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Public Sector Discount Rates: A Comparison of Alternative Approaches

3 Thinking About Discount Rates

It has been seen that the discount rate captures how a decision-maker trades-off future versus present benefits. This may seem like a difficult concept to observe or measure, but in fact people make this type of trade-off all the time. When deciding whether to spend now or to invest, people have to balance their own individual preferences for consumption in the present with the fact that investment is productive, and can therefore generate more consumption for the future.

By making this type of decision, people implicitly reveal how they discount the future. This section shows that, in equilibrium, the discount rate can be thought of as the rate which just balances individuals' preferences for investment with the rate of return on investment. Although it involves strong assumptions, this is a key insight as it provides the basis for the two main ways of thinking about the discount rate. These are:

  • opportunity cost of capital approaches - based on observing market rates of return as a measure of how people can trade-off consumption in the future versus the present
  • time preference approaches - based on peoples' preferences for how they wish to trade-off future versus present consumption

It will be seen that in a large competitive market with no distortions, these two approaches are equated in equilibrium. That is, the rate at which people wish to trade-off their own present and future consumption will equal the rate at which markets allow them to shift consumption through time via investment. As long as these conditions hold, both approaches should therefore give the same discount rate. This provides the basis for setting private sector discount rates by reference to market rates of return (that is, on an opportunity cost of capital basis).

However, it is unlikely that these conditions hold for public sector projects. As a result, the equivalence between time preference and opportunity cost approaches can break down. It is then necessary to choose which of the two approaches is most appropriate for determining public sector discount rates, or whether they can be combined in some way.

3.1  Time preference

When considering whether to spend money now or invest for the future, individuals typically postpone a dollar's worth of consumption now only if they are compensated with more than a dollar of consumption in the future. The rate at which an individual needs to be compensated for postponing consumption is known as the rate of time preference.[5]

This is usually specified in percentage terms, in the same way as an interest rate.[6] It varies:

  • for a given individual according to how much that individual is consuming/investing at any given time, and
  • from individual to individual according to personal preferences.

As a result, time preference captures how individuals are willing to trade-off present and future consumption. The fact that individuals typically require a positive rate of return to postpone consumption amounts to saying that individuals value a dollar now more than a dollar in the future. In other words, people behave as if they ‘discounted' the value of amounts received in the future.

3.2  The optimal level of consumption and investment

Spending one's income now means sacrificing the opportunity to invest and yield more consumption potential for the future. As a result, individuals must balance the preference to bring consumption forward against the fact that investment is productive. A rational decision-maker manages this trade-off by continuing to invest an additional dollar of income as long as the rate of return from that investment more than compensates for the sacrifice of present consumption.

It is typically assumed that the more an individual invests now, the more unwilling that person is to sacrifice further, and therefore the greater the required increase in future consumption that is needed as compensation. In other words, the rate of compensation that an individual requires to make an investment is assumed to increase the more that is invested now.

This means that an individual continues to invest until the rate of return obtained from the last unit of investment is just sufficient to compensate for the corresponding loss in present consumption. Or, stated differently, rational decision-makers continue to invest until their willingness to trade present for future consumption is equated to the rate of return that can be earned on their investment.

3.3  Market rates of return

For many individuals interacting in a competitive market economy, they can be thought of as borrowing and lending to plan their own consumption over time such that in equilibrium each individual's willingness to trade consumption over time is equated to the rate of return available in the market.

Moreover, in the economy as a whole, market rates of return themselves vary according to the aggregate amount of capital supplied by individuals. It is usually assumed that there are decreasing returns to capital, so that the rate of return on investment declines the more that is invested. Therefore in a well-functioning market, the rate at which individuals are willing to trade consumption over time is jointly determined along with the market rate of return.

This last statement provides an important insight into how to think about the discount rate. Specifically, it states that (in a well-functioning market), the rate at which individuals wish to trade-off consumption over time is equal to the rate at which the market allows them to make this trade-off. Stated differently, in equilibrium, market rates of return indicate:

  • the rate of return on productive capital that is available to individuals in the market (that is, the opportunity cost of capital), and
  • the minimum rate of return that individuals require to sacrifice a unit of present consumption (that is, time preference).

If presented with the option to finance a new investment project, this reasoning indicates that the rate of return on that project should be no less than the market rate of return. Otherwise the rate of return on the new project would be inferior to the rate of return on existing investment possibilities and not exceed the cost to investors of sacrificing present consumption.

This reasoning therefore provides the basis for discounting at market rates of return. It states that discount rates should be set by reference to both the rate of return that is demanded by individuals to postpone consumption and the rate of return that can be earned by individuals on a comparable investment project. In a well-functioning market with no distortions, these two rates are expected to be equal in equilibrium.

This provides a convincing rationale for why market rates of return are used to discount private decisions about how individuals should invest. Indeed, it provides the basis for how companies discount their investments (see section 4). However, it is not clear that this rationale necessarily extends to investments by the public sector.

3.4  Public sector discount rates

By definition, there are no large competitive markets for public sector investments. Public sector projects are typically very different from private projects. They are likely to give rise to externalities and have distributional implications. Therefore there is no mechanism to elicit peoples' time preferences for public sector projects. Nor are there reliable ways to estimate the rates of return on a broad range of public sector investments (financial and social-sector) for the purposes of setting opportunity costs.[7] In addition, public projects must be financed by either taxation or debt. In both cases a present transfer of real resources is made from private to public sectors. In addition, taxation (and possibly debt - to the extent that it is simply delayed taxation) involves deadweight losses that should be included as a cost of undertaking public projects.[8]

Despite the fact that there are no well-functioning markets for public sector projects, the considerations for thinking about the discount rate are the same. Namely:

  • What is the rate of return that a decision-maker could earn on a hypothetical next best available alternative? That is, what is the opportunity cost of a public project?
  • What rate of return would a decision-maker require to sacrifice a unit of present consumption in order to invest in a public project?

In principle, these two rates of return would also be equated in equilibrium, as a public sector decision-maker would continue to invest until their willingness to trade present for future consumption is equated to the rate of return that can be earned on their investment. However, in the absence of markets for public projects, it is not possible to rely on the usual market signals. Furthermore, even in ‘perfect' markets, equilibrium prices have efficiency properties but are not necessarily associated with ‘optimal' outcomes, particularly as the latter depend on distributional considerations.

As a result, there are two different ways of thinking about public sector discount rates. These are:

  • The social opportunity cost of capital approach, and
  • The social rate of time preference approach

These two approaches are considered in turn in the following two sections.

Notes

  • [5]The term consumption is used frequently in the following sections. It is important to stress that consumption should be interpreted more broadly than the everyday material sense of the word. Specifically, consumption should be taken to mean the use of currently available resources to deliver a benefit, of any kind, in the present. This includes any immediate social or non-material benefit that people value. For example, consumption could refer to the use of current resources to deliver social services which generate benefits in the present. Consumption of any durable good occurs over the lifetime of that good, not simply when it is purchased.
  • [6]For example, a rate of time preference of 5% means that in order to convince an individual to delay $100 of consumption by a year, that individual would need to be offered (at least) $105 in a year's time. It should also be noted that time preference need not always be positive. If people expect little or no income in the future, they may be willing to save at zero or even negative rates of return. However, this discussion is concerned with the general case.
  • [7]Furthermore, some public sector projects may be sufficiently large for general equilibrium effects to arise.
  • [8]That is a tax, by altering the prices at which economic transactions would otherwise be traded, typically causes some consumers to be less willing to buy, and some producers to be less willing to sell, than in the absence of the tax. This distortion gives rise to a 'deadweight loss' or 'excess burden' of taxation, and should be regarded as a cost of public financing. As this concerns the measurement of costs, rather than problem of setting the discount rate, it is not discussed further here.
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