Cost-Benefit Analysis Research Paper

1. Foundations Of Cost–Benefit Analysis

CBA is concerned primarily with efficiency in the allocation of resources. As such, it follows directly from the body of neoclassical economic theory (or resource allocation theory). Yet whereas the main body of neoclassical theory deals with the nature of private decisions by households and firms, CBA focuses on public decisions. It sets forth the requirements for any public decision, or policy, to be efficient; that is, for the policy to contribute to an ‘improvement’ in the allocation of economic resources. CBA seeks to answer the question: will an alteration in the current pattern of resource allocation improve efficiency in the use of national resources? Insofar as CBA is directed at allocative efficiency, it can be viewed as an attempt to replicate for the public sector the decisions that would be made if private markets worked satisfactorily. In private markets, no explicit attention is given to social goals such as equity. Indeed, private markets tend to respond to actual demands and resource constraints, where demand is partly a reflection of the distribution of income, and economists do not generally regard private markets as operating unsatisfactorily simply because they fail to produce goods for people who cannot afford to pay for them. Similarly, the focus of cost–benefit analysis is on allocative efficiency, and implies that public sector decisions should be guided by these same demand (not desire) and resource cost considerations. It is presumed that if there are concerns about the acceptability of the income distribution that gives rise to the pattern of demands, or to the impact of the policy’s benefits and costs on the income distribution, these concerns will be taken into account through other policies with explicitly redistributive goals.

As with the neoclassical theory that guides market analysis, CBA rests on the analytical underpinnings of modern welfare economics. Modern welfare economics shares the utilitarian presumption that aggregating the wellbeing (utilities) of the individuals who make up society is a valid measure of social wellbeing. CBA provides a basis for inferring changes in utilities, which are unobservable, from economic choices and outcomes, which are observable. These outcomes, especially if they are revealed in markets, express the value of changes in utilities in terms of a money metric. At one level, then, CBA can be thought of as the accounting protocol of welfare economics for measuring in terms of a money metric the changes in utilities caused by changes in public policy.

The principle of Pareto efficiency lies at the heart of welfare economics. An allocation of goods is Pareto-efficient if there exist no alternative allocations that make at least someone better off without making anyone else worse off. The intuitive appeal of Pareto efficiency is obvious: one would have to be malevolent to oppose a reallocation that betters the situation of someone without harming anyone else.

Although the Pareto criterion seems unobjectionable as a basis for judging the relative desirability of public policies, it would be largely useless as the basis for choice because policies without some losers are extremely rare in the real world. This limitation of the Pareto criterion prompted efforts to develop a normative welfare criterion with more general applicability to actual decisions. A more serviceable criterion for CBA arose out of proposals by Nicholas Kaldor and J. R. Hicks: a change in the allocation of resources should be regarded as increasing welfare if either the Pareto criterion is met or the persons who have gained by the reallocation could compensate those who have been harmed by it so as to leave everyone at least as well off as they would have been without the reallocation. Any resource allocation that meets this criterion is said to be a ‘potential Pareto improvement.’ This criterion expands the set of situations and policies about which statements may be made as to whether economic welfare has been increased, decreased, or left unchanged.

In resting on this criterion, CBA becomes an accounting protocol that enables the analyst to determine whether a reallocation has the potential to be Pareto improving. As a decision rule, this criterion seeks the greatest potential Pareto improvement by choosing projects that maximize the excess of social benefits over social costs.

CBA gained a distinct identity in the 1930s as a formal technique for systematically measuring benefits and costs of flood control projects sponsored by the US federal government (for an overview, see Steiner 1974). As the scope of governments grew, and economists gained influence as policy analysts, the use of CBA expanded well beyond the evaluation of public works projects. In the USA, for example, Executive Order 12291 (February 17, 1981) requires that federal regulatory agencies subject proposed regulations with estimated costs of over $100 million to CBA. Continuing advances in empirical research methods further expand its range of application. Natural resource economists, for instance, use survey methods to estimate benefits necessary for applying CBA to environmental policies.

2. Social Benefits And Costs: Concepts And Measurement

2.1 The With Without Principle Of Evaluation

The evaluation of public projects in terms of the potential Pareto improvement principle requires that analysts determine if the value of the output in the economy with the proposed project would be greater than the value of the economy’s output without the project. Note that this comparison must be made ex ante (based on the prediction of results). It therefore requires the prediction of the future under two scenarios: one with the project and one without it. This with without principle is important for defining and measuring both social benefits and social costs.

Although CBA is forward looking, its application often requires analysts to draw on past experience as a basis for prediction. In such cases, the outcome of a similar policy previously implemented is observed but the counterfactual—what would have occurred with-out it—is not. Analysts must infer the counterfactual in order to make the with without comparison. For example, in order to assess the social costs and benefits of an existing irrigation project, analysts must infer the value of crops and environmental quality that would have been produced without the project for comparison with those observed to occur with it. This ex post CBA (based on actual results) could then be used as an empirical basis for predicting the social costs and benefits for an ex ante CBA of a proposed irrigation project with similar features.

2.2 A Comprehensive Framework: Standing

Costs and benefits in CBA derive from the preferences of the individuals who make up society. But what defines society? And are all preferences legitimate? These questions have come to be known as issues of ‘standing’ (Whittington and MacRae 1986). Recognizing that the citizens of a country share a common constitution, which sets out values and rules for making collective choices, and participate in the same national economy, most analysts define society at the national level. The evaluation of social benefits andu social costs requires that the protocol for the analysis be a comprehensive one in which all of the adverse and beneficial effects of the policy are tabulated, regardless of who in the society is harmed or helped by them. It follows that all effects accruing to national citizens (or perhaps residents) be counted.

Comprehensively taking account of effects accruing to all those with standing means that CBA differs from financial analysis. Considering only the revenue flows to government agencies is generally inadequate be-cause it does not take account of all the impacts of policies on citizens. It also means that analysts working for sub-national governments should resist pressures to ignore national costs and benefits that accrue outside of their jurisdictions. For example, a city may view a grant from the central government as only a benefit, while from the social perspective it involves an offsetting national cost.

An accounting that accepted all preferences as legitimate would be too broad. For example, most observers would not view the pleasure that psycho-paths get from physically assaulting people as an appropriate part of the utilitarian calculus. Where to draw the line between legitimate and illegitimate preferences, however, is sometimes difficult. One approach is to rely on the existing legal framework for guidance (Zerbe 1998), yet doing so assumes that existing laws are moral.

2.3 The Concept Of Social Benefits: Willingness To Pay

The fundamental concept for guiding the measurement of social benefits is the aggregate willingness to pay of those with standing for the impacts of a policy. The analyst wishes to know the maximum amounts individuals would be willing to pay for policy impacts that they view as beneficial, and the minimum amounts individuals would be willing to accept as compensation for policy impacts that they view as harmful. In other words, the analyst would like to know how much each individual’s wealth would have to be adjusted in conjunction with the policy change so that the individual’s utility remained unchanged. The algebraic sum of these wealth adjustments for all individuals measures the social value of the impacts of the policy in terms of dollars. Although some theoretical caveats apply (Blackorby and Donaldson 1985), policies with larger positive sums have larger social benefits.

Note that the amounts that people are willing to pay to obtain a policy’s impacts depends on their levels of wealth. For example, provision of a public good, such as improved environmental quality, may convey the same physical effect on all people. However, people with more wealth would be willing to pay more for this benefit than those who are poorer. An obvious implication of the dependence of individuals’ willing-ness to pay on their levels of wealth is that the aggregate willingness of a society to pay for a policy impact depends on the distribution of wealth among its members. Thus, the social benefits used in CBA are contingent upon the particular distribution of wealth that exists in the society.

2.4 Categories Of Social Benefits: Active And Passive Use

The impacts of public policies can be divided into two broad categories. In the first category are impacts that change observable behaviors of individuals. These behavioral changes are labeled ‘active use.’ For ex-ample, preserving a wilderness area may facilitate birdwatching, an observable behavior. Any such behavior provides at least the possibility of making an inference about willingness to pay through its observation.

Many policies also produce impacts that are valued by people without changing observable behaviors. The realization of these values is labeled ‘passive use.’ Analysts have found it useful to identify three distinct categories of passive use.

First, a policy may have an ‘option value’ (Weisbrod 1964). People may value a good because they anticipate the possibility of using it in the future. Only when they actually use it, if ever, will their behavior be observable. For example, a person may be willing to pay something now to preserve a national park in Alaska with the hope of visiting it someday. The person’s circumstances, however, may never allow the visit to be made.

Second, a policy may have ‘existence value’ (Krutilla 1967). People may value a good even if they never anticipate actively using it. For example, a person may be willing to pay to preserve a wildlife habitat that would be completely closed to the public. One motivation for the willingness to pay may be a belief in the intrinsic value of the natural order. Another motivation may be altruism: a desire to make the good available either to the current generation, or to bequeath it to future generations.

Third, a policy may have a ‘donor value’ (Hochman and Rodgers 1969). People may be willing to pay something for a policy that distributes goods in a way they view as desirable. The motivation may be altruistic, say in providing more to those who otherwise would be consuming less. It may also be motivated by values of equality or fairness. The inclusion of donor values integrates individual preferences over the distribution of wealth into the efficiency framework, broadening it substantially from a normative perspective. While some studies have attempted to attach explicit weights to benefits and costs depending on the characteristics of who bears them, most analysts suggest an alternative approach—namely that the distributional consequences of a proposed resource reallocation be displayed as a supplement to the cost–benefit calculation based purely on efficiency. Such a display enables decision-makers to perceive fully the distributive implications of the proposals being discussed.

2.5 The Measurement Of Social Benefits

How can willingness to pay be measured? It would be ideal if analysts could elicit willingness-to-pay amounts directly from individuals through structured conversations. If securing this information from all citizens were too costly or impossible, surveys of population samples could be used as the basis for estimating aggregate willingness to pay for the population. This approach, called ‘contingent valuation,’ is conceptually attractive because it potentially allows the analyst to elicit a willingness-to-pay amount for impacts that involve both active and passive use.

The use of contingent valuation to measure willing-ness to pay has become increasingly common, especially in the evaluation of environmental policies (Bateman and Willis 2000). A blue ribbon panel convened by the US National Oceanic and Atmospheric Administration concluded that contingent valuation could be a reasonable basis for estimating passive use values in natural resource damage assessment (Arrow et al. 1993).

Nevertheless, the use of contingent valuation re-mains controversial. One source of concern is the cognitive demands that it places on respondents in terms of understanding the policy being valued. Unless respondents understand what is being valued, and believe their answers to be consequential in influencing the policy choice, they cannot be expected to give meaningful answers to serve as the basis for an inference about the willingness to pay of the entire population. Considerable research, mainly by environmental economists, is contributing to the craft of designing effective questionnaires for contingent valuation. Another source of concern is the fear that respondents will answer strategically in the sense of giving false answers that they believe will lead to a better outcome for themselves than would result from truthful answers. Both theory and evidence suggest that giving respondents referendum-type questions about public goods minimizes the dangers of strategic responses. That is, rather than directly asking a respondent to state her willingness to pay, she is given a random dollar amount and asked if she would vote for the policy if it would cost her that amount in higher taxes or increased costs for other goods. An estimate of mean or median willingness to pay for the sampled population can be inferred statistically from sample responses.

The conceptual and practical problems in conducting contingent valuations commonly lead analysts to estimate willingness-to-pay amounts through inferences from observation of the behavior of individuals, especially in markets. Demand analysis plays an especially important role in such estimation. A per-son’s demand schedule for a good tells how much of a good the person wishes to purchase as a function of the price of the good, holding all other prices and the person’s utility constant. The height of the demand schedule at each level of consumption gives the person’s willingness to pay for an additional unit of consumption. The difference between the willingness to pay for this unit and the amount that the consumer actually pays is its ‘consumer surplus.’ Adding up the surpluses for each of the units consumed gives the total consumer surplus that accrues to the person from participation in the market or experiencing services produced by the public sector.

If a policy measure either satisfies a demand that has not been met, or changes the price of a good or service that a person is already consuming, the consumer surplus of the person will be changed. This change is the person’s willingness to pay for the impact of the policy measure. (Graphically, the consumer surplus is the area under the demand schedule but above the market price from zero units to the number of units actually purchased.) If the good or service produced by the public sector is a private good, in that it does not generate external, or spillover, costs or benefits, then the market demand schedule for the good (that is, the horizontal sum of all the individuals’ demand schedules) provides the basis for estimating changes in consumer surplus, and hence changes in the aggregate willingness to pay of individuals for the effects of the policy.

The market demand schedule must be estimated from observed price and quantity data. The standard econometric procedures result in the direct estimation not of the demand schedule described above, which holds the utilities of individuals constant (the Hicksian or compensated demand schedule), but of one that holds their incomes constant (the Marshallian or market demand schedule). Quite often these demand schedules are sufficiently similar so that measuring consumer surplus in terms of the market demand schedules provides good approximations of the aggregate of individuals’ willingness-to-pay amounts (Willig 1976).

Estimation of willingness to pay is more difficult when policy impacts do not correspond to changes in markets for traded goods. For example, though most people would be willing to pay positive amounts for improvements in environmental quality, there is no market for this public good. People may convey information about their willingness to pay for changes in environmental quality, however, by their action in other markets. So, for instance, housing values may change to reflect changes in levels of noise pollution near airports, thereby providing a so-called ‘shadow’ price for quiet. In general, shadow prices refer to inferences of marginal social value when it is not revealed through market prices.

This approach is based on what is called the ‘hedonic price model,’ which provides a theoretical basis for statistically isolating the independent effects of the various characteristics of a product on price. It has been used extensively to estimate the benefits of air quality improvements and health risk reductions from wage and housing value variation. An important use of the hedonic price model in CBA has been to estimate the ‘value of life,’ defined as the amount that people are willing to pay for reductions in the risks of death that they face (see Viscusi 1993). Analysts can take advantage of prior research to find estimates of relevant shadow prices (Boardman et al. 1997). For example, a large number of studies conducted across a number of countries suggest that commuters value reductions in their travel times at between 40 and 50 percent of their after-tax wage rate (Waters 1996).

2.6 The Concept Of Social Costs: Opportunity Costs

The implementation of policies usually requires the use of economic inputs that could be used to produce other things. CBA uses the concept of ‘opportunity cost’ to value these particular policy impacts. The opportunity cost of an input is the value of the goods and services that the input would have produced in its best alternative use. This value is just the willingness to pay for these goods and services on the part of those who would have consumed them if they had been produced.

Opportunity cost may or may not correspond to the accounting cost of inputs used to implement policies. If purchasing the input in a competitive market does not alter the price in the market, then opportunity cost and accounting cost are identical. For example, buying books for a local reading project is unlikely to affect prices so that the purchase cost of the books represents their opportunity cost. If purchasing the input in a competitive market increases the market price, then opportunity cost will be less than the accounting cost based on the post-purchase price. For example, buying concrete for a dam in a local market may drive up the price of concrete, as the marginal costs of producing concrete increase. However, some of the payments at the higher price will be to more efficient suppliers with lower marginal costs. These payments in excess of marginal costs, called ‘rents,’ are simply transfers from the project budget to the efficient suppliers and therefore do not contribute to opportunity cost. The opportunity cost of inputs purchased in noncompetitive markets may be larger, smaller, or equal to their accounting cost. For example, the opportunity cost of the time of people compelled to serve on juries may be larger or smaller than the legally set payments they receive from the court.

2.7 The Measurement Of Social Costs

The problems encountered in measuring social opportunity costs are very similar to those confronted in measuring social benefits. A commonly encountered problem in CBA is the measurement of the opportunity cost of unemployed labor. The conceptually correct measure is the value of the forgone leisure to each worker. The accounting cost of the project is certainly an overestimation of the opportunity cost of otherwise unemployed labor. Alternatively, zero is probably an underestimation of the opportunity cost. Rarely do analysts have enough information about the value of the forgone leisure to estimate the conceptually correct opportunity cost for unemployed labor so they usually use some fraction of accounting cost as an approximation (Haveman and Krutilla 1968).

Another commonly encountered problem in CBA is the appropriate measurement of the opportunity cost of government revenues. Standard practice is to treat a dollar of accounting cost raised through taxation as the equivalent of a dollar of opportunity cost. Raising revenue through taxes, however, usually involves inefficiencies, or ‘deadweight losses,’ that reduce social welfare. The amount by which the social cost of a dollar of tax revenue exceeds its nominal value is called its excess marginal burden. Expenditures funded by tax increases, and revenues allowing tax reductions, should be adjusted by the marginal excess burden of the relevant tax. A number of estimates of marginal excess burden have been made for various components of the US tax system (Jorgenson and Yun 1990).

An appropriate accounting of opportunity costs helps clarify when the inclusion of so-called secondary benefits is correct (Haveman and Weisbrod 1975). The primary benefits of a project derive from its direct effects. For example, the primary benefit of stocking a lake with game fish is to increase the supply of fishing days. The improved fishing might very well have secondary effects, such as the construction of a nearby hotel. It is usually incorrect to attribute any benefits to the secondary effects because they involve offsetting opportunity costs—the hotel requires resources that could have been used to build it elsewhere. Such secondary effects may involve benefits, however, if they use otherwise unemployed resources such as labor. In such cases, the benefits produced may not be fully offset by opportunity costs. A final point on opportunity cost: resources already expended have zero opportunity cost if they are no longer available for other uses. These previously expended resources are known as ‘sunk costs.’ Because it is forward looking, CBA ignores sunk costs.

3. Timing Of Costs And Benefits: Discounting

The social benefits and costs generated by a public program often extend over long periods. Because waiting is costly, the amount that people value a dollar of benefits or costs in the future is less than if that value were obtained in the present. In an ideal economy, markets for lending and borrowing funds (also known as capital markets) balance the preferences of lenders who require a payment for giving up use of their funds (hence, delaying consumption) and the preferences of borrowers who invest in projects with future payoffs. In this situation, the market interest rate that is the outcome of this balancing serves as the basis for adjusting costs and benefits occurring in the future to make them commensurate with costs and benefits occurring in the present. This adjustment for time is called discounting. In particular, if r is the annual market interest rate, then a dollar of cost or benefit that will be realized after N years in the future would have a present value of 1/(1+ r)^N . Maximizing the present value of net benefits would maximize potential Pareto efficiency.

This simple solution results if capital markets are competitive and not restricted or distorted, for example because of taxes on savings (consumption) or on the returns from investment. When such distortions exist, the solution becomes more complicated. Such taxes insert wedges between the marginal valuation of funds by lenders and borrowers. With such wedges, it is not clear which of the values is appropriate for discounting: the before-tax rate of return of borrowers who invest (the marginal rate of return on private investment), or the after-tax return faced by lenders (the marginal rate of pure time preference). Another distortion is general price inflation. Market interest rates reflect expectations about inflation. They correspond to projections of costs and benefits in inflated (nominal) dollars. When costs and benefits are projected in terms of current (real) dollars, typically the most convenient method, nominal discount rates must be converted to real discount rates.

Although some controversy remains, most analysts do seem to agree that the social discount rate should reflect the fact that both consumption and investment are foregone when the public sector uses resources. Thinking of the discounting problem in terms of shadow price of capital provides a way of taking account of these effects (Bradford 1975, Boardman and Greenberg 1998). It involves using the marginal rate of return on private investment to convert any foregone investment to the stream of future consumption that it would have produced. The consumption equivalents of foregone investment are then added to any foregone consumption to express all resource costs in terms of consumption, which can then be appropriately discounted using the marginal rate of social time preference.

4. Accounting For Uncertainty

As CBA involves prediction, it can rarely be done with certainty. The standard approach to dealing with uncertainty is to estimate expected net benefits. The first step is to convert the problem from one of uncertainty to one of risk by assuming a plausible distribution of benefits. The second step involves finding the expected value, basically the weighted average, over this distribution. Third, society is assumed to be risk-neutral, so that the expected values can be treated as commensurate with certain values. For example, a project with certain opportunity costs of $15 million and a 20 percent chance of yielding $5 million in benefits and an 80 percent chance of yielding $20 million in benefits would have expected benefits of $17 million and expected net benefits of $2 million.

The calculation of expected net benefits, however, does not fully take account of individual preferences for risk. Individuals may not be willing to trade certain amounts for expected values of the same magnitude. In such cases, the appropriate measure of benefits is ‘option price,’ the individual’s willingness to pay for the particular distribution of outcomes associated with a policy (Graham 1981). As individuals are generally risk averse, policies that reduce risk generally have option prices larger than expected benefits. The difference, ‘option value,’ is a premium individuals are willing to pay for the reduced risk. As option price can only be elicited through contingent valuation surveys, it is rarely estimated. Unfortunately, relatively little progress has been made in the theoretical determination of the magnitude or even sign of option value. For policies involving substantial risks, especially if the risks are social in the sense that everyone realizes the same outcome, the use of expected benefits may introduce substantial error into CBA. Even when the policy being evaluated is not inherently risky, analysts may be uncertain about their predictions of its costs and benefits. It is common, therefore, for analysts to test how sensitive their estimates of costs and benefits are to particular assumptions. This process, called ‘sensitivity analysis,’ typically involves changing the assumed values of a few key parameters to see how net benefits change.

5. The Maximum Net Benefits Rule

Assuming that all of the costs and benefits of a policy have been correctly measured, discounted, adjusted for uncertainty, and aggregated, positive net benefits indicate that the policy is potentially Pareto improving: the excess of benefits over costs would permit the policy to be implemented in conjunction with a set of compensatory transfers such that at least someone would be better off without anyone being worse off. Thus selecting policies on the basis of positive net benefits, the Kaldor-Hicks criterion discussed above, guarantees that adopted policies are potentially, but not necessarily actually, Pareto-improving.

The rule can be stated as follows: choose from among all possible policies those that offer the largest sum of net benefits. In the special case of mutually exclusive policies, the one with the largest net benefits should be selected. In the special case of completely independent policies, all those with positive net benefits should be selected. Note that this rule says nothing about a benefit–cost ratio, which is a common calculation made by CBA analysts. The use of a benefit– cost ratio criterion is appropriate only if the policies are independent of each other, in which case the set of projects with benefit–cost ratios greater than one corresponds to the rule of adopting policies with positive net benefits.

6. Further Reading

A number of textbook-length treatments of CBA are available for those wishing to explore it in much more depth (Boardman et al. 2001; Dinwiddy and Teal 1996, Zerbe and Divily 1994, Gramlich 1990, Sugden and Williams 1978).

Bibliography:

1. Arrow K, Solow R, Portney P, Leamer E, Radner R, Schuman H 1993 Report of the NOAA Panel on contingent valuation. Federal Register 58: 4601–14
2. Bateman I J, Willis K G (eds.) 2000 Valuing Environmental PBibliography: Theory and Practice of the Contingent Valuation Method in the US, EC, and De eloping Countries. Oxford University Press, Oxford, UK
3. Blackorby C, Donaldson D 1985 Consumers’ surpluses and consistent cost–benefit tests. Social Choice and Welfare 1: 251–62
4. Boardman A E, Greenberg D H 1998 Discounting and the social discount rate. In: Thompson F, Green M T (eds.) Handbook of Public Finance. Marcel Dekker, New York
5. Boardman A E, Greenberg D H, Vining A R, Weimer D L 2001 Cost–Benefit Analysis: Concepts and Practice. Prentice-Hall, Upper Saddle River, NJ
6. Boardman A E, Greenberg D H, Vining A R, Weimer D L 1997 Plug-in shadow price estimates for policy analysis. Annals of Regional Science 31: 299–324
7. Bradford D F 1975 Constraints on government investment opportunities and the choice of discount rate. American Economic Review 65: 887–99
8. Dinwiddy C, Teal F 1996 Principles of Cost–Benefit Analysis for De eloping Countries. Cambridge University Press, New York
9. Graham D A 1981 Cost–benefit analysis under uncertainty. American Economic Review 71: 715–25
10. Gramlich E M 1990 A Guide to Benefit–Cost Analysis. Prentice Hall, Upper Saddle River, NJ
11. Haveman R H, Krutilla J V 1968 Unemployment, Idle Capacity, and the Evaluation of Public Expenditures. Johns Hopkins University Press, Baltimore, MD
12. Haveman R H, Weisbrod B A 1975 Defining benefits of public programs: some guidance for policy analysts. Policy Analysis 1: 169–96
13. Hochman H M, Rodgers J D 1969 Pareto optimal redistribution. American Economic Review 59: 542–57
14. Jorgenson D W, Yun K Y 1990 Tax reform and US economic growth. Journal of Political Economy 98: S151–93
15. Krutilla J V 1967 Conservation reconsidered. American Economic Review 57: 777–86
16. Steiner P O 1974 Public expenditure budgeting. In: Blinder A S, Solow R M, Break G F, Steiner P O, Netzer D (eds.) The Economics of Public Finance. Brookings Institute, Washington, DC
17. Sugden R, Williams A H 1978 The Principles of Practical Cost–Benefit Analysis. Oxford University Press, New York
18. Viscusi W K 1993 The value of risks to life and health. Journal of Economic Literature 31: 1912–46
19. Waters W G 1996 Values of travel time savings in road transport project evaluation. In: Hensher D et al. (ed.) World Transport Research. Elsevier, New York, Vol. 3
20. Weisbrod B 1964 Collective consumption services of individual consumption goods. Quarterly Journal of Economics 78: 71–7
21. Whittington D, MacRae D 1986 The issue of standing in cost–benefit analysis. Journal of Policy Analysis and Management 5: 665–82
22. Willig R D 1976 Consumer’s surplus without apology. American Economic Review 66: 589–97
23. Zerbe R O 1998 Is cost–benefit analysis legal? Three rules. Journal of Policy Analysis and Management 17(419): 56
24. Zerbe R O, Divily D D 1994 Benefit–Cost Analysis in Theory and Practice. HarperCollins, New York