The Defense of Discounting

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(A) The Tastes Defense
(B) The Dynastic Defense
(C) The Decentralization Defense

Including the time discount rate into our social welfare function would certainly make things easier. But how are we to justify it? If we follow Pigou, Ramsey and company in their reasoning, there seems to be no "ethical" justification for putting a utility discount into the social welfare function. How might this be disputed?

(A) The Tastes Defense

The inventors of intertemporal preferences, Eugen von Böhm-Bawerk (1886) and Irving Fisher (1930), believed that discounting future utility was an irrationality. This was the line that Arthur C. Pigou (1920), Frank Ramsey (1928) and Roy Harrod (1948) took -- which is precisely why they felt that it should not be included in the intertemporal social welfare function. As Roy Harrod reiterates forcefully:

"After all, pure time preference is a weakness; a man may choose to sacrifice 2 units of utility -- of utility not money -- in 20 years from now for sake 1 unit now; but in 20 years' time he will presumably regret having done so. Unfortunately he will not then be able to reverse the process. On the assumption -- unwarranted, no doubt, some of you may think -- that a government is capable of planning what is best for its subjects, it will pay no attention to pure time preference, a polite expression for rapacity and the conquest of reason by passion." (R.F. Harrod, 1948: p.40).

But there are articulate defenses in the opposite direction as well (e.g. Ludwig von Mises, 1949: Ch. 18). One could say that positive time preference is just that: a preference and not a personal weakness or defect that ought to be "corrected". It need not be justified, it just "is" and de gustibus non est disputandum (we cannot quarrel over tastes). In this view, for someone to say it is an "irrational preference", as Pigou (1920: p.25) did, is oxymoronic.

So the simplest, defense for including a discount factor in the social welfare function is that, well, people have positive time-preference -- and a preference is a preference is a preference. It should be respected by the social planner. Removing time preference from the social welfare function, far from being "ethical", can in fact be deemed unduly authoritarian as it disregards people's tastes. Arguments to this end were forwarded by Peter T. Bauer (1957) and Otto Eckstein (1957).

Yet this is not a perfect argument for if we are going to stick to "preferences" argument, then should not the preferences of future generations be taken into account? If their opinion had any bearing on the present, then it would be precisely to discount the utility of the earlier generations. Clearly, we are at an impasse.

Of course, all this is wordplay. As Maurice Allais (1947: Ch. 4) and Jan de Van Graaff (1957: p.103) note, the optimal level of savings is a political and ethical question, for which the market's solution is only one among many. Bauer (1957) would probably agree -- but would cast his vote in favor of non-interference nonetheless.

But if we agree to this, then are we not conceding too much to posterity? If we are to explicitly consider the question as a political one, one must wonder whether future generations should have any claim at all! In effect, only living members are involved in the political process and those are, effectively, the only ones social welfare functions should respect. As Stephen Marglin explains:

"I, for one, do not accept the Pigovian formulation of social welfare. If I am going to play the neoclassical, or rather neo-Benthamite, game, in which individuals are assumed to have well-defined preferences that are identical to their utilities, I want to play the rest of the bourgeois-democratic game of philosophical liberalism as well: in particular, I want the government's social welfare function to reflect only the preferences of present individuals. Whatever else a democratic society may or may not imply, I consider it axiomatic that a democratic government reflects only the preferences of the individuals who are presently members of the body politic." (Marglin, 1963).

And why not? After all, we cannot second-guess the desires of people who are not born yet and perhaps we should not even try. Who is to argue on their behalf and should we believe them? Why should we make room in our polity for current political representatives for future generations that do not exist? To do so might be as undemocratic as, say, allowing clergymen a dominant position in current political affairs because they are the "representatives" of supernatural beings and human afterlife -- concepts which are no more vague and speculative than "future generations". Of course, the clergy have had such power in the past, but it is clearly not part of the modern "bourgeois-democratic" conception of political life.

If we were to agree that only "present members of the body politic" should count, this might seem to turn the balance towards the Eckstein-Bauer corner of the debate, restoring the ethical legitimacy of positive time preference. But perhaps future generations do have political representatives in the present -- namely, that the living individuals themselves are their advocates, however imperfect. In other words, current people do have "social tastes" which incorporate the interests of future generations. They actually want the social welfare function to reflect these.

A strict behaviorist would contend that this is nonsense. If people's tastes incorporate this advocacy for future generations, their behavior should reflect this. People's high time preference rate demonstrates that they do not really care much about them -- and that is the only accurate measure of their concern.

But what if, contends the opposite camp, living individuals have a discrepancy between their "personal tastes" and "social tastes". Might people really want zero (or at least low) discount rates for society, even while possessing a personal high time preference rate? This does not necessarily dismiss the behavioral argument, but rather sharpens it by dividing people's behavior into two: people's political choices (e.g. voting for recycling and environmental protection laws) reflect their "social tastes", but people's personal economic choices (e.g. how much recycling they themselves do) reflect their "personal tastes". Any behaviorist would be forced to admit that, indeed, people's political behavior usually does not match their personal behavior.

But should not these two types of tastes be consistent with each other? Not necessarily. As outlined by Stephen Marglin (1963), there are at least two ways to argue this. The first argument, credited to Gerhard Colm, is simply that the "frame of reference" is different in personal and social considerations. People wear two hats on the relevant time discount rates. Individuals may have defective telescopic faculties when making decisions about what they want to save individually, but when asked what "society" should save, the individual might recommend a different (i.e. a much lower) discount rate. Again, think of the penchant for Westerners to individually generate enormous amounts of waste while condemning Western wastefulness at the same time.

The second argument, articulated by William J. Baumol (1952) and Amartya Sen (1961), is only subtly different in that it emphasizes the "free-rider" aspects of the problem. Specifically, people will vote for policies with low discount rates (e.g. municipal recycling programs) in the expectation that others will comply with them, while personally they will perform actions which reflect their personal high discount rate (e.g. not bother to recycle their own garbage). They might not feel they are being "inconsistent" in their personal and social tastes because they expect others to comply with the laws that they have voted for.

Both these cases reinforce Pigou's arguments for disregarding personal discounting. People's social tastes are for zero or very low discounting and this is what should be included in the intertemporal social welfare function. Their personal taste for high discounting, as revealed by their individual actions, should not be considered sufficient justification for its inclusion. Viewed from this prism, the Pigou-Ramsey social welfare function is not authoritarian at all, but complies with what people "really" want when they are in a "social" frame of mind or when they are voting.

However, this puts us right back in our dilemma. The "tastes" defense does not seem, on its own, to be capable of justifying the inclusion of positive time preference in our social welfare function. Pigou, Ramsey, Harrod and company would be overjoyed.

(B) The Dynastic Defense

Is there a median position where we can include the "reality" of personal discounting into a social welfare function, without contaminating it with its "unethical" features? One maneuver consistent with utilitarian ethics is to transform our concern with "generations" into a concern for "dynasties". [although suggested much earlier, Robert Barro (1974) was perhaps the first prominent modern economist to perform this trick explicitly]. Specifically, let us eliminate all future generations from our social welfare function, so that the social planner is concerned with the utility of the current generation only, i.e. the social welfare function is simply:

S = å h=1H u0h(c0h)

where u0h(キ) and c0h are the utility function and consumption plan of the hth living household, H are the total number of households alive at the initial time period t = 0. Thus, backing away from Pigou and Ramsey and moving towards Marglin, we now have "society" defined merely as the living individuals and not future ones.

Although Marglin's argument would imply future generations have no "legitimate claims" on the current generation, that does not mean that they cannot have "emotional claims". The trick is to take this to the extreme and argue that currently living individuals have "dynastic" utility functions. By this we mean that a living individual is altruistic towards his "dynasty", i.e. his utility takes into account the utility of his progeny. Thus, the future is reintroduced into the story not because it is "ethical" to do so, but merely because that is what current living individuals do anyway.

The implications of this become interesting. The utility of the current generation depends upon not only their own consumption but also on the utility of their children. But, by the same logic, the utility of their children depends, in turn, on the utility of their children and so on ad infinitum through the ensuing dynasty. To see this clearly, let h denote the "dynasty" stemming from the living agent h and suppose that there is only one child per adult (no population growth). Then we can stipulate that u0h = u0h(c0h, u1h), so the utility of the household h living at t = 0 depends on the utility of their direct descendent, the household h that is living at t = 1. As u1h itself is a function of consumption at t = 1 and the utility of their progeny (generation h at t = 2), then u1h = u1h(c1h, u2h), which we can plug that back into the original generation's utility so u0h = u0h (c0h, u1h(c1h, u2h)). Iterating further, the utility of generation t = 2 of dynasty h is a function of their consumption (c2h) and the utility of their progeny, u3h, i.e. u2h = u2h(c2h, u3h). We can proceed in this manner for all future generations of dynasty h. Thus, recursing all the utilities of a dynasty into themselves, the utility of household h at the initial time period t = 0 is the stream of utilities achieved by the entire ensuing dynasty in the future, i.e.

u0h = u0h(c0h, u1h(c1h, u2h(c2h, u3h(c3h, ....))))

Since currently-living individuals are myopic (it is a "personal" weakness, as Pigou allowed), then a positive rate of time preference can be introduced without ethical implications. The discount factor indicates that a household is a little bit selfish (or more accurately, just plain short-sighted) in the sense that they do not consider the utility of their children to be quite as important as their own. Specifically, let us propose that the utility function u0h is an additively separable function with positive time preference. Let us assume that every generation of dynasty h has the same utility function uh(キ) which is dynasty-dependent but time-independent. Furthermore, from the perspective of the current living agent (living at t = 0), the utility of his descendent at time t = 1 is b uh(キ), where 0 < b < 1 is the "discount factor" which we assume to be the same across dynasties and generations. Consequently, we can rewrite the utility of the current living member of household h as:

u0h = uh(c0h) + b uh(c1h) + b2 uh(c2h) + ...

or simply:

u0h = å t=0¥ bt uh(cth)

The rest is simplicity itself. Taking our social welfare function, as Marglin (1963) suggests, over currently living people alone, we see that:

S = å h=0H u0h = å h=0H å t=0¥ bt uh(cth)

so, switching summation signs:

S = å t=0¥ å h=0H bt uh(cth)

Finally, assuming that all households within a generation have the same capacity for pleasure, then uh(キ) = u(キ) for all h = 1, 2, .., H, and therefore (for Benthamite fairness) the same contemporaneous consumption allocation, cth = ct for all h = 1, 2, .., L, so our social welfare function becomes S = åt=0¥ Lキbt u(ct). Letting Lキu(ct) = U(Ct), where U and Ct are the aggregate utility and aggregate consumption of generation t, then we obtain:

S = å t=0¥ bt U(Ct)

which is a simple infinite-horizon social welfare function with a time discount factor. In continuous time, this can be expressed as:

S = ò 0¥ U(Ct)e-r t dt

where r is the rate of time preference. These are exactly the Samuelson social welfare functions we were hoping for earlier.

In sum, from the dynastic perspective, the burden of taking the utility of future generations into account is shouldered by currently-living individuals rather than the social planner. But since the social planner takes the utility of current-living individuals and because these take the utility of their descendants into account, then we can regard the resulting social welfare function with intertemporal discounting, S = ò0¥ U(Ct)e-r t dt, to be "ethically defensible". Including time preference into the social welfare function does not imply that our social planner is a moral desperado, but merely that our households have "defective telescopic faculties".

(C) The Decentralization Defense

A different argument in favor of discounting, which we shall consider later in more detail, is the "decentralization" defense, originally attributed to Robert Becker (1980). This is perhaps the best-known argument and, by far, the most popular today. But it requires an entire overhaul of our understanding of the intertemporal social welfare function.

In a nutshell, the "decentralization" thesis argues that time preference should be included in the social welfare function because, well, it is really not a social welfare function at all! Instead of conceiving of the Ramsey problem as an exercise in normative economics, the decentralization argument considers it to be one of positive economics. They insist that a "properly" [sic] formulated model of the market, with infinitely-lived (!), intertemporally-optimizing, myopic (?) consumers and firms, with perfect foresight (!) and facing perfectly working capital markets (!), will yield exactly the same solution as the Ramsey social planner. In this view, the entire social welfare maximization exercise is merely a mathematical summary of the actual workings of the market. Consequently, adding time preference to the social welfare function is, in fact, necessary because consumers are myopic and the Ramsey social welfare function, over which we have been losing sleep, is really nothing other than the utility of the representative consumer.

Although the decentralization argument stretches credulity to an enormous degree, it is the most widely accepted argument today for including time preference. It has interesting implications for it has modified the nature and significance of optimal growth theory.

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