Kenneth Arrow and the Overdemandingness Argument for Discounting Future Health Benefits

post by Paul Kelleher

There are a number of different arguments in the economics literature for assigning less value to future benefits than to present ones (this includes health benefits). This practice is called discounting, and standard economnic analyses of programs that produce benefits in the future will discount those benefits at some positive rate. For example, a cost-benefit analysis using a discount rate of 3.0% will say that 1.3 expected lives saved in 10 years are equivalent in value to 1 life saved today. 

One common argument in defense of discounting is what I shall call the Overdemandingness Argument. This argument takes the form of a reductio ad absurdum. Here is an example of it in the literature (I give other examples in a paper on discounting out just today):

There has been considerable debate about the value of [the discount rate] since Ramsey. He argues that it is ethically indefensible to use a positive value, as this would discount future generations’ well-being relative to the present one. However, Arrow shows that weighting all generations’ welfare equally results in very high rates of savings being required of the current (or even of every) generation. He demonstrates that, under reasonable parameter values, the current generation could be required to save approximately two-thirds of its income! To avoid this result, a positive pure rate of time preference should be employed. (Moore et al. 2004, p. 804)

As stated here, the Overdemandingness Argument is woefully incomplete. For it relies on a crucial, unstated premise, namely Premise 3 in the following more complete version of the argument:

1. Assume a discount rate of 0%. (This means a benefit provided today will be not be valued more than an exactly similar benefit provided at any point in the future.)
2. So long as the current generation’s consumption is not perilously close to zero, a dollar productively invested today on behalf of future generations will enable them to derive more “raw” (i.e. undiscounted) benefit than that dollar could provide if consumed by the current generation.
3. We have a moral obligation to maximize total net benefits across time.
4. Therefore, the current generation has an obligation to sacrifice its own consumption for investment in behalf of future generations.
5. But Conclusion 4 is absurd, so there must be something wrong with the argument that leads to it.
6. The only plausible weakness is Premise 1.
7. Therefore, Premise 1 is false, and a positive discount rate should be used to convey that future benefits are less valuable than present ones.

Premise 3--the premise that Moore et al. left unstated--could be rewritten thus: we have a moral obligation to pursue efficiency singlemindedly. This view is called consequentialism in moral philosophy, and utilitarianism is its most well-known variant.  If the Overdemandingness Argument does not contain a premise about consequentialism, it is incomplete. Once that assumption is added, the argument is complete, and premises 1-3 do logically entail the ostensibly problematic Conclusion 4. But in order for the Overdemandingness Argument to be a successful argument in favor of discounting, Premise 1 must be the only possible problematic premise. And it is precisely because they leave Premise 3 unstated that the economists I quoted above view Premise 1 as entirely responsible for the problematic Conclusion 4. However, someone who rejects that conclusion may now choose to reject consequentialism (Premise 3) instead. The Overdemandingness Argument's case against Premise 1 is therefore significantly weakened.

Despite being cited favorably by the economists quoted above, Kenneth Arrow saw very clearly that the assumption of consequentialism is doing essential work in Overdemandingness Argument. As he writes in "Discounting, Morality, and Gaming" (pdf),

But with zero time preference [i.e. no discounting] and a long horizon, the savings become inordinately high, possibly approaching one as the horizon goes to infinity. A reconciliation must be based on the notion that individuals are not morally required to subscribe fully to morality at any cost to themselves. (p. 13, emphasis added)

The substance of this observation is correct, but Arrow’s wording is not innocuous. He assumes here that morality is consequentialist, and thus that any deviation from consequentialism is a deviation from morality. However, many who reject consequentialism claim that morality itself permits deviations from consequentialism’s dictates. Indeed, Arrow at one point suggests precisely that:

I find this to be an incredible and unacceptable strain on the present generation...I therefore conclude that the strong ethical requirement that all generations be treated alike, itself reasonable, contradicts a very strong intuition that it is not morally acceptable to demand excessively high savings rates of any one generation, or even of every generation. (p. 16, italics added)

If it is indeed a substantive question whether morality is consequentialist or not, then this will be a question about which many economists, qua economist, wish to remain neutral. Often, this will be because economists are not formally trained to evaluate answers to this philosophical question. But even if they, like Arrow, are willing and able to make philosophical headway on the question, it is doubtful that economists, qua economist, ever need to do this. To see why, consider the following remark by Arrow and colleagues in their chapter on discounting in the 1995 report of the Intergovernmental Panel on Climate Change (pdf):

Economists are in general agreement that cost-benefit analysis, including discounting, is useful in examining policies with long or complex time paths, or policies whose effects extend across generations. At the same time, cost-benefit analysis, and the techniques that go with it, including discounting, focus on economic efficiency, and therefore have limitations as a guide to policy. (p. 130, emphasis added)

If economists are to focus on efficiency only, then it is not clear why the technique of discounting should be a part of the economist’s repertoire in the first place. After all, one can focus exclusively on efficiency (e.g. investigate its nature, make recommendations for its measurement, rank policies with respect to it, etc.) without recommending the singleminded pursuit of it. But, as we have seen, it is only the singleminded pursuit of efficiency that could generate the worry that current generations will be crushed under the weight of a duty to maximize future well-being. Since economists, qua economist, do not recommend the singleminded pursuit of efficiency, I conclude that they have no “overdemandingness”-related reason to discount the raw results of their efficiency-focused inquiry.

Of course, this does not show that discounting the value of future benefits is wrong. It just shows that one common reason for doing so is unsound.