Social opportunity cost vs. social rate of time preference [part 2/2]🍋
The NZ Treasury's new approach to public-sector discount rates applied to risky projects
As outlined in part 1, the New Zealand Treasury has modified its public-sector discount-rate methodology. While it previously used a social opportunity cost of capital (SOC) for all projects, it now uses a social rate of time preference (SRTP) for “non-commercial” projects, whilst retaining the SOC for “commercial projects”.1
Part 1 concludes that use of the SRTP can induce the wrong decision on the acceptance or rejection of a risk-free non-commercial public sector project.
Risky projects
Risk-free projects are a useful benchmark. However, risk is an inescapable feature of the real-world, so it should not be assumed away.
Consider a non-commercial project requiring an investment now of $100m and delivering an uncertain payoff in ten years’ time with $160m expected. I’ll assume that the current ten-year real government bond rate is 4%.2 If the payoff had no risk, it would be $160m for certain and would warrant discounting at 4%, giving rise to a present value for the future payoff of $108m, which exceeds the investment now of $100m and therefore the project would be socially desirable.
Suppose the uncertainty in the payoff is positively correlated with the general state of the economy at that time. This is “systematic” risk. The parties who will experience the consequences of this systematic risk are the general public, and the risk (in the form of the project’s benefits being higher or lower than their expectation of $160m) will be felt by the general public. This risk will be systematic if it is correlated with GDP at the time. An example of this is a health project whose benefits are the saving of Quality Adjusted Life Years (QALYs), which are conventionally valued at GDP per capita.3 Higher GDP means higher benefits from the project, and therefore positive systematic risk.
Furthermore, people in general are averse to risks, and especially to systematic risks because these cannot be mitigated by diversification. The expected rate of return on a typical portfolio of equities is about 6% more than the government bond yield, and this “market-risk premium” is a manifestation of the risk aversion of those who own equities, either directly or indirectly through an investment intermediary (such as a fund managing a KiwiSaver account).4 The 6% premium is a manifestation of the risk aversion of a large proportion of the general public, and therefore a good indicator of the risk aversion of the rest. So, it should be used for public-sector projects whose systematic risk matches that of a typical portfolio of equities, with a higher or lower rate used if the project’s systematic risk is higher or lower, i.e., if its beta is more or less than 1. If its beta is zero, no adjustment for systematic risk is warranted.
However, the Ramsay model does not allow for systematic risk. This is unsurprising because it was developed in 1928, which was over 30 years before the concept of systematic risk was even recognised in the economics literature and reflected in the first (1964) version of the Capital Asset Pricing Model (CAPM). Versions of CAPM are currently the premier models for determining the premium for risk in any SOC.5 So, the Ramsay model is unsuitable for assessing a risky non-commercial project. The model does allow for annihilation risk — but this is not systematic risk and constitutes only a small fraction (about 1/40th) of the Ramsay discount rate whilst systematic risk is the dominant component of the default rate in Treasury’s SOC model.6
In a paper accompanying The Treasury’s work, Grimes notes that under certain conditions the SOC and SRTP coincide, and therefore either could be applied to a risk-free project. He then adds that “In each case, an appropriate risk premium would be added to the risk-free rate.”7 However, The Treasury does not add an allowance for risk to its SRTP, contrary to the advice of Grimes.
Returning to my example of a risky project, suppose that the systematic risk on it is similar to that on equities in general. Its discount rate should then be raised by 6% to compensate the general public for the risk they face on that project. Doing so raises the discount rate from 4% to 10%, and the present value of the project’s payoff then falls to $62m, which is less than the investment of $100m. This signals that the project should be rejected.
Equivalently expressed in compounding terms, faced by a project costing $100m now and delivering a payoff in ten years with an expectation of $160m and subject to systematic risk comparable with equities in general, investing the $100m instead into equities with the same systematic risk (at 10% per annum compounded for ten years) would give rise to an expected payoff of $260m, which would just compensate taxpayers for the risk they would experience. This expected payoff of $260m is far higher than the expected payoff of $160m from investing in the project. Accordingly, the expected payoff of $160m on the proposed project would not adequately compensate taxpayers for the systematic risk they would experience. Adoption of the project would therefore leave society worse off, consistent with the results of the discounting exercise using a rate of 10%. Accordingly, it is not in society’s best interests to discount the project’s benefits using an SRTP of 2% when the real government borrowing rate is 4% and the compensation for systematic risk is 6%.
Conclusions
In summary, Treasury has changed it discount rate methodology for assessing non-commercial projects, from use of the SOC to a schedule of SRTP rates determined in part by the Ramsay model. Using that latter model the Treasury estimates the SRTP at 2% real for payoffs in years 1-30, and lower rates for payoffs in later years determined in accordance with the Weitzman analysis. SOC rates are market based, and designed to determine the market value of the project. The market value of a non-commercial public-sector project is not meaningful and therefore it might seem that market-based rates are irrelevant to them. However, even when not being used in discounting exercises to determine market values, market costs of capital are still project costs relevant to the assessment of non-commercial projects. This can be demonstrated through compounding exercises.
Market costs of capital are still project costs relevant to the assessment of non-commercial projects.
In particular, if a project with payoffs up to 30 years away has some systematic risk, the Ramsay model will not take account of it. This may lead to accepting some projects whose expected payoffs are insufficient to compensate society for the systematic risk it bears, and such projects should be rejected. Even if a project with payoffs up to 30 years away has no such risk, but the current real government bond rate is more or less than 2%, the Ramsay model will again lead to accepting some projects whose benefits do not cover the cost of borrowing to finance them (and are therefore undesirable to society), and rejecting some projects whose benefits do cover the cost of borrowing to finance them (and are therefore desirable to society).
The Ramsay model is only suitable for a project with no systematic risk and when the real government bond rate is currently about 2%. Even in these idealised conditions, it has no advantage over simply using the current real government bond rate. These comments about the Ramsay model also apply to any discount rate that does not appropriately allow for systematic risk or fails to apply the current government bond rate to risk-free projects.
By Martin Lally
See Updated Public Sector Discount Rates for Cost-Benefit Analysis, Treasury Circular 2024/15, 2024.
The current rate is actually about 2.8%. See Table B2 on the RBNZ’s website. These rates change over time whilst the SRTP is fixed for three years, so the estimation process for the SRTP will only match the real government bond rate outside the triennial reset times by chance. I use a 4% rate to magnify the point I’m making.
See M. Lally, The Value of Lives in New Zealand, Monash Bioethics Review, forthcoming; and:
There are various ways of estimating this premium. The Treasury uses an estimate of 7%, but this is for the simplified Brennan-Lally version of the Capital Asset Pricing Model, in which the premium is the expected rate of return on the market portfolio of equities less the government bond rate net of the corporate tax rate. Without the corporate tax rate adjustment, which is not required for non-commercial projects because neutrality with the private sector is not necessary, the premium would be about 6%. I therefore use 6%.
The Ramsay model was published in 1928 (F. Ramsay, A Mathematical Theory of Saving, The Economic Journal, pp. 543-559) whilst the first version of the CAPM was published in 1964 (W. Sharpe, Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, The Journal of Finance, pp. 425-442). The version of the CAPM used generally by the private sector in New Zealand, and by the Treasury for its SOC, was published in 1992 (M. Lally, “The CAPM Under Dividend Imputation”, Pacific Accounting Review, 1992, pp, 31-44).
The default systematic risk allowance within Treasury’s SOC is 4.69% (the product of the market risk premium of 7% and the default asset beta of 0.67) whilst the default SOC is 8%: see The Treasury, 2008, Public Sector Discount Rates for Cost Benefit Analysis. So, most of the 8% is for systematic risk.
See page 10 of A. Grimes, How Should the New Zealand Government Discount Future Payoffs, discussion paper prepared for The Treasury, 2023.
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