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6.4 Measurement and parameter values

The SRTP offers a formula expressed in terms of easily interpreted parameters. However, the question arises of how transparently this can be made operational? Doing so requires decision-makers to specify the values of their pure rate of time preference, p, and their aversion to intertemporal inequality, θ. Both of these values represent abstract constructs that cannot be easily gauged intuitively.

Consider the variable, θ, which reflects the decision-maker's degree of aversion to unequal consumption streams across time, or the ‘aversion to intertemporal inequality'. It is a measure of the sacrifice that a decision-maker is willing to make for the purposes of redistributing consumption over time. It is related to the concavity of the welfare evaluation, or scoring function, U(c).

Supposing consumption is expected to grow over time, people in the future will enjoy higher material living standards than those in the present. If the decision-maker has some preference for smoothing the living standards of society over time, one can carry out the thought experiment of what loss the decision-maker would be willing to tolerate when making a redistribution across time.

An analogy can be made with using a 'leaky bucket' to transfer water from where it is plentiful to where it is scarce. How leaky a bucket would the decision-maker be willing to tolerate before judging the waste to imply that the benefit of the transfer exceeds its benefit? In the same way, suppose that a decision-maker can redistribute consumption over time, but only through a leaky budget envelope. That is, transferring consumption from one time period to another would involve some irretrievable loss or leak. How much of a leak would a decision-maker be willing to tolerate when making a transfer?[25]

Attempting to answer this question can be used to gauge the meaning of different values of θ. For example, assuming annual per capita consumption growth of 2 per cent, setting θ=1 (as assumed in the UK in the specification of SRTP) implies that the decision-maker would be willing to smooth consumption by taking $1 from ten years in the future in return for $0.82 for the present. In this way, examining the implications of different values can be used to gauge what choices most closely match the decision-maker's values.

Rather than trying to specify these variables directly, following the kind of thought experiment discussed above, some economists have tried to infer peoples' underlying preferences for trading-off time and inequality by reference to how people make actual decisions that involve making these trade-offs (that is, by using ‘revealed preference' approaches). Examples include looking at savings and investment decisions and studying the degree of redistribution implied by income tax systems.

Whilst these studies can be used to provide some information about how individuals make the relevant trade-offs, they have very strong limitations. In particular, much of this research involves estimating individuals' preferences in contexts that are not always directly comparable with how individuals might be expected to behave with regards to public sector investment decisions.[26]

This is essentially the same criticism discussed above in relation to SOC-based approaches. Namely that relying on the results of such studies assumes that decision-makers should trade-off the future for public decisions in the same way that individuals do for their own private decisions (or decisions made in other contexts that may not be strictly comparable).

As a result, this research may be used only to help guide a broader discussion about what parameter values are reasonable. A more appropriate way of doing this is to point out the implications of different parameter choices, and choose a parameter combination that most closely matches the decision-maker's social values.

The preceding sub-sections have suggested that that SOC appears to be easier to measure than SRTP. This discussion need not be repeated in detail here, except to restate the general conclusions that a first-best measure of SOC is not clearly observable in all cases and that the risk-premiums on private projects may not always be a good indicator of the risk-premiums required by the government.

The longest maturity on New Zealand government bonds is approximately 20 years, and even in international markets, securities with horizons of more than 30 to 40 years are unlikely to be traded with sufficient volume and liquidity to provide a reliable 'noise-free' signal of how markets discount the long term, and a representative signal of how the long term is valued.

Therefore, rather than SOC being an entirely objective or technical exercise, taking the next-best alternative use of public funds to be a private sector investment with similar risk characteristics amounts to imposing a potentially significant assumption. As a result, there may be no clear benchmark from financial markets to help determine either the risk-free or the risk-based component of SOC. If this is the case, SRTP may be the only feasible approach for valuing outcomes in the very long term. The issue of discounting over long time horizons is considered further in section 7. A brief summary of the comparisons is given in Table 3.

Table 3 Comparison of the Two Approaches
1. Capturing opportunity cost 2. Capturing time preference
  • The current market-based social opportunity cost (SOC) approach is likely to overestimate the public sector discount rate for many projects, as it assumes full crowding out.
  • A social rate of time preference (SRTP) approach that does not account for the shadow price of capital is likely to underestimate the public sector discount rate.
  • The current market-based SOC may overestimate the public sector discount rate if CBA fails to account for socially-motivated preferences.
  • SRTP is difficult to quantify in a transparent way.
3. Accounting for risk 4. Overall measurability
  • The market-based SOC may overestimate the public sector discount rate, as governments may be better placed to handle risk.
  • A pure SRTP does not account for risk in the discount rate: risk is dealt with separately in CBA.
  • The SOC is observable for public projects that have a clear market alternative, but not all public projects
  • The SRTP requires an explicit statement of value judgements, and requires dealing with abstract theoretical constructs.


  • [25]The ‘leaky bucket’ experiment was introduced by Atkinson (1970) in discussing the concept of inequality aversion. A somewhat different approach was used by Okun (1975) who discussed transfers between groups of individuals. For its use in the present context, see Creedy (2007).
  • [26]The alternative approaches to ‘measurement’ are critically examined by Creedy (2007).
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