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Public Sector Discount Rates: A Comparison of Alternative Approaches

6 Comparison of alternative approaches

Sections 4 and 5 have looked at two seemingly very different approaches to determining the discount rate. Under the social opportunity cost of capital (SOC) approach, the discount rate is interpreted as the rate of return that the government foregoes when it invests public funds on behalf of society. Under the social rate of time preference (SRTP) approach, the discount rate is interpreted as the rate of return required by a 'socially-minded' decision-maker in order to defer a unit of consumption from the present to the future.

This section attempts to weigh the advantages and disadvantages of these two approaches with reference to choices faced by governments. A crucial point to stress is that neither approach offers a completely objective way of determining public sector discount rates. Value judgements are inevitable.

SOC-based approaches can seem appealing, as basing discount rates on observable market returns appears to be more objective than approaches based on SRTP. However, the very decision to select a SOC-based approach carries a number of implicit assumptions and value judgements. SRTP-based approaches require more transparent statements of the decision-maker's value judgements.

The following discussion is organised into four subsections. The first two subsections seek to assess how SOC and SRTP compare in relation to the way they reflect the government's opportunity cost and the government's time preference rate. Accounting for public sector risk and the overall ease and practicality of measurement are discussed in the next two subsections. This is followed by a brief summary and a selection of international approaches.

6.1  Reflecting opportunity cost

The key rationale for the SOC approach is that if the return on public projects does not at least meet the hurdle of the next best rate of return available to the government, then government investment displaces, or crowds-out, an investment that would have generated more overall value.

Under the New Zealand Treasury's current approach, share market returns are considered to be the most appropriate measure of the next best alternative to the government. This is because the companies that constitute the market face incentives to carry out the most productive investments in the economy (both locally and overseas), and these returns are available to the public. Moreover, the government does in fact invest in the share market through the New Zealand Superannuation Fund. It could choose to substitute between this investment and other public projects.

However, this approach to defining the SOC assumes that, in the absence of undertaking a public sector project, the next-best use of the funds would be to invest in a private sector project of equal magnitude and risk. In other words, it assumes that a public sector project fully crowds-out or displaces a private sector investment of the same cost and risk profile. This is a key judgement. It is clearly the appropriate counterfactual for private sector investment decisions. However, in most cases the appropriate counterfactual for setting the government's opportunity cost is likely to be one of the following two other possibilities.

  1. The funds for the public project would never have been raised. In this case the next best use of the funds would have involved a mixture of consumption and investment by private individuals and businesses, most likely with a lower risk-return profile. Therefore, to the extent that private consumption (as opposed to investment only) has been displaced as a result of the public project, the relevant measure of opportunity cost should also reflect the rate at which private individuals are willing to trade-off current and future consumption by saving. This rate is far from clear, but it would generally be expected to be lower than the opportunity cost of a risky private investment.[21] Therefore, allowing for the fact that consumption (and not just investment) is displaced by the financing of a public project would tend to lower the opportunity cost of capital relative to the current approach.
  2. The funds would have been invested in an alternative public project. In the case of core public service delivery, it is unlikely that the government would consider not raising the funds as a feasible counterfactual. In most cases it is also unlikely that the government would be willing freely to substitute between public service delivery and investment in the Superannuation Fund (or any other private investments). In this case, the appropriate measure of opportunity cost would be defined by reference to an alternative method of delivering a comparable service. This may be observable for some projects for which there are well-defined private alternatives (for instance communications networks). However, this is unlikely to be observable for most social-sector projects. For such cases, setting the SOC by reference to share market returns is a strong assumption.

As a result, a SOC approach based on share market returns does not provide an objective measure of the opportunity cost of public projects for all cases.

However, an SRTP approach does not account for the fact that raising public funds crowds out at least some private investment. For instance, supposing a public sector project costs $100m and that half of this money would have been allocated towards private investment in the absence of the public project, so that the remaining half displaces private consumption. The relevant opportunity cost of the public project is:

  • $50m of present consumption which is displaced, and
  • The present value, in consumption terms, of the remaining $50m that would otherwise have been invested at a private rate of return. That is, the present value of the $50m invested at a private rate of return, but discounted at the SRTP.

Therefore, an SRTP approach should take account of the fact that a public project displaces not only present consumption, but also private investment that would have generated a stream of future consumption. The present value of such consumption streams that are displaced should be recognised as a cost of the public project when conducting the cost-benefit analysis (CBA). This is known as the shadow price of capital. Estimating the shadow price of capital raises additional challenges, but methods have been proposed in the CBA literature.[22]

In summary, a SOC based on share market returns tends to overestimate social opportunity cost, as it assumes full crowding-out. On the other hand, a SRTP approach is likely to underestimate this cost, as it assumes no crowding-out of private investment projects. A pragmatic solution might involve either of the following approaches.

  • Take a weighted average of a market-based SOC and SRTP. The weights can depend on the proportion of investment and consumption in the counterfactual case where resources are left in private hands. However the assignment of these weights is not a simple matter, and such an approach may yield an intermediate number which does not cope well with addressing the variability of individual projects.
  • Apply a SOC-based discount rate in cases where the main effect of a proposal is to displace or alter the use of capital in the private sector, and apply an SRTP-based discount rate when a proposal primarily and directly displaces private consumption.

Notes

  • [21]It is often set by reference to some measure of government bond yields as a proxy for a risk-free rate of saving.
  • [22]See for example Boardman et al. (2006), Boardman et al. (2008), Lind (1990) and Parker (2011)
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