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Public Sector Discount Rates: A Comparison of Alternative Approaches

7 Time-varying discounting

The discussion has so far assumed that future costs and benefits are discounted at a constant proportionate rate, however long the time horizon under consideration. As explained in Section 2 above, this is referred to as constant exponential discounting.

One concern that has been raised with constant exponential discounting is that, even with a low discount rate, the compounding effect of applying a constant rate can cause decision-makers to attach a very low value to more distant future outcomes. Some people are concerned that this builds 'short-termism' into political decision-making.

This section outlines some of the characteristics of an alternative model of discounting, namely time-varying or hyperbolic discounting, which involves applying a progressively lower discount rate for more distant outcomes.

7.1  Discounting over the long term

Even with relatively low discount rates, constant exponential discounting causes the discount schedule - that is, the weights that the decision-maker attaches to future time periods - to converge towards zero for more distant net benefits: this is illustrated above in Figure 1. In practical terms, this means that decision-makers effectively 'stop caring' about outcomes in the future, provided these outcomes are distant enough.

As is evident from the Figure 1, discount factors of less than 10% are reached within timeframes that are reasonable for some public sector projects, even with relatively low discount rates.[27] In particular, constant exponential discounting can imply the following.

  • It is not worth present generations incurring a small cost now to avoid potential costly events in the distant future.
  • The outcomes of distant generations are discounted relative to each other in the same way that more proximate generations are discounted. Some people may argue that, beyond some time horizon, T, they have no particular preference for discounting the wellbeing of generation T + 1 much more than the wellbeing of generation T.[28]

As mentioned in Section 6, there may not be any market instruments that can be used reliably to gauge rates of return in the distant future. That is, an opportunity cost of capital approach is likely to break down in the context of very long term projects.

7.2  Hyperbolic discounting

In response to these concerns, some people have proposed using time-varying discount rates whereby progressively lower rates are used as the time period at which net benefits are received becomes more distant. This approach is known as hyperbolic discounting. It has the effect of scaling-up the weight attached to the more distant future relative to exponential discounting. Clearly, this is distinct from the idea of using a lower exponential rate for longer-term projects.

In the last decade or so, some countries - most notably the UK, France, Denmark and Norway - have adopted hyperbolic discount rates as their default guidance for public sector CBA.

Two main rationalisations have been suggested for hyperbolic discounting in the case of individual decisions. Both are based on uncertainty about the future.

First, it can be shown that if the discount rate is expected to be constant over time, but there is uncertainty over its precise value, then the term structure of discount rates declines over time.[29]

Second, under a Ramsey SRTP formulation of the discount rate, suppose the following assumptions are introduced. There is uncertainty over the future growth rate of per capita consumption, gt, and this uncertainty is positively correlated, so that there is some tendency for positive or negative consumption shocks to accumulate. In this case, it can be shown that the decision-maker's discount rate declines over time. The reason for this result is that, given a preference for consumption smoothing, the decision-maker cares more about a negative shock than an equal and opposite positive shock. This asymmetry introduces a precautionary effect which causes the decision-maker to place a greater weight on the future, and hence to lower the discount rate, relative to a situation of complete certainty. The longer the time horizon, the more time there is for positive and negative shocks to accumulate, and so the variance of potential outcomes increases with time. This increasing uncertainty raises the strength of the precautionary effect, causing decision makers to apply a declining discount rate schedule.

Other arguments relate to statements about basic value judgements, involving a compromise between the situation under which there may be said to be a ‘dictatorship' of the present (constant exponential discounting) and a 'dictatorship' of the future (zero discounting).[30]

7.3  Time inconsistency

One issue that arises under hyperbolic discounting is that it results in time-inconsistent decisions. Specifically, with hyperbolic discounting it is possible that a decision-maker may wish to change an investment decision taken in the past, even though the forecasts of the costs and benefits made at the date of the decision turn out to be correct.

This problem arises because when making a decision now that has impacts at some future time t, the decision-maker uses a long-term (low) discount rate to evaluate the impact between periods t and t + 1. However, when time t actually arrives, he or she will apply a short-term (high) discount rate to period t + 1. In other words, when the future arrives the decision-maker's relative valuation of benefits in subsequent periods is lower than when the decision was originally taken. This could cause the decision maker to want to change the decision from that point onwards.

In such cases, the decision-maker's wish to make a different decision is due solely to the passage of time, because hyperbolic discounting applies different discount rates according to when in time things are evaluated. Constant exponential discounting does not encounter this problem as it treats time consistently in the sense that the relative valuation of any two benefits separated by a given time interval does not depend on when they are evaluated.

Time inconsistency raises an interesting question, as it effectively introduces two 'versions' of the decision maker. One is a forward-looking version who discounts more distant outcomes at a low rate, and the second is a more present-focussed person who discounts the immediate future at a high rate. This comes into conflict when the more distant future becomes the immediate future.


  • [27]Specifically, discount factors of less than 10 per cent are reached within 80 years at a discount rate of 3 per cent; and within 50, 35 and 25 years for discount rates of 5, 7 and 10 per cent respectively.
  • [28]Although this view does not take into account the wealth effect in the Ramsey equation.
  • [29]See, for example, Weitzman (2007).
  • [30]See Chichilnisky (1997) and Li and Lofgren (2000) for alternative specifications.
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