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About the article
Published Online: 2013-03-28
Zerbe et al. (2011, p. 84), accessed 29 August, 2012.
For a recent review and discussion in a BCA context see Boardman, Moore and Vining (2010).
The discount factor that society should apply to consumption in period t is given by . It equals the product of U´(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.
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.
If U(c)=ln(c), then U´=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).
We would like to thank an anonymous referee for pointing out an error in this formula in a draft of this article.
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.
Data source: http://www.econ.yale.edu/~shiller/data/chapt26.xls (accessed June 30, 2011).
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.
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.
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.
That is, , where i is the actual rate of inflation.
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.
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).
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).
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.
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).
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).
For a schedule of US-derived declining rates, which are based on Newell and Pizer (2003), see Moore et al. (2004).