Breakdown of the discount rate

A6.5 The STPR has two components:40

'time preference' - the rate at which consumption and public spending are discounted over time, assuming no change in per capita consumption. This captures the preference for value now rather than later.

'wealth effect' - this reflects expected growth in per capita consumption over time, where future consumption will be higher relative to current consumption and is expected to have a lower utility.

A6.6 The STPR is expressed as:

r = ρ + µg

where:

r is the STPR

ρ (rho) is time preference comprising pure time preference (δ, delta) and catastrophic risk (L)

µg is the wealth effect. The marginal utility of consumption (µ, mu), multiplied by expected growth rate of future real per capita consumption g

A6.7 As recognised in the 2003 Green Book there are a range of estimates of the individual components of the discount rate.41 Research continues to illustrate a range of plausible estimates but concludes that the overall discount rate of 3.5% remains within that range and is justifiable.42

A6.8 The way in which the STPR is applied in the Green Book requires each component to be specified. This facilitates sensitivity analysis and clarifies treatment where individual components of the discount rate should be adjusted (e.g. for health discounting). The overall values ascribed to specific components of the STPR are retained from the 2003 edition as set out below. The calculation of the STPR is shown in Box 29.

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40 Based on Ramsey F.P. (1928) "A Mathematical Theory of Saving" Economic Journal, Vol. 38, No. 152, pp. 543-559

41 See discussion paper: Spackman, M. (2016) "Appropriate time discounting in the public sector" GRI Working Paper No. 182. Grantham Research Institute on Climate Change and Environment. London School of Economics.

42 See Freeman, Groom and Spackman (2018) "Social Discount Rates for Cost-Benefit Analysis: A Report for HM Treasury" published on the HMT Green Book web page