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More appropriate discounting: the rate of social time preference and the value of the social discount rate

  • Mark A. Moore EMAIL logo , Anthony E. Boardman and Aidan R. Vining

Abstract

Recently, a number of authors, including Burgess and Zerbe, have recommended the use of a real social discount rate (SDR) in the range of 6–8% in benefit-cost analysis (BCA) of public projects. They derive this rate based on the social opportunity cost of capital (SOC) method. In contrast, this article argues that the correct method is to discount future impacts based on the rate of social time preference (STP). Flows in or out of private investment should be multiplied by the shadow price of capital (SPC). Using this method and employing recent United States data, we obtain an estimate of the rate of STP of 3.5% and an SPC of 2.2. We also re-estimate the SDR using the SOC method and conclude that, even if analysts continue to use this method, they should use a considerably lower rate of about 5%.


Corresponding author: Mark A. Moore, Beedie School of Business, Simon Fraser University, 500 Granville St., Vancouver, BC, V6C 1W6, Canada

The authors wish to thank Daniel Cole, David Greenberg, David Weimer and two anonymous referees for helpful comments. We would also like to thank Joy Begley for assistance with the WRDS database.

  1. 1

    Zerbe et al. (2011, p. 84), accessed 29 August, 2012.

  2. 2

    For a recent review and discussion in a BCA context see Boardman, Moore and Vining (2010).

  3. 3

    The discount factor that society should apply to consumption in period t is given by . It equals the product of (ct), the derivative of U(ct) with respect to ct, which is the marginal utility of consumption, and the discount factor for utility of consumption, e-ρt.

  4. 4

    Given that , then the rate of change of the absolute value of the discount factor, which equals divided by , is ρ+gε, where, , is the rate of change in per capita consumption, and , which is the absolute value of the elasticity of the marginal utility of consumption with respect to consumption. We drop the time subscript on c for simplicity.

  5. 5

    If U(c)=ln(c), then =1/c and ε=1. In this case, the marginal utility of consumption equals the inverse of per capita consumption. Therefore, a 10% reduction in the per capita consumption of the current generation (for example, from $50,000 to $45,000) is equivalent to a 10% reduction in the per capita consumption of a richer future generation (for example, from $100,000 to $90,000).

  6. 6

    We would like to thank an anonymous referee for pointing out an error in this formula in a draft of this article.

  7. 7

    Such considerations have led Kula (1984) and the European Commission (2008) to suggest that ρ can be inferred from the population’s annual death rate, which is an estimate of a representative individual’s instantaneous probability of death. While this might make sense for individuals who discount the future since they may not be around to enjoy it, it is not compelling from a societal perspective.

  8. 8

    Data source: http://www.econ.yale.edu/~shiller/data/chapt26.xls (accessed June 30, 2011).

  9. 9

    We computed this average in two ways. One method regresses the natural logarithm of real per capita consumption on time and the other computes the average annual growth rate based on the per capita consumption in 1947 and 2009.

  10. 10

    Evans and Sezer (2004) assume an iso-elastic utility function and that tax rates are set such that each tax payer sacrifices an equal absolute amount of utility. Based on this model, they infer that e=ln(1–t)/ln(1–T/Y), where t=marginal tax rate and T/Y=average tax rate.

  11. 11

    That is, (1–t)≥WACC, where the weighted average cost of capital is computed as: WACC=weke+wd(1-t)kd, where, ke is the cost of equity, kd is the cost of debt, we is the proportion of equity, wd is the proportion of debt, and t is the corporate tax rate.

  12. 12

    That is, , where i is the actual rate of inflation.

  13. 13

    This estimate measures total returns to the S&P 500, that is, dividends plus capital appreciation from 31 Dec 1947 to 31 Dec 2010. The returns are lower in more recent time periods. For example, the average return is 9.11% for 1987–2011, and only 1.17% for the most recent decade.

  14. 14

    Federal Reserve Bank of St. Louis Economic Research (FRED) using Moody’s “Seasoned Aaa” corporate bonds (AAA) for 1948–2011, available at http://research.stlouisfed.org/fred2/data/AAA.txt (accessed July 26, 2011).

  15. 15

    Federal Reserve Bank of St. Louis Economic Research (FRED) using Consumer Price Index for All Urban Consumers: All Items for 1947–2011, available at: http://research.stlouisfed.org/fred2/data/CPIAUCSL.txt (accessed July 27, 2011).

  16. 16

    This estimate is consistent with previous estimates of the pre-tax ROI in the US, which range between 5% and 8% (Cline, 1992; Nordhaus, 1999; Portney and Weyant, 1999). Nonetheless, we should point out that our estimate is sensitive to the tax rate and the debt to assets ratio. Damodaran computes the actual average US corporate tax rate (by dividing taxes paid for 5891 firms by the taxable income as reported to shareholders) as 15.48% (See “Cost of Capital by Sector” on http://pages.stern.nyu.edu/~adamodar/, accessed 28 August 2012). Using this lower tax rate, results in a much lower ROI of 5.27%. The estimated ROI increases as the debt to assets ratio decreases and vice versa.

  17. 17

    See FRED: www.research.stlouisfed.org/fred2/categories/106 (for GDP) and www.research.stlouisfed.org/fred2/categories/112 (for investment), accessed July 28, 2011.

  18. 18

    Based on Federal Reserve Bank of St. Louis Economic Research (FRED) Real Government Consumption Expenditures and Gross Investment, available at http://research.stlouisfed.org/fred2/categories/107 and Real GDP, available at www.research.stlouisfed.org/fred2/categories/106 (accessed August 23, 2012).

  19. 19

    Federal Reserve Bank of St. Louis Economic Research (FRED) using 10 year constant maturity US Treasury Bond rates for 1953–2011, available at http://research.stlouisfed.org/fred2/data/GS10.txt (accessed July 26, 2011). The nominal, pre-tax average monthly yields on bonds are converted to real, after-tax rates by adjusting for taxes and inflation. Shoven and Topper (1992) calculate that the personal tax rate on savings is 30%, which we use in our calculations. To measure the rate of inflation that consumer/savers expected, we use the implicit forecasts of 1-year ahead expected inflation from the Federal Reserve Bank of Philadelphia Livingston survey, http://www.philadelphiafed.org/research-and-data/real-time-center/livingston-survey/, accessed July 24, 2011. For details on our procedure, see Moore et al. (2004, pp. 800–801).

  20. 20

    For a schedule of US-derived declining rates, which are based on Newell and Pizer (2003), see Moore et al. (2004).

References

Arrow, K. J. (1995). Intergenerational equity and the rate of discount in long-term social investment. Paper presented at the IEA World Congress. Available at: http:www-econ.stanford.edu/faculty/workp/swp97005.pdf. Accessed on 11 February 2008.Search in Google Scholar

Arrow, K. J., Cline, W. R., Maler, K. -G., Munasinghe, M., Squitieri, R., & Stiglitz, J. E. (1996). Intertemporal equity, discounting and economic efficiency. In: J. P. Bruce, et al. (Eds.), Climate change 1995 (pp. 128–144). Cambridge, UK: Cambridge University Press.Search in Google Scholar

Belfield, C. R., Nores, M., Barnett, S., & Schweinhart, L. (2006). The high/scope perry preschool program: cost-benefit analysis using data from the age-40 followup. The Journal of Human Resources 41(1), 162–190.10.3368/jhr.XLI.1.162Search in Google Scholar

Boardman, A. E., Moore, M. A., & Vining, A. R. (2010). The social discount rate for Canada based on future growth in consumption. Canadian Public Policy 36(3), 323–341.10.3138/cpp.36.3.325Search in Google Scholar

Boardman, A. E., Greenberg, D. H., Vining, A. R., & Weimer, D. L. (2011). Cost-benefit analysis: concepts and practice (4th ed). Upper Saddle River, N.J.: Prentice Hall.Search in Google Scholar

Bradford, D. F. (1975). Constraints on government investment opportunities and the choice of discount rate. American Economic Review 65(5), 887–899.Search in Google Scholar

Burgess, D. F., & Zerbe, R. O. (2011). Appropriate discounting for benefit-cost analysis. Journal of Benefit-Cost Analysis 2(2), Article 2.10.2202/2152-2812.1065Search in Google Scholar

Checherita, C., & Rother, P. (2010). The impact of high and growing government debt on economic growth: an empirical investigation for the euro area. European Central Bank Working Paper No. 1237.Search in Google Scholar

Chen, D., & Mintz, J. (2011). New estimates of effective corporate tax rates on business investment. Cato Institute Tax & Budget Bullletin # 64. Feb.Search in Google Scholar

Cline, W. R. (1992). The economics of global warming. Washington, DC: Institute for International Economics.Search in Google Scholar

Cole, D. (2010). Blog on ‘Law, Economics and Cycling.’ Dec 25, Available at: http://cyclingprof.blogspot.ca/2010/12/revised-report-on-principles-standards.html.Search in Google Scholar

Cropper, M. L. (2012). How should benefits and costs be discounted in an intergenerational context? Resources for the Future Discussion Paper 12-42.10.2139/ssrn.2165532Search in Google Scholar

Eckstein, O. (1958). Water resource development: the economics of project evaluation. Cambridge, Mass: Harvard University Press.Search in Google Scholar

European Commission. (2008). Guide to cost-benefit analysis of investment projects. Available at: http://ec.europa.eu/regional_policy/sources/docgener/guides/cost/guide2008_en.pdf. Accessed on 25 October 2011.Search in Google Scholar

Evans, D. J. (2005). The elasticity of marginal utility of consumption: estimates for 20 oecd countries. Fiscal Studies 26(2), 197–224.10.1111/j.1475-5890.2005.00010.xSearch in Google Scholar

Evans, D. J., & Sezer, H. (2004). Social discount rates for six major countries. Applied Economic Letters 11(9), 557–560.10.1080/135048504200028007Search in Google Scholar

Feldstein, M. (1972). The inadequacy of weighted discount rates. In: R. Layard (Ed.), Cost-benefit analysis (pp. 311–332). Harmondsworth, UK: Penguin.Search in Google Scholar

Frederick, S., Loewenstein G., & O’Donoghue, T. (2002). Time discounting and time preference: a critical review. Journal of Economic Literature 40(2), 351–400.10.1257/jel.40.2.351Search in Google Scholar

Gollier, C., Koundouri, P., & Pantelidis, T. (2008). Declining discount rates: economic justifications and implications for long-run policy. Economic Policy 23, 759–795.10.1002/9781444307238.ch4Search in Google Scholar

Gordon, R. J. (2012). Is U.S. economic growth over? faltering innovation confronts the six headwinds. NBER Working Paper 18315.10.3386/w18315Search in Google Scholar

Harberger, A. C. (1972). On measuring the social opportunity cost of public funds. In: Project evaluation: selected papers. Chicago: University of Chicago Press.Search in Google Scholar

HM Treasury. (2003). The Green Book: appraisal and evaluation in central government. London: TSO. Available at: www.hm-treasury.gov.uk/d/green_book_complete.pdf.Search in Google Scholar

Hepburn, C. J., & Koundouri, P. (2007). Recent advances in discounting: implications for forest economics. Journal of Forest Economics 13(2–3), 169–189.10.1016/j.jfe.2007.02.008Search in Google Scholar

Jenkins, G. P. (1973). The measurement of rates of return and taxation for private capital in Canada. In: W.A. Niskanen et al. (Eds.), Benefit cost and policy analysis (pp. 211–245). Chicago: Aldine.Search in Google Scholar

Kula, E. (1984). Derivation of social time preference rates for the United States and Canada. Quarterly Journal of Economics 99(4), 873–882.10.2307/1883131Search in Google Scholar

Lind, R. C. (Ed.). (1982). Discounting for time and risk in energy policy. Baltimore and Washington, DC: Johns Hopkins University Press and Resources for the Future.Search in Google Scholar

Marglin, S. A. (1963). The opportunity costs of public investment. Quarterly Journal of Economics 77(2), 274–289.10.2307/1884403Search in Google Scholar

Mirrlees, J. A., & Stern, N. H. (1972). Fairly good plans. Journal of Economic Theory 4(2), 268–288.10.1016/0022-0531(72)90153-6Search in Google Scholar

Moore, M. A., Boardman, A. E., Vining, A.R., Weimer, D. W., & Greenberg, D. H. (2004). Just give me a number!: practical values for the social discount rate. Journal of Policy Analysis and Management 23(4), 789–812.10.1002/pam.20047Search in Google Scholar

Newell, R. G., & Pizer, W. A. (2003). Discounting the distant future: how much do uncertain rates increase valuations? Journal of Environmental Economics and Management 46(1), 52–71.10.1016/S0095-0696(02)00031-1Search in Google Scholar

Nordhaus, W. D. (1999). Discounting and public policies that affect the distant future. In: P. R. Portney & J. P. Weyant (Eds.), Discounting and intergenerational equity (pp. 145–162). Washington, DC: Resources for the Future.Search in Google Scholar

Nordhaus, W. D. (2007). A review of the Stern review on the economics of climate change. Journal of Economic Literature 45(3), 682–702.10.1257/jel.45.3.686Search in Google Scholar

OECD. (2010). OECD StatExtracts: Taxing Wages at www.stats.oecd.org/Index.aspx (accessed on July 21, 2011).Search in Google Scholar

Portney, P. R., & Weyant, J. P. (Eds.). (1999). Discounting and intergenerational equity. Washington, DC: Resources for the Future.Search in Google Scholar

Prescott, E. (2002). Prosperity and depressions. American Economic Review 92(2), 1–15.10.1257/000282802320188916Search in Google Scholar

Ramsey, F. P. (1928). A mathematical theory of saving. Economic Journal 38(151), 543–559.10.2307/2224098Search in Google Scholar

Reinhart, C. M., & Rogoff, K. S. (2009). This time is different: eight centuries of financial folly. Princeton, NJ: Princeton University Press.Search in Google Scholar

Rothstein, J., & Rouse, C. E. (2011). Constrained after college: student loans and early-career occupational choices. Journal of Public Economics 95(1–2), 149–163.10.1016/j.jpubeco.2010.09.015Search in Google Scholar

Shiller, R. (2005). Irrational exuberance (2nd ed). Princeton: Princeton University Press. Data source: Available at: http://www.econ.yale.edu/~shiller/data/chapt26.xls (accessed on June 30, 2011).Search in Google Scholar

Shoven, J.B., & Topper, M. (1992). The cost of capital in Canada, the United States and Japan. In: J.B. Shoven & J. Whalley (Eds.), Canada-U.S. tax comparisons (pp. 217–235). Chicago, IL: University of Chicago Press.Search in Google Scholar

Spackman, M. (2004). Time discounting and of the cost of capital in government. Fiscal Studies 25(4), 467–518.10.1111/j.1475-5890.2004.tb00547.xSearch in Google Scholar

Stern, N. (2007). The economics of climate change: the Stern review. New York: Cambridge University Press.10.1017/CBO9780511817434Search in Google Scholar

Weitzman, M. L. (2001). Gamma discounting. American Economic Review 91(1), 260–271.10.1257/aer.91.1.260Search in Google Scholar

Weitzman, M. L. (2007). A review of the Stern review on the economics of climate change. Journal of Economic Literature 45(3), 703–724.10.1257/jel.45.3.703Search in Google Scholar

Zerbe, Jr., R. O., Davis, T. B., Garland, N., & Scott, T. (2010). Toward principles and standards in the use of benefit-cost analysis. Benefit-Cost Analysis Centre, University of Washington, 10 November. Accessed on 28 December 2010.Search in Google Scholar

Zerbe, Jr., R. O., Davis, T. B., Garland, N., & Scott, T. (2011). Toward principles and standards in the use of benefit-cost analysis. Benefit-Cost Analysis Centre, University of Washington (Available at: http://evans.washington.edu/files/Final-Principles-and%20Standards-Report--6_23_2011.pdf), Accessed on 29 August 2012.Search in Google Scholar

Published Online: 2013-03-28

©2013 by Walter de Gruyter Berlin Boston

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