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# Discount rate methodology

## Summary

This note considers whether the 2050 Calculator should use the standard Green Book discount rate (3.5%) or the Stern-adjusted lower discount rate (of 3% and declining). It concludes we should use the former.

## HMT Green Book discount rate

The Treasury’s Green Book sets out the definition and de-construction of the Social Time Preference Rate (STPR). The STPR is the rate used for discounting future benefits and costs in order to trade-off the value society attaches to present, as opposed to future, consumption.

The STPR, represented by r, is the sum of these two components, i.e.

r = ρ + μ.g

There are two components to the STPR:

• ρ: rate at which individuals discount future consumption over present consumption, on the assumption that no change in per capita consumption is expected
• μ.g: per capita consumption is expected to grow over time and therefore future consumption will be plentiful relative to the current position and thus have lower marginal utility. This effect is represented by the product of the annual growth in per capita consumption (g) and the elasticity of marginal utility of consumption (μ).

The term ρ comprises two elements:

• L: catastrophe risk: the likelihood that there will be some event so devastating that all returns from policies, programmes or projects are eliminated, or at least radically and unpredictably altered. Examples are technological advancements that lead to premature obsolescence, or natural disasters, major wars etc.
• δ: pure time preference: reflects individuals’ preference for consumption now, rather than later, with an unchanging level of consumption per capita over time.
 The values of these factors are as follows: r = ρ + μ.g 3.5 = 1.5 + (1*2)

However over the longer term (beyond 30 years), uncertainty over the future suggests the discount rate should decline. So the discount rate becomes:

Table 1 – Standard Green Book discount rate

 Period of years 0–30 31-75 76–125 126–200 201–300 301+ Discount rate 3.5% 3.0% 2.5% 2.0% 1.5% 1.0%

The Stern Review concluded that in the context of climate change we should use a lower discount rate. The Stern Review argues that in the case of climate change, ρ should be lower because:

• L: catastrophe risk: this is lower when considering economy-wide action to cut emissions than when looking at individual projects because the risk of the world ending is less than the risk of an individual project becoming obsolete.
• δ: pure time preference: Stern reflected an ethical judgement that it was not appropriate to discount on the basis of birth date.

On this basis supplementary guidance from HMT provides an adjusted profile of discount rates, set out below.

Table 2 – Stern-adjusted discount rates

 Period of years 0–30 31–75 76–125 126–200 201–300 301+ Discount rate 3.0% 2.57% 2.14% 1.71% 1.29% 0.86%

## Which discount rate should we use in the Costs Calculator?

The HMT supplementary guidance suggests using both discount rates as a sensitivity test of the results. However we need to decide which rate we use as a default; unfortunately the guidance is not very clear on this. However there are three arguments which tend to support the idea of using the standard 3.5% as the default discount rate:-

 Issue Supports the use of the following discount rate Precedent. The most recent climate change Impact Assessment looking out to 2050 used 3.5% as its discount rate . 3.5% Time horizon. The supplementary guidance suggests that this lower discount rate should be used where “the effects under examination are very long term (in excess of 50 years)”. However the Costs Calculator looks out just 40 years ahead. 3.5% Net benefits. The guidance and verbal advice from the Treasury indicates that the Stern adjusted discount rate should be applied to net cost-benefits. But the Costs Calculator only considers costs. 3.5%

Therefore we will use 3.5% as our default choice of discount rate (as set out in table 1). But users will be able to sensitivity test this.