1 The Pareto criteriononwhich a CBAis raised has regard also to the economist’s basic maxim that the value to be attributed to a good or bad at any point in time is that value which is placed on it by the persons themselves at that point in time. Its applicationrequires, inparticular, that, if a personvalues a sum, say
$400, expected to be received with equal certainty ten years from now as exactly equivalent in welfare to $60 received this year, the economist accepts this trade-off as part of his ‘objective’ data.
If, however, gainers or losers in the projects being ranked are expected not to be alive at the common terminal date of the projects or at the common commencement date, it is easily shown that a positive figure calculated by reducing all gains and losses to a single date – for instance, to a terminal value as proposed or the currently more popular present value – does not infact meet the Pareto criterion.
Although not necessary for its demonstration, it will simplify the exposition if, for the time being, we conceive of a public project for which the finance is raised wholly by reducing current consumption. Further simplification is gained by assuming also the existence of institutions so accommodating as to produce a single rate of discount that is the rate of time preference common to all people affected by the project, this rate being exactly equal to the current yield on all investment.
With these highly convenient assumptions, it would follow in the usual way – that is, with the implicit proviso that all persons affected are expected to remain alive over the investment period – that the benefit–cost ratio would remain constant no matter what point of time was adopted in discounting and/or compounding gains and losses. Inasmuch as a benefit–cost ratio greater than unity entails an excess of benefits over costs, it also meets a Pareto criterion.
Thus, the problem addressed inthis chapter is that which arises whenthe itali-cized proviso above is not met; that is, when gainers and losers come into being at some point of time later than the commencement of the project or else expire before its terminal date. To illustrate, suppose a benefit of $1,000 is to be received by person X inyear 100. The commonrate of discount r, which also corre-sponds to X ’s rate of time preference, is such, we shall suppose, as to discount this $1,000 to the sum $2 inyear zero. But eventhough this r remains constant over his ownlifetime, if personX is borninyear 60, he cannot properly be said to be indifferent as between receiving $1,000 in year 100 and receiving $2 in
QUAH: “CHAP32” — 2007/1/25 — 08:03 — PAGE 172 — #2 year zero whenhe is infact not alive inyear zero, this being 60 years before he was born.
2 This difficulty has been circumvented up to now by assuming (implicitly) that each person affected by the project remains alive during the entire investment period, which assumption is incidentally too strict, as we shall see later. A popu-lar alternative that simplifies matters wonderfully is to adopt a particupopu-lar ‘social’
rate of discount, one the economist is to accept as a political datum and one to be used to cover any number of years, whether or not more than one generation is involved. Yet, as indicated earlier, the implications of introducing politically determined valuations or parameters into what are putatively economic calcula-tions are unacceptable. Such a device entails a rejection of the economist’s basic maxim (that only the person himself is to determine the valuation of the effect on him of the good or bad) and therefore also of an economic or Pareto criterion.
And inso far as the political authority inquestionis requiring the economist to come up with a strictly economic calculation, the economist’s surrender to such a requirement not only prevents the economist from discharging his responsibility, but involves him in deception.
3 Let us first highlight the inter-generational problem by a simple three-person model, one that may also be interpreted as a three-generation model.
InFigure 32.1, chronological time is measured as t along the horizontal axis, and the logarithm of the net benefit for persons X and Y , and of the net loss for person Z, is measured as B along the vertical axis. The three sloping lines are to be conceived as ‘time-indifference’ curves for the three persons who alone are affected by a particular project, it being assumed that each person is indifferent between any two points. Although not essential to the analysis, it simplifies further to assume a common rate of time preference for the three persons r, say one that
B
QUAH: “CHAP32” — 2007/1/25 — 08:03 — PAGE 173 — #3 Pareto criterion and generational time 173 indicates indifference between having $1 at any time t and having $2 twenty years later. All three indifference lines therefore slope upward from left to right at the same angle.
Consider first case (i), in which person Z, who lives from year 80 to year 140, is shown to be indifferent between losing consumption equal to $100 in year 80 and losing consumption equal to $200 in year 100. Person X , who lives from year 40 to year 100, is indifferent between consuming $120 in year 80 and consuming
$240 inyear 100. As there is anoverlap of 20 years betweenthe lifetimes of Z and X , extending from year 80 to year 100, a Pareto comparison can be made without violating the basic maxim. Whether year 80 is chosen or year 100 or any year between80 and 100, the ratio of X ’s gainto Z’s loss – 6/5 – remains valid. If, for instance, the year chosen is year 80, Z actually loses $100 of consumptioninthat year, whereas X , who actually gained $30 of consumption in year 40, would agree to accept, instead, $120 in year 80. Thus, whether or not X actually postpones consumption, his gain of $30 in year 40 is equivalent to a gain of 120 in year 80.
Consequently, a potential Pareto improvement is realized in year 80, since X ’s gainof 120 inthat year exceeds the loss of $100 by Z.1
The same exercise may be carried out for persons Y and X inasmuch as, between years 40 and 60, their lifetimes overlap. Y is indifferent between consumption of 7.5 inyear 20 and 15 inyear 40, whereas X actually receives 30 inyear 40. In this case, both persons gain. But if, for argument’s sake, we change Y ’s gainof 7.5 in year 20 into a loss of 7.5, equivalent to a loss of 15 in year 40, since it is thenexceeded by X ’s actual gainof 30 inyear 40, a potential Pareto improvement againexists.
Now consider case (ii) in which persons Y and Z alone comprise the community affected by the project. Since there is no point of time common to the two of them, a direct comparison between their actual or equivalent gains or losses is not possible.
Y ’s gainof 7.5 inyear 20 canbe compounded forward as far as year 60 whenhe is still alive, but Z’s loss of 100 is suffered inyear 80, at the start of his life. Were it possible meaningfully to compound Y ’s gain forward beyond year 60 or to discount Z’s loss backward from year 80, we should be able to talk of the project producing a potential Pareto loss for the Y –Z community – or, if the signs were reversed, a potential Pareto gain. But it is not possible, and therefore a valid comparison of gains and losses cannot be made for any single year.
For example, Y cannot be indifferent as between receiving 7.5 in year 20 and receiving 60 inyear 80, as he will not be alive inyear 80. Nor cana valid comparison be made for year 60, as Z cannot be indifferent between losing 100 in year 80 and losing 50 in year 60, 20 years before he is born. Inasmuch as the basic maxim cannot be met in a case where no common point of time is shared by Y and Z, a Pareto comparison of their gains and losses is not possible.
1 Clearly, discounting these two sums in year 80 to present values, or else compounding them to terminal values, simply multiplies each sum by the same scalar, leaving the benefit–loss ratio unchanged at 6/5.
QUAH: “CHAP32” — 2007/1/25 — 08:03 — PAGE 174 — #4 It should be evident that we can multiply the number of persons and also reduce the time overlap between successive persons indefinitely. But once a time gap between any two persons exists, their comparison via compounding or discounting through time must be ruled out as aninvalid procedure.
We conclude then that, in the absence of some dependable mechanism enabling us to transform the project’s original net benefit stream into some new pattern over generational time, it is not possible to compare gains and losses on the Pareto criterion. Inparticular, where a time gap exists betweentwo or more persons affected by the project in question, a potential Pareto improvement cannot be said to be met by a cost–benefit calculation that results in a positive discounted present (or compounded terminal) net benefit.
4 Among other facile but inoperative proposals to somehow circumvent the prob-lem, inadditionto the adoptionof a politically determined social rate of discount, is that of recourse to the oft-touted economist’s Nirvana, ‘a well-defined social welfare function’. However we imagine this abstraction to be created, it is even more far-fetched thanthe idea of a social rate of discount.2
It has also beenproposed that projects that show modest benefits inthe first years to be succeeded by heavy losses falling on future generations could be made acceptable if a state agency were established charged with appropriating a portion of the gains accruing in the early years, investing it at market rates of return. By the time the heavy losses occurred, the amount invested would have compounded to a sum that would fully compensate for the losses.3But until such an agency is indeed established, the economist cannot interpret the results of his CBA as if in fact it exists.
5 The questionthennaturally arises: when, over a period that covers two or more generations, the terminal years show an excess of benefits over costs which, as argued, cannot be said to result in a Pareto improvement, just what criterion can it be said to meet?
In fact, the answer is quite simple. Indeed, the answer is deducible from the proposal considered above, that a state agency be established to act in such ways as
2 This “well-defined social welfare function” may be visualized perhaps as emerging from a sort of conclave representatives of present and future generations who, between them, will debate and eventually reach agreement about what is an equitable inter-generational distribution of real income and, possibly, other momentous issues. Yet, whatever that distribution of income agreed upon, even if it could somehow be brought about, it does not ensure that a positive DPV or CTV can be interpreted as realizing a potential Pareto improvement.
3 The reverse of a hypothetical investment stream – one that imposes costs on current generations from which future generations will reap great benefits – would seem to be more difficult for our state agency to handle. But although one cannot appropriate a portion of the gains of future generations so as to compensate losers in the present, as much may be achieved by compensating present generation for their losses by ‘eating’ into the existing stock of capital. In practice, this would translate into the state’s taking action to increase current consumption through a reduction in income tax, the fall in revenue being met by a fall in public investment (or else by an issue of bonds that would ‘crowd out’ current commercial investment).
QUAH: “CHAP32” — 2007/1/25 — 08:03 — PAGE 175 — #5 Pareto criterion and generational time 175 to ensure that, in implementing projects that show a positive net terminal benefit, no generation suffers a net loss. With such an investment project, it would be possible to make sure that each generation then enjoyed a potential Pareto improvement.
Since such an agency does not, in fact, exist, and a potential Pareto improve-ment in any period over the entire lifespan of the project could be assured only if such an agency did exist, the required potential Pareto improvement is hypo-thetical only – contingent, that is, on the actual establishment of the agency. In other words, the standard potential Pareto improvement, which rationalizes the economist’s acceptance of projects that show an excess of net benefits, must itself be regarded as potential only, so long as such an agency itself remains a potential, and not an actual, institution.
It must be concluded, therefore, that the excess net benefit criterion, when realized for a long-lived project does not in fact meet the standard economist’s test of a potential Pareto improvement: the criterion confers no more than a potential Pareto improvement.
On reflection, moreover, it will transpire that a time span long enough to cover two or more generations is not necessary for interpreting a positive excess net benefit as no more than a potential Pareto improvement, for even for projects with short lifespans, say of five years or less, it will almost be impossible to avoid some generational overlap. In fact, it is enough for a person who contributes to the cost of the project to expire before receiving the later benefits to warrant regarding the net excess benefit criterion as fulfilling only a potential improvement.
6 It cannot be denied that a potential Pareto improvement is less compelling a sanction in warranting the economist’s excess net benefit criterion than is the more generally accepted potential Pareto improvement. Certainly, for those who are apt to regard CBA, or allocative economics in general, as a normative study, at least in the sense that the economist’s criterion would command a consensus or near-consensus, would be disconcerted to discover that the criterion involved no more thana potential improvement.
For those economists like ourselves, however, who regard CBAas an exercise in positive economics, there need be no heart searching. For the decision to sanction a proposed project is not the economist’s responsibility. It is the responsibility of the political decisionmaker – ina liberal democracy, that of the community’s representatives. Yet, inorder for decisions to be takeninfull awareness of the economic implications of cost–benefit calculations, the economist has a duty to explainits limitations. He is to emphasize inparticular that the values he attributes to the goods and bads produced by the project are all derived, ultimately, from the subjective valuations of the persons affected by the project: also that the excess of net benefits over costs that is calculated must be interpreted not so much as a material improvement for the community as a whole, nor even as a potential improvement over the given time span, but as a potential improvement – with no account being taken of the distribution of gains or losses over time, whether progressive or regressive onbalance.
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QUAH: “CHAP33” — 2007/1/25 — 14:03 — PAGE 177 — #1