Thaler on Discounting

This is a companion to “Richard Thaler, Nobel Laureate” and “Thaler’s Non-Revolution in Economics“. See also the long list of related posts at the end of “Richard Thaler, Nobel Laureate”.

Richard Thaler, the newly minted Noble laureate in economics, has published many papers, including one about discounting as a tool of government decision-making. The paper, “Discounting and Fiscal Constraints: Why Discounting is Always Right”, appeared in August 1979 under the imprimatur of the think-tank where Thaler was a consultant. It was also published in the October 1979 issue of the now-defunct Defense Management Journal (DMJ). Given the lead time for producing a journal, it’s almost certain that there is no substantive difference between the in-house version and the DMJ version. But only the in-house version seems to be available online, so the preceding link leads to it, and the quotations below are taken from it.

The aim of Thaler’s piece is to refute an article in the March 1978 issue of DMJ by Commander Rolf Clark, “Should Defense Managers Discount Future Costs?”. Specifically, Thaler argues against Clark’s conclusion that discounting is irrelevant in a regime of fiscal constraints.*

Clark took the position that a defense manager faced with fiscal constraints should simply choose among alternatives by picking the one with the lowest undiscounted costs. Why? Because the defense manager, unlike a business manager, can’t earn interest by deferring an expenditure and investing the money where it earns interest. To put it another way, deferring an expenditure doesn’t result in a later increase in a defense manager’s budget. Or in the budget of any government manager, for that matter.

Viewed in perspective, the dispute between Thaler and Clark is a tempest in a teaspoon  — a debate about how to arrange the deck chairs on the Titanic. Discounting is of little consequence against this backdrop:

  • uncertainty about future threats to U.S. interests (e.g., their sources, the weapons and tactics of potential enemies, and the timing of attacks)
  • uncertainty about the actual effectiveness of U.S. systems and tactics (e.g., see this)
  • uncertainty bout the costs of systems, especially those that are still in the early stages of development
  • a panoply of vested interests and institutional constraints that must be satisfied (e.g., a strong Marine Corp “lobby” on Capitol Hill, the long dominance of aviation in the Navy, the need to keep the peace within the services by avoiding drastic changes in any component’s share of the budget)
  • uncertainty about the amounts of money that Congress will actually appropriate, and the specific mandates that Congress will impose on spending (e.g., buy this system, not that one, recruit to a goal of X active-duty personnel in the Air Force, not Y).

But the issue is worth revisiting because it reveals a blind spot in Thaler’s view of decision-making.

Thaler begins his substantive presentation by explaining the purpose of discounting:

A discount rate is simply a shorthand way of defining a firm’s, organization’s, or person’s time value of money. This rate is always determined by opportunity costs. Opportunity costs, in turn, depend on circumstances. Consider the following example: An organization must choose between two projects which yield equal effectiveness (or profits in the case of a firm). Project A will cost $200 this year and nothing thereafter. Project B will cost $205 next year and nothing before or after. Notice that if project B is selected the organization will have an extra $200 to use for a year. Whether project B is preferred simply depends on whether it is worth $5 to the organization to have those $200 to use for a year. That, in turn, depends on what the organization would do with the money. If the money would just sit around for the year, its time value is zero and project A should be chosen. However, if the money were put in a 5 percent savings account, it would earn $10 in the year and thus the organization would gain $5 by selecting project B. [pp. 1-2]

In Thaler’s simplified version of reality, a government decision-maker (manager) faces a choice between two projects that (ostensibly) would be equally effective against a postulated threat, even though their costs would be incurred at different times. Specifically, the manager must choose between project A, at a cost of $200 in year 1, and project B, at a cost of $205 in year 2. Thaler claims that the manager can choose between the two projects by discounting their costs:

A [government] manager . . . cannot earn bank interest on funds withheld for a year. . . .  However, there will generally exist other ways for the manager to “invest” funds which are available. Examples include cost-saving expenditures, conservation measures, and preventive maintenance. These kinds of expenditures, if they have positive rates of return, permit a manager to invest money just as if he were putting the money in a savings account.

. . . Suppose a thorough analysis of cost-saving alternatives reveals that [in year 2] a maintenance project will be required at a cost of $215. Call this project D. Alternatively the project can be done [in year 1] (at the same level of effectiveness) for only $200. Call this project C. All of the options are displayed in table 1.

Discounting in the public sector_table 1

[pp. 3-4]

Thaler believes that his example clinches the argument for discounting because the choice of project B (an expenditure of $205 in year 2) enables the manager to undertake project C in year 1, and thereby to “save” $10 in year 2. But Thaler’s “proof” is deeply flawed:

  • If a maintenance project is undertaken in year 1, it will pay off sooner than if it is undertaken in year 2 but, by the same token, its benefits will diminish sooner than if it is undertaken in year 2.
  • More generally, different projects cannot, by definition be equally effective. Projects A and B may be about equally effective by a particular measure, but because they are different they will differ in other respects, and those differences could be crucial in choosing between A and B.
  • Specifically, projects A and B might be equally effective when compared quantitatively in the context of an abstract scenario, but A might be more effective in an non-quantifiable but crucial respect. For example, the earlier expenditure on A might be viewed by a potential enemy as a more compelling deterrent than the later expenditure on B because it would demonstrate more clearly the U.S. government’s willingness and ability to mount a strong defense against the potential enemy. Alternatively, the earlier expenditure on B might cause the enemy to accelerate his own production of weapons or mobilization of troops. These are the kinds of crucial issues that discounting is powerless to illuminate, and may even obscure.
  • For a decision to rest on the use of a particular discount rate, there must be great certainty about the future costs and effectiveness of the alternatives. But there seldom is. The practice of discounting therefore promotes an illusion of certainty — a potentially dangerous illusion, in the case of national defense.
  • Finally, the “correct” discount rate depends on the options available to a particular manager of a particular government activity. Yet Thaler insists on the application of a uniform discount rate by all government managers (p. 6). By Thaler’s own example, such a practice could lead a manager to choose the wrong option.

So even if there is certainty about everything else, there is no “correct” discount rate, and it is presumptuous of Thaler to prescribe one on the assumption that it will fit every defense manager’s particular circumstances.**

Thaler does the same thing when he counsels intervention in personal decisions because too many people — in his view — make irrational decisions.

In the context of personal decision-making — which is the focal point of Thaler’s “libertarian” paternalism — the act of discounting is rational because it serves wealth-maximization. But life isn’t just about maximizing wealth. That’s why some people choose to have a lot of children, when doing so obviously reduces the amount that they can save. That’s why some choose to retire early rather than stay in stressful jobs. Rationality and wealth maximization are two very different things, but a lot of laypersons and too many economists are guilty of equating them.

If wealth-maximization is your goal, just stop drinking, smoking, enjoying good food, paying for entertainment, subscribing to newspapers and magazines, buying books, watering your lawn, mowing the grass, driving your car (except to work if you have no feasible alternative), and on into the night. You will accumulate a lot of money — if you invest wisely (there’s the rub of uncertainty) — but you will live a miserable life, unless you are the rare person who is a true miser.
__________
* If you are unfamiliar with the background of the Clark-Thaler exchange, and the reference to fiscal constraints, here’s the story: Since 1969 the Secretary of Defense has required the military departments to propose multi-year spending programs that are constrained by an explicit ceiling on each year’s spending. Fiscal guidance, as it is called, was lacking before that. But, in reality, defense budgets have always been constrained, ultimately by Congress. Fiscal guidance represents only a rough guess as to the total amount of defense spending that Congress will approve, and a rougher guess about the distribution of that spending among the military departments.

** Thaler’s example of a cost-saving investment is also a stretch, given how government budgets are decided. I gave it a pass in order to make the point that it wouldn’t save Thaler’s argument even if it were realistic. Here’s the missing reality:

Even if the Secretary of Defense (the grand panjandrum of defense managers) makes the kinds of moves counseled by Thaler, and even if his multi-year program sails through the Office and Management and Budget without a scratch, Congress has the final say. And Congress, though it pays attention to the multi-year plans coming from the Executive Branch, still makes annual appropriations. When it does so, it essentially ignores the internal logic of the multi-year plans (assuming that the Defense plan has an internal logic after it has been subjected to Pentagon politics). Instead, Congress divides the defense budget into various spending programs (see the list for national defense, here), and adjusts each program to suit the tastes, preferences, and moods of staffers, committee members, and committee chairman. Thus it is unlikely that the services’ maintenance and procurement budgets will emerge from Congress as they entered, with cross-temporal tradeoffs intact. A more rational budgeting strategy, from the perspective of the Secretary of Defense, is to submit plans that accord with the known preferences of Congress. Such plans may not incorporate the kind of trivial fine-tuning favored by Thaler, but they will more likely serve the national interest by yielding a robust defense.

Discounting in the Public Sector

This post is an adaptation of an article that I wrote 25 years ago. It appeared in the May-June 1989 issue of Program Manager, a magazine published in 1972-2003 by the Defense Systems Management College and its successor, the Defense Acquisition University. Several years before the article appeared, I had begun to question the soundness of the federal government’s official policy about discounting. which is stated in Circular A-94, issued by the Office of Management and Budget, Executive Office of the President.

The point of this post is to refute the case for discounting in benefit-cost or cost-effectiveness analyses of government projects. Part of my argument against discounting is made in “Discounting and ‘Libertarian Paternalism’.” This post makes a more complete case against the use of discounting in analyses of government projects.

DISCOUNTING: WHY AND WHY NOT

Discounting is a valid exercise in the evaluation of personal and business alternatives. A business, for example, will use discounting to compare alternative investments in new equipment; for example:

Implementation of project A will cost $1 million a year in years 1-5; project A will yield an annual net cash flow of $1 million in years 6-15.

Implementation of B will cost $1.5 million a year in years 1-4; B will yield $1.1 million a year in years 5-15.

Instead of undertaking either project, the firm could purchase equally risky bonds with a yield of 5 percent.

Should the firm undertake project A or project B? Discounting reveals the answer (though, for the sake of simplicity, I’m omitting risk, uncertainty, taxes, and inflation): The net present value of A, discounted at 5 percent, is $1.72 million; of B, $4.34 million. B is the preferred alternative, all other things being equal.

This result would seem backwards to a person who is used to thinking in terms of gross numbers, irrespective of the timing of outlays and returns. For example, A costs $5 million and returns $1 million a year (20 percent) when it’s up and running; whereas, B costs $6 million and returns $1.1 million a year (18.33 percent) when it’s up and running. Thus an analysis that omits timing would favor project A. But timing is important. Even though B costs more than A, B yields a greater return, and sooner (by a year). Over the relevant time span, the extra year and extra annual return of $0.1 million make B the more profitable alternative.

However, the result is sensitive to the selection of a discount rate and time horizon, both of which are judgment calls. A range of discount rates and time horizons would be chosen, to see if the preference for B is robust or weak. If A is judged less risky than B, it would be appropriate to apply a lower discount rate to A than to B. If A is likely to have a longer productive life than B (less likely to become obsolete, for example), the time horizon for A would be longer than for B.

Discounting makes sense in the private sector, despite the sensitivity of results to changes in assumptions about costs, returns, discount rate, and time horizon. For one thing, the discount rate — however uncertain — is relevant to the decision-maker; it represents the rate of return that the decision-maker could earn if he chose not to undertake project A or project B. It is his discount rate, not one chosen arbitrarily for him by someone else. For another thing, the returns (such as they turn out to be) belong to the decision-maker. When all is said and done, he (or the principal for whom he is acting) will choose a course of action that is meant to maximize his wealth or his profits. Accordingly, different decision-makers, in different circumstances, will use discount rates and time horizons appropriate to their circumstances. Discounting isn’t a one-size-fits-all procedure.

That said, it doesn’t make sense if to discount if you’re analyzing alternative projects for a government decision-maker. Why not?

1. Government is funded (ultimately) by taxes. Taxpayers have myriad discount rates. The use of a particular rate to represent a (fictional) “social” rate amounts to gross presumption.

2. Further, there’s usually a misalignment of costs and benefits. Those who bear the costs (taxpayers) aren’t likely to reap the benefits in proportion to the costs they bear. Discounting doesn’t apply when X bears the costs and Y reaps the benefits.

3. Given (1) and (2), the proponent of discounting will resort to the use of an internal rate of return (e.g., cost reductions generated by maintenance projects that can then be applied to investments in new weapon systems). The use of an internal rate of return turns out to be a horse-before-the cart proposition: the correct choice determines the discount rate; the discount rate doesn’t determine the correct choice.

Now, for the details.

THE FICTIONAL “SOCIAL” DISCOUNT RATE

The academic justification for discounting the costs of alternative government projects goes like this:

The appropriate rate of discount for public projects is one which measures the social opportunity cost. The decision to devote resources to investment in a public project means … that these resources will become unavailable for use by the private sector. And this transfer should be undertaken whenever a potential project available to the government offers social benefits greater than the loss sustained by removing these resources from the private sector. The social rate of discount, then, must be chosen in such a way that it leads to a positive number for the evaluated net benefits of a public project if and only if its gross benefits exceed its opportunity costs in the private sector. (William J. Baumol, “On the Social Rate of Discount,” American Economic Review, September 1968, pp. 789-90)

In mathematical notation:

[NPV(public benefits) > NPV(private costs)] → Undertake public project

In the next section I’ll address the almost-certain misalignment of benefits and costs.  Here, I’ll assume for the sake of argument that benefits flow only to those taxpayers who foot the bill for a public (i.e., government) project, and do so in perfect proportion to the taxes levied on each of them. Would that unlikely condition justify the public project?

Consider this example:

There is a two-person economy consisting of Adam and Eve.

If a public project is undertaken, both will be taxed the same amount and both will receive the same benefits.

Taxes are levied in year 1; benefits are received in year 2.

Adam’s discount rate is 5 percent; Eve’s discount rate is 10 percent. That is, Eve has a “high” time-preference, relative to Adam; she places more emphasis on the present, as against the future.

The public decision-maker uses a discount rate of 7.5 percent.

The dollar value of the benefits accruing to Adam and Eve can be estimated.

The net present value of the sum of those benefits exceeds the net present value of the sum of the costs borne by Adam and Eve.

Nevertheless, Eve is probably made worse off by the undertaking of the public project. Adam is probably made better off, but at Eve’s expense. Why? Let’s say that Adam and Eve each pay $100 in taxes in year 1, and that the public project breaks even (returns exactly 7.5 percent), so that each of them receives $107.50 worth of benefits in year 2. Adam, given his 5 percent discount rate, would have been made whole with benefits of $105 in year 2, so he gains $2.50. Eve, on the other hand, would have been made whole with benefits of $110 in year 2, so she loses $2.50.

All of that assumes, of course, that both Adam and Eve place any value on the benefits delivered by the public project, let alone the same value. How does the government decision-maker know what value Adam and Eve place on the benefits delivered by his project? He doesn’t; he’s just a presumptuous fellow who wants to spend Adam and Eve’s money to satisfy his own sense of how things should be.

THE MISALIGNMENT OF COSTS AND BENEFITS

Professor Baumol admits that “no optimal [social discount] rate exists” (op. cit., p. 798). Actually, no “social” discount rate exists, except in the minds of arrogant economists and government officials.

How does “society” benefit if Adam is made happy at Eve’s expense? It doesn’t, because there’s no such thing as a social-welfare function, that is, a collective degree of happiness (or unhappiness) in which Adam’s gain somehow cancels Eve’s loss.

It only gets worse in the usual case, where the benefits from a government program do not flow to taxpayers in proportion to the taxes that they pay. It would be a major miracle if benefits were somehow aligned perfectly or even passably well with tax payments, especially given progressive tax rates and deliberately regressive benefit payments (e.g., Social Security, Medicare, Medicaid, housing subsidies, food stamps).

With millions of taxpayers and non-taxpayers in the mix — each with his own discount rate, and each receiving benefits (or not) that are disproportionate to the taxes that he pays — how can anyone say with a straight face that any government project can be justified by applying a “social” discount rate to its benefits and costs?

THE IRRELEVANT INTERNAL RATE OF RETURN

Given the foregoing, insurmountable objections, the die-hard defender of public-sector discounting hops on his deus ex machina: the internal rate of return. One such die-hard is Richard Thaler (also a notorious paternalist and purported libertarian), who essayed his views in “Discounting and Fiscal Constraints: Why Discounting is Always Right” (Center for Naval Analyses, Professional Paper 257, August 1979).

In Thaler’s simplified version of reality, a government decision-maker (manager) faces a choice between two projects that would deliver equal effectiveness (benefits). Specifically, the manager must choose between project A, at a cost of $200 in year 1, and equally-effective project B, at a cost of $205 in year 2 (op. cit., pp. 1-2). Thaler continues:

A [government] manager . . . cannot earn bank interest on funds withheld for a year. . . .  However, there will generally exist other ways for the manager to “invest” funds which are available. Examples include cost-saving expenditures, conservation measures, and preventive maintenance. These kinds of expenditures, if they have positive rates of return, permit a manager to invest money just as if he were putting the money in a savings account.

. . . Suppose a thorough analysis of cost-saving alternatives reveals that [in year 2] a maintenance project will be required at a cost of $215. Call this project D. Alternatively the project can be done [in year 1] (at the same level of effectiveness) for only $200. Call this project C. All of the options are displayed in table 1.

Discounting in the public sector_table 1

(op. cit., pp. 3-4)

Thaler believes that his example clinches the argument for discounting because the choice of project B (an expenditure of $205 in year 2) enables the manager to undertake project C in year 1, and thereby to “save” $10 in year 2.

Thaler’s “proof” is deeply flawed, as discussed in “Discounting and ‘Libertarian Paternalism’.” I’ll focus here on the essential emptiness of Thaler’s argument:

1. Even granting the availability of cost-reduction measures, their payoffs will vary widely. Thaler conveniently conjures projects C and D, with costs of $200 and $215 in years 1 and 2, respectively. He could just have well conjured a project D with a cost of $205 in year 2 — throwing A + D into a tie with B + C — or a project D with a cost of $203 in year 2 — causing A + D to look better than B + C.

2. In other words, the “correct” discount rate depends on the options available to a specific manager of a specific government activity. Yet Thaler insists on the application of a uniform discount rate by all government managers (op. cit., p. 6). By Thaler’s own example, such a practice could lead a manager to choose the wrong option.

3. To put it another way, the analyst should consider the specific options that are available to a specific manager, by constructing packages of projects that would cost the about the same in every year. Having done so (and assuming away a great deal of uncertainty about the costs and benefits of the options), the manager can then choose the package that delivers the most bang for the buck — when the bang is needed, in his judgment. There is no need to apply a discount rate. The relevant (and idiosyncratic) “discount rate” is a product of the correct choice, not a determinant of it.

FINAL WORDS ABOUT THE FUTILITY OF DISCOUNTING FOR GOVERNMENT DECISION-MAKING

Even if there were such a thing as a “social” discount rate, and even if the costs and benefits of government programs were well aligned, discounting would be an inadvisable practice in analysis for government decision-making. If a decision is to depend on the application of a particular discount rate, there must be great certainty about the future costs and benefits of alternative courses of action. But there seldom is (see “Analysis for Government Decision-Making: Demi-Science, Hemi-Demi-Science, and Sophistry“). The practice of discounting simply fosters an illusion of certainty — a potentially dangerous illusion, in the case of national defense.