Abstract

For more than 20 years, economists have converted annual losses from injuries to natural resources caused by oil spills or hazardous-substance releases into their present-value equivalents using a 3% real discount rate. A 1999 technical paper from the National Oceanic and Atmospheric Administration provided three data series from 1981 through 1998 supporting a 3% real discount rate. However, data series for 1981 through 2016, which provide a proxy for the social rate of time preference for consumption by the public, support a lower discount rate. Furthermore, recent conceptual developments imply a lower discount rate for environmental services than for produced goods and services. We present several lines of evidence that support a real discount rate of not more than 2% for assessing intragenerational natural resource damages.

Federal and state agencies, as well as Indian tribes, acting on behalf of the public as natural resource trustees can pursue damages for injuries to natural resources resulting from oil spills and hazardous substance releases under the Oil Pollution Act (OPA) and the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), respectively. Compensation for natural resource injuries is based on the present value of losses experienced by the public over time (Desvousges, Gard, Michael, & Chance, 2018; Dunford, Ginn, & Desvousges, 2004). Consequently, a discount rate is needed to convert annual losses into their present-value equivalents.

After providing more background on the process for assessing natural resource damages (NRD), we explore the conceptual, institutional, and empirical bases for the appropriate discount rate for NRD purposes. We focus on the intragenerational discount rate, since most NRD assessments involve injuries within the lifetime of the current generation.

NRD assessment

In general, natural resource injuries can result in two types of losses incurred by the public: ecological service losses and human-use service losses. The former refers to losses of physical, chemical, or biological functions of habitat, fish, birds, and other natural resources. The latter refers to losses of active or passive uses of natural resources by the public, including fishing, boating, wildlife viewing, swimming, and beach use.

The goal of the NRD assessment process is to compensate the public for the service losses caused by an oil spill or a hazardous-substance release (Dunford et al., 2004). For ecological service losses, the compensation is usually based on the cost of one or more restoration projects that are expected to provide ecological service gains over time that will equal or exceed the ecological service losses caused by the spill or release (Desvousges et al., 2018). In contrast, human-use service losses are usually monetized, and the trustees use the recovered funds to implement one or more human-use restoration projects (Flores & Thacher, 2002).

It is noteworthy that the compensation for both ecological service losses and human-use service losses requires discounting. Both the ecological services losses over time from a spill or release and the ecological service gains over time from restoration projects are converted into their present value equivalents using habitat equivalency analysis (HEA) or resource equivalency analysis (REA; Desvousges et al., 2018; Dunford et al., 2004).1 Similarly, monetized human-use service losses over time are converted into their present values using discounting.

Natural resource damages are assessed from the later of the year of a spill/release or 1981 (the year after the passage of CERCLA in December 1980). So damages for hazardous substance releases will not extend back more than 36 years into the past. Damages for oil spills only go back to the year of the spill, which is likely to be relatively recent. Similarly, many losses (especially from oil spills) will not continue very far into the future, and many restoration projects will not produce ecological service gains beyond 30 or 40 years. In summary, the service losses and gains for many incidents will occur approximately within the lifetime of the current generation.2 This definition of “intragenerational,” which is consistent with Freeman’s definition (2003, p. 204), avoids the complications of discounting for intergenerational effects (effects that occur over the lifetimes of multiple generations), which are beyond the scope of this article.3

Conceptual basis for the NRD discount rate

In an NRD assessment, the value of the public’s consumption of ecological services and/or human-use services over time is discounted. Thus, the discount rate should reflect tradeoffs between the public’s past, present, and future consumption of such services. Those tradeoffs are reflected in the social rate of time preference (SRTP).

The SRTP literature extends back to Ramsey (1928), who argued that the goal of policy makers should be to maximize a social welfare function equal to the discounted value of the utility from current and future consumption.4 That goal leads to the familiar Ramsey equation,

r=ρ+(gε),(1)...

 

where r = social discount rate (i.e., SRTP), ρ = pure rate of time preference, g = percentage change in per capita consumption, and ε = absolute value of the elasticity of the marginal utility of consumption (Moore, Boardman, & Vining, 2013a, p. 4).

The pure rate of time preference reflects the rate of decrease in utility from having to wait for consumption, which will be positive within the same generation. The second term on the right side of Equation (1) reflects “the idea that society prefers more equality in per capita consumption over time than would otherwise occur (i.e., consumption smoothing), given that consumption will be higher in the future because of economic growth” (Moore et al., 2013a, p. 5). In particular, ε is a “measure of society’s preference for reducing inequality in per capita consumption over time” (Moore et al., 2013a, p. 5). Since ε is non-negative, positive economic growth leads to r ≥ ρ.

The standard Ramsey equation includes no uncertainty in the growth of per capita consumption (g). In reality, future consumption growth is uncertain. Karp & Traeger (2014) show that incorporating uncertain future consumption growth into the Ramsey framework leads to the modified formula

r=ρ+(μ · ε)(ε2· σ2)/2,(2)...

 

where μ = expected value of the percentage change in per capita consumption (g) and σ = standard deviation of the expected growth rate in per capita consumption (Karp & Traeger, 2014, p. 288). Notice that uncertainty regarding the percentage change in per capita consumption lowers the SRTP, because the third term on the right side of Equation (2) is negative.

Usually, the public is averse to uncertainty in per capita consumption. Adding risk aversion regarding uncertainty in per capita consumption to Equation (2) leads to the formula

r=ρ+(μ · ε)(ε2· σ2)/2(RIRA · |1ε2| · σ2)/2,(3)...

 

where RIRA = relative intertemporal risk aversion (Karp & Traeger, 2014, p. 288). Since RIRA typically is positive, the additional term on the right side of Equation (3) will be negative, further reducing the SRTP.

Recently, several economists (Echazu, Nocetti, & Smith, 2012; Gollier, 2010; Gollier & Hammitt, 2015; Karp & Traeger, 2013) have expanded Ramsey’s analysis by recognizing the consumption of two different categories of goods and services: produced and environmental. For simplicity, we will refer to the former as produced goods and the latter as environmental services. Under this expanded analysis, the SRTP for environmental services depends on the pure rate of time preference and the following factors:

  • Environmental services share (i.e., the weight that society attaches to environmental services relative to produced goods),

  • Elasticity of substitution between environmental services and produced goods,

  • Rate at which the environmental services share and the elasticity of substitution change over time,

  • Degree of multivariate risk aversion and its rate of change, and

  • Resistance to intertemporal inequality and its rate of change (Echazu et al., 2012, p. 2).

Gollier & Hammitt (2014) focus on the effect of these considerations on the relative prices of environmental services versus produced goods over time. They conclude that the discount rate for environmental services depends on the growth rates in the two categories of goods and services, as well as the uncertainty about those growth rates (Gollier & Hammitt, 2014, p. 288).

As noted in the previous section, ecological damages in NRD are measured as the present-value cost of one or more appropriately scaled restoration projects using HEA or REA. Since HEA and REA are equating the present value of environmental services provided by restoration projects over time to the present value of service losses from a spill/release over time, the discount rate for environmental services would be used in HEA and REA. However, the discount rate for produced goods would be used to estimate the present value of the cost of the scaled restoration projects, because those costs involve labor, capital, and energy (i.e., marketed goods). Different discount rates for environmental services and produced goods would not have any other effects on HEA or REA. Presumably, the present value of monetized human use service losses would use the discount rate for environmental services, since the values for the forgone human use services are estimated using nonmarket valuation techniques.

Institutional basis for the NRD discount rate

In 1986 the U.S. Department of the Interior (DOI) promulgated regulations for assessing NRD under CERCLA (see 43 CFR Part 11). The DOI regulations indicate that the discount rate specified in Office of Management and Budget (OMB) Circular A-94 Revised (dated March 27, 1972) should be used in NRD assessments (43 CFR Sec. 11.83(e)(2)). Section 8(b)(1) in that circular requires the use of a 7% real discount rate for benefit–cost analyses of regulatory programs, which “approximates the marginal pretax [real] rate of return on an average investment in the private sector” (OMB 1992, p. 9) in 1992, when the circular was last updated.

In contrast, OMB Circular A-4, providing guidance on regulatory analyses, which was last updated in 2003, requires federal agencies to use both a 3% and a 7% real discount rate in benefit–cost analyses.

The 7 percent rate in Circular A-4 is aligned with the discount rate used for Federal spending programs, as outlined in Circular A-94. The 7 percent rate was based on the opportunity cost of capital, and thus is most appropriate when the project is displacing investment. The 3 percent rate was based on the rate that the average saver uses to discount future consumption. (Council of Economic Advisors [CEA], 2017, p. 1)

The CEA (2017, p. 2) further explains that the 3% real rate approximated the real rate of return on long-term government debt in 2003, which is a proxy for the SRTP.

The National Oceanic and Atmospheric Administration (NOAA) first developed the NRD assessment regulations for oil spills in 1996 (see 15 CFR Part 990). For scaling restoration actions, the NOAA regulations require a “riskless discount rate representing the consumer rate of time preference” (15 CFR Sec. 990.53(d)(4)). In the preamble to 1996 regulations, NOAA recommended a 3% real rate as “a reasonable choice for the social rate of time preference” (61 Federal Register, January 5, 1996, p. 454).

NOAA provided empirical support for its recommendation of a 3% real discount rate in a 1999 technical paper (National Oceanic and Atmospheric Administration [NOAA], 1999). Specifically, NOAA used three lines of evidence for its choice of a 3% real discount rate. The first line of evidence was an analysis by Freeman (1993), who concluded that “a discount rate of 2 to 3 percent is appropriate in discounting social costs and benefits” accruing to people in the same generation (NOAA, 1999, p. 5). Freeman (1993) based his opinion on a chapter in a book written by Lind (1982) and a working paper by Barro and Sala-i-Martin (1990). According to Freeman (1993, p. 208), Lind (1982) found that real discount rates from 1926–1978 ranged between 0% (the historical real rate of return on Treasury bills) and 4.6% (the real after-tax return on a portfolio of common stocks).5 Barro and Sala-i-Martin (1990) developed a weighted average of the real discount rate across nine industrialized countries between 1959 and 1989. In that 30-year period the real discount rate exceeded 2.5% in only eight years. Barro and Sala-i-Martin’s (1990, Table A2) measure of the real discount rate was the interest rate paid on 3-month Treasury bills minus the change in the Consumer Price Index over the three months (i.e., the real rate of return on 3-month Treasury bills).

The second line of evidence in the NOAA paper was the real discount rate used by the U.S. Department of the Interior when evaluating government projects, which was based on the interest rate paid on 3-month Treasury bills less the rate of inflation. Using that definition, the real discount rate “averaged about 3 percent” over the 15 years ending in 1998 (NOAA, 1999, p. 6).

The third line of evidence in the NOAA paper was the real rate of growth of gross domestic product (GDP) in the United States. That growth rate “averaged about 3 percent” over the 15 years ending in 1998 (NOAA, 1999, p. 6). Presumably, the rationale for the rate of growth of real GDP as a proxy for the SRTP is that it reflects the opportunity cost of forgoing consumption in one year in return for compensation in a subsequent year. However, a substantial portion of GDP involves economic activity not associated with the production and use of consumer goods and services (as discussed in the next section). Accordingly, an estimate of the real change in the public’s expenditures on consumer goods and services may be a more appropriate SRTP proxy (i.e., the real per capita growth rate in personal consumption expenditures).

In conclusion, both the DOI and NOAA regulations for NRD assessment have led to the common use of a 3% real discount rate. However, the empirical basis for that real discount rate involves data through the late 1990s. As recently noted by the Council of Economic Advisors, “empirical evidence suggests that real interest rates around the world have come down since the last evaluation of the rates” (CEA, 2017, p. 1). The DOI and NOAA regulations also do not account for recent conceptual developments on the appropriate discount rate for environmental services relative to produced goods.

Alternative empirical estimates of the NRD discount rate

In this section, we present alternative empirical estimates of the SRTP from 1981 through 2016 for both the institutional and conceptual bases for the SRTP in NRD assessments. Typically, values after general price inflation is eliminated are discounted in NRD assessments, which requires a “real” discount rate (i.e., a discount rate net of inflation). Since most interest rates available to the public reflect nominal rates of return, an empirical estimate of inflation is required in order to derive an empirical estimate of the SRTP. Consequently, we present potential measures of inflation in the next subsection. Then we evaluate five potential measures of SRTP, including the Ramsey equation.

Alternative inflation measures

There are two common measures of price inflation for consumer goods and services in the United States: the Consumer Price Index (CPI) and the Personal Consumption Expenditures Index (PCEI).6 The CPI is produced monthly by the U.S. Bureau of Labor Statistics (BLS) based on changes in the prices paid by urban consumers for a representative basket of goods and services (Bureau of Labor Statistics [BLS], 2018a). According to the BLS, the CPI is the most widely used measure of inflation. For example, it is used as an economic indicator, as a deflator of other economic series (e.g., national product and income accounts), and to adjust government payments (e.g., Social Security payments) and wages for millions of American workers (BLS, 2018b). Between 1981 and 2016, the CPI increased at an average annual rate of 3.02% (Federal Reserve Bank of St. Louis [FRED], 2018c).7,8

The PCEI is produced by the U.S. Bureau of Economic Analysis, and it measures the change in prices paid for goods and services purchased by the personal sector in the U.S. national income and product accounts (McCully, Moyer, & Stewart, 2007). The PCEI differs from the CPI in four main ways: formula effect, weight effect, scope effect, and “other effects.”

  • The formula effect accounts for the different formulas used to calculate the two indices. The PCE price index is based on the Fisher–Ideal formula, while the CPI is based on a modified Laspeyres formula.

  • The weight effect accounts for the relative importance of the underlying commodities reflected in the construction of the two indexes. For example, the PCEI has a higher weight on medical care, while the CPI has higher weights on housing and transportation.

  • The scope effect accounts for conceptual differences between the two indices. The PCEI measures spending by and on behalf of the personal sector, which includes both households and nonprofit institutions serving households; the CPI measures out-of-pocket spending by households. The “net” scope effect adjusts for CPI items out of scope of the PCE price index less items in the PCE price index that are out of scope of the CPI.

  • “Other effects” include seasonal adjustment differences, price differences, and residual differences (Bureau of Economic Analysis [BEA], n.d.).9

The PCEI is primarily used for macroeconomic analysis and forecasting – it is the Federal Reserve’s preferred measure of inflation. Between 1981 and 2016, the PCEI increased at an average annual rate of 2.61% (FRED, 2018b).10

Both the CPI and the PCEI have their strengths and weaknesses as inflation measures. Instead of selecting one of the measures, imposing our perspective on their relative merits, we use both measures in our analysis. This provides a sensitivity analysis of the effect of inflation measures on the empirical estimates of SRTP. Since the CPI increased at a higher rate than the PCEI between 1981 and 2016, the former produces a lower real discount rate than the latter for a specified nominal discount rate. In the Conclusions we investigate the impact of a lower discount rate on natural resource damages.

Treasury bill rates

Since 1981, the U.S. Department of the Treasury has sold three types of marketable securities to the public in nominal dollars to finance the federal debt (U.S. Department of the Treasury, 2018b):

  • Bills – issued in denominations of $100 with maturity dates of three months, six months, and one year;

  • Notes – issued in denominations of $1000 with maturity dates of two to 10 years;

  • Bonds – issued in denominations of $1000 with the most common maturity date being 30 years.

As noted in the previous section, the rate of return on 3-month Treasury bills was the foundation of two of the three lines of evidence in the NOAA technical paper on the discount rate for NRD assessments (NOAA, 1999). Such short-term securities would have a very low default risk, as well as a small differential between expected and actual inflation. The average annual nominal rate of interest on 3-month Treasury bills was 4.25% between 1981 and 2016 (FRED, 2018d).11 This translates into an average annual real rate of interest of 1.22% or 1.64% depending on the measure of inflation.

Treasury inflation-protected securities (TIPS) rates

In 2003, the U.S. Treasury Department began selling inflation-protected securities, known as TIPS, with maturities of 5, 10, and 30 years. The principal of a TIPS increases with inflation and decreases with deflation, as measured by the Consumer Price Index. When a TIPS matures, the owner is paid the adjusted principal or the original principal, whichever is greater. TIPS pay interest twice a year, at a fixed rate. The rate is applied to the adjusted principal; so, like the principal, interest payments rise with inflation and fall with deflation (U.S. Department of the Treasury, 2018a). The unweighted average yields for all TIPS with remaining terms to maturity of more than 10 years was 1.56% between 2003 and 2016 (FRED, 2018e).12

Real GDP growth rate

The U.S. Bureau of Economic Analysis (BEA) produces a quarterly estimate of real gross domestic product (GDP), which is a measure of the market value of the production of all goods and services in the U.S. economy, including government expenditures and net exports. This economic measure is much broader than the consumption of goods and services by the public. The BEA uses three methods to estimate real GDP: the deflation method, the quantity extrapolation method, and the direct valuation method (see BEA, 2016, for more details). However, most components of real GDP are estimated using the CPI (BEA, 2017b, p. 2). The average annual rate of growth in real GDP was 2.69% between 1981 and 2016 (BEA, 2018).13 As noted in the previous section, the real GDP growth rate was one line of evidence in the 1999 NOAA technical paper, presumably because it is a proxy for the opportunity cost to the economy of forgoing production in one year in exchange for compensation in a subsequent year.

PCE per capita growth rate

Personal consumption expenditures (PCE) are the primary measure of consumer spending on goods and services in the U.S. economy. They account for about two-thirds of domestic final spending (BEA, 2017a, p. 1). The BEA adjusts PCE for inflation using the PCEI, and then divides by a population estimate to obtain its estimate of real PCE per capita. The average annual rate of growth in real PCE per capita was 2.02% between 1981 and 2016 (FRED, 2018c).14 Since PCE focuses on consumer spending (excluding government spending and net exports), the growth rate in real PCE per capita is probably a better measure of the opportunity cost of forgone consumption by the public than the growth rate in real GDP.

Ramsey equation

Many economists have estimated the SRTP using the basic Ramsey equation (e.g., Moore, Boardman, & Vining, 2013b; Nordhaus, 2007; Stern, 2006). However, Burgess & Zerbe (2013, pp. 392–394) identify several disagreements among economists on the estimates for each of the three components of the basic Ramsey equation, leading to substantial differences in empirical estimates of the SRTP, ranging from close to 0% up to almost 9%. For example, Stern (2006) estimated a SRTP of 1.4% in his review of the economic effects of climate change, while Nordhaus (2007) estimated a SRTP of 5.5% for the same effects, almost four times Stern’s estimate. In our view, there is no definitive SRTP estimate based on the basic Ramsey equation.

Not surprisingly, there are several challenges in estimating the SRTP using the expanded Ramsey equation, which include uncertainty and risk aversion, and allow different SRTPs for produced goods and environmental services. Nevertheless, Gollier (2010) estimated a 1.5% discount rate for environmental services compared with a 3.2% discount rate for produced goods using plausible assumptions and a Cobb–Douglas functional form for utility. Even though the SRTP estimates based on the expanded Ramsey equation are sensitive to the underlying assumptions, and perhaps some value judgments, it appears that the SRTP for environmental services will be less than the SRTP for produced goods under a wide range of circumstances (Karp & Traeger, 2013).

While there appears to be a consensus among economists that the discount rate for environmental services is lower than the discount rate for produced goods, there is no consensus on the magnitude of the difference between the two rates. A practical alternative for the purposes of NRD assessment would be to provide a range for the difference in the two rates. For example, if the discount rate for produced goods is 2%, then the discount rate for environmental services might be

  • 1% (i.e., half of the rate for produced goods, which is consistent with the proportion in Gollier, 2010);

  • 1.5% (i.e., three-fourths of the rate for produced goods); or

  • 2% (i.e., the rate for produced goods as a conservative upper bound estimate).

Summary

Table 1 summarizes the empirical estimates of the SRTP presented in this section. Several results in this table are noteworthy. First, the range of SRTP estimates goes from 1.22% to 2.69%. Thus, even the upper-bound estimate of the SRTP for 1981 through 2016 is less than the 3% real discount rate currently used in NRD assessments. Second, the range of SRTP based on 3-month Treasury bill rates (i.e., 1.22% to 1.64%) is much lower than the range of SRTP based on growth rates of the U.S. economy (i.e., 2.02% to 2.69%). As noted in Section 3, the NOAA (1999) lines of evidence for the discount rate for NRD assessments emphasize the Treasury bill rates. Third, the TIPS rate falls with the range of SRTP based on 3-month Treasury bill rates, but that comparison is undermined by the difference in the time periods for the data series. For the years 2003–2016, the average TIPS rate falls between the average annual growth rate of the U.S. economy based on changes in real GDP (1.85%) and the real PCE per capita (1.32%). Fourth, the average of the real rates in Table 1 (excluding the TIPS rate), which gives equal weight to Treasury bill rates and the growth rates for the U.S. economy, is 1.89%.

TABLE 1

Social rate of time preference estimates: 1981–2016.

Economic measureReal
Annual change in gross domestic product (GDP)   2.69% 
Annual change in personal consumption expenditures (PCE) per capita   2.02% 
Treasury inflation-protected securities (TIPS) (2003–2016 only)   1.56% 
 Nominal Real using CPI Real using PCEI 
3-month Treasury bill rate 4.25% 1.22% 1.64% 
Economic measureReal
Annual change in gross domestic product (GDP)   2.69% 
Annual change in personal consumption expenditures (PCE) per capita   2.02% 
Treasury inflation-protected securities (TIPS) (2003–2016 only)   1.56% 
 Nominal Real using CPI Real using PCEI 
3-month Treasury bill rate 4.25% 1.22% 1.64% 

Notes: 3.03% = average annual change in consumer price index (CPI); 2.61% = average annual change in personal consumption expenditures index (PCEI).

Sources: See Appendix Tables 13.

Conclusions

The empirical estimates in the previous section clearly support a discount rate below 3% for NRD assessment purposes. For 1981 through 2016, the upper-bound estimate of the discount rate for produced goods is 2.7%, while the average for four estimates of the discount rate for such goods (excluding the TIPS rate) is 1.9%. This average is consistent with a recent analysis by the Council of Economic Advisers, which concluded that SRTP for regulatory programs “should be at most 2 percent” (CEA, 2017, p. 1).

As noted above, recent research suggests that the discount rate for environmental services, which are relevant for NRD assessments, is less than the discount rate for produced goods. In particular, Gollier (2010) estimated the discount rate for environmental services as about half of the discount rate for produced goods. Furthermore, discount rates in the past are a matter of record – there is no uncertainty about past discount rates and presumably no risk aversion to historical discount rates. However, future discount rates are uncertain and the public may be risk-averse to fluctuations in the uncertain rates. Uncertainty and risk aversion tend to lower the SRTP, as demonstrated above. Thus, we might expect the discount rate for future losses and restoration gains to be lower than the average discount rate in the past. This reinforces the conclusion that 2% is an upper bound for the appropriate discount rate for NRD assessments.

A reduction in the discount rate for NRD assessment from 3% to 2% leads to two main questions:

  • (1)

    Would a 2% discount rate result in less restoration or more restoration for the injuries from a spill or release?

  • (2)

    Would the change in the scale of restoration at a 2% discount rate be substantial?

Not surprisingly, the answers to both questions depend on the characteristics of the injuries from the spill/release and the gains from the relevant compensatory restoration project.

To illustrate the impact of a lower discount rate on the required compensatory restoration, suppose that a release initially lowers ecological services by 80% but those services naturally recover at a linear rate over a 40-year period. As shown in Table 2, the aggregate loss (i.e., the debit) from such a release depends on when the release occurred. Releases that occurred further in the past have a larger debit for a specified discount rate. However, a lower discount rate decreases the debit when most of the injuries from a specified release occurred in the past. In contrast, a lower discount rate increases the debit when most of the injuries occur in the future.

TABLE 2

Impact of discount rate on scale of restoration for ecological injuries.

Discount rate
Damage elements3.0%2.5%2.0%1.5%1.0%
Debit for injury from      
1981–2015 3360 2972 2631 2333 2071 
1991–2025 2500 2321 2158 2010 1875 
2001–2035 1861 1813 1771 1732 1697 
2011–2045 1384 1417 1452 1492 1536 
Credit/acre for gains from      
2021–2055 9.0 9.9 10.9 12.0 13.3 
Restoration acres for injury from      
1981–2015 375 301 242 194 155 
1991–2025 279 235 199 167 141 
2001–2035 207 184 163 144 127 
2011–2045 154 144 134 124 115 
Discount rate
Damage elements3.0%2.5%2.0%1.5%1.0%
Debit for injury from      
1981–2015 3360 2972 2631 2333 2071 
1991–2025 2500 2321 2158 2010 1875 
2001–2035 1861 1813 1771 1732 1697 
2011–2045 1384 1417 1452 1492 1536 
Credit/acre for gains from      
2021–2055 9.0 9.9 10.9 12.0 13.3 
Restoration acres for injury from      
1981–2015 375 301 242 194 155 
1991–2025 279 235 199 167 141 
2001–2035 207 184 163 144 127 
2011–2045 154 144 134 124 115 

Notes: Debits and credits are estimated as discounted service acre-years. Inputs: base year for discounting, 2017; injured acreage, 100; initial service loss, 80%; first year of restoration service gains, 2021; years to recovery, 40; restoration service gain at maximum, 50%; years to maximum service gain, 5; at maximum service gain, 35.

Suppose that a restoration project will begin providing ecological services in the year 2021. Further, assume that the project will produce gains of 50% in ecological services when it reaches its peak productivity in five years, and then that 50% gain will continue for another 30 years. The middle of Table 2 shows that a lower discount rate will increase the credit per acre from such a restoration project.

The scale of restoration projects that fully compensate the public for ecological losses from a spill/release is determined by dividing the debit by the credit per acre from the restoration projects (Dunford et al., 2004). As shown at the bottom of Table 2, a lower discount rate reduces the scale of restoration projects to fully compensate the public. The reduction in scale is largest for spills/releases that began further in the past, while it is smallest for more recent spills/releases. In particular, many hazardous-substance releases began prior to the enactment of the Clean Water Act in 1972 (33 U.S.C. §1251 et seq.). Thus, NRD actions for hazardous-substance releases are more likely to involve injury periods beginning in 1981 than those for oil spills, which would have an injury period beginning closer to the present. Consequently, a lower discount rate is likely to lower the restoration acreage for a hazardous-substance release more than it would lower the restoration acreage for an oil spill.

In some instances, releases of highly toxic substances can result in perpetual ecological service losses. Similarly, the permanent preservation of habitat can produce perpetual gains in ecological services in some cases. Such instances introduce the complications of tradeoffs of ecological services across the lifetimes of multiple generations. There appears to be a consensus in the economics literature that a lower discount rate is appropriate in discounting economic effects across multiple generations (Defrancesco, Gatto, & Rosato, 2014, p. 4; Freeman, 2003, pp. 204–5). Furthermore, many economists support declining (e.g., hyperbolic) discount rates for annual losses and gains over very long time horizons (Arrow et al., 2014; Groom et al., 2005; Traeger, 2011; Weitzman, 1998). While our study focuses on intragenerational discounting, we recommend future research on the effects of intergenerational discounting for NRD assessment.

Another potential topic for future research on the discount rate for NRD assessment would be the difference of the discount rate for environmental services from that for produced goods. In particular, more research on the potential magnitude of the difference in those discount rates would help ensure that the public is fully, but not excessively, compensated for losses of environmental services from spills/releases.

One final observation is noteworthy. The discount rate next year is likely to be comparable to the discount rate this year, barring a major exogenous change in the economy next year. Analogously, the average discount rate over the next five years is likely to be more similar to the average discount rate over the last five years than the average discount rate over the last 30 years. Thus, a more accurate estimate of the debit from a spill/release in present value terms may result from using a discount rate that matches the time period of the NRD losses. For example, if a release occurred in 1992 and the public experienced losses from that release through 2012, then the average discount rate from 1992 to 2012 may provide a more accurate estimate of the debit than the average discount rate from 1981 to 2016, because the latter reflects discount rates outside the relevant injury period. Similarly, if a release leads to injuries from 1997 to 2028, then the debit from 1997 to 2018 could be based on the average discount rate in those years. The discount rate for the debit in 2019–2028 could be based on the average discount rate for the last 10 years, under the assumption that tradeoffs in ecological services over the next 10 years would be similar to tradeoffs over the last 10 years, other things being equal. A comparable approach could be used for the average discount rate for the credit per acre from restoration projects. For example, if the restoration project is expected to provide credits for 35 years, then the average discount rate over the last 35 years could be used to estimate the credit per acre from the project.

In this last example, with significantly different durations for losses from natural resource injuries and gains from restoration actions, it may be appropriate to use different discount rates for losses and gains. Shorter durations for losses compared restoration gains are more likely for oil spills than for hazardous-substance releases, because of shorter recovery periods following oil spills. Thus, different discount rates for losses and gains may be more applicable to oil spills than for hazardous-substance releases.

For clarity, the NOAA and/or the DOI could provide its preferred measure of historical discount rates on an annual basis going back to 1981. Then the agencies could direct NRD practitioners to use an average of the historical rates over the injury period in the past for discounting past losses. Future losses could be discounted using the average of historical discount rate over the duration of the future losses (e.g., losses extending 10 more years into the future would be discounted using the average historical discount rate for the last 10 years). Finally, future restoration gains would be discounted using the average of historical discount rates over the duration of the future gains. This temporal-matching approach to discounting may provide a more accurate estimate of the compensation required to make the public whole for a spill/release than using the same discount rate for losses and restoration gains regardless of the duration of those losses and gains.

Appendix

TABLE 1

Inflation indices for U.S. economy, 1981–2016.

YearConsumer price index (CPI)aChange in CPIPCE price indexbChange in PCE price index
1981 90.933 10.4% 47.908 8.9% 
1982 96.533 6.2% 50.553 5.5% 
1983 99.583 3.2% 52.729 4.3% 
1984 103.933 4.4% 54.724 3.8% 
1985 107.600 3.5% 56.661 3.5% 
1986 109.692 1.9% 57.887 2.2% 
1987 113.617 3.6% 59.650 3.0% 
1988 118.275 4.1% 61.974 3.9% 
1989 123.942 4.8% 64.641 4.3% 
1990 130.658 5.4% 67.440 4.3% 
1991 136.167 4.2% 69.652 3.3% 
1992 140.308 3.0% 71.494 2.6% 
1993 144.475 3.0% 73.279 2.5% 
1994 148.225 2.6% 74.803 2.1% 
1995 152.383 2.8% 76.356 2.1% 
1996 156.858 2.9% 77.981 2.1% 
1997 160.525 2.3% 79.327 1.7% 
1998 163.008 1.5% 79.936 0.8% 
1999 166.583 2.2% 81.110 1.5% 
2000 172.192 3.4% 83.131 2.5% 
2001 177.042 2.8% 84.736 1.9% 
2002 179.867 1.6% 85.873 1.3% 
2003 184.000 2.3% 87.572 2.0% 
2004 188.908 2.7% 89.703 2.4% 
2005 195.267 3.4% 92.261 2.9% 
2006 201.558 3.2% 94.729 2.7% 
2007 207.344 2.9% 97.102 2.5% 
2008 215.254 3.8% 100.065 3.1% 
2009 214.565 −0.3% 100.000 −0.1% 
2010 218.076 1.6% 101.653 1.7% 
2011 224.923 3.1% 104.149 2.5% 
2012 229.586 2.1% 106.121 1.9% 
2013 232.949 1.5% 107.532 1.3% 
2014 236.704 1.6% 109.150 1.5% 
2015 236.987 0.1% 109.532 0.3% 
2016 240.009 1.3% 110.721 1.1% 
Mean  3.03%  2.61% 
YearConsumer price index (CPI)aChange in CPIPCE price indexbChange in PCE price index
1981 90.933 10.4% 47.908 8.9% 
1982 96.533 6.2% 50.553 5.5% 
1983 99.583 3.2% 52.729 4.3% 
1984 103.933 4.4% 54.724 3.8% 
1985 107.600 3.5% 56.661 3.5% 
1986 109.692 1.9% 57.887 2.2% 
1987 113.617 3.6% 59.650 3.0% 
1988 118.275 4.1% 61.974 3.9% 
1989 123.942 4.8% 64.641 4.3% 
1990 130.658 5.4% 67.440 4.3% 
1991 136.167 4.2% 69.652 3.3% 
1992 140.308 3.0% 71.494 2.6% 
1993 144.475 3.0% 73.279 2.5% 
1994 148.225 2.6% 74.803 2.1% 
1995 152.383 2.8% 76.356 2.1% 
1996 156.858 2.9% 77.981 2.1% 
1997 160.525 2.3% 79.327 1.7% 
1998 163.008 1.5% 79.936 0.8% 
1999 166.583 2.2% 81.110 1.5% 
2000 172.192 3.4% 83.131 2.5% 
2001 177.042 2.8% 84.736 1.9% 
2002 179.867 1.6% 85.873 1.3% 
2003 184.000 2.3% 87.572 2.0% 
2004 188.908 2.7% 89.703 2.4% 
2005 195.267 3.4% 92.261 2.9% 
2006 201.558 3.2% 94.729 2.7% 
2007 207.344 2.9% 97.102 2.5% 
2008 215.254 3.8% 100.065 3.1% 
2009 214.565 −0.3% 100.000 −0.1% 
2010 218.076 1.6% 101.653 1.7% 
2011 224.923 3.1% 104.149 2.5% 
2012 229.586 2.1% 106.121 1.9% 
2013 232.949 1.5% 107.532 1.3% 
2014 236.704 1.6% 109.150 1.5% 
2015 236.987 0.1% 109.532 0.3% 
2016 240.009 1.3% 110.721 1.1% 
Mean  3.03%  2.61% 
a

All urban consumers: all items, monthly, seasonally adjusted. Source: FRED, 2018a.

b

Chain-type price index, seasonally adjusted, fourth quarter, 2009 = 100. Source: FRED, 2018b.

TABLE 2

Rate of return on selected Treasury securities, 1981–2016.

Year3-month Treasury bill rate (%)aTIPS average long-term yield (%)b
1981 14.03 NA 
1982 10.61 NA 
1983 8.61 NA 
1984 9.52 NA 
1985 7.48 NA 
1986 5.98 NA 
1987 5.78 NA 
1988 6.67 NA 
1989 8.11 NA 
1990 7.49 NA 
1991 5.38 NA 
1992 3.43 NA 
1993 3.00 NA 
1994 4.25 NA 
1995 5.49 NA 
1996 5.01 NA 
1997 5.06 NA 
1998 4.78 NA 
1999 4.64 NA 
2000 5.82 NA 
2001 3.39 NA 
2002 1.60 NA 
2003 1.01 2.54 
2004 1.37 2.21 
2005 3.15 1.94 
2006 4.73 2.27 
2007 4.35 2.34 
2008 1.37 2.20 
2009 0.15 2.24 
2010 0.14 1.72 
2011 0.06 1.19 
2012 0.09 0.17 
2013 0.06 0.66 
2014 0.03 0.85 
2015 0.05 0.81 
2016 0.32 0.69 
Mean 4.25 1.56 
Year3-month Treasury bill rate (%)aTIPS average long-term yield (%)b
1981 14.03 NA 
1982 10.61 NA 
1983 8.61 NA 
1984 9.52 NA 
1985 7.48 NA 
1986 5.98 NA 
1987 5.78 NA 
1988 6.67 NA 
1989 8.11 NA 
1990 7.49 NA 
1991 5.38 NA 
1992 3.43 NA 
1993 3.00 NA 
1994 4.25 NA 
1995 5.49 NA 
1996 5.01 NA 
1997 5.06 NA 
1998 4.78 NA 
1999 4.64 NA 
2000 5.82 NA 
2001 3.39 NA 
2002 1.60 NA 
2003 1.01 2.54 
2004 1.37 2.21 
2005 3.15 1.94 
2006 4.73 2.27 
2007 4.35 2.34 
2008 1.37 2.20 
2009 0.15 2.24 
2010 0.14 1.72 
2011 0.06 1.19 
2012 0.09 0.17 
2013 0.06 0.66 
2014 0.03 0.85 
2015 0.05 0.81 
2016 0.32 0.69 
Mean 4.25 1.56 
a

Secondary market, monthly, not seasonally adjusted percentage. Source: FRED, 2018d.

b

Treasury inflation-indexed long-term average yield, not seasonally adjusted, daily. Source: FRED, 2018e.

TABLE 3

Inflation indices for U.S. economy, 1981–2016.

YearReal GDP ($ billion)aChange in real GDPReal PCE per capita ($)bChange in real PCE per capita
1981 6,618 2.6% 17,479 -0.8% 
1982 6,491 −1.9% 17,952 2.7% 
1983 6,792 4.6% 18,937 5.5% 
1984 7,285 7.3% 19,604 3.5% 
1985 7,594 4.2% 20,378 3.9% 
1986 7,861 3.5% 21,103 3.6% 
1987 8,133 3.5% 21,498 1.9% 
1988 8,475 4.2% 22,278 3.6% 
1989 8,786 3.7% 22,589 1.4% 
1990 8,955 1.9% 22,491 −0.4% 
1991 8,948 −0.1% 22,407 −0.4% 
1992 9,267 3.6% 23,196 3.5% 
1993 9,521 2.7% 23,663 2.0% 
1994 9,905 4.0% 24,278 2.6% 
1995 10,175 2.7% 24,667 1.6% 
1996 10,561 3.8% 25,218 2.2% 
1997 11,035 4.5% 26,035 3.2% 
1998 11,526 4.4% 27,206 4.5% 
1999 12,066 4.7% 28,276 3.9% 
2000 12,560 4.1% 29,220 3.3% 
2001 12,682 1.0% 29,685 1.6% 
2002 12,909 1.8% 30,014 1.1% 
2003 13,271 2.8% 30,887 2.9% 
2004 13,774 3.8% 31,725 2.7% 
2005 14,234 3.3% 32,386 2.1% 
2006 14,614 2.7% 33,134 2.3% 
2007 14,874 1.8% 33,292 0.5% 
2008 14,830 −0.3% 32,344 −2.8% 
2009 14,419 −2.8% 31,999 −1.1% 
2010 14,784 2.5% 32,717 2.2% 
2011 15,021 1.6% 32,959 0.7% 
2012 15,355 2.2% 33,156 0.6% 
2013 15,612 1.7% 33,585 1.3% 
2014 15,982 2.4% 34,508 2.7% 
2015 16,397 2.6% 35,147 1.9% 
2016 16,662 1.6% 35,987 2.4% 
Mean  2.69%  2.02% 
YearReal GDP ($ billion)aChange in real GDPReal PCE per capita ($)bChange in real PCE per capita
1981 6,618 2.6% 17,479 -0.8% 
1982 6,491 −1.9% 17,952 2.7% 
1983 6,792 4.6% 18,937 5.5% 
1984 7,285 7.3% 19,604 3.5% 
1985 7,594 4.2% 20,378 3.9% 
1986 7,861 3.5% 21,103 3.6% 
1987 8,133 3.5% 21,498 1.9% 
1988 8,475 4.2% 22,278 3.6% 
1989 8,786 3.7% 22,589 1.4% 
1990 8,955 1.9% 22,491 −0.4% 
1991 8,948 −0.1% 22,407 −0.4% 
1992 9,267 3.6% 23,196 3.5% 
1993 9,521 2.7% 23,663 2.0% 
1994 9,905 4.0% 24,278 2.6% 
1995 10,175 2.7% 24,667 1.6% 
1996 10,561 3.8% 25,218 2.2% 
1997 11,035 4.5% 26,035 3.2% 
1998 11,526 4.4% 27,206 4.5% 
1999 12,066 4.7% 28,276 3.9% 
2000 12,560 4.1% 29,220 3.3% 
2001 12,682 1.0% 29,685 1.6% 
2002 12,909 1.8% 30,014 1.1% 
2003 13,271 2.8% 30,887 2.9% 
2004 13,774 3.8% 31,725 2.7% 
2005 14,234 3.3% 32,386 2.1% 
2006 14,614 2.7% 33,134 2.3% 
2007 14,874 1.8% 33,292 0.5% 
2008 14,830 −0.3% 32,344 −2.8% 
2009 14,419 −2.8% 31,999 −1.1% 
2010 14,784 2.5% 32,717 2.2% 
2011 15,021 1.6% 32,959 0.7% 
2012 15,355 2.2% 33,156 0.6% 
2013 15,612 1.7% 33,585 1.3% 
2014 15,982 2.4% 34,508 2.7% 
2015 16,397 2.6% 35,147 1.9% 
2016 16,662 1.6% 35,987 2.4% 
Mean  2.69%  2.02% 
a

Chained 2009 dollars, seasonally adjusted annual rate. Source: BEA (2018).

b

Chained 2009 dollars, fourth quarter, seasonally adjusted annual rate. Source: FRED (2018c).

Acknowledgements

The author wishes to thank Dr. Ted Tomasi at Cardno in Newark, Delaware, for constructive suggestions on an earlier draft of this article.

Funding

This research did not receive any funding from government agencies, businesses, or not-for-profit organizations.

Notes

1.

Technically, implicit monetary values for ecological service losses from an incident and ecological service gains from restoration projects are discounted in HEA and REA. Under certain simplifying assumptions (Dunford et al., 2004), the two implicit monetary values are equal and cancel out of the loss and gain calculations. Thus, it appears that physical units of ecological services are discounted in HEA and REA, even though the discounting actually applies to the implicit monetary values.

2.

The median age of the current U.S. population is approximately 38 years (www.statista.com/statistics/241494/median-age-of-the-us-population/), and the average life expectancy of the current population is about 79 years (www.cdc.gov/nchs/fastats/deaths.htm). So the lifetime of the current generation would cover natural resource losses and gains from 1981 until about 2059.

3.

The complications include difficult intergenerational equity issues (see Groom, Hepburn, Koundouri, & Pearce, 2005; Howarth, 1996; Khanna & Chapman, 1996; Portney & Weyant, 1999) and the possibility of declining discount rates over time (Arrow, Cropper, Gollier, Groom, Heal, Newell, Nordhaus, Pindyck, Pizer, Portney, Sterner, Tol, & Weitzman, 2014; Traeger, 2011; Weitzman, 1998).

4.

As noted in Arrow et al. (2014), Ramsey’s formula can be used to estimate the social discount rate for both intragenerational and intergenerational discounting by varying the time index.

5.

The NOAA paper indicates that Lind’s range for the real discount rate was 1% to 6% (NOAA, 1999, p. 5). Actually, Lind (1982, p. 74) concluded that the range was from -1% to 6%, but the highest estimate provided in his chapter was 4.6%, so the basis for 6% as the upper end of his range is unclear.

6.

There are variants of both indices that exclude segments of the economy with relatively volatile prices (e.g., food prices and energy prices). For simplicity, we focus on the annual indices for all goods and services.

7.

See Appendix Table 1 for the annual CPI percentages.

8.

A simple average over time for normalized data series can be biased, in which case a geometric mean is a better measure of central tendency (Fleming & Wallace, 1986). However, most of the normalized data series presented in this paper have at least one negative observation, which precludes the use of a geometric mean. Furthermore, the compound annual average for the data series is almost identical to the simple annual average, which suggests relatively little bias in the latter.

9.

See McCully, Moyer, & Stewart, 2007, for more details on the differences between the CPI and PCEI.

10.

See Appendix Table 1 for the annual PCEI percentages.

11.

See Appendix Table 2 for the annual 3-month Treasury bill rates.

12.

See Appendix Table 2 for the annual TIPS rates.

13.

See Appendix Table 3 for the annual GDP real growth rates.

14.

See Appendix Table 3 for the annual PCE growth rates per capita.

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