is the value of H10 compared to H0 ? Compounding costs does not make the problem go away.
6. The alleged logic of NICE
Representing NICE, Claxton, Culyer and Sculpher et al (2006) claimed that to avoid discounting costs and benefits at the same rate is ‘plainly illogical’. But their own logic is highly questionable on three accounts.
First, in a section on ‘Is health tradable?’ they wrote the following:
‘Discounting the future requires the assumption that things are tradeable over time. No one disputes that wealth is indeed tradeable over time. One can forego consumption now, invest it, and enjoy consumption in the future. Likewise, our valuation of costs should reflect the opportunities we forgo by incurring cost now and the opportunities provided by delaying costs to some future date. This can be done either by discounting future costs to the present period or equivalently compounding current costs to an appropriate future period. To claim that health should not, in principle, be discounted or that it should be discounted in some other way must rest on a claim that health, unlike wealth, is not tradeable over time.’
The logic of the above paragraph seems to be as follows:
(1) Discounting the future requires the assumption that things are tradable over
(2) Health can be traded over time.
(3) Costs can be traded over time.
(4) So benefits must be discounted at the same rate as costs.
I fail to see that (4) follows logically from (1) – (3).
Second, Claxton et al proceeded to give an example similar to that of Viscusi. They chose the same discount rate – 3,5 % - for compounding costs to terminal value and discounting benefits to present value. They showed that ‘decisions based on present or terminal values (…) generate identical ICERs’ and are ‘equivalent’. But again, this is only true if benefits are discounted at the same rate as costs, so with this example and statement, they either simply skirted the issue of whether there should be equal discounting, or they were implicitly assuming that equality between present and terminal ICERs is more important than consistency between (a) discounting of benefits in formal economic evaluation and (b) actual societal preferences for time of benefit. Again it seems to me that this would be to let the tail wag the dog. As noted earlier, a fully reasonable position for decision makers is to want a different discount rate for benefits than for costs. If this is their position, economists are going to have to live with present and terminal ICERs being different. For consistency in decision making, a good idea is then presumably to stick to the clearly most common approach, i.e. to calculate present value ICERs.
Third, Claxton et al attempted to justify equal discounting by focusing on opportunity cost:
‘The true cost of health gained is health gain foregone – at whatever dates these gains or losses may occur. Put in this fashion, the illogicality of wanting to discount health foregone at a different rate from health gained becomes plain’.
But this is not helpful. Consider the following example:
(1) The true costs of 5 lives gained in ten years at present cost C is what health gains C alternatively could buy ( = health foregone).
(2) Assume that C could buy 4 lives now.
(3) From (1) and (2) it follows that the true cost of 5 lives gained in ten years is 4 lives foregone now.
The question then remains: How much do decision makers value 5 lives in ten years compared to 4 lives now? Focusing on health foregone does not make that question go away.
Interestingly, Gravelle et al (2007), when arguing against Claxton et al’s advocacy for equal discounting of costs and benefits on grounds of increasing social value of health, did not seem to have a problem with Claxton et al’s consistency requirement. They merely argued that the requirement would be met also by their alternative approach.
On the other hand, Claxton et al in a recent review and continuation of the discounting debate seem to have come to a new position (2009, submitted). After some further mathematical analysis they conclude that ‘the appropriate discount rates to apply depend on social values and positive empirical questions’. This seems to be a step in the right direction
The purpose of the above analyses has been to show that efforts over the last 30 years to justify equal discounting of costs and benefits on grounds of pure logic in various ways are misconceived and/or logically flawed.
This does not mean that there cannot be – underneath all the unsound arguments - some sound basis for equal discounting, in other words ‘a baby in the bathwater’. In fact, there is a possible justification for equal discounting in microeconomic theory. While presumably being at the back of many economists’ minds (but not all, I suspect) when they advocate equal discounting, this justification is often missing in the literature, including in the papers discussed above. In the following I carefully spell out this possible justification. When it is stated precisely, it becomes clear that it applies only for a specific, limited purpose of economic analysis and not necessarily for societal priority setting decisions.
Assume that the purpose of an evaluation is to estimate the strength of individual preferences for different streams of health benefits in time. Instead of ‘strength of preference’ we may use the concept of ‘individual utility’. The question is then for instance: How much individual utility is produced by an intervention that yields health gain H in a year (H1) compared to one that yields H now (H0)?
To answer this question one can either ask people directly about their preferences for H1 relative to H0, or one can model U(H1) relative to U(H0) on the basis of microeconomic and welfare economic theory. The two will not necessarily lead to the same result. Some investigators will prefer the empirical approach, while others may distrust stated preferences and prefer to model. Assume that a decision maker is interested in the answer that the theoretical model would give. Then it can be shown that there is a theoretical case for equal discounting.
The model goes as follows: Consumers strive to maximise utility from wealth by adjusting consumption of different goods such that at the margin, rates of substitution on the value side are equal to rates of transformation on the purchasing side. This applies also to choices between present and future consumption, i.e. choices between consumption and saving. The rational consumer is willing to save up to a point at which the utility loss he suffers from delaying a marginal unit of consumption a year is exactly compensated by the increase in consumption that he/she achieves through the interest obtained on the saved money. So if the market rate of interest for instance is 5 %, one may infer that the utility at time zero of a unit of consumption one year later will be 5 % less than the utility at time zero of that same consumption at time zero. Since all consumers face the same market rate of interest, they will all tend to have this 5 % trade off at the margin between consumption now and consumption in a year.
Assume that the analyst wants to estimate the total individual utility at time zero of different streams in time of consumption of goods in general. All individuals’ degree of discounting of future consumption is (according to the model) approximated by the market rate of interest to which they all have adjusted their saving at the margin. So the appropriate discount rate for future consumption equals the market rate of interest, which again is the appropriate rate for discounting costs.
Now assume that analyst wants to estimate the total individual utility at time zero of different streams in time of health benefits. Assume furthermore that over time, individuals value health relative to other goods at a constant rate, i.e. the individual willingness to pay for health, or the ‘dollar value of health’, is constant. Then it seems reasonable to assume that individuals at the margin discount health benefits at the same rate as they discount other goods. The latter is, as noted above, observable (at least approximately) in the market rate of interest. This is at the same time the appropriate rate for discounting costs. So the appropriate rate for discounting health benefits is the same as the appropriate rate for discounting costs.
This is a logical line of argument for equal discounting in the
‘different-benefit-times’ decision problem. There are two problems with it. First, according to stated preference studies,
individual time preferences for health may in fact not be consistent with the
discount rate suggested by the theoretical model (Lipscomb et al, 1996). Lipscomb
et al argue that the discrepancies are not worrisome in overall tendency or
size. This is probably a matter on which different investigators may have different
views. Second, and more importantly, one must bear in mind the limited nature
of the question to which the above line of argument responds: What is the strength
of individual preferences for - or individual
utility of - different streams of health benefits in time? Societal decision
makers may find this information useful. But societal decision makers are not
necessarily individual utility maximisers. Indeed, in some countries – for instance
Note finally that the above conclusion applies irrespective of how health benefits are valued. I emphasise this, because some economists seem to think that even if a case can be made for discounting natural units of health or QALYs at a rate different from the discount rate for costs, there is no way around equal discounting if health is valued in monetary terms. But the above point has nothing to do with how utility is measured. The point is the distinction between utility maximisation and maximisation of some wider societal value function.
Main papers on discounting health benefits have missed a distinction between two quite different evaluation problems: (1) How much does the time of program implementation matter for value and (2) how much does the timing of health benefits from programs implemented at a given time matter? The papers have focused on logical and arithmetic arguments that are at best trivial and miss the real value issue, at worst simply flawed. I find this state of affairs remarkable in itself.
At the end of the day there is a sensible argument for equal discounting of costs and benefits rooted in microeconomic theory of rational, utility maximising consumers’ saving behaviour. But even this argument is problematic, first because the model is not clearly supported by empirical observations of individuals’ time preferences for health, second because it relates only to evaluation in terms of overall individual utility. It does not provide grounds for claiming that decision makers with a wider societal perspective, which may include concerns for fair distribution, need to discount health benefits and costs equally. Altogether I conclude that the issue of discounting future health benefits is less a matter of pure logic, and more a matter of empirical research and societal values, than what has been suggested by leading health economists in the last three decades.
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