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OAQPS Economic Analysis Resource Document

8.3 Discounting Benefits and Costs

    The manner in which the benefits and costs of a regulatory action are discounted to account for differences in their timing is perhaps the most contentious of all methodological issues in the economic analysis of environmental policy.  The reasons for this are both simple and complex.  The simplicity derives from the fact that the mere mechanics of discounting can have a decisive impact on whether benefit-cost results favor a particular action because environmental regulation often involves costs now and benefits later.  When discounting is used, the future benefits decline in comparison to the present costs.  When a higher discount rate is used, the results are less favorable for the action generating the future benefits.  The complexity derives from the fact that the decision to discount future events involves implicit acceptance of certain political and economic philosophies, and the selection of an appropriate discount rate requires consideration of what some policymakers might perceive as complex economic concepts.  
    With the controversy and complexity of discounting as background, the Journal of Environmental Economics and Management (JEEM) in 1990 devoted an entire issue to the conceptual, empirical, and practical considerations of the discounting issue.  This issue of JEEM helped elucidate many of the issues, but it did not—nor did it intend to—arrive at a set of recommended rules for applying discounting methods in environmental policy evaluation.  In 1996, EPA convened the Economic Consistency Workgroup.  This workgroup commissioned a series of “White Papers” to address a number of methodological issues, including social discounting.  These white papers will provide the basis for the issuance in 1998 of an agencywide guidance document for economic analysis.  The white paper on discounting is an important reference point for the current document.

8 Methodological

 8.0 Intro

 8.1 Specifying the Time
   Period of Analysis

 8.2 Specifying a Baseline
   for Analysis

 8.3 Discounting Benefits
   and Costs

 8.4 Addressing Uncertainty
    Abstracting from these earlier and ongoing assessments of discounting methods, the following discussion addresses discounting considerations in economic analysis of OAQPS regulations.  The issue is addressed by first describing why discounting is necessary to evaluate both private decisions and public policies.  Then, the mechanics of discounting in net present value methods are presented.  The discussion then focuses more specifically on which discount rate is appropriate for annualizing capital costs, and it presents prescriptions other researchers have made for costing methods that are consistent with principles of welfare economics.  Economists have recently defined the openness of capital markets as a key determinant of the aggregate social cost of a policy intervention.  That issue is addressed here both in the context of aggregate social benefit-cost analysis found in EAs and the more narrowly scoped assessment of impacts found in an EIA.  The discussion concludes with a recommendation for capital cost discounting in economic analysis of OAQPS policies.  
  8.3.1    Basic Considerations in Discounting
    Discounting is the process by which the different time streams of benefits and costs of a particular action can be placed on a comparable basis.  Discounting is relevant for private consumption and investment decisions and therefore is relevant, in a somewhat more complicated manner, for public decisions that affect consumption and investment patterns of individuals affected by the decision.  Discounting and Private Decisions
    In this context, private decisions refer to choices made by households and firms that affect the allocation of their own resources over time.  The general premise is that both households and firms are not indifferent to the time pattern of resource allocation.  Both prefer to either consume (households) or receive profits (firms) and income (households) sooner rather than later.  There are two basic models demonstrating time preferences for consumption and investment.
    Consumption.  For ease of presentation, the term household is used synonymously with the individual consumer.  While some models distinguish between individual and group (household) decisions, those distinctions are not addressed here.   
    Households are typically viewed as seeking to maximize their utility over time.  Utility (U) is dependent on the consumption of goods and services (C):
    U = U(C) (8.1)
    More consumption yields higher utility (i.e., MU/MC $ 0).  The need to discount can be evaluated by considering consumption over two time periods.  This evaluation can be extended to more time periods without loss of generality.  The two-period objective function is specified as follows:
    V =U(C0) + U(C1)/(1+p) (8.2)
where V is the present value of the utility gained from consumption in the current (0) and next (1) period and p is the single-period discount rate for consumption.  Generally, p > 0, reflecting the notion that a unit of consumption deferred to the next period is valued less by the household than if the unit were consumed presently.  In this context, p is often referred to as the marginal rate of time preference or the consumption rate of interest.  Therefore, when households evaluate the consequences of an action that alters consumption patterns over time, for instance, by investing (reducing consumption) today to generate future benefits (increased consumption) in the future, they will generally require more consumption in the future to compensate for a given level of foregone consumption today.
    Investment.  Investment is the process of expending funds today to purchase an asset (capital) that generates a stream of future income.  Although asset characteristics differ across households and firms, the underlying concept of an opportunity cost of the investment is relevant across all asset types.  Consider an investment requiring I0 of funds today that returns income of Y1 a year from now.  The net present value (NPV) of this action can be expressed
    Z = Y1/(1+r) – I 0 (8.3)
where Z is the NPV of the investment and r is the single-period discount rate.  Generally, r > 0, reflecting the notion that income received next period is valued less than current income.  This discount factor, r, is conceptually distinct from the consumption rate, p, referenced above, in that it reflects the opportunity cost of capital committed to the investment rather than the disutility of deferring consumption.   The reason to discount future income streams generated by an investment is that committing funds to that particular asset requires foregoing income streams from alternative investments.  The term, r, reflects the rate of return on alternative assets.  Thus, the I0 worth of funds allocated to this investment could generate a return of I0(1+r) next period if  invested elsewhere.  Therefore, the expected income next period, Y1, must be discounted by the factor (1+r) to appropriately value the investment.  Having performed the appropriate discounting, the investment should be undertaken if the NPV, Z, is positive.
    Another way to characterize the situation is in terms of capital’s rental cost.  Investing ties up capital in the ownership of the asset.  By not allowing these funds to flow elsewhere, the capital is “rented” in the form of this particular asset.  Ignoring the issues of asset service life, depreciation, and capital gains, the rental cost of capital is rCI0, also referred to as the annualized cost of capital.
    Summary Point.  The motivation for discounting in private decisions is similar, whether the decisionmakers are households or firms and whether the economic activity is consumption or investment.  In all cases, the future is discounted relative to the present.  Households discount future consumption because they prefer present consumption.  Firms and households discount the future returns from an investment because the capital tied up in the investment could be invested elsewhere.  The mechanics of discounting are essentially the same in both situations, with the  consumption rate of time interest (p) determining the value of consumption streams and the opportunity cost of capital (r) determining the value of investment streams.  However, as discussed below, these two discount rates will, in general, differ.  Therefore, discounting methods must account for these differences.  Discounting and Public Policy Decisions
    While the private decisions just described are driven by the benefits and costs accruing to the individual household or firm making the decision, public policy decisions must account for the benefits and costs accruing to the entire society, empowering the public decisionmakers.  Hence, the term social benefit-cost analysis (SBCA) is used for the types of public decisions faced by EPA.
    Assuming that public policies have the objective of raising society’s welfare, the time preferences of that society are relevant to the benefit-cost criterion for public policy analysis.  As described above, people generally demonstrate a preference for current consumption over future consumption.  Moreover, investing funds in a particular project foregoes an income stream generated by another use.   Therefore, policies that require investment and alter the time pattern of consumption must account for these temporal factors, hence the need to discount in SBCA.
    Economic welfare measures are generally derived from the consumption of goods and services.  As a result, SBCA should be ultimately translated to corresponding effects on society’s consumption patterns over time.  Differences in consumption across time periods can be compared after adjusting for the consumption rate of interest, which is the rate of return at which individuals are willing to trade off current consumption for future consumption.
    At this point, the distinction between the benefits and costs of a regulatory action is important.  The appropriate welfare measure for benefits is the amount that parties are willing to pay to obtain these benefits.  An example might be the amount parties are willing to pay to reduce the population risk of cancer by 0.1 percent.  For all intents and purposes, this can be viewed as a consumption equivalent, and the multiperiod consumption model presented above applies.  Then, benefits that accrue over time can be compared and aggregated using the consumption rate of interest.
    The social cost of a regulatory action is the value of opportunities foregone by allocating resources to the activity.  Society could have otherwise used the funds for current consumption or  invested those funds in other economically productive activities (thereby enhancing future consumption).  Once costs are expressed in consumption equivalents, they can be discounted at the same rate as benefits.  Special discounting issues related to the social opportunity cost of mandated capital expenditures and its connection to the capital cost estimated in an EIA are addressed in more detail below.
    The need to discount in benefit-cost analysis of public policies can be summarized as follows:
    1.    Environmental regulation implicitly aspires to raise social welfare.
    2.    Social welfare, as modeled in economics, is determined by consumption of market and nonmarket goods and services; therefore, the effects of a particular policy or regulation should be transformed to consumption equivalents to evaluate its welfare consequences.
    3.    The evaluation of the social welfare consequences of policies that affect current and future patterns of consumption should account for the fact that individual members of society are generally observed to value current consumption more than future consumption.
    4.    Discounting is the mechanism by which these preferences are imposed on social welfare measures of policy options.
    The two-stage discounting procedure can be used to discount benefits and costs of a regulatory action in a theoretically consistent manner.
  8.3.2    The Two-Stage Discounting Procedure
    The shadow price of capital approach calls for converting all mandated private capital costs to annualized consumption equivalents by using an estimate of the pre-tax private rate of return to generate the annual stream of costs (foregone consumption) ( Kolb and Scheraga, 1990).  This cost stream can then be converted to a present value using the consumption rate of time preference.  The cost value can then be compared to the present value of benefits, which is computed using the consumption rate of time preference exclusively.  This method is applied by using the two-stage discounting method discussed in this section.
     The two-stage discounting procedure uses two different discount rates (see  Scheraga, 1989).  This approach is a variant of the shadow price of capital approach in that capital costs are adjusted upward to reflect the social cost of displaced investment before benefits and costs are discounted at the consumption rate of interest.  The steps involved in the two-stage discounting process are as follows:
    1.    Annualize capital costs over the expected lifetime of the capital equipment using the opportunity cost of capital.  In ISEG, 7 percent is typically used as the opportunity cost of capital (consistent with OMB Circular A-94).  After annualizing capital costs, add annual noncapital costs to annualized capital costs to yield total annual costs.
    2.    Discount the stream of annualized costs at the consumption rate of interest.  In general, this rate will be lower than the opportunity cost of capital.  As described below, 3 percent is commonly used for the consumption rate of interest.  The stream of benefits is also discounted using this rate.
These procedures result in present value cost and benefit estimates that can be directly compared with one another and with other present value estimates.
    To illustrate how the two-stage discounting procedure works, consider the following example. A regulatory option will impose $20 million in capital costs during the first year for equipment that is expected to last 15 years.  In addition, there will be $5 million in annual operating costs, also beginning in the first year.  Benefits of $8 million will be realized each year over the 15-year time period.  The question is whether the $8 million in annual benefits exceed the costs.
Stage 1:  Annualize Costs
    To estimate the present value of the costs of the regulation over the useful life of the capital, it is first necessary to annualize the capital costs, using the opportunity cost of capital.  Annualization is the calculation of the value that, if paid out in equal annual amounts over a specified period and discounted, would be equal to the present value.  Annualization is the calculation of the value x that solves Eq. (8.4).
Eq. (8.4)

    I    =    the present value of the capital investment,
    x    =    the annualized value,
    i     =    the discount rate, and
    n     =    the number of years over which the value is annualized.
Note that the annualized costs are evaluated as if they occur at the end of each year.   The annualized capital cost can be computed by manipulating Eq. (8.4) to solve for x as follows

Eq. (8.5)

In this example, the annualized cost of I = $20 million over n = 15 years at i = 7 percent is approximately $2.2 million.  For purposes of calculating the total annual costs of the regulation, the annualized capital cost of $2.2 million is added to the $5 million in costs incurred each year for a total annual cost of $7.2 million.  
Stage 2:  Compute “Consumption Equivalent” Present Value of Costs and Benefits
    In the second stage, the annual values estimated in the first stage are converted into a present value, using the consumption rate of interest.  This calculation can be performed using  Eq. (8.4), with the following values:  x = $7.2 million (total annual cost), i = 0.03 (the consumption rate of interest), n = 15 years.  The present value of an annual cost of $7.2 million over 15 years at a 3 percent discount rate is $85.9 million.
    To calculate the present value of benefits, the same procedure described above for the second stage of the cost calculation is used.  In this example, the annual benefits are $8 million per year.  The present value of a 15-year annual stream of benefits, using a 3 percent discount rate, is $95.5 million.  This regulatory option would therefore yield positive present value net benefits of $9.6 million ($95.5 million benefits minus $85.9 million costs) over the period of analysis.
    It is important to note that in this example the calculation of present value benefits and costs is not necessary to determine the correct decision.  Once the annualized total costs are estimated, enough information is revealed to determine the annualized net benefits of the regulation.  In cases such as this, in which both benefits and costs can be expressed at a constant rate over the same time period, calculating the present value of net benefits is redundant.  Instead, annual costs (with capital costs annualized using the opportunity cost of capital) can be compared with annual benefits.  If annual benefits exceed annual costs in each year, then the net benefits of the rule will be positive.
    If, however, benefits vary across years or accrue over a time period different from the one in which costs are incurred, the full calculation is necessary to determine whether the net benefit condition is met.  In such cases, the analyst will typically calculate the present values of both the cost and benefit streams.  Alternatively, the present value of the stream of benefits can be calculated and then annualized over the time period in which the costs are imposed to facilitate an annual comparison.
    Regardless of whether costs are expressed on an annualized or present value basis, it is critical that
  • any calculations make proper use of discounting procedures and rates to arrive at the correct annualized or present value, and
  • the same procedures be used to calculate benefits and costs when these values are to be compared.  In other words, if costs are expressed in annualized terms, benefits should be expressed on the same basis.
  8.3.3    Discounting Issues Deserving Further Attention:  Nonmonetized Benefits and Long Time Horizons
    Although reviewing all the economic theory relating to the discounting of benefits is beyond the scope of this economics manual, discounting nonmonetized benefits and benefits accruing to future generations merits some further discussion.
     As mentioned above, EPA guidelines indicate that benefits should be discounted using the rate of time preference.  It is important to note that both quantified and monetized benefits should be discounted.  On conceptual grounds, benefits that are quantified but not monetized can be discounted in the same manner as monetized benefits.  The absence of monetary values simply means that nonmonetized benefits cannot be compared directly to monetized benefits or costs.  However, if  these benefits are quantified by some nonmonetary metric (e.g., adverse health effects avoided) there is no reason, in principle, why future effects should not be discounted relative to present effects.  The underlying premise is that these quantified effects positively affect utility, thereby carrying some (apparently unmeasurable) value society is willing to pay.  Thus, discounting these benefits is no less warranted than discounting monetized benefits.
    Discount rates essentially reflect choices revealed in credit markets by the current generation.  In some instances, however, the benefits of a regulatory action may accrue well into the future (e.g., reducing the threat of catastrophic climate change).  These situations raise unique questions about intergenerational equity.  Because the parties benefitting from such regulations are not yet born, it is not clear whether a market-based rate of time preference adequately incorporates the expected utilities of future generations.
    Analysts disagree whether long time horizon problems merit special consideration.  Some economists and policy analysts argue that benefits accruing to future generations should not be discounted at all.  Others believe that intergenerational concerns can often be addressed by using a social rate of time preference—the rate of time preference modified to reflect intergenerational equity considerations ( EPA, 1997j).  The draft EPA white paper on discounting suggests that when faced with a situation involving intergenerational concerns, the analyst should acknowledge that both sides of this debate have merit and calculate the present value of future benefit streams using both a zero discount rate (not discounting at all) and the rate of time preference (effectively discounting all expected future benefits in the same way) ( Arnold, Sussman, and Deck, 1997).  The analyst should refer to OP’s forthcoming Guidelines for Economic Analysis (referenced in Section 1) for further guidance on discounting methods for long time horizon problems.
  8.3.4    Discount Rates and the Capital Costs of the Regulation
    The basic premise of the two-stage discounting method is that a different rate should be used to annualize the capital costs of a regulation than is used to discount streams of benefits and costs through time.  In EIAs or EAs performed by ISEG, the selection of the rate to annualize costs is at least as important, if not more so, than the rate used to compute present values of the net benefits.  This is particularly true when all costs (and/or benefits) are computed on an annualized basis, as they are with many of the analyses performed in ISEG.  In those cases, the rate used to compute present values is moot, and the only discount rate that matters is the rate used to annualize capital costs.  As a result, the selection of the proper rate to annualize capital costs is of paramount importance in ISEG analyses.  Conceptual Issues
    Government can intervene to achieve public policy objectives in essentially two ways.  One is to use public funds to produce a good or service that the private sector cannot or does not have the incentive to produce (e.g., national defense).  The other is to mandate private expenditures to achieve a public objective.  The importance of distinguishing between public programs and mandated private expenditures relates to the opportunity costs of the funds spent on the activity.  Although much of the discussion surrounding social discount rates draws from examples of public expenditure (see  Lind, 1990), mandated private expenditure is relevant to the discussion of environmental regulation and is the point of departure here.
    Sectoral vs. Economywide Measures of Social Costs.  Before proceeding, important points must be made regarding factors that often complicate the dialogue on costs, economic impacts, and social welfare.  One is the need to distinguish between the social cost measured in the economic sector directly affected by the regulation and the total social cost of a regulation.  Section 5 of this document demonstrates how to estimate social cost-based measures (i.e., producer and consumer surplus) of the regulation in the directly affected industries (markets).  There may be differences between those measures and the “true” social cost due to the indirect effect that changes in the regulated market might have on other sectors of the economy.  This issue has typically been viewed from a pragmatic standpoint.  Except in cases where the direct impacts in one market are extremely large and/or cut across many sectors of the economy (e.g., climate change) it is usually acceptable to ignore the muted indirect impacts in other markets and take the impacts in the directly affected markets as the appropriate measure.  When the impacts are too large to ignore, it may require the use of general equilibrium modeling approaches to capture these impacts ( e.g., Hazilla and Kopp, 1990).  General equilibrium considerations are not addressed in the present discussion.   Instead, the key issues relate to the emerging literature on discount rates (as summarized in the EPA White Paper), namely, that the assumption one has about corresponding effects in the capital market determines the appropriate rate for estimating aggregate social costs.
    This section continues with a discussion of methods for annualizing capital costs in a typical EIA.  The primary objective of an EIA is to estimate the magnitude of a regulation’s cost and the distribution of the burden of those costs among the producers and consumers in a particular regulated industry.  EIAs generally give a first-order approximation of the total social cost of a regulation.  The second part of the discussion considers factors that may impart differences between the social costs estimated in an EIA and the “true” aggregate social costs of a regulation.  Of particular concern is the role that assumptions on the mobility of capital may have on differences between these two estimates.  Because the EIA is often the basis for the cost estimate in a full SBCA required in an EA, the discussion attempts to reconcile the two measures.  This identifies the critical assumptions and parameters determining their difference and allows the analyst or policymaker to choose between methods based on the reasonableness of the underlying assumptions and parameters.  Estimating Capital Costs in Economic Impact Analysis
    The CAA as amended requires that an EIA be performed to estimate the costs of a set of pollution control responsibilities and to determine how those costs are distributed among producers and consumers in the regulated industry.  As part of an EA, the SBCA compares the social costs of a regulation to its social benefits to help policymakers assess whether the regulation is justified under the provisions of EO 12866—Regulatory Planning and Review.  As indicated in Section 2 of this document, EAs (SBCAs) are required only for regulations deemed to be economically significant.  Therefore, while many OAQPS regulations require an EIA, relatively few lead to SBCAs (EAs).  Nonetheless, it is important that EIAs generate information that is transformable to a full SBCA.  Specifically, the EIA should produce an estimate of the social cost of a regulation that is theoretically consistent and therefore comparable to estimates of social benefits, should the comparison be called for in a subsequent SBCA.
    Typically, the EIA is preceded by an analysis that estimates the cost of regulatory compliance for each pollution source subject to the regulation.  The pollution sources in the analysis may constitute a full and exhaustive census of all facilities in the regulated industry or,  more likely, an array of model facilities or some combination of actual and model facilities.  Consistent with the goal of estimating the size and distribution of social costs among different parties affected by the regulation, and given that the distribution of these costs is largely determined by economic behavior, an EIA ideally employs an analytical framework that captures the effect of the control responsibilities in a market setting.  The modeling mechanism for capturing these market effects is discussed in Section 5.
    The firm that is faced with pollution control responsibilities will incur the cost of the required capital equipment.  Operating and maintenance (O&M) costs are ignored here to focus on the capital discounting issue.  The current discussion also ignores the need to periodically replace the capital equipment and simply assumes that the service life of the capital is infinite.  As a consequence, the annualized cost of the capital purchase is rK where K is the purchase price of the compliance capital and r is the firm’s cost of capital.  The cost of capital represents what it must give up (annually) to make this capital purchase.  This is either the foregone opportunity to invest K worth of internal funds in another investment, to distribute K worth of funds to shareholders, or to repay a party for lending it the funds to invest K in pollution control.  In any case, the cost of compliance capital reflects the rate of return the funds can achieve in another use.
    As indicated in Section 5, a market model can be constructed to simulate economic behavior on the part of producers responding to compliance requirements and consumers responding to any corresponding change in price.  As a result, the burden will, in general, be shared by producers and consumers as measured by changes in producer and consumer surplus.  For ease of exposition, the present discussion assumes that the producer absorbs the entire cost of the regulation (i.e., no change in market prices or consumption occur), but the main result can be generalized to cases where the burden is shared with consumers.
    If producers absorb the full cost of a regulation, then their pre-tax profits decline by the amount of the compliance cost.  This is given by

    )A= -rK (8.6)

However, producers pay taxes (T) to the government, based on their level of profits (A)

    T = t C A (8.7)

where t is the tax rate on profits.  Because producer profits decline by the amount of the compliance cost, their taxes fall as well.   As a result the net post-tax loss to the producer is

     ) PS = )A C (1–t) = -rK C (1–t). (8.8)

However, there is also the net loss in tax receipts to the government

     ) GS =  -rK C t. (8.9)

The total welfare loss due to the regulation, as measured in the market for the regulated product, is

     )WF = )PS + ) GS =
     -rK C t  – rK C (1–t) = -rK.

Therefore, pre-tax measures, such as the market rate of return on capital, determine the absolute size of welfare effects, though the distribution is affected by taxes.  This demonstrates the point that the private cost of capital is the appropriate measure for estimating welfare impacts (annualized capital costs) in the regulated market.
    General Conclusion about Discounting Costs in EIAs.  An EIA can and should vary the market assumptions to generate a case between the full-cost pass-through and absorption extremes presented here, wherein the burden is shared between consumers and producers in the affected markets (and taxpayers).  The magnitude of these impacts, however distributed, will still be determined by the producers’ cost of capital.  Thus, the prescription for capital discounting seems clear for EIAs—use the pre-tax rate of return on capital to measure the welfare impacts on the direct parties of interest.  In fact, the EPA White Paper on discounting, which recommends against the use of the pre-tax rate of return on capital for estimating the social cost of a regulation under some circumstances, specifically recommends the use of this rate in the estimation of private-sector economic impacts in all circumstances.  The (potential) difference between economic impacts and social costs is discussed in more detail below.  Reconciling Social Costs in an EIA with “True” Social Costs
    In contrast to the sector-specific emphasis of the EIA, most of the theoretical literature on the discount rate for SBCAs implicitly addresses the issue from a more aggregate (economywide) perspective.  In that context, the cost of a regulation is what society gives up by mandated private expenditures on pollution control.  The sectoral and economywide perspectives are reconciled here and the extent to which they affect selection of the discount rate and calculation of social costs is addressed.
    Capital Market Factors.  Following  Lind (1990) the current literature suggests that selection of the social discount rate depends on which of the following hypotheses about the capital market holds:
  • The supply of capital to the economy is fixed (“closed economy”).
  • The supply of capital to the economy is variable (“open economy”).
Each is discussed in turn below.
    Capital Costs Under the Closed Economy Hypothesis.  Under the closed economy hypothesis, mandated pollution control expenditures, by definition, displace other forms of private investment.  As a result, the social opportunity cost of the mandate is the pre-tax private rate of return of capital (i.e., the value of market goods and services that could have been generated had the displaced private investment occurred).  More to the point of the present discussion, if the fixed capital/closed economy assumption holds, then the estimate of net welfare impacts from an EIA, which derives from the pre-tax rate of return of private capital, is a valid measure of social costs.
    Argument for Lower Capital Cost Under the Open Economy Hypothesis .  The gist of the open economy argument is capital supplied to any one industry is almost perfectly elastic;  therefore, virtually limitless capital can be supplied to that industry without affecting the world price for capital.  Moreover, the effect of environmental regulation’s capital requirements on the U.S. economy, much less any one industry, is small relative to the global supply of capital and all other global capital demands.  Thus, it is seen as unlikely that the global price of capital will change in response to a particular environmental regulation.  Because the capital price does not change, the argument goes, all investments opportunities that would have been taken in the absence of the regulation will still be taken (i.e., no capital is displaced as a result of the regulation).  For now, this is taken to mean that society does not forego investment opportunities to fund pollution control; rather it foregoes consumption.  The consistency of the no-capital-displacement assertion with a model of global capital market equilibrium is addressed in more detail below.  
    If one accepts the notion that a regulation’s capital requirements replace consumption rather than investment, the crucial point is that the opportunity costs of consumption and investment generally differ because of tax distortions in the U.S. and most other market economies.  As discussed above, the opportunity cost of consumption is generally lower than the opportunity cost of capital.  This point is demonstrated by reference to a model of a perfectly functioning, undistorted capital market.  In such a world, the market rate of interest would simultaneously equal both the consumption rate of time preference and the private rate of return of capital.  Any distinction about which discount rate to use would be moot—the market interest rate would serve the purpose.  However, capital markets in most market economies, including the U.S., have a systematic distortion stemming from the fact that capital income is taxed and consumption (for all intents and purposes) is not.  Therefore, capital investments must generate a pre-tax rate of return that is sufficient to satisfy the investor’s willingness to trade consumption, which is purchased with post-tax income, between time periods.  Therefore, in equilibrium, the capital market should produce the following relationship:

Eq. (8.11)

The consumption rate of interest (p) equals the after-tax rate of return on private capital investment (r), which is presented as taxed at the rate, trK.  In short, the price at which individuals trade consumption through time (p) is lower than the rate at which capital generates consumable goods and services (r).  Thus if pollution control expenditures replace consumption, the social costs are lower than if they replace capital investment.
    The gap between the consumption rate of interest and the rate of return of capital has long been recognized and has been the impetus for the shadow price of capital (SPC) approach for discounting costs ( Bradford, 1975).  The SPC view is operationalized into the two-stage discounting procedure described above.  Because it is a common practice in EIAs and SBCAs to express costs on an annualized basis, the critical point is that the pre-tax rate of return of capital should be used to compute the annualized cost.  Thus, the social cost process outlined in the  EIA discussion is entirely consistent with the SPC approach.
    While the SPC view explicitly recognizes the difference between consumption and investment opportunity costs, the two-stage method still follows the implicit assumption that pollution control expenditures displace private capital investment.  That is the premise of stage 1, in which the capital allocated to pollution control is converted to its consumption equivalent, that is, the amount of consumption (income) that could have been generated by a private investment.   However, the open economy adherents would reject the stage 1 adjustment, or at least make it so that the consumption rate of the interest, p, is used in the stage 1 annualized cost assessment, thereby making the entire adjustment process redundant.   In other words, the open economy view holds that no investment is displaced by the regulatory requirement; therefore, no upward adjustment for the opportunity cost of capital is necessary.
    As a practical matter, this suggests that the market adjustment made in the EIA model, which is based on the private capital cost of r, leads to an overstatement of the true social opportunity cost of the regulation if the open economy assumption holds.  Under the limiting case of capital with an infinite service life, the degree of overstatement is roughly given by the ratio of the two discount rates, r/p.  For instance, if the EIA impacts are computed using a market rate of, say, 7 percent and the corresponding consumption rate of interest is 3 percent, EIA social cost impacts would overstate true aggregate social cost impacts by a factor of more than two.  The distortion is reduced when finite capital service lives are considered.
    Reconciling the Difference Between the Open Economy and Closed Economy Measures.  It has thus far been argued that the pre-tax rate of return of capital, r, should generally be used for an EIA and that the consumption rate of interest, p, may be appropriate for estimating aggregate social costs under some circumstances.  Given that this approach will lead to sectoral impacts that exceed social impacts, who in society receives the offsetting gains that are ignored in a typical EIA?
    As demonstrated above, when investable funds are assumed fixed, the losses to the private sector and government (which sum up to the total social cost) equal the private cost of capital.  However, when capital is fully mobile through a global capital market, the argument has been made that no investment has been displaced, only consumption.  From the aggregate welfare perspective, the funds needed for pollution control in Industry X  are reallocated from nontaxed activity (consumption) to a taxed activity (investment).  Therefore, the government receives an increase in tax revenue directly from the new investment activity in the amount of (trK C rK).  Drawing again from the full-cost absorption example, Eqs. (8.9) to (8.10) are restated as follows:
Eq. (8.12), (8.13), and (8.14)
indicating that the after-tax rate of return of capital is the appropriate measure of social costs.  In an efficient capital market, the after-tax rate of return of capital equals the consumption rate of interest (Eq. 8.9).  Therefore, the consumption rate of interest would be used for discounting costs in this case.
    In essence, while taxpayers were shown to bear part of the burden through a loss in profits tax under the closed economy/EIA model, they bear none of the burden in the open economy model.  So regarding the question of who gains in the aggregate social cost computation versus the sectoral impacts computation of social cost?  The taxpayer.
    More on Global Capital Markets and the Implications for Social Cost.  The open economy arguments put forward by Lind (1990) and the EPA white papers on discounting (Arnold, Sussman, and Deck 1997) rely largely on heuristic descriptions of the global capital market and international flows of funds.  To illuminate the displacement issue further, a simple model of a global capital market is put forth here.
    The global supply of capital is a function of the global price of capital (r):

Eq. (8.15), (8.16), (8.17), and (8.18)
Therefore, if the regulation imposes capital requirements that cause Industry X to increase its demand for investable funds, those funds must be supplied by some combination of an increase in global capital supply, displacement of capital invested in Industry X, displacement of capital to other U.S. industries, or displacement of capital to the rest of the world.
    The common interpretation of the open economy hypothesis is that no investment is displaced by the claims on the capital market placed by regulatory capital requirements.  Yet the global capital market equilibrium just described suggests that the capital needed for the expenditure mandated by the regulation must be diverted either from consumption or other capital uses to maintain a global equilibrium.  But if the capital price does not change at all, there is no mechanism by which capital supplies will increase or capital will be diverted from other capital uses to fund the regulated industry’s capital requirements.  
    Perhaps a more correct interpretation of the implications of a global capital market can be stated as follows. The investment requirements for a typical industry-level regulation are so small relative to world capital markets that
  • the effect on the global capital price is indetectable and
  • the displacement of global consumption, U.S. investment, and non-U.S. investment is imperceptibly small, relative to baseline values.
Thus, the notion that the global markets are essentially unaffected by the regulation’s capital requirements would not be far from the truth.  In other words, a regulation requiring $20 million worth of capital expenditures is, no doubt, too small to materially alter the world capital rate or to have a noticeable effect on net global investment.  However, it seems quite a different matter to conclude that the $20 million did not involve the displacement of other capital.  Re-establishment of a global capital market equilibrium suggests that the $20 million must be supplied to Industry X through some combination of displaced consumption and displaced capital in other uses.  Thus, the opportunity costs of the capital allocated to Industry X’s compliance requirements will be a weighted average of the opportunity costs of displaced consumption and investment.   
    The extent to which displaced global consumption and displaced non-U.S. investment—rather than displaced U.S. investment—supplies the capital for Industry X’s regulatory compliance will bring the (U.S.) social opportunity cost closer to the lower-bound (consumption rate) value proposed above.  Again, this is because the regulation causes the substitution of taxed activity (U.S. investment) for nontaxed activity (consumption and non-U.S. investment).  This reduces the burden borne by U.S. taxpayers in terms of reduced profit taxes from Industry X.  Of course, the extent to which it is consumption and non-U.S. investment that is displaced, rather than U.S. investment, is an empirical issue.  Practical Concerns for the Policymaker and Analyst
    The implications of the open economy model and the subsequent reduction in the social cost estimate raise a number of questions that are potentially crucial to the policy assessment.  Two particularly important points are raised here.
  • Is it reasonable to assume that pollution control will not affect other investment opportunities for the regulated industry?
Whether private investment is displaced by pollution control seems, at least, an empirical question worthy of further pursuit, rather than a foregone conclusion by those advocating either the higher or lower discount rate.  Macroeconomic studies of the relationship between government deficits and investment suggest that government deficits do not crowd out private investment (e.g.,  Evans, 1985).  These findings have supported the notion that open global capital markets work to prevent federal deficits from crowding out investment and raising interest rates.  The  Lind (1990) article thus implies that the crowding out effect is not a terribly important consideration in the selection of a social discount rate for public expenditures.   This has sparked the drawing of similar conclusions for the analysis of pollution control requirements and support for the use of the consumption-based discount rate (i), as described above.  However, empirical studies that have looked specifically at mandated pollution control expenditures typically find a relationship between pollution control and other investment.   Viscusi (1983) shows that environmental regulation can reduce productive investment due to the uncertainty it implies for investment returns.   Gray and Shadbegian’s (1997) study of environmental regulation in the pulp and paper industry finds that pollution control expenditures almost fully crowd out “productive” investment.
The degree of friction in the regulated industry’s access to capital markets will largely determine whether investment crowding takes place.  If access to credit markets is constrained for pollution control investments, there is a stronger case that other private investments would be displaced and the opportunity cost would be captured by r, rather than i. These issues may be worth further scrutiny in an EIA if the regulated industry is dominated by small companies with limited debt capacity.
To summarize the point, the potential for fully mobile global capital to mitigate the social costs of public programs is an important theoretical development in the economics literature.  However, the application of this principle to the particular environmental regulation being analyzed should be justified empirically.
  • Even when private investment is not displaced, is it reasonable to assume that tax revenues will be unaffected by pollution control investment?
The exact canceling out of tax effects as implied by Eq. (8.13) is unlikely to occur in practice.  First, the corporate tax rate (t) will generally differ from the tax rate on investment income (trK) for U.S. citizens, which itself may differ from the tax rate on foreign investment income.  Second, the tax effects on regulated producers will be affected by rules governing cost recovery of depreciable assets.  Third, there are state taxes to consider.  Finally, the tax outcome is further complicated by the extent to which the funds used for pollution control capital are provided through debt, equity, or retained earnings.  While it is possible to address some of these tax complications in an EIA, resource limitations will likely make it impractical to quantify the effect of these factors on the selection of a discount rate.
  8.3.5    Empirical Evidence on Discount Rates
    At this point, the reader may be misled to the conclusion that once one resolves the conceptual issues surrounding which discount rate to use (consumption rate or return to capital), the entire discounting problem has been solved.  Unfortunately this is not the case, because complex capital markets generate a wide range of market rates that vary by factors such as the time commitment of funds and the degree of risk of the investment.  As a result, there is no clear consensus about the appropriate rate to use either for the consumption rate of interest or the rate of return of capital.  Some empirical evidence is presented below.  Consumption Rate of Interest
    Market rates of return on relatively risk-free lending (e.g., Treasury bills) are often viewed as the appropriate proxy for the consumption rate of interest.   Lind (1990),  Moore and Viscusi (1990), and  Freeman (1993) all argue for real (inflation-adjusted) rates in the 1 to 4 percent range for the consumption rate of interest.   Lipscomb, Weinstein, and Torrance (1996) recommend a rate of 3 percent as the most reflective of real riskless rates of return.  There is precedence elsewhere in EPA for using a 3 percent rate as representative of the consumption rate of interest ( EPA, 1996).  Rate of Return on Private Capital
    The 7 percent rate recommended by  OMB (1992) is the point of departure for any discussion of private cost of capital in regulatory analysis.  This rate is supposed to reflect the marginal pre-tax rate of return on an average private-sector investment.  The OMB circular also stipulates that “analyses should show the sensitivity of the discounted net present value and other outcomes to variations in the discount rate.  The importance of these alternative calculations will depend on the specific economic characteristics of the program under analysis” [Section 8(b)(2)].  Therefore, there seems to be some leeway to modify the analysis to reflect industry-specific real rates of return that are lower or higher than percent as part of a sensitivity analysis.  For an EIA, knowledge of industry- (and firm-) specific capital cost factors will provide a more accurate analysis of distributional effects.  Moreover, if the flow of capital funds is limited to the point that pollution control is thought to displace other forms of investment within the regulated sector (i.e., the “closed economy” assumption holds), then these foregone rates of return represent the magnitude of the social cost.  Industry-specific rates of return on capital can be obtained from secondary data sources, such as Dun & Bradstreet.
  8.3.6    Discounting Recommendations
    The first, and strongest, recommendation is to use the pre-tax rate of return on private capital investment to discount costs for the typical EIA.  “Typical” means an EIA for a regulation that mandates control responsibilities for a specific industry.  The rationale for this is that the private cost of capital determines the magnitude of these control cost responsibilities and therefore the size of the burden that will be determined by the sum of changes in producer and consumer surplus within the regulated sector, the focal point of an EIA.  The OMB-recommended discount rate (7 percent) is the suggested default value for the real private cost of capital.  If warranted, industry- and firm-specific rates of return can be used to modify this rate via sensitivity analysis.  Also, to the extent that an EIA addresses compliance requirements for the public sector, government borrowing costs should be considered, rather than the private rates.    
    A case has been stated that pollution control requirements in general may not displace other private investment in the U.S. economy.  If so, then the sector-specific social cost estimate from the EIA, which uses the pre-tax rate of return of capital, must be transformed to a (lower) social cost value for SBCA, one based on the consumption rate of interest.  Table 8-1 provides an example for the simplifying case of a regulation whose costs are entirely capital expenditures with an infinite service (i.e., expenditures are annualized into perpetuity).

Table 8-1

The cost estimate is reduced by more than 50 percent.  However, before making this transformation, the analyst should examine the empirical justification for doing so.  Most importantly, does the evidence support the case that investment will not be displaced for the regulation in question?  This may depend on characteristics of the industry and on the nature of the control responsibilities themselves.   It is unlikely that a clear answer will result from this inquiry, so the analyst’s most prudent strategy may be to present benefit-cost results both with and without the social cost transformation outlined above.  This allows the analyst to determine whether the transformation has a decisive impact on the benefit-cost results and if the issue warrants further scrutiny.

2 The white papers and agency guidance document are, at the time of this writing, evolving documents.  Latest versions can be obtained from the Economy and Environment Division of EPA’s Office of Policy (formerly Office of Policy, Planning, and Evaluation).
3  In October 1992, OMB issued a revised version of its Circular A-94, which contains guidance on discounting in regulatory analyses.  OMB’s 1996 economic analysis guidance defers to the 1992 Circular.  EPA’s Office of Policy continues to examine this issue through the development of its new EA guidance document, and changes in EPA’s recommended discounting methods may be forthcoming.
4 The discount rate reflecting the opportunity cost of capital, as specified in OMB Circular A-94, is currently estimated to be 7 percent.  This represents the average of the returns on low-yielding capital investments, such as housing, and the returns on high-yielding investments, such as corporate capital.  OMB’s EA guidance recommends using the opportunity cost of capital for discounting in EAs of regulations ( OMB, 1996).
5 This example is borrowed directly from the document,  Guidance on the Preparation of Economic Analyses in OPPT, Office of Pollution Prevention and Toxics, Economic Analysis and Policy Branch, September 1998c.
6 This is identical to the types of calculations made to determine mortgage payments or car payments.
7 Details on taxation of private capital investments and how that may differ between suppliers and demanders of capital are presented below.
8 This is not inconsistent with the views attributed to Blinder (1985) and stated in Lind (1990, p. S-15) that crowding out (in their case due to deficit financing) is more likely to be small, rather than nonexistent when viewed in the context of global capital markets.
9 Personal and corporate tax rates are probably more similar in the mid-1990s than they have been historically.  Corporate tax rates in 1997 ranged from 15 to 38 percent (IRS Form 1120 instructions), while personal tax rates ranged from 15 to 39.6 percent (IRS Form 1040 instructions).  However the highest personal income tax rates apply only to very high income households ($271,050 in taxable income).  The amount of tax withheld from investment income accruing to foreign entities depends on the status of income tax treaties (or conventions) between the U.S. and the foreign country of interest.  Foreign residents (sometimes limited to citizens) of those countries are often taxed at a reduced rate or are exempt from U.S. income taxes on certain income received from within the U.S. ( IRS, 1998).
10 Refer to Section 5 for a description of the typical industry-level analysis that is the focus of this document.
11 The magnitude of the cost difference is amplified by the infinite life assumption.  If the capital equipment has a useful life of, for example, 15 years, then the annualized cost at 3 percent is only about one-quarter less than the annualized cost at 7 percent.

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