Social opportunity cost vs. social rate of time preference [part 1/2]🍋
The NZ Treasury's new approach to public-sector discount rates applied to risk-free projects
The New Zealand Treasury has modified its public-sector discount-rate methodology, as outlined in the recent Treasury Circular 2024/15. 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 Treasury expects to review the rates every three years. The Circular directs readers to a link containing background papers, including papers on the methodologies underlying the SOC and the SRTP. Treasury have retained their previous methodology for calculating the SOC.2
Dieter Katz, in a recent Asymmetric Information post, described these changes and explored some consequences.
In this post I’ll dig deeper into how Treasury came up with the rate for the SRTP. I’ll explain how using it may induce the wrong decision on the acceptance or rejection of risk-free non-commercial public-sector projects. In part 2, I’ll explain how this conclusion extends to risky projects.
The social opportunity cost of capital approach
The SOC methodology is intended to determine the market value of a project. It accords with standard private-sector practice in relying on market costs of capital, most particularly the yield to maturity on government bonds plus a premium for risk determined from expected rates of return on listed equities. Since the private but not the public sector pays company tax, the SOC is raised to offset the tax difference and therefore match the value that the private sector would place on the project.
The SOC default rate is 8% real, but a different rate can be used if its systematic risk does not accord with the default value of 0.67. This SOC rate is applied to “commercial” projects, i.e., those that might be undertaken by both the public and private sectors.
The social rate of time preference approach
By contrast, the SRTP is a discount rate applied to the benefits and costs of public-sector projects, so as to determine those projects whose adoption would be beneficial to society. It does not use market costs of capital.
There are various ways of estimating the SRTP. The Treasury Circular’s links to relevant material suggest that it is based upon Treasury’s Working Paper 25/01, because the conclusions in that Working Paper exactly match the rates prescribed in the Treasury Circular.3 The Working Paper estimates the rate at 2% real for payoffs in years 1-30, using the Ramsay (1928) model, and lower rates for payoffs in later years in accordance with the Weitzman (1998) analysis.4
The Ramsay model involves a number of components, of which the largest is the product of the expected growth rate in real consumption per capita and the elasticity of marginal social welfare with respect to consumption. The Treasury applies these rates to “non-commercial” projects.
This post focuses upon the use of the Ramsay model to determine the 2% discount rate on non-commercial projects with payoffs up to 30 years hence.
As noted, the role of the SOC is to determine the market value of a project. In so far as non-commercial projects are clearly identifiable, and therefore the public sector is not competing with the private sector over these projects (now or in the future), the market value of a non-commercial project is not meaningful.
It might then seem that the public sector would be free to choose its discount rate methodology for these projects without being bound to the use of market costs of capital. This conclusion is not correct. 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 even non-commercial projects. This can be demonstrated through compounding exercises.
Assessing risk-free projects
Since the New Zealand government runs fiscal deficits, the marginal effect of the public sector undertaking a non-commercial project is to increase public-sector borrowing, which incurs the government borrowing rate.
Suppose a non-commercial project requires an investment now of $100m and generates real non-commercial benefits of $130m (for certain) in ten years. Suppose also that the current real ten-year government borrowing rate is 4%.5
Using the SRTP of 2%, the present value of the future payoff is $107m, which exceeds the investment now of $100m and therefore the project seems desirable. However, if the real ten-year government borrowing rate was 4%, the present value of the future payoff using that rate is $88m, which is less than the investment now of $100m, signalling that the project should not be adopted.
To more clearly appreciate the social undesirability of this project, suppose the government borrowing for the project was structured so that all interest and principal payments occurred in ten years. At that point, the (compounded) sum of interest and principal payments would be $148m, which exceeds the project payoff at that time of $130m. Investing in the project would therefore inflict a loss on society of $18m in ten years’ time, for certain. So, the project should be rejected.
Discounting the project’s benefits using the government borrowing rate and comparing this to the initial investment is mathematically equivalent to the compounding exercise, and therefore provides the correct signal even though the market value of the project is not meaningful here. So, discounting a risk-free non-commercial project at any rate other than the government borrowing rate may lead to a wrong decision (in this example, by accepting a project that leaves society worse off). Even if the project’s benefits arrive outside the lifetimes of those currently living (an “inter-generational project”), the generation receiving benefits of $130m will not be thankful for the accompanying need to pay $148m to the capital suppliers.
Discounting a risk-free non-commercial project at any rate other than the government borrowing rate may lead to a wrong decision.
It might be argued that the benefits of a risk-free project to society are quite different to the benefits to a private-sector firm, and therefore the SRTP could differ from the government borrowing rate. For example:
“It is possible that individuals in their political roles as citizens might be more concerned about future social outcomes than is reflected in their day-to-day decisions about their own personal consumption and investment. … This would mean that the discount rate implied by a market-based SOC would be too high for certain public projects, particularly in the social sector, as it would overlook preferences that would tend to lower the discount rate. An SRTP approach is a direct way of trying to capture these preferences.”6
However, in the context of the above example, the preferences of “individuals in their political roles as citizens” are reflected in the figure of $130m ascribed to the project payoffs. By contrast, the figure of $148m is payment to capital suppliers at the prevailing government borrowing rate of 4% per year and those lenders neither know nor care how government uses the money. Since 4% is the rate paid, it must be the rate used to determine the payment in ten years (of $148m), and therefore it must also be the rate used in the mathematically equivalent discounting process. At such a rate, the payoff of $130m does not cover the payment to capital suppliers and the project therefore leaves society worse off.
The example above is concerned with a situation in which the current real government bond rate exceeds the SRTP and the difference in rates leads to acceptance of the project when using the SRTP and rejection when using the real government bond rate. Of course, there will be occasions when the two rates match, and other occasions when they give rise to the same decision despite the rates differing. In such cases no harm would be done in using the SRTP. However, there will sometimes be times when risk-free projects that should be adopted (when properly assessed using the government bond rate) are instead rejected when using the SRTP, and therefore society would be worse off by applying the SRTP. There will also sometimes be times when risk-free projects that should be rejected (when properly assessed using the government bond rate) are instead accepted when applying the SRTP, and therefore society would again be worse off by using the SRTP.
The extent of this problem depends upon the variation over time in the real government bond rate, and it is substantial. The yields on inflation-indexed government bonds issued in November 1995 and maturing in February 2016 ranged from 1.0% to 5.9% over their life. Those issued in November 2012 for maturity in September 2025 have so far ranged from -1.0% (the minus sign is not a typo) to 2.8%.7 An SRTP of 2% is within the range but well above the lowest yield of -1.0% and well below the highest yield of 5.9%. With such variation over time in the real government bond rate, it is highly likely (in respect of risk-free projects) that use of a SRTP of 2% will frequently lead to decisions that leave society worse off.
The analysis above assumes that the government is running a deficit, and therefore finances public-sector projects by borrowing. If the government was not running deficits, and therefore financed projects from taxes, those taxes would come from taxpayers just as a firm investing in a project with equity finance acquires those funds from its shareholders. Taxpayers have alternative uses for those funds, and an alternative with the same (zero) risk would be for taxpayers to invest the $100m into government bonds (which pay the government bond rate). To benefit society, the proposed project must do at least as well as this, i.e., deliver payoffs in ten years of at least the $148m taxpayers would receive if they retained the $100m and invested it in government bonds for ten years.8 However, undertaking this project provides a payoff of only $130m in ten years, which is inferior to taxpayers retaining the funds and using them in other ways. One such way is to invest in government bonds that deliver $148m in ten years. Since the project must do at least as well as the government bond rate per year to make taxpayers better off, the present value of its benefits must be discounted using the government bond rate and this must be at least the initial investment. So, regardless of whether a risk-free non-commercial public-sector project is financed by government borrowing or taxes, the benefits must be discounted using the government borrowing rate.
The above analysis assumes that the SRTP rate of 2% is based entirely upon Treasury’s Working Paper 2025/1, and therefore upon the Ramsay model. However, Treasury has drawn my attention to an OIA request that indicates that the 2% rate places some (unspecified) weight on the estimate for the Ramsay model (using an earlier version of Treasury’s Working Paper 2025/1) and some on the prevailing real government bond rate.9 The weights are unclear because both approaches gave rise to an estimate of 2% at the time. In so far as some weight is placed upon the real government bond rate prevailing at the reset point, the resulting estimate of the SRTP will tend to be closer to the prevailing real government bond rate. This reduces errors arising from using an SRTP in assessing projects at that time. It does nothing to address errors arising from the real government bond rate changing over the following three years whilst the SRTP remains fixed.
Regardless of whether a risk-free non-commercial public-sector project is financed by government borrowing or taxes, the benefits must be discounted using the government borrowing rate.
The Ramsay model is only suitable for a project with no systematic risk and when the current real government bond rate is about 2%. Even in these idealised conditions, it has no advantage over simply using the current real government bond rate.
Risk-free projects are a useful benchmark. However, risk is an inescapable feature of most real-world projects. In part 2 of this post, I’ll extend this analysis to risky projects.
By Martin Lally
See Updated Public Sector Discount Rates for Cost-Benefit Analysis, Treasury Circular 2024/15, 2024.
See Public Sector Discount Rates for Cost Benefit Analysis, The Treasury, 2008.
See C. Parker, Deriving Values of the Social Rate of Time Preference, New Zealand Treasury Working Paper 25/01, 2025.
See F. Ramsay, A Mathematical Theory of Saving, The Economic Journal, 1928, pp. 543-559, and M. Weitzman, Why the Far-Distant Future should be Discounted at its Lowest Possible Rate, Journal of Environmental Economics and Management, 1998, Nov, 36 (3), pp. 201-208. The significance of years 1-30 is presumably that New Zealand government bonds exist with terms to maturity up to 30 years.
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 page 18 of J. Creedy and H. Passi, Public Sector Discount Rates: A Comparison of Two Approaches, New Zealand Treasury Working Paper 17/02, 2017.
These need not be New Zealand government bonds. One could instead invest in the default-free bonds of another government and take out a forward contract to deal with the exchange rate risk. The Interest Rate Parity Theorem would ensure the same result as investing in New Zealand government bonds.
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