Public Finance, 2nd Edition

24

THE RATE OF DISCOUNT FOR

PUBLIC INVESTMENTS

THREE FACTORS RELEVANT TO PRESENT

VALUE CALCULATIONS

The Opportunity Cost of Public Funds

Reinvestment of Project BeneWts

The Social Rate of Time Preference

THEORETICAL CONSIDERATIONS FROM NORMATIVE PUBLIC

EXPENDITURE AND TAX THEORY

The First-Best Environment

The Second-Best Environment

THE BRADFORD MODEL OF THE PUBLIC SECTOR RATE

OF DISCOUNT

One-Period Government Investments

n-Period Government Investments

OTHER VIEWS ON THE APPROPRIATE RATE OF DISCOUNT

Marglin±Feldstein: The Social Rate of Time Preference

Harberger and Sjaastad±Wisecarver: The Opportunity Cost of Funds

Conclusion

EMPIRICAL EVIDENCE ON THE PUBLIC RATE OF DISCOUNT

What Do the Experts Say?

Discounting Within the Federal Government

Concluding Observations

What rate of discount should the government use for computing

the present values of various investment alternatives? As indicated in

Chapter 23, this question has stirred considerable debate among public

sector economists, one which goes far beyond attaching a particular numer-

ical value to the public rate of discount. There is a fundamental conceptual

disagreement over exactly what the public discount rate is meant to re-

present.

731

Roughly speaking, the division within the profession is threefold. One

group, following Arnold Harberger,

1

believes that the rate of discount for

public projects ought to reXect the opportunity cost of public funds, much as

the discount rate for private investments measures the opportunity cost of

capital to the Wrm. A second group, following Stephen Marglin and Martin

Feldstein,

2

argues that the discount rate, per se, has nothing whatsoever to do

with opportunity cost. It simply reXects society's rate of time preference, the

social marginal rate of substitution between the present and future. The

opportunity cost of public funds is relevant, but is properly accounted for

by means of a separate shadow price applied directly to these funds. It is not

relevant for discounting a future stream of net beneWts. A Wnal group remains

eclectic (e.g., Peter Diamond, Roland McKean),

3

arguing that it is pointless to

associate the rate of discount with any one concept such as opportunity cost

or time preference. Rather, the rate of discount is simply one shadow price

among many in a second-best environment that depends, as do all shadow

prices, on the structure of that environment. Under some assumptions, the

appropriate discount rate will appear to represent the opportunity cost of

public funds; under diVerent assumptions, society's rate of time preference.

Yet it is always possible to describe reasonable assumptions under which there

is no obvious relationship between the discount rate and either concept.

The eclectic view is unassailable on strictly theoretical grounds. The

public rate of discount is determined by equations such as Eqs. (22.46) or

(22.88), appropriately modiWed to have an intertemporal interpretation. But

it bears reemphasizing that most issues in cost±beneWt analysis cannot be

decided by appealing strictly to theory. Ultimately governments must chose

some rate of discount to apply consistently to all projects. Proponents in each

of the Wrst two groups would undoubtedly concede the theoretical point

that the appropriate rate of discount is model sensitive. Nonetheless, they

argue that their principles oVer reasonable and practical guidelines for real-

world policy evaluation. In contrast, attempts to estimate equations such

as Eqs. (22.46) and (22.88) are bound to be loaded with assumptions, to be

highly subjective, and unlikely to produce a consensus public rate of dis-

count.

Despite their diVerences of opinion, virtually all public sector economists

agree that the present value of government projects depends crucially upon

732 THE RATE OF DISCOUNT FOR PUBLIC INVESTMENTS

1

A. Harberger, Project Evaluation: Collected Papers, Markham Publishing Chicago, 1974.

See also ``The Opportunity Costs of Public Investment Financed by Borrowing,'' in R. Layard,

Ed., Cost-BeneWt Analysis, Penguin Education, Penguin Books, Ltd., Harmondsworth, Middle-

sex, England, 1972.

2

M. Feldstein, ``The Inadequacy of Weighted Discount Rates,'' in R. Layard Ed., Cost±

BeneWt Analysis; S. Marglin, ``The Opportunity Costs of Public Investment,'' Quarterly Journal

of Economics, May 1963.

3

P. Diamond, ``The Opportunity Costs of Public Investment: Comment,'' Quarterly Journal

of Economics, November 1968; R. McKean, ``Tax Wedges and Cost±BeneWt Analysis,'' Journal of

Public Economics, February 1974.