A Critique of Weinstein & Stason’s Consistency Argument for Time-Discounting (wonky)

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?

Here’s an example from Paul Menzel, in an essay on discounting in a recent volume:  

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.[1]

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).

(Key: $10’ = $10,000, $70’ = $70,000; “LY” means “life-year saved/generated”)

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:

1. B should clearly be given priority over A3, since for the same price ($10,000) B produces seven times the benefit of A3.
2. A3 is equivalent to A2.
3. A2 is equivalent to A1.
4. A1 is equivalent to A.
5. Therefore, B should be given the same priority over A as it has over A3.
6. This is achieved by discounting the future health benefits at the same rate as costs (in this case, by 5% per year).
7. Therefore, future health benefits should be discounted at the same rate as costs.
8. 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:

1. B is statically-superior to A3.
2. A3 is statically-equivalent to A2.
3. A2 is statically-equivalent to A1.
4. A1 is dynamically-equivalent to A.
5. 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.[2]

 

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[1] 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.

[2] 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.

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Weinstein and Stason's original "consistency argument":

 

 

Comments

[Daniel S. Goldberg]

Can you say more about why this is "super-important?"

[Paul Kelleher]

Here's my favorite:

If one discounts health benefits at 5% per year, one will view as equivalent one billion lives lost 425 years from now and one life lost today.

Others from Menzel:

“Comparison of mobile coronary care units (MCCU) with a prevention program of screening children for elevated cholesterol and following it up with recommended dietary changes found a cost-effectiveness advantage for MCCU of over 2:1 when costs and added life were uniformly discounted at 5.0%. It found an opposite 3:1 advantage for screening, however, when the years of added life were not discounted.”

“A well-known study of Pap smears to screen for cervical cancer revealed that if costs and benefits were uniformly discounted at 5.0%, then, begun at age 20, they had a relatively modest cost of $10,000 per added year of life [if] done every 4 years. They caught more cancers if done every 3 years, but at a marginal cost of $185,000 per year of life. If those added years of life were not discounted, however, even screening at 3-year intervals on average saved at the relatively modest marginal cost rate of $20,000/year of life.”

[love actuary]

It's not clear to me that this is hogwash. Taken personally when I ask you: knowing that you are going to die at some point, would you rather have 1 year of life tacked on to that point immediately, or one year tacked on to that point in 40 years? Given that you may not be around in 40 years, the answer is clearly that you would prefer to have the extra year of life right now, thus some difference in value.

But we're dealing with entire populations and I think the analogy still holds. Would you rather improve everyone's wellbeing (say, an additional 1 LY) today, or wait 40 years to do so? You would rather improve everyone's wellbeing today, as in 40 years there will only be a fraction of the current population still alive. Not to mention the 40 years-worth of individuals who will be born in the mean time.

Thus why is it silly to assume that we should not discount the benefits? The benefit delivered in the future seems naturally worth less than that delivered today. Perhaps we disagree with their mechanism for discounting?

[Paul Kelleher]

"Love Actuary",

Thanks for your comment. Before addressing it, I just want to make it clear that here I am critiquing *just one*, *specific* argument for discounting. So I did not say here that discounting is "hogwash" or "silly," as you imply. I claimed only that this specific argument for it doesn't work. I have critiqued other arguments here (pdf): http://bit.ly/xljGdu

But now to your specific arguments for discounting. Your first thought experiment certainly will lead people to say they want the earlier life year "tacked on", and for the reason you envisage: that unless the earlier life year is tacked on, the person may well be dead in 40 years. But that is simply not a good thought experiment for testing the quite *general* claim that discounters make, which is that a health benefit--any health benefit--is more valuable the sooner in time it occurs. You foresee that I take issue with your suggestion that we can easily move from the intrapersonal to the interpersonal case, but even if we stick to the intrapersonal case, it is not at all clear that people discount nonlifesaving benefits (which is what the discounters say we should do). Imagine, for example, that we asked people this: ould you rather have a serious nonfatal health condition adversely affect your 40s or your 50s? It's not at all clear to me that most people would say "my 50s." Menzel (in the paper I link to in the post) reports this:

"Redelmeier and Heller (1993) found a fairly low individual-utility time preference in comparing present nonlifesaving health benefits with similar benefits in 5-10 years in the future: a mean of 0.25% as an annual discount rate. Also, 62% of their respondents expressed a zero discount rate, and 10% had a *negative* discount rate (preference for the later benefit)."

In short, once we move beyond lifesaving benefits, it's not clear that people's intrapersonal preferences are as you say they are.

I also don't understand why you assume I would "rather improve everyone's wellbeing today, as in 40 years there will only be a fraction of the current population still alive." I certainly don't yet see why that gives me reason to choose today's beneficiaries rather than tomorrow's, especially if my obligation is to society rather than to any specific individual. Are you assuming that I have some obligation to today's individuals that I don't have to tomorrow's? I would want to see an argument for that thesis. I don't agree it can just be assumed.

[Daniel S. Goldberg]

Hmmm. I get why the discounting matters a lot for what we'd like to see as the accuracy of cost-effectiveness types of analysis.

I'm less clear on why the discounting matters a great deal ethically.

(Disclosure: I'm ultimately unclear on why cost-effectiveness analysis is seen to matter ethically so much. I mean, we might have ethical obligations to do all sorts of inefficient things. So the fact that a given intervention is cost-effective or cost-saving may or may not be all that helpful in the normative inquiry.

Interestingly, Norman Daniels's recent paper in THC goes some way to both clarifying and deepening my confusion. It clears things up because it offers some account of why measurable assessments of lives is highly relevant to what policies we ought to pursue. It deepens my confusion in the sense that Daniels ultimately concludes -- plausibly, I think -- that the arguments simply aren't dispositive and we have no choice but to rely on public reason to have any hope of reaching acceptable policies.

[Paul Kelleher]

Daniel, if efficiency ever matters, then discounting matters, since discounting affects how efficient a policy/program/project is said to be. One is entitled to be indifferent about the issue of discounting only if one says efficiency never matters. You're willing to say that, right?

[Paul Kelleher]

I meant to ask at the end: You're *not* willing to say [efficiency never matters], right?

[Daniel S. Goldberg]

I absolutely agree that if efficiency ever matters, than discounting matters.

And I also agree that there are cases in which efficiency matters.

I am perhaps less sanguine about the weight of those cases ("weight" being intentionally ambiguous here).

If one were to doubt that efficiency is a particularly weighty phenomenon for ethical analysis, then one would not be inclined to see the issues of discounting as particularly weighty.

(Recognizing, of course, that reasonable people might well disagree on how important efficiency considerations are).

[Paul Kelleher]

I guess I just don't understand the hesitation to concede that efficiency is very important. Suppose we have to choose between (1) preventing 100 deaths by treating and (in effect) curing 50 people of AIDS today or (2) preventing 500 deaths from AIDS through a prevention program whose benefits (i.e. "deaths averted") do not accrue until 2050. Who would say that the efficiency consideration (the fact that 450 more deaths can be averted with program 2) is not "particularly weighty"? I'm surprised you would be inclined to say this, given your interest in social determinants and prevention.

Or am I missing something?

[Paul Kelleher]

Another typo!: Program (1) should say it prevents 50 deaths. But it doesn't really matter. 50 and 100 are still a lot less than 500.

[Daniel S. Goldberg]

Well, I might be confused, but couldn't one argue that what is most morally significant about saving 450 more lives by 2050 is not captured by the idea that it is more efficient.

There might be all sorts of plausible reasons for favoring one of these options over the other, but I'm not particularly sure why analyses of their respective efficiencies add much. Rather, all the usual kinds of ethical considerations (justice, distribution, future publics, identified vs. statistical victims, etc.) seem to me to be what really matter. Ethically, why should I care whether the arrangement saves money or not?

I guess part of the issue turns on what you mean by "efficiency" in this context. What do you mean? (no intention to be snarky here).

[Paul Kelleher]

I think we're using "efficient" to mean different things. You seem to be using it to mean "saves money." I'm using it to mean "produces most benefits (with the budget we've got)."

Of course you are right that we might have *other* reasons besides efficiency to select one policy over another. All I'm saying is that efficiency (in the sense I mean) is important. As for the suggestion that "justice, distribution, future publics, identified vs. statistical victims, etc." might be what's doing the work, I would respectfully suggest that each and every one of these implicates a complex *set* of considerations, a set that is surely going to include efficiency (in the sense I mean).

[Daniel S. Goldberg]

Sounds reasonable.

My disagreement is more with the notion that a health intervention must "pay for itself" to be justified, which seems to me to be dubious. Sometimes ethics might require a significant expenditure that is not recouped. I'm thinking of the prevention paradox (or one of them, at least): the fact that preventing some chronic illnesses is not cost-saving because those people will live longer and ultimately require more health care expenditures does not imply that we ought not prevent those chronic illnesses.

[Paul Kelleher]

Yeah, that's what efficiency means here. Indeed, efficiency in cost-effectiveness and cost-benefit analysis *is* a form of recouping investment: what's recouped is a (health) benefit, not money back into the coffers.

[Daniel S. Goldberg]

How can the value of that benefit can be operationalized other than in terms of money?

[Paul Kelleher]

Cost-effectiveness analysis uses quality-adjusted life years (QALYs) as its unit of measurement, e.g.

[Daniel S. Goldberg]

Ah yes (although don't some analyses use DALYs instead or in addition?)

This is a very helpful conversation, thanks. Aside from reminding me I need to go back and read my Broome, I think what generally bugs me about CE analysis is the tendency to naturalize inappropriately by simply presuming that the increase in welfare is self-evidently ethical, without actually supplying the inferences and assumption that would ground the ethical conclusion.

What I mean is that it is of course possible to supply all sorts of consequentialist claims and arguments that would ground a claim that cost-effective or cost-saving interventions are ethically optimal. But IMO those arguments are in much health policy, health economics, and HSR discourse frequently left unstated and unargued. There are myriad reasons to doubt that a particular intervention that is cost-effective or cost-saving is ethically optimal simply by virtue of the fact that it is cost-effective or cost-saving (which is what gives rise to my [roughly deontological?] notion that we may have ethical obligations to do all sorts of inefficient things).

Of course, as a philosopher, you are not likely to make such an error, to naturalize without justification a particular arrangement of goods and services as it relates to health and its distribution. So I suppose my brief is not with those who endeavor to supply the claims and justify the conclusions, but with what I perceive as the great majority that do not.

[Franklindmadoff.wordpress.com]

It's absolutely appropriate to discount a future year of life 40 years hence for both the time-value-of-money and probability that that investment will make a difference.

The big disconnect here is that a year of life in the future is probably worth a lot more 40 years hence in current dollar terms (well above the rate of inflation) because people will be a hell of a lot more productive 40 years hence than they will be today.

In 1900 the average worker made around 500/yr, yet 70K/yr is about $2700 in 1900 dollars, more than 3x the avg wage at the time. In other words, economic growth dramatically outstripped inflation. We are richer today than we were 100+ years ago and will likely be substantially richer 40 years in the future.

So it's really a question of what discount rate you choose and what rate of economic growth you impute to adjust the value of that future year of life. Intuitively I think that the discount factor ought to be higher than the life-year adjustment and certainly not greater than the present life year.

Ultimately I don't think the effective rate of discounting itself is very instructive here in terms of strictly adjusting for inflation or even economic growth. The reason we ought to discount that future life year is probably because a life saved today is far more certain than solving problems 40 years hence. In other words, if we're investing in future life saving technology, or what have you, preferentially over current lives it ought to be because expected value of those future lives saved far out number current and more marginal uses of those resources (in terms of the raw number of lives saved, quality of life, etc). So, in other words, an investment in something like antibiotic development ought to be easily defensible, but investing in an orphan drug to save the lives of people with some rare disorder 40 years hence with current technology... not so much.