1 All the well-known criteria proposed for evaluating public investment streams embody in one form or another a DPV procedure.1A distinction must be made, however, between(a) the older type of criterion, which simply applies what is thought to be an appropriate discount rate to the stream of benefits (positive or negative) in question, and (b) a newer type of criterion, in which provision is made for the allocation of the resulting benefits of a project as between consumption and further investment and within which category there can be differences between behavioural, institutional and political assumptions.
The differences withinthe (a) category are elucidated ina comparisonof equations (28.1)–(28.4) which follow. Those within the (b) category are basically less controversial and may be represented by equation (28.5) alone. The latter differences, as we shall see, arise only from the degree of elaboration thought to be appropriate, and deserve only passing mention.
2 In order to economize on inessential elaboration of the analysis, the practice common in the literature of ignoring (initially at least) uncertainty in order to focus on a critical part of the logic of investment criteria is followed here.
Although, in general, there may be different rates of time preference for the different groups affected by the project and also different yields on private invest-ment according to risk, an analysis conducted in terms of such generality adds only anelegant complexity to the expositionthat is more likely thannot to obscure the basic outlines of the argument. We shall, therefore, regard the rate of time preference r as a single figure (or weighted average of the rates of time prefer-ence of all groups affected by the project) and the yield ρ also as a single figure (or weighted average of the different rates of returnonsums invested by the project).
If we write PV (B) as a shorthand for the DPV of the stream of all the (net) benefits, B0, B1, B2, . . . , BT, some of which may be negative, and K as the
1 Mishan’s proposed normalization procedure (1967c) is an exception, one that informs this and the following chapter.
QUAH: “CHAP28” — 2007/1/25 — 08:03 — PAGE 154 — #2 initial outlay, then under the older type of criteria (a) we may distinguish four alternatives:
3 Criterion (28.1), the staple of textbook instruction, is superficially plausible enough. If r is rate of time preference, the community is indifferent between receiving the stream of benefits (B) = B1, . . . , BT, and receiving its present value PVr(B). In particular, any project with a benefit stream that meets criterion (28.1) tells us that the present value of that stream of benefits exceeds the value of its initial outlay at time zero and, therefore, introducing the project realizes a potential Pareto improvement.
The rationale for criterion (28.2) is no less plausible. It suggests that, if funds equal to K are to be spent on a public project, the average yield from the project should be no less than the ρ per annum that the sum K could fetch if it were placed in the private investment sector instead. If, over the period, the benefit stream yields onaverage more thanρ, the PVp(B) > K criterionwould be met, and there would be a net gain from adopting the investment project.
Clearly, criterion (28.3) is a generalization of (28.1) and (28.2) extended to cover all the different rs an d ρs in the economy. Since the weights, the ws, are the fractions of K contributed by separable components of the reduced amount of consumption and of the reduced amounts of private investment, the resultant weighted rate of return represents society’s actual opportunity yield per dollar of investing a sum K ina public project. Ingeneral, then, ρ will vary according to whether K is raised by tax finance, loan finance or as a mixture of both. Although (28.3) was originally proposed by Krutilla and Eckstein (1958), it was advanced againby Harberger (1968) inconnectionwith a rise ininterest rates inresponse to government borrowing,2which is supposed to check both private investment
2 Not surprisingly, Chicago School economists favour loan finance of public investments. Others favour tax finance, either on the grounds that it tends to reduce the volume of private investment less than does loan finance (see Musgrave, 1969) or else on the grounds that loan finance entails future tax levies inorder to service the debt.
QUAH: “CHAP28” — 2007/1/25 — 08:03 — PAGE 155 — #3 Critique of DPV criterion (I) 155 and consumption.3 With such a weighted discount rate, Harberger (1968: 308) claimed (erroneously, as we shall see) that the ‘so-called reinvestment problem disappears’.4
This criterionis also opento a more serious reservation. Inessence, it is pre-Keynesian, ignoring as it does the stabilizing effect of ‘liquidity preference’ – the shape of the demand curve to hold the total stock of securities in the economy – on rates of interest. If, therefore, government borrowing for the public project has no effect or a negligible effect on interest rates, there may be no ‘crowding out’ of private investment and no reduction in current savings.
In so far as the economy is close to full employment, any government expen-diture on a public project that is financed by borrowing – by an issue of bonds – must add to aggregate demand in the economy, and is therefore inflationary.5
If, incontrast, there is ample slack inthe economy, the additionto aggregate demand arising from spending a sum K as initial outlay on a public project has no inflationary effect. In such circumstances, the cost of the public project could be negative, as argued in Chapter 13.
We turn finally to the well-known Arrow–Lind paper of 1970, which produced criterion(28.4) as a modificationof the popular criterion(28.2), PVρ(B) > K. We shall accept without criticism their argument that the risks associated with public projects, whendivided among a large populationof taxpayers, are felt by each taxpayer to be negligible compared with the sense of risk apprehended by investors inprivate enterprise. A personcanthenbe supposed to be indifferent betweena rate of return ρ on private investment and the greater certainty of a somewhat lower rate of return q on his money when it is invested instead in a public project – a risk premium equal to (ρ − q) being attributable to the greater risk entailed by investing in the private-investment sector. A potential Pareto improvement may then be realized if funds are removed from private investment, so forgoing yield ρ, and placed instead in a public investment at a yield greater than q. For
3 However, Dreze (1974: 60) asks whether if government borrowing does affect the rate of interest and, if so, whether a higher rate of interest increases current saving. His answer is simply that ‘there undoubtly exist cases where government borrowing does not affect the rate of interest, but is simply offset by rationing of private investment’. Dreze compares his view with that of Arrow (1966), who argues that the divergence between ‘the rate of interest implicit in consumption decisions and any market rate is so great that it must be accepted that savings are largely independent of the latter’ and thengoes onto say that the issue is ‘to decide whether some consumers do react, at least, for some forms of consumption’.
4 Indeed, all formulae that assume a voluntary increase in savings in response to a rise in interest rates are suspect, for, in the absence of a well-functioning capital market – one in which interest rates move freely so as to bring the current flow of savings into equilibrium with the current flow of investment – an additional $1 million saved (although, by definition, entailing a reduction of current consumption by $1 million) may have no effect whatever on the current demand for investment.
5 Equilibrium mechanisms that are invoked by the inflation can act eventually to reduce aggregate consumption and/or investment. But there is no simple theory from which we may deduce reductions in the rate of inflation.
QUAH: “CHAP28” — 2007/1/25 — 08:03 — PAGE 156 — #4 then, everyone who invests in the public project will be made better off by a yield of a little more than q thanby the higher yield ρ from private investment.
Hence, the proposed criterion (28.4), PVq(B) > K, for investments in the public sector.
This proposed criterion (28.4) is, however, no less vulnerable than the other three. Even though we assume that the government is not permitted to undertake any investments comparable with those undertaken in the private sector, adherence to this criterion might deprive the economy of worthwhile investments. If the sum K is raised wholly by taxation, it may involve a reductioninconsumptiononly.
The opportunity rate that is to be forgone on the sum K raised by taxationis then no more than society’s rate of time preference r. It follows that a Pareto criterion would be met if the public project were to yield more than r, as incriterion (28.1).
Insum, although this (28.4) criterionis aninteresting, though controversial variationof the (a) type of criteria, it is – apart from the above criticism – subject to a more fundamental critique along with the other three.
4 We turn briefly to the newer type (b) criterion, which recognizes that more care has to be taken of the reinvestment aspect of the returns on an investment project. Such criteria canbe formulated as
PVr(B) > AK (28.5)
where A is the ratio of the social opportunity costs both of the public project itself and of the actual alternative use of the outlay K. Let us consider these two social opportunity costs.
Marglin’s (1963a) treatment, in his classic article, assumes that the required sum K is raised from tax revenue and that, of every dollar so raised, a fraction θ1comes from an initial reductioninprivate investment with yield ρ, the remaining fraction (1 − θ1) coming from a reduction in current consumption.6Inaddition, θ2is the fractionof each dollar of any returnthat is placed inthe private investment sector.
Under these conditions, an amount K left inthe private sector of the economy would generate a stream of consumption over the future which, when discounted at r, would converge to aK, a being greater than unity.7 This aK is the ‘social opportunity cost’ of a project requiring a nominal outlay of K.
However, the employment now of criterion PVr(B) > aK canbe justified only if the stream of benefits are entirely consumed as they occur. If, instead, the fraction (1 − θ2) of each of the benefits is consumed as it occurs, the remainder being invested in the private sector at ρ, and the returns to these investment components
6 Infact, Marglinproduces three models inthis paper. His third model introduces alternative and less plausible behaviour assumptions, while his first model is little more than a stepping stone to the second model, which is treated above as the Marglinmodel.
7 In order for the infinite stream of consumption thus generated to converge, when discounted at r, to a finite sum, Marglin assumes that θ2p > r.
QUAH: “CHAP28” — 2007/1/25 — 08:03 — PAGE 157 — #5 Critique of DPV criterion (I) 157 treated inthe same way, the consumptionstream so generated canbe discounted at r to a present value of αPVr(B), with ∝ greater thanunity. The corrected criterion αPVr(B) > aK canthenbe writtenas8
PVr(B) > AK A = a
α
Later contributions that explicitly recognized the reinvestment problem pro-duced models which, though interesting in themselves, repropro-duced the same essential features of the Marglin model. Feldstein’s three papers (1964a,b, 1972), for instance, extend the formulation to cover other behavioural and institutional parameters. Bradford’s (1975) paper is of the same family and, though he begins somewhat differently, his results conform to the same basic formula as Mar-glin’s.9 As there is no fundamental novelty of conception in the later papers adopting this approach, remarks onthe Marglinmodel are applicable also to their analyses.
Without doubt, the introduction of the type (b) criteria, which face up to the reinvestment problem, is an important step forward in the art of project evaluation and goes far to remedy the defect inherent in the older DPV formulae. Yet, the insight that inspired the innovation was channelled into the conventional mould.
It is possible, however, to break out of this conventional DPV mould by adopt-ing, instead, a normalization procedure with the singular feature that each of a stream of benefits is compounded forward to a terminal date rather than being discounted backward to the present, a procedure that is illustrated in the following chapter.
8 Ina limiting case, where θ1= θ2= 0, a will equal α, an d PVr(B) > AK becomes equal to PVr> K.
(InBradford’s 1975 model, θ1and θ2are denoted, respectively, as αtand αt+1and, when these are equal, his criterionalso reduces to PVr(B) > K.)
9 Bradford’s (1975) paper, in some ways a development of his earlier paper of 1970, constructs a model which closely resembles that of Marglin. This resemblance is easier to appreciate by comparing Marglin’s equation (8), condensed and cast in discrete form, with Bradford’s equation (15), using a common notation. Marglin’s criterion then appears as
∞
where Btis the tth benefit from the public project, Ktis the tth net outlay, and atis the shadow price of a dollar of the tth net outlay. The discount factor to be applied to Bt, an d Ktis δt. Bradford’s public investment benefit stream is finite (and not infinite as is Marglin’s), and his shadow prices at and αtvary with t. For the special case αt= at, both reduce to the general form PVr(B − K) > 0, which form includes the possibility also of a stream of net outlays.
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