Valuing future life and future lives: A framework for understanding discounting

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Abstract

This article offers a conceptual framework for separating the distinct theoretical concepts that are often confounded in discussions of discounting. Two distinctions are emphasized: (a) the difference between discounting a future outcome because it confers less utility and discounting future utility per se, and (b) the differences between discounting one’s own future utility and discounting the utility of others who will be alive in the future. Within this framework, I discuss and clarify the continuing controversy over discounting future life and future lives.

Introduction

Many personal and public decisions have consequences that extend across time. Lying in the sun confers an attractive tan in the near future but unattractive wrinkles in the distant future. Vaccination is painful and inconvenient, but prevents future disease. Using coal as a fuel source reduces the costs of electricity for this generation, but contributes to global climate warming that may harm future generations.

In most formal analyses, future consequences are given less weight or “discounted” relative to more immediate consequences. Typically, discounting is codified via the discounted utility model (DU), which dictates that the overall value, V, of a sequence of outcomes (x0, x1,  , xt), equals the sum of the discounted utilities of each of the individual consequences, where δt is the discount factor applied to the utility in period t:V(x0,x1,,xt)=u(x0)+δ1u(x1)++δtu(xt)

In most applications of DU, discount rates range from 2% to 10% per year (Lyon, 1990). The choice of the discount rate is often critical. It can determine the cost-effectiveness of “Pap” smears (Eddy, 1990), hypertension treatment (Coyle & Tolley, 1992), and screening programs for gastrointestinal parasites (Anderson & Moser, 1985); the appropriate strategy for dealing with heart disease (Cretin, 1977), kidney failure (Klarman et al., 1968, Stange and Sumner, 1978), prostate tumors (Woodward, Boyarsky, & Barnett, 1983), and tropical pathogens (Barnum, 1987); and the appropriateness of circumcising male infants (Ganiats, Humphrey, Taras, & Kaplan, 1991), performing elective hysterectomies (Cole & Berlin, 1977), saving premature babies (Boyle, Torrance, Sinclair, & Horwood, 1983), implementing a national vaccination program for hepatitis (Krahn & Detsky, 1993), recovering helium from natural gas production (Owen, 1983), and building a national nuclear waste storage facility (Schulze, Brookshire, & Saddler, 1981).

Although the discount rate is a crucial parameter in many policy decisions, it is often assigned with little explicit justification. As Baumol (1970) comments: “Despite the critical nature of [the discount rate], in some calculations it is assigned a value almost cavalierly, with little attempt to show that the selected figure is not chosen arbitrarily and capriciously” (p. 273). Similarly, Krahn and Gafni (1993) remark: “Most analyses, including those who take great care to measure costs and consequences, pull their discount rates either out of the air or off the shelf, and the lucky number is most often 5%” (p. 415).

The lack of explicit justification for the magnitude of the discount rate reflects a more fundamental failure to identify the theoretical basis for discounting. As Goodin (1982) comments:

Justifications [for discounting] tend … to come in the rushed preliminaries to more detailed discussions … We are asked to make do with brief allusions to an ill-sorted jumble of slightly different arguments having rather different bases and quite different implications (p. 54).

When justifications for discounting are offered, they often differ across analyses. Sometimes discounting is justified by appealing to concepts of investment and opportunity costs. Elsewhere, discounting is used to reflect the common assumption that people have a time preference – that they care less about future utility than current utility. In still other cases, discounting has been used to reflect uncertainty or anticipated decreases in the utility of future consumption. For distant future consequences, discounting has been used to reflect diminished empathy for future generations.

Fig. 1 outlines a conceptual framework for sorting out the factors that are often conflated in discussions about discounting.1 The left side lists six factors that may affect the expected amount of utility a future outcome confers: (1) its probability, (2) changes in the objective consequence itself, (3) changes in utility functions, (4) utility from anticipation, (5) utility from memory, and (6) opportunity costs. These factors must be distinguished from time preference (δ, in the upper right corner of Fig. 1) which pertains to the relative weight given to future utility. Strictly, the DU model expresses time preference, because the discount factor operates on utility itself. This time preference relevant to outcomes that occur later within one’s own life must, however, be distinguished from an intergenerational time preference, which pertains to the degree of concern one has for the welfare of future individuals. There is an important difference between discounting one’s own future utility and discounting the utility of someone else who will be alive in the future. The type of time preference pertinent to distant outcomes might be considered an empathic discount rate, representing the diminution of empathy felt for people who are more temporally remote (η in the lower right corner of Fig. 1).

Much of the debate surrounding discounting has been sustained by the tendency to confuse the distinct theoretical concepts represented in Fig. 1. Resolving these distinct concepts helps illuminate several areas of controversy, including the magnitude of the discount rate, the appropriateness of discounting all outcomes at the same rate, and the legitimacy of applying conventional discount rates to distant future outcomes.

Section snippets

Probability

The passage of time may reduce the probability that a future consequence will actually occur. For example, the government may collapse before your bond matures, you may die before getting a chance to cash it in, and so on. Similarly, when calculating the number of expected cancers caused by a future radiation spill, it seems reasonable to account for the possibility that scientists will have a cure by then, or even to incorporate the possibility that civilization will already have been

Time preference (discounting future utility)

The previous sections outlined six factors that may affect the expected amount of utility a future consequence confers. Each consideration could be explicitly represented in models of intertemporal choice – by including a probability term to account for uncertainty, by permitting the utility of consumption to depend on time, by including arguments in the utility function for anticipation and memory, and so on. However, none of the considerations discussed thus far justifies the type of

Intergenerational time preference (discounting the future utility of others)

When evaluating outcomes that affect people who are not yet born, the concept of time preference discussed in the previous section (which refers to the degree of concern people have for their own future welfare) must be replaced with the concept of an intergenerational time preference (which refers to the degree of concern people have for the welfare of other people who will be alive in the future). Although these two types of time preference are often confounded, there is no close connection

Conclusions

This article proposes a framework for organizing the reasons why an individual or society might discount future outcomes relative to more immediate outcomes. Two distinctions are emphasized: (1) the difference between discounting a future outcome because it confers less utility and discounting future utility per se, and (2) the difference between discounting one’s own future utility and discounting the utility of others who will be alive in the future.

Being clear about the various bases for

Acknowledgements

I thank Geoffrey Brennen, Zoe Chance, Andrew Colman, Kerri Frederick, Matthew Selove, and an anonymous referee for comments received on prior drafts.

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