Richard O. Zerbe Jr.

Xi Han

David Layton

Tom Leshine

October 2002

This report reflects a history of the use of discount rates by government agencies along with a history of the values of real interest rates. The major conclusion of this report is that there is little consistency in government decisions to use or not to use discount rates or in their choice of particular rates when they are used. This article is organized as follows: section two deals with the concept of discount rates; section three examines various discount rates used by government agencies; section four analyzes why discount rates differ among government agencies; and section five looks at the history of real interest rate in U.S. We do not suggest here what discount rates should be used.

Discount rates reflect simply the particular use of interest rates to find the earlier value of expected returns. Interest rates are used by lenders and borrowers to determine the amount of some future payment. Thus if P is the amount borrowed today and r is the interest rate, then the future value F, or the amount to be paid back at time T, will be given by

The interest rate r is called the discount rate when it is used to solve for P given the other values. Thus in using the following equation (2) the practice is called discounting and r is said to be the discount rate.

P = F/(1+r)^T (2)

Thus the use of discount rates must be as old as the use of interest rates. We will focus here simply on the use of such rates in more modern times and in particular their use by government agencies.

Interest rates and thus discount rates may be expressed in real or nominal terms. Nominal rates are market rates which by their nature contain an expected inflation factor. Real rates are nominal rates from which expected inflation (in practice usually actual inflation) has been removed. The real rate R is related to the nominal rate r as through the expected inflation rate, I^e as follows:

R = (1+ r)/(1+I^e) -1 (1)

which may be expressed approximately as

R @ r - I^e (2)

Thus if the nominal interest rate is 7%, expected inflation is 2%, the real interest rate R would be 4.90% or approximately 5%.

The conceptually correct procedure is to use real rates to discount real benefits and costs (constant-dollar values) and to use nominal rates to discount nominal benefits and costs (current-dollar values). To mix real with nominal values is to allow inflation in one part of the calculation but not in the other.

There is little consistent practice in government both in the choice of a particular discount rate, and in the decision of whether or not to use discount rates. This inconsistency is found across different levels of government, among different government agencies at the same level, and across time within the same agency.

Thus not all Federal agencies use the same discount rates, nor do they always use discounting at all. Bazelon and Smetters (1999, p 219) note that, "In many cases, federal agencies do not discount. " and further, "congressional cash-based budget planning does not discount either." Federal agencies often treat a dollar spent now exactly the same as a dollar spent next year (e.g. yearly budgets, mandatory spending). Further, "changes in spending beyond the five or ten-year budget window . . .are essentially discounted at an infinite rate." The following then briefly goes over the history of discount rates used by different federal agencies.

I. Discount Rates Used by Office of Management and Budget (OMB)

According to the OMB Circular No. A-94, dated March 27, 1972 , "Discount Rates to be Used in Evaluating Time-Distributed Costs and Benefits", a real rate of 10 percent was recommended by OMB for use from March 27, 1972 until October 29, 1992. This rate represents an estimate of the average rate of return on private investment, before taxes and after inflation.

This Circular applies to all agencies of the executive branch of the Federal Government except the U.S. Postal Service. And the 10 percent real discount rate applies to the evaluation of Government decisions concerning the initiation renewal or expansion of all programs or projects, other than those specifically exempted (decisions concerning water resource projects, the Government of the District of Columbia, and non-Federal recipients of Federal loans or grants). There have been two additional exceptions to the use of this rate according to Lyons (1990). The first is that agencies were allowed to use a different rate when an alternative rate can be justified. However, the acceptable basis for using a different rate are not spelled out. The second exception to the 10 percent rule has been lease or purchase decision, for which the OMB Circular No. A-104, dated June 14, 1972, "Comparative Cost Analysis for Decisions to Lease or Purchase General Purpose Real Property", specified a real rate of 7 percent. This rate represents an estimate of the internal rate of return on general purpose real property leased from the private sector, exclusive of property taxes and expected inflation. This rate is influenced by IRS tax treatment of real property and by separate handling of property taxes in Circular A-104; and it is specific to lease-or-purchase decisions and is not comparable to before tax rates of return that the OMB specified in Circular A-94.

In October 1992, the OMB Circular No. A-94 was extensively revised. According to the OMB Circular No. A-94, dated October 29th, 1992 ,"Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs", two basic types of discount rates have been specified: (1) a discount rate for public investment and regulatory analyses; and (2) a discount rate for cost-effectiveness, lease-purchase, internal government investment and asset sale analyses.

For the base case of public investment and regulatory analyses, OMB now suggests a real discount rate of 7 percent. This rate is said by OMB to approximate the marginal pretax rate of return on an average investment in the private sector in recent years.

For the cost-effectiveness, lease-purchase, internal government investment and asset sale analyses, OMB discount rates are based on interest rates on Treasury Notes and Bonds with maturities ranging from 3 to 30 years. The rate used may be either nominal or real, depending on how benefits and costs are measured. Analyses that involve constant-dollar costs should use the real Treasury borrowing rate on marketable securities of comparable maturity to the period of analysis. This rate is computed using the Administration's economic assumptions for the budget, which are published in January of each year. Real Treasury rates are obtained by removing expected inflation over the period of analysis from nominal Treasury interest rates.

The history of nominal interest rates used by OMB is presented in Table 1. These nominal rates are used for discounting nominal flows, which are often encountered in lease-purchase analysis.

And the history of real interest rates used by OMB is presented in Table 2. These real rates are used for discounting real (constant-dollar) flows, as is often required in cost-effectiveness analysis.

II. Discount Rates Used by Department of Energy (DOE)

Since 1996, the Department of Energy reports its discount rate yearly. The DOE discount rate is based on long-term Treasury bond rates averaged over the previous 12 months. The nominal, or market rate, is converted to a real rate using the projected rate of general price inflation from the Economic Report of the President's Council of Economic Advisors, to correspond with the constant-dollar analysis approach that is used in most federal life-cycle cost (LCC) analyses. Federal agencies and contractors to federal agencies are required by 10 CFR 436 to use the DOE discount rate when conducting LCC analyses related to energy conservation, renewable energy resources, and water conservation projects for federal facilities.

According to NISTIR 85-3273-10, October 1995, the Department of Energy uses a real discount rate of 4.1 percent or a nominal discount rate of 7.6 percent for 1996 (the projected rate of general price inflation was 3.4%).

According to NISTIR 85-3273-11, July 1996, the Department of Energy uses a real discount rate of 3.4 percent or a nominal discount rate of 6.6 percent for 1996 (the projected rate of general price inflation was 3.1%).

According to NISTIR 85-3273-12, April 1997, the Department of Energy uses a real discount rate of 3.8 percent or a nominal discount rate of 6.9 percent for 1997 (the projected rate of general price inflation was 2.9%).

According to NISTIR 85-3273-13, April 1998, the Department of Energy uses a real discount rate of 4.1 percent or a nominal discount rate of 6.6 percent for 1998 (the projected rate of general price inflation was 2.4%).

According to NISTIR 85-3273-14, July 1999, the Department of Energy uses a real discount rate of 3.1 percent or a nominal discount rate of 5.7 percent for 1999 (the projected rate of general price inflation was 2.5%).

According to NISTIR 85-3273-15, April 2000, the Department of Energy uses a real discount rate of 3.4 percent or a nominal discount rate of 6.3 percent for 2000 (the projected rate of general price inflation was 2.8%).

According to NISTIR 85-3273-16, April 2001, the Department of Energy uses a real discount rate of 3.3 percent or a nominal discount rate of 6.1 percent for 2001 (the projected rate of general price inflation was 2.7%).

According to NISTIR 85-3273-17, April 2002, the Department of Energy uses a real discount rate of 3.2 percent or a nominal discount rate of 5.6 percent for 2002 (the projected rate of general price inflation was 2.3%).

The following table sums up all the discount rates used by DOE from 1996 until 2002:

III. Discount Rates Used by Other Federal Agencies

The Congressional Budget office (CBO) since 1990 has used a real rate of 2% (Thompson and Green, 1998; Bazelon and Smetters, 1999, p222). Analysts are directed to perform sensitivity analysis using plus and minus 2 percent around this rate (Bazelon and Smetters, 1999, p222).

The General Accounting Office (GAO) generally uses lower discount rate than the OMB recommended rates based on the average nominal yield on treasury debt minus the inflation rate. They recommends the use of a very low discount rate when analyzing policies with large intergenerational effects involving human life. They use especially lower rates (close to zero) for projects with strong intergenerational health effects. The logic seems to be that the individual's growth in productivity would offset the interest rate. Thus if the discount rate is 2.5% and the productivity growth rate is 2%, the GAO would suggest what is usually called a net discount rate of 0.5%.

Water resource projects, contracting out, and federal energy management programs are exempt from GAO and OMB guidelines. These projects fall under different regulations. Water resource projects have been justly criticized in the past for using nominal interest rates with real dollar benefits and costs (see Lyons, pS-31). The current guidance for water resource projects is the approved Economic and Environmental Principles and Guidelines for Water and Related Land Resources Implementation Studies (Principles and Guidelines, 1983). It requires the agencies to calculate present values of projects using the discount rate established annually for the formulation and economic evaluation of plans for water and related land resources plans. And the guidance for federal energy programs can be found in the Federal Register of January 25, 1990, and November 20, 1990 (Volume 55). In these guidances, the Department of Energy (DOE) states that measuring the interest rate on U.S. Treasury bonds and removing the effects of inflation is the appropriate procedure for setting a market-based discount rate to be used in performing life cycle cost analyses for purposes of estimating and comparing the cost effects of investing in greater energy efficiency in Federal buildings. The discount rate will be set by DOE for one-year intervals coinciding with the Federal fiscal year, and the supporting tables for use in life cycle cost analysis are to be made available in an annual supplement to the Life Cycle Costing Manual for the Federal Energy Management Program (NIST 85-3273) issued at the beginning of each fiscal year.

The rates used by the Corp of Engineers have varied from as low as 2.5% to as high as 8.75% over the period from 1957 through 1980 . (Zerbe and Dively, 1994, p277-278.) There also have been peculiar practices required of the Army Corp and the Bureau of Reclamation by which real rates are to be used with nominal benefits and costs. This practice of combining real and nominal values makes no sense and economists at the Corp and at the Bureau of Reclamation with whom we (Zerbe) have talked recognize this. We are unable to determine the origin of this practice.

In short, there is a lack of consistency for Federal government use of discount rates. The range of federal rates used by federal agencies is then from 2% to 7% in real terms, though the effective real rate used by the Bureau of Reclamation and the Corp of Engineers could be even higher when market rates , which include an expected inflation component, are applied to expected real benefits and costs.

In so far as government rates are based on Treasury bond rates which is the case with OMB lease purchase decision and with the rates used by the Bureau of Reclamation and the Corp of Engineers, it is recommended that bonds be chosen whose terms correspond with the time period of the project. This means that longer lived projects would be evaluated with larger interest rates.

The yields on Treasury instruments (over the period from January 1979 to February 2002) would yield a low real rate of 2.1% in February 2002 on 3-year notes and a high real rate of 7.9% in February 1982 for 30-year projects (the current OMB circular A-94). Such rates normally increase with time due to inflation risk. If this logic is extended to very long lived projects it suggests quite large discount rates.

As far as we can discern no one has systemically collected information for discount rates used by various state governments. There appears to be no general knowledge of how the use of discount rates vary across state governments or what rates they use, although this knowledge can be gathered state by state. The justification for government rates has ranged from using the rate on government bonds (the government cost of capital) to using the rate on private capital to using the social rate of time preference.

Little has been published about municipal use of discount rates. Consequently we attach an Appendix that contains an unpublished survey of municipal rates that some of us undertook (Zerbe and Dively, 1993). A random sample of 72 cities with populations over 100,000 were asked a series of questions of their use and understanding of the use of capital budgeting and discount rates. About 37% reported they use such rates and as many as 46% may use them indirectly through consultants. That is, over half of municipal governments with populations over 100,000 do not use discount rates in their planning. The roughly 40% of municipal governments that use rates generally use a real rate in the 2.5% - 3.5% range. The only variable we found that is correlated with the use of discount rates is that cities with independently elected officials are more likely to use (and to understand) discount rates than other cities. Some municipal government consciously avoid benefit cost analysis and the use of discount rates. Interesting, expressed rationale in many cases is the desire to make decisions on a purely political basis which they find is complicated by the use of benefit cost analysis and the attendant use of discount rates.

The basis for the choice of discount rates varies among agencies and appears to have been significantly influenced by academic literature at the Federal level. The issues that have motivated these debates involve questions of whether risk should be treated differently for government investments than for private investments, and whether the rate of time preference on the one hand or the opportunity cost of capital on the other is the more appropriate for government rates. In the case of municipal governments, however, the driving force appears to simply be the rate the municipality must pay on its bonds.

There has been a debate in the economics literature for some time whether rates should reflect the social rate of time preference (SRTP) or the opportunity cost of capital (OCR). The SRTP is the rate at which individuals are willing to trade off present for future consumption. Some agencies base their choice of rates on a social rate of time preference (e.g., Congressional Budget Office, and General Accounting Office). This rate is commonly equated with the risk free rate of return on government bonds, though there is no definitive SRTP rate. Other federal agencies such as OMB, base their rates on the price of capital in the private sector-the before tax rate of return to private capital. Others, most commonly municipal governments, base their rate on their own costs of capital which they see as the interest they must pay to issue bonds so that in practice those that base their rate on the SRTP and pragmatically on the cost of generating government capital tend to choose about the same rates. The OCR rates tend to be significantly higher than the rates based on the yield on government bonds so that OCR rates are generally significantly higher than rates used by municipalities or rates based on the SRTP.

A parallel debate has concerned whether or not government discount rates should include a risk premium as they do in the private sector. In general, private rates of return are said to equal the risk-free rate plus a risk premium depending on the market risk of the equity. The return to equities above government bills is said to have averaged 6 percentage points a year during the past century, an astronomical difference when compounded over time (Bazelon and Smetters. 1999). Bazelon and Smetters conclude that there is no good reason for the government to use different rates from the private sector.

A paper by Lind and Arrow (1970), however, suggests that government should use a risk-free rate. Bazelon and Smetters note that this view has "had considerable influence inside the Washington Beltway" (p214).

Table 4 shows realized real interest rates, that is actual interest rates minus actual inflation, for various yields and time periods. The actual real rates for 20-year United States Treasury Bonds varies from 2.46% to 5.17%. The rates are similar though slightly higher for 30-year Treasury Bonds. Rates for periods with little inflation and with little change in inflation have a particular appeal since rates during these periods are likely to be less influenced by expectations of inflation or by changes in inflation. Because of low levels of inflation and/or a low variance in inflation rates, three periods of particular interest are the periods 1881-1951, 1885-93, 1890-1915. During these periods, actual real rates on American Railroad bonds varied between 3.76% to 4.62%. Rates on Prime Commercial Paper in the latter period averaged 5.24%. In the period 1885-93, inflation was zero throughout. In this eight-year period, the average yield on American Railroad bonds was 4.62% with a standard deviation of 0.13%. The range of rates two standard deviations to either side of this 4.62% rate is between 4.36% to 4.88%.

The smallest actual real rates mentioned in Table 4 are for the period 1953-88-89 and are about 2.5% for 20-year bonds. But, as is now well recognized, part of this period included egregious misjudgments about what the rate of inflation would be. The highest rates in Table 2 are those for the period before 1900. These should not be given as much weight as more recent rates. The rate of 4.62% for the period of greatest economic stability, 1885-1893, lays well within the range of rates derived from the expected real rates in Table 1 of 3.5% to 5.5%. A range of rates during this period of greater economic stability based on four standard deviations around the mean is included in this range.

The figures here are supported by calculations from another source. Table 5 shows long-term realized real interest rates calculated by Barro (1993).

Period	Real Interest Rate (percent)
1840-1860	9.1
1867-1880	9.1
1880-1900	6.3
1900-1916	3.1
1920-1940	4.9
1947-1960	-0.2
1960-1980	1.2
1980-1990	4.8
Weighted Average 1840-1990	4.87
Weighted Average 1840-1990 without 1947-60	5.38

The above data use realized real interest rates which subtract actual inflation from the nominal discount rate. This results in a bias when the realized or actual rates differ from the expected rates. We can make this clearer through the following relationships. The expected real rate of return (ERR) is recognized to be the conceptually correct measure of the discount rate to use with inflation adjusted income streams because it represents the rate at which people are willing to lend or to borrow. This is approximately equal to the market or nominal rate of return minus expected inflation. That is, the expected real rate is approximately calculated as follows (see equation 2):

ERR = Nominal Rate - Expected Inflation (6)

The realized real rate of return (RRR) is different; it is the nominal rate of return minus actual inflation. That is:

RRR = Nominal Rate -Actual Inflation (7)

The difference in the expected real rate and the realized real rate is then equal to

ERR - RRR = (Actual Inflation - Expected Inflation) (8)

That is, the realized real rate of return is given by

RRR = ERR + (Expected Inflation - Realized Inflation) (9)

Equation (9) shows the source of the bias. The realized real rate will only be the unbiased rate with expected inflatioin equals realized inflation. If realized inflation exceeds expected inflation, the realized real rate will be lower than the expected real rate of return by the difference between actual and expected inflation. The estimate of the expected real rate of return will then be too low. If expected inflation exceeds actual inflation, the reverse is true. Systematic bias between the expected real rate and the realized real rate will be smaller in the long run; otherwise people will learn to gain from exploiting this bias. Thus, in calculating real rates of return, the longer the time period used the better.

In practice often short period discount rates are used as representative of the rates applying over longer periods. The use of short periods can result in biased estimates when there is a significant divergence between actual and expected inflation. For example, real discount rates are low during the 1950's and 1960's because expected inflation was less than actual inflation. Since actual inflation experienced is usually used to calculate real interest rates, the subtracted amount is too large in this situation. Similarly, net discount rates (nominal retes minus productivity growth) during the period from 1950 through 1973 are low by historical standards because the rate of growth of capital relative to the rate of growth of labor was unusually high by historical standards not only in the United States but also in most other developed countries. These differential rates of growth produced a relatively high rate of growth of wages and a relatively low rate of return to capital so that the net discount rate during this period contains a downward bias when judged by long-term historical standards and by the experience since 1980.

With the above definitions in hand we can establish the proposition that real interest rates during the 1953-1990 period understate the real discount rate to be applied to future periods.

From the previous discussion it is sufficient to establish that during most of the 1950-1991 period, actual inflation exceeded expected inflation by significant amounts. That this is the case that is well recognized (Barro, 1993; Theis, 1982; Walsh, 1987; Huizanga and Miskin, 1984; Nelson and Plosser, 1982.) Table 6 shows the difference between expected inflation according to the Livingston Index and actual inflation by decade. A negative number means that actual inflation exceeded expected inflation, and a positive number indicates that expected inflation was larger.

* Calculated from Barro (1993) p176-177.

Table 6 suggests that a real interest rate calculated using actual inflation during the period 1950-1979 would underestimate the real interest rate by about 1.3 percentage points. The downward bias is probably greater than this since the Livingstone index used to calculate expected inflation produces less of a difference between expected and actual interest rates than other measures. Real interest rates during the period 1947-1980 were about 1%. For the whole period 1840 through 1990, omitting the war years, the real interest rates averaged 5%.

Table 6 suggests the proposition that the realized real rates of the 1980's, 1990 and 1991 will be better predictors of rates in the future than earlier post-war rates. Table 6 suggests that the real interest rate calculated using actual inflation in the 1980's and 1990's has a upward bias but that this upward bias is much smaller than bias of the previous three decades. In addition, Huizinga and Mishkin (1984), Nelson and Plosser (1982), and Walsh (1987) present evidence to suggest there has been a shift in the structural real rate process beginning about October 1979. This suggests that expected real rates during the post-war period, before the 1980's, understate expected real rates in the near future. Expected real rates have been higher during the 1980's than earlier in the post-war period (Walsh, 1987). Walsh finds that a 1% change in nominal rates during the period 1979 QIV to 1984 QIII was on the average produced by a 0.8% change in expected real rates and by a 0.2% change in expected inflation.

Even aside from a change in structure, to some extent, changes in rates have a random walk component. That is, if the rate goes up there is no tendency to return to any average or trend line value (See Nelson and Plosser, 1982, for example). Thus, the use of the 1953-90 period to calculate actual real rates will lead to substantial errors in the calculation of the real discount rate because it includes a substantial period with a downward bias for expected real interest rates, and because the most recent period, the period since 1979, has shown higher expected real rates which should be given greater weight given the evidence of a change in the structural rate process and in the existence of auto correlation among rates. These considerations, taken together, suggest the real discount rate during the 1980's should be given more weight than the 1953-90 period as a whole.

We have suggested that examining actual real rates in the post-war period, except for the 1980-90 period, will yield biased estimates of real discount rates and that net discount rates during this period may also be biased. Several alternatives are possible. We can examine expected instead of actual discount rates, and we can examine longer time periods. We do both of these below. Table 7 shows expected real rates calculated from several sources.

The rates shown in Table 7 vary from 2.09 to 5.82%. The 2.09% real rates result from use of the Livingstone poll. Unlike all of the other polls this is based on a survey of economists. The other polls based on expectations of businessmen and may more accurately reflect what the market expects. These real rates are significantly higher than the 1% or less that is sometimes cited.

In court cases, the value of life is usually determined by taking the present value of expected lifetime earnings, or, in some states, of earnings minus consumption. An issue is what discount rate to use. One way of avoiding the issue of using realized versus expected real interest rates is to calculate the net discount rate. The net discount rate is found by subtracting the growth in earnings from the nominal or market interest rate. This procedure has led to arguments for a total offset method, which is simply the use of a zero discount rate applied to the assumption of the continuation of the existing earnings level, perhaps with a life cycle earnings adjustment. The net discount rate may be defined approximately as:

Net Discount Rate = Market Interest Rate - Nominal Wage Growth (4)

An exact definition can be made by referring to equation (3). If we define k as [(1+R)/(1+G)] -1, we can more formally define k as the net discount rate. Note that the above expression for K will approximately equal R-G. If R and G contain the same inflation component, then k will also equal r -g where the lower case letters refer to real components. Equation (3) may now be written solely in terms of real components as:

(5)

Clearly the use of the net discount rate will give the same answer as the use of nominal or real rates since equation (5) is the same as equation (3).

The net discount rate will be influenced by capital labor ratios and by technological progress. If the growth of capital relative to labor were especially high during some historical period the rate of growth of wages to the interest rate would be particularly large, and the use of this period as a guide to the future net discount rate would be biased downward. The use of a time period such as from 1953 to 1990 to calculate net discount rates raises the question of whether or not this is reasonably representative of the future.

The period from about 1950 to about 1973 was the "golden age of growth" for a period running from about the end of the Napoleonic Wars, say from 1820, to the present for all of the developed countries. For developing nations including the United States, as shown in Table 8.

GDP per person during this period increased at significantly higher rate than in other periods, an average rate of 3.8 % per person per year for all developed countries, a rate far greater than occurs elsewhere in this period. For example, the growth rate during the period from 1870 to 1950 is about 1.3% per year in GDP per person. In the U. S. this period is not quite as dramatic but nevertheless clearly stands out as is shown in Table 9.

1	Time Period	1820-70	1870-1913	1913-50	1950-73	1973-89
2	GDPa	4.5	3.9	2.8	3.6	2.7
3	GDP per Headb	1.5	1.8	1.6	2.2	1.6
4	Net Non-Residential Capital Stockc			1.69	3.84	2.59
5	Adusted Labor Inputs d			0.85	1.67	1.87
6	Capital. minus Labor growth			0.84	2.17	0.72
7	Productivity: Output per Man Houre	–	1.9	2.4	2.5	1.0

Table 6 shows that the period 1950-1973 was a period of unusual growth in capital relative to labor and that therefore wages should be unusually high during this period relative to the return to capital, that is relative to interest rates.

We now examine the net discount rate over a longer period than the post war-period. Table 10 below shows the net discount rate from 1890 to 1990. Column F shows the net discount rate using wage compensation. Column E shows the net discount rate using total compensation. Total compensation figures are not reported before 1948; they differ from wages in including fringe benefits. Benefits were not increasing as a percentage of wages before W.W.II, and immediately following . This is suggested by the fact that the percentage increase in wages is the same as for total compensation for the 1953-59 period. Thus the wage should give an accurate figure for the net discount rate for the pre-war period. In the post-war period, the yearly increase in fringe benefits has been about 0.6 percentage points greater than the increase in wages. This is shown by Table 10 below.

If we use the growth of wages before the war, not counting the depression, we find that real earnings grew at about 2.17 % per year. Since these are changes in real compensation, they must be subtracted from changes in real interest rates to obtain a net discount rate. Comparing this with our expected real rate of about 3.5 to 5 percent in Table 7 gives a rate of about 1.3% to 2.8% as the net discount rate.

A direct determination of real rates earnings and total compensation gives a similar result as shown in Tables 10 and 11.

Column D in Table 10 shows the net discount rate. Column C shows the figures using the rate of return on commercial paper and manufacturing wages. Column E shows the net discount rate using total compensation. The shaded areas show the applicable net discount rate for the indicated periods. The use of Commercial paper rates give a downward bias to the rates since these are very short term rates and are used only because they are available for long time periods. Table 11 shows the net discount rate for selected periods. For the period before W.W.II , the rate of growth in earnings is used in calculating the net discount rate, and for the period after the war, the growth in total compensation is used. The war periods should be disregarded because controls on wage and interest rates do not allow the calculation of accurate figures. A depression as severe as that during the 1930's is unlikely to occur again so the depression years should also be eliminated. The argument for treating the period 1950-as special has already been made here. Finally, the period 1946-49 shows negative real interest rates and represents the effect of a continuation of war time controls so that this period also should not be included. The figure of 2.47 % appears to represent the better figure. The period producing this rate eliminates the war periods, the depression years, the period from 1950-1970 because of its special nature, and the period 1946-49 when controls led to a negative real discount rate. This rate is especially supportable because of the downward bias from using commercial paper rates. A net discount rate of zero or less than 1.0 percent appears to be without justification.

Table 8: Average Net Discount Rates for Selected Periods
Av. Net Discount Rate w/o War Periods	1.44 %
Av. Net Discount Rate w/o War Periods & 1950-70	1.71%
Av. Net Discount Rate w/o War Periods & Depression	1.91 %
Av. Net Discount Rate w/o War, Depression and Period 1946-1969	2.47 %

• Federal Government agencies are inconsistent, among themselves and sometimes internally and sometimes over time, in their use of discount rates.
• In some cases Federal agencies use nominal discount rates with real benefits and costs in defiance of logic and theory.
• Federal Government agencies have no recommendations as to the use of discount rates when considering the far future.
• Little information is available on the use of discount rates by state governments.
• A bit less than half of municipal governments with populations over 100,000 appear to use discount rates.
• Municipalities sometimes avoid the use of benefit-cost analysis with its associated discount rates for polictical reasons.
• Their use is positively correlated when the presence of independly elected finanacial examiners.
• Projects analysis should use real discount rates with real benefits and costs.
• Real rates should be calculated using expected inflation rather than actual inflation, though the use of actual inflation is the usual practice.
• Over the 1953-1989 period, expected real rates vary between about 2% and 5%.
• Over the period from 1857-1989, expected real rates vary betweeen about 2% and 9.4%.
• Thus, there is considerable volatiliaty in expected real rates over long periods.
• The use of post war realized or actual real rates, particularly in the 1950-1975 period result in rates that are biased downward.
• Net discount rates over the 1890-1991 period vary beween 6.9% and -1.34%.
• Average net discont rates over this period eliminating periods of war and depression are about 2.5%.

Net discount rates during the 1950-1973 period are lower than during other historical periods probably since 1820.

Net discount rates during the period 1950-73 are biased downward when applied to future net discount rates.

A figure of about 5% is a reasonable estimate of the real discount rate.

Not only is this about the long term historical average, but it is about the rate that has prevailed in the most recent period. Long-term real productivity growth has been about 1.5-2.0 percent per year which suggests a net discount rate of about 3.0 to 3.5 percent.

Boardman, Greenberg, Vining, and Weimer. Cost Benefit Analysis in Practice, 2001.

Klein, Linda. "Discounting Guide, Report No. 01-11-01", Cost Analyst Division.

Almost nothing is known about municipal use of techniques for evaluation of capital projects and the associated discount rate for project evaluation. In response to this lack of specific knowledge we surveyed municipal use of discount rates for capital project analysis through telephone and written surveys for 72 American cities in the fall of 1990 and the Spring of 1991.

The results suggest that substantial efficiency gains are available from the introduction of capital budgeting techniques into municipal decision making, and that one way in which efficiency can be realized is by providing for independently elected financial officials. The presence of these officials is associated with the greater use of discount rates by cities, and quite probably with greater efficiency in capital budgeting decisions. The survey showed that most cities do not use discount rates, but instead a variety of ad hoc and political techniques to choose capital projects. The most common technique for choosing a discount rate was the city's cost of capital.

Two types of discount rate surveys were used. First, telephone interviews were held with officials from the budget offices of 27 randomly selected cities with populations greater than 105,000 scattered throughout the country. Second, written surveys were sent to the budget directors of 81 randomly selected cities, of which 51 were returned, representing a 63 percent response rate. We used both telephone and written surveys to determine if there were differences in replies by type of survey instrument. We could determine no differences. Six cities were duplicated between the two groups in order to assess the validity of combining the surveys. Thus, a total of 72 different cities responded to the survey.

The sample of cities provide a diverse sample of major U.S. municipalities. Only cities with populations in excess of 100,000 were included since smaller cities are less likely to have the types of projects that require discount rate analysis. The responding cities represented 37 states and ranged in population from Eugene, Oregon at 112,669 to Los Angeles, California at 3,485,398. The list of cities is shown in Table 1.

Both the telephone and written surveys asked the same questions about the discount rate. The telephone surveys contained a substantial introductory discussion to elicit the level of understanding about benefit-cost techniques for capital budgeting techniques. We found in discussions that lack of knowledge about the function of discount rates seems a very good proxy for lack of knowledge about evaluative capital budgeting techniques in general. The specific discount rate questions were:

In addition, the surveys gathered information about the types of utilities operated by the responding cities. This information was collected since utilities often have capital projects that are the subject of detailed financial analysis.

At the conclusion of the survey processes, the results for the six cities that were in both the telephone and written samples were compared. In general, the responses to the two types of surveys were sufficiently similar to allow the samples to be combined.

The surveys revealed that the use of discount rates among major cities is less prevalent than had been assumed. Less than half of the cities sampled (37.5 percent) use discount rates for project evaluation, and several of these indicated that the use is infrequent. Furthermore, the surveys suggested that many municipal finance officials are completely unaware of the concept of discount rates or of benefit cost analysis. Officials in about 15 cities indicated that they had never heard of the term, and several others confused it with the lending rates set by the Federal Reserve Board. The same lack of knowledge showed up in telephone interviews we conducted in which we attempted assiduously to make sure we were speaking with the highest level and best qualified city employee.

As part of the telephone survey, cities that do not use discount rates were asked to explain how they evaluate projects. Most of the responses indicated that projects were identified based on perceived needs or political priorities, without any form of comparative quantitative analysis. In a few cases, cities indicated that they relied on recommendations from experts, who might use cost-benefit analysis in making those recommendations. Thus, the actual use of discount rates may be greater than 37.5 percent, with an upper bound of 43%, if this implicit use by consultants is included.

About half of the cities using discount rates indicated that different rates may be used in some cases. This typically involves rates used for projects paid for by special enterprise funds, including airports or water systems. The approach for setting discount rates is usually the same regardless of the funding source, but the actual rate may vary. For example, cities that use the current cost of capital for setting the discount rate may have different costs of capital for different purposes.

Cities use a wide range of approaches for selecting discount rates, with a few cities relying on a combination of approaches. Nine distinct types of approaches were identified. These are listed below in the order of frequency:

The average discount rate used by the 38 percent of cities that used a discount rate was a nominal rate of 7.89 percent, with a range between 5.00 and 10.00 percent. The real rate appears to have been about 3 percent given that expected inflation was about 5% at the time. A real discount rate of 3% is consistent with the range of 2.5% to 5% recommended by Lyons (1990), by Zerbe(1992) and by Lesser and Zerbe (1994). The real (inflation adjusted) cost of capital can be reasonably represented by the after tax rate on long term (20 year bonds) government bonds and by the rate of return of safe financial instruments such as long term railroad bonds or the rate of return on commercial paper. The rates on these instruments over the period from 1900 to 1990 show a range of real rates of between about 2.5 to 5 % (Zerbe, 1992). We think this is a reasonable range to use as the discount rate for government projects. Only three cities have rates outside of our recommended range, and one (Baltimore) is right at the edge of the lower range., and one is a bit less than 0.5 percentage points below our lower range. The third city, Lincoln Nebraska, has a real rate of zero, which seems clearly inappropriate.

Lincoln is also the only city that uses discount rates that clearly has an inappropriate method (uses the inflation rate). The eight cities (category 2) that use the current return on invested funds use short term rates for long term projects, and their rates tend to fall into the bottom of the range. Nevertheless, these rates tend to be within the recommended range.

There is no unanimity among the cities regarding the frequency with which the discount rate should be revised. Five different approaches were mentioned:

In practice, revisions as needed, continuous revisions, revisions after each bond issue, and monthly revisions probably amount to the same thing. Yearly revisions presumably give less variability in rates used, but probably do not yield a difference in average rates.

We considered the following variables in connection with the use of discount rates.

Geographical location. Cities in some sections of the country might make more extensive use of discount rates because of prevailing practices or the presence of educational institutions emphasizing such techniques. The survey revealed some such geographical differences. Discount rates seem to be used more often by cities in the West Coast, Great Lakes, and Middle Atlantic states. Discount rates seem to be the least used by cities in the New England and Southern states. The surveys revealed no obvious reason for these differences.

As a more sophisticated statistical approach a logit equation was run in which the dependent variable was a binary variable, the use or non-use of the discount rate. In a logit equation the coefficients represent the effect of the variable on the log of the odds-here the odds of using a discount rate. In each equation there were two independent variables; independently elected financial officials was run separately with population, population growth and city age. In all of these two variable runs, independently elected financial officials is significant at better than the 5% level. The cities growth rate is close to significance at the 11% level, and the other variables are not significant. The Tables in the Appendix report the statistics for three of the runs with two variables.

The major result of the data analysis to compare differences in means is that cities with independently elected officials are more likely to use (and to understand) discount rates than other cities. A test of the differences in means suggests that cites with higher population growth rates are less likely to use discount rates. Older cities may be more likely to use discount rates, but cities with larger populations may be more likely to use them. The presence of utilities and bond rating appear not to be correlated with the use of discount rates. The survey also revealed that discount rates appear to be used more frequently in cities in the West Coast, Great Lakes and Middle Atlantic states. They are least used by the New England and Southern states. The survey revealed no obvious reason for these differences.

Most municipal governments may not use discount rates and appear not to understand present value analysis. A number of these were rather forthright about political concerns dominating investment decisions and gave as a reason for not using discount rates that their use would make politically based decisions more difficult. This explanation is consistent with the major finding that the presence of independently elected finance officials significantly increases the use of discount rates and the understanding of present value analysis. Such officials may reduce the discretion of others in an administration. It seems possible that the existence of such officials is cost-effective from a financial perspective.

A potentially important finding is that cities with independently elected finance review officials are more likely to use a discount rate, suggesting the possibility that the presence of these review officials produces a higher standard of analysis. What this study strongly suggests most strongly is that there is substantial opportunity for improving the efficiency of capital budgeting by municipal governments. It also suggests that one way to do this is to have an independently elected financial official.

Of the approximately 40% of municipal governments that use discount rates almost all use some variant of the cost of capital to determine the rate. The range of rates they exhibit, at least at the point in time we examined, is almost entirely within the range we have determined to represent the range for the real after tax return to government bonds which in turn appears consistent with social rate of time preference rate suggested by economic theory (Zerbe and Lesser, 1994) Thus, municipal use of discount rates is more consistent among municipalities and more consistent with theory than are rates used by different divisions within the Federal government. The Federal Office of Management and the Budget (OMB) (in circular A-94) at the time this survey was written recommended and often required a real (inflation adjusted) rate of 10%, far higher than theory would suggest. Congressional agencies use other rates (Lyons, 1990).

A complete explanation of why certain cities use discount rates would require further research. Such research might focus on the role of state laws in influencing city budget practices, the form of city government, a more comprehensive review of the types of capital projects undertaken by cities, and on the educational backgrounds of budget officers in different parts of the country.

There is no unanimity among cities regarding the frequency with which the discount rate should be revised or reexamined. We found no statistically significant relationship between population size and the probability of using a discount rate, although there is some suggestion that there is a weak, positive correlation. Older cities appear are more likely to use a discount rate. We do not know why older cities may be more likely to use a discount rate. Cities that are growing faster are less likely to use discount rate, and this appears to be due mainly to the fact that older cities are more slowing growing and are more likely to use a discount rate than newer cities. Neither the importance of city utilities nor the cities bond rating are correlated with the use of a discount rate.

Albuquerque, NM No – – – –

Anaheim, CA Yes 9.00 4.00 Current return on funds Annually

Anchorage, AK No – – – –

Arlington, TX No – – –

Atlanta, GA Yes 7.50 2.5 Current cost of capital Continuously

Baltimore, MD Yes 7.48 2.48 Current cost of capital As needed

Baton Rouge, LA Yes 7.02 2.02 Estimate by consultant Each bond issue

Birmingham, AL No – – – –

Boise, ID No – – –

Boston, MA No – – –

Bridgeport, CT No – – – –

Buffalo, NY Yes 8.00 3.0 Estimate by consultant Annually

Charlotte, NC No – – – –

Cincinnati, OH Yes 8.00 3.0– Current cost of capital Annually

Columbus, OH No – – – –

Corpus Christi, TX No – – – –

Dallas, TX No – – – –

Dayton, OH Yes 7.75 2.75– Current return on funds As needed

Denver, CO Yes varies varies– Current cost of capital; As needed

current return on funds

Des Moines, IA No – – – –

Detroit, MI No – – – –

Eugene, OR Yes 8.50 3.5 Current return on funds As needed

Fort Wayne, IN No – – – –

Fresno, CA No – – – –

Hartford, CT No – – – –

Honolulu, HI No – – – –

Houston, TX No – – – –

Indianapolis, IN Yes 7.50 2.5 Bond yields for other cities Annually

Jackson, MS No – – – –

Jersey City, NJ No – – – –

Kansas City, MO No – – – –

Knoxville, TN No – – – –

Lincoln, NE Yes 5.00 0 Inflation rate Annually

Little Rock, AR No – – –

Los Angeles, CA Yes varies – Current cost of capital Continuously

Louisville, KY Yes 8.00 3.0 Bond yields for other cities Monthly

Madison, WI No – – – –

Memphis, TN No – – – –

Miami, FL Yes 7.00 2.00 Estimate by consultant Annually

Milwaukee, WI Yes 7.00 2.00 Current cost of capital Annually

Minneapolis, MN Yes 10.00 5.00 Taxpayer cost of capital As needed

Mobile, AL No – – – –

Nashville–Davidson, TN No – – – –

New Orleans, LA No – – – –

Oakland, CA No – – – –

Omaha, NE No – – – –

Orlando, FL No – – – –

Paterson, NJ No – – – –

Peoria, IL No – – – –

Philadelphia, PA Yes varies – Long-term bond rate As needed

Phoenix, AZ No – – – –

Pittsburgh, PA Yes 8.50 3.50 Current cost of capital; Annually

cost of existing debt

Portland, OR Yes 7.50 2.50 Current return on funds As needed

Raleigh, NC No – – – –

Richmond, VA No – – – –

Rochester, NY Yes varies 3.75 Estimate by consultant As needed

Sacramento, CA Yes 8.75 3.75– Current return on funds As needed

Saint Paul, MN No – – – –

Saint Petersburg, FL No – – – –

Salt Lake City, UT No – – – –

San Diego, CA No – – – –

San Francisco, CA Yes 7.50 2.50– Current cost of capital; Continuously

cost of existing debt;

inflation plus real rate

San Jose, CA No – – –

Santa Ana, CA No – – – –

Seattle, WA Yes 7.50 2.50– Inflation plus real rate As needed

Spokane, WA Yes 8.50 3.50– Current return on funds As needed

Stockton, CA No – – – –

Syracuse, NY No – – – –

Tucson, AZ Yes 10.00 5.00– Current cost of capital, Continuously

modified by risk of project

Tulsa, OK Yes varies – Current return on funds As needed

Winston–Salem, NC No – – – –

Yonkers, NY Yes 7.50 2.50– Bond yields for other cities Annually

Average 8.06 3.06

1. Forrester, John P. "Municipal Capital Budgeting: An Examination", Journal of Pubic Budgeting and Finance, 13, (2) Summer 1993

2. Havrilesky, Thomas, "New Evidence on Expected Long Term Real Interest Rates", Journal of Forensic Economics, Summer, 1988

3. Judge, George G. R. Carter Hill, William E. Griffiths, Helmut Lutkepohl and Tsoung-Chao Lee, An Introduction to the Theory and P{ractice of Econometrics, Second Editon, New York: John Wiley & Sons, 1988

4. Lind, R. C., "Reassessing the Government's Discount Rate Policy in Light of New Theory and Data in a World Economy With Integrated Capital Markets," Journal of Environmental Economics and Management 18:S-8 - S-28 (1990).

5. Lyons, Randolph, "Federal Discount Rate Policy, The Shadow Price of Capital and Challenges for Reforms", 18 Journal of Environmental Economics and Management S29-S50 (1990).

6. Zerbe, Richard O. Jr. "Recommendations for Government Discount Rate Policy", No. 92-1, Working Papers in Public Policy Analysis and Management, Graduate School of Public Affairs, (1992)

7. Zerbe, Richard O. Jr. and Dwight Dively, Benefit Cost Analysis in Theory and Practice, Harper Collins (1994).

8. Zerbe, Richard O. Jr. and Jonathan Lesser, "Discounting Procedures for Environmental and Other Projects: A Comment on Kolb and Scherage", JPAM, Winter, 1994

The following three tables show the coefficients for the two variable logit runs. The sample sizes are 45, 44, and 45 for the three cases.

Appendix

Nominal or real interest rates and are used to discount economic loss to present value in tort cases. Nominal discount rates are market rates in current dollars, that is, unadjusted for inflation. Real rates are nominal rates adjusted for inflation. Similar definitions apply to nominal and real wage growth. The relationships are approximately as follows:

Market Rate (Nominal Rate) = Real Rate + Inflation (1)

Real Rate = Nominal Rate - Inflation. (2)

As long as the market discount rate is used with nominal wages and the real discount rate is used with real wages, the use of the nominal and real rates will give the same answer as long as the inflation component is the same. This may be seen by writing out the expression for the net present value of a wage stream:

(3)

where

g is the nominal or market growth wages in wages,

W_ois the wage one period before the initial period, and

r is the nominal or market discount rate.

The nominal growth rate, G, will equal [(1 + I)(1 + g)]-1 where

I is the Inflation rate and

g is the real (inflation adjusted) growth rate.

Similarly, the nominal discount rate, r, will equal [(1 + I) (1+ r)]-1

where r is the real (inflation adjusted) discount rate.

The expression containing the inflation components will then divide out as long as the inflation components are the same in the denominator and numerator so that equation (4) may be written as:

(4)