Ramsey discounting calls for subtracting climate damages from economic growth rates

ABSTRACT

The Ramsey equation ties the utility discount rate and the elasticity of marginal utility of consumption together with per capita consumption growth rates to calculate consumption discount rates. For many applications, per capita consumption growth rates can be approximated with per capita output growth rates. That approximation does not work for climate change, which drives an ever-increasing and increasingly uncertain wedge between output and consumption growth. NAS (2017), in a central recommendation and illustrative example, conflates the two. The correct, consumption-based discounting method generally decreases consumption discount rates and, thus, increases the resulting Social Cost of Carbon Dioxide (SC-CO₂).

KEYWORDS:

• Discounting
• Ramsey equation
• climate change

JEL CLASSIFICATION:

• D6
• H43
• Q5

Acknowledgements

Without any implications, we thank Don Fullerton, Ken Gillingham, Bob Kopp, Kian Mintz-Woo, Billy Pizer, and Richard Zeckhauser for helpful comments. All remaining errors are our own.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ This alone is an area where NAS (2017) clears up prior confusion: The more commonly used term to describe the optimal social cost of the marginal tonne of CO₂ emitted is ‘Social Cost of Carbon’ or ‘SCC’. That is inaccurate. For example, an SCC of $100 per tonne of carbon, C, equals $27 per tonne of carbon dioxide, CO₂, as one tonne of C = tonnes of CO₂.

² Yet another important contribution: splitting the daunting process of calculating the SC-CO₂ into individual modules. While often interrelated, these modules can, for the most part, be tackled independently before integrating them into a coherent whole.

³ Note that we do not go as far here as Heal (2017), who argues that the Ramsey equation does not apply because of climate damages. It does. It just requires the use of the correct that subtracts climate damages from economic output, as we show here.

⁴ See, e.g. Gollier (2012) for an overview. See Broome (2012) and Kelleher (2017) for ethical perspectives, Arrow et al. (1996) for introducing the distinction between descriptivist and prescriptivist approaches to discounting into the climate debate, and references in footnote 6 for how uncertainties influence the resulting discount rates.

⁵ One important critique and extension, also referenced by NAS (2017) in a footnote though not further elaborated on, notices that in Equation 2 conflates risk across states of nature and risk across time, in form of the elasticity of intertemporal substitution (EIS). Separating risk aversion and the EIS is a potentially important extension that, in fact, replaces the Ramsey equation altogether in determining appropriate discount rates (e.g. Epstein and Zin 1989; Epstein and Zin 1991; Weil 1990).

⁶ The difference is variably described as ‘marginal’ versus ‘nonmarginal’ (e.g. Dietz and Hepburn 2013; Foley, Rezai, and Taylor 2013) or as ‘exogenous’ versus ‘endogenous’ approaches to discounting (e.g. Dietz et al. 2006), with the first of each pair of terms applying to output-based growth rates and the second to consumption-based ones adjusted for climate damages. Note that general-equilibrium approaches such as Nordhaus (1992, 2017)’s DICE model naturally use the latter. NAS (2017), too, notes that outputs from integrated assessment models like DICE are in ‘consumption-equivalent’ units (167). Many others explore the role of uncertainty in determining the discount rate, which generally declines as a result. For some of the recent intellectual history, see Weitzman (1998, 2001, 2010), Newell and Pizer (2003) and Gollier and Weitzman (2010). For digestible summaries of the main arguments, see Arrow et al. (2013), Arrow et al. (2014) and Groom et al. (2005).

⁷ In fact, NAS (2017) is clear that the reason for using the Office of Management and Budget’s 3 rather than 7% discount rate is that ‘the 3.0 percent rate is intended to reflect the rate at which society discounts future consumption’ (160, emphasis added), and it refers to ‘the rate of growth in consumption’ (176) in its reference to U.S. Government Interagency Working Group on Social Cost of Carbon (2015) justifying a 2.5% discount rate.

⁸ On page 175, the NAS report argues that the growth rates are to emerge from the ‘socioeconomic’ module, whose task is to project growth rates in business-as-usual real GDP per capita over the coming decades (NAS 2017, 72–74).

⁹ Not to be overly precise, but since it will matter for comparison with Table 1, the exact rates thus calculated are 1.98, 3.04 and 4.00%, respectively.

¹⁰ See footnote 9 for comparison.