post by Paul Kelleher
UPDATE: I have a follow-up post here that offers a hypothesis as to why W&S accept what most others believe is a patently false premise (i.e. that programs A1 and A2 are equivalent).
In 1996, an expert panel appointed by the U.S. Public Health Service released a report on improving the methods of cost-effectiveness analysis in health policy. That report, known in the biz as the Washington Panel Report, included a chapter on discounting the health benefits produced by medical interventions. Discounting is a super tricky issue that raises questions of ethics and economics, which is why I like it. It is also a super important issue, as I hope will be made plain by this post.
The Washington Panel recommended (1) that both the future costs of health promoting policies and their future benefits should be discounted, and (2) that costs and benefits should be discounted at the same rate. What does this mean? Put simply, to discount is to treat as less valuable. So consider costs first. The main reason for treating a dollar in the future as less valuable than a dollar today is that today’s dollar can be invested productively to yield more than one dollar in the future (even after adjusting for inflation). This means a cost of 100 (inflation-adjusted) dollars borne in 20 years can be covered by an investment of less than $100 today. Hence, future costs should be discounted relative to present costs.
So that’s discounting costs. What does it mean to discount health benefits that lie in the future?
At a 3.0% discount rate over 20 years…the present value of 10 years of future life drops to less than 6 years.
This means that a cost-effectiveness analysis that discounts health benefits at 3% per year will treat 10 life-years gained in 20 years and 6 life-years gained today as roughly equivalent benefits. Thus, if one discounts health benefits, it means that one treats what look like identical health outcomes—10 extra life-years now, 10 extra life-years in the future—as more or less valuable depending on where they occur in time.
The Washington Panel offers a few arguments in favor of discounting health benefits at the same rate as costs. They label one of these the “consistency argument.” This argument is drawn wholesale from a 1977 NEJM paper by Weinstein and Stason (W&S). (Weinstein is also an author on the Panel’s chapter on discounting). I want now to lay out W&S’s argument as I understand it, and then to explain why I think it fails. For reference (and to enable readers to keep me honest), I have included W&S's own presentation of this argument at the end of this post.
Here’s W&S’s main thesis:
For consistency, the same discount factor [that is used for costs] should be applied to future health benefits (i.e. quality-adjusted life years) as well. (719)
To argue for this, W&S construct an “example that illustrates the chain of logic for discounting future health benefits” at the same rate as future costs. (Their own presentation of this example is included in its entirety at the end this post.) Their example involves a comparison between five potential health-generating programs, which I have listed in the following table (this table is basically the same table Erik Nord has used to make it easier to compare W&S’s five programs).
W&S ask: Should program A or program B receive higher priority? (Let me note here that I believe all monetary amounts in this example are intended to be in constant [i.e. inflation-adjusted] dollars). Program A costs $10,000 today and would create 1 additional life-year in 40 years; program B also costs $10,000 today, but will create 1 additional life-year now. If the answer to W&S’s question is that B should receive priority over A, then this means there is reason to discount the (seemingly identical) future health benefit generated by A. So, should B receive higher priority than A?
In order to answer this question, W&S construct a chain that links A to B via programs A1, A2, and A3. Here’s how they do it. First, they argue that A is equivalent to A1 since a cost of “$70,000 in 40 years has a present value (at 5 per cent) of $10,000 and because the benefits of both programs, A and A1, are the same [i.e. 1 LY].” Here W&S point out that at a 5% rate of growth (which is assumed for the sake of argument), a financial investment of $10,000 today will yield $70,000 in 40 years. So (assuming that rate of growth) there is a plausible sense in which $10,000 today and $70,000 in 40 years are indeed “equivalent.”
Next, W&S argue that A1 and A2 are also equivalent, because A2 “simply translates both the benefits and the costs of Program A1 from the future to the present.” This claim is somewhat opaque, but I think W&S mean this: regardless of when costs are borne and health benefits are gained, A1 and A2 both secure 1LY for the (inflation-adjusted) sum of $70,000. And there is, again, clearly a sense in which $70,000 per LY now and $70,000 per LY in 40 years are equivalent.
Next, W&S argue that A2 and A3 are equivalent because A3, by promising 1/7 of a LY for $10,000, thereby promises 1 full LY for $70,000–the same as A2.
W&S are now in a position to run through the chain of equivalences they have constructed in order to show that B should be given higher priority than A. Here’s how that goes:
- B should clearly be given priority over A3, since for the same price ($10,000) B produces seven times the benefit of A3.
- A3 is equivalent to A2.
- A2 is equivalent to A1.
- A1 is equivalent to A.
- Therefore, B should be given the same priority over A as it has over A3.
- This is achieved by discounting the future health benefits at the same rate as costs (in this case, by 5% per year).
- Therefore, future health benefits should be discounted at the same rate as costs.
- Therefore, A’s health benefit should be reported as 1/7th of a life-year.
Is this a good argument for discounting future health benefits? I don’t think so. The argument seems to commit a fatal fallacy, the fallacy of equivocation. To see this, note that A is equivalent to A1 only in a very specific sense. That is, A can be said to be equivalent to A1 only because there exists an economic mechanism that converts $10,000 now into $70,000 in 40 years. Call this form of equivalence productive or dynamic equivalence.
This is quite different from the sense in which A1 and A2 are equivalent. A1 and A2 are equivalent in a much simpler sense that doesn’t involve dynamic considerations: $70,000 per life-year is straightforwardly equivalent–let us say statically equivalent–to $70,000 per life-year. It is only by distinguishing dynamic-equivalence from static-equivalence that we can say, without logical contradiction, that $70,000 is equivalent to both $70,000 and $10,000.
Finally, W&S claim that A2 is equivalent to A3, by which they mean A2 is statically-equivalent to A3.
Now that we have properly distinguished between different sorts of equivalence, we can see where W&S’s argument breaks down. They argue:
- B is statically-superior to A3.
- A3 is statically-equivalent to A2.
- A2 is statically-equivalent to A1.
- A1 is dynamically-equivalent to A.
- Therefore B is superior A.
Put this way, the argument clearly does not go through, since the conclusion uses a term that does not appear in any of the premises. Moreover, even if the conclusion were put in terms of either static-equivalence or dynamic-equivalence, the conclusion would still not follow from the premises. This is because the chain of logic grinds to a halt at premise 4, which is the only premise that mentions dynamic equivalence. Premise 4 can therefore not provide the needed bridge from B to A.
Since this is the only argument W&S provide in support of the thesis that future health benefits should be discounted, they have given us no reason to do so. As I noted, the Washington Panel gives other arguments, so maybe the pratice of discounting benefits is justified after all. That's a question for another post.
 In a recent paper in Health Economics, Erik Nord critiques several so-called “consistency” arguments, including W&S's. I unfortunately found it hard to follow the details of Nord’s analysis. I explain in a second footnote at least one respect in which Nord’s critique differs from mine.
 In the first footnote I noted that Erik Nord critiques this argument of W&S’s in a recent paper. Nord does not invoke the distinction between dynamic and static equivalence. But I think he implies such a distinction in the following remarks:
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 $ 70 000 in 40 years. It is a seven times larger cost
Since I think we should concede that there is a sense in which $70,000 now is equivalent to (an inflation-adjusted) $70,000 in 40 years, I think it unwise to simply dictate, as Nord does, that these are "not equivalent." It seems to me better to acknowledge the sense in which they are equivalent, but to distinguish this sense from the other kind of equivalence at work W&S’s argument.
Weinstein and Stason's original "consistency argument":