How Should the New Zealand Government Discount Future Payoffs?

Executive Summary#

This report responds to a Treasury request “to provide an independent expert perspective on New Zealand public sector discounting, specifically hyperbolic discounting. In this context and based on the provider’s existing expert knowledge of the literature and international experiences, from the perspectives of theory, methodologies and applied policy:

In providing a perspective, this report considers the rationales for using different formulations of the social discount rate (SDR), including reviewing and critiquing the literature related to the setting of the SDR and, in one instance, extending that literature. Key points in the paper are as follows:

• Treasury currently adopts a default real discount rate of 5% p.a. when evaluating public sector projects, with 6% being used for some sectors; robustness checks can incorporate a lower rate of 2%. The default discount rate incorporates both the risk-free discount rate plus a default risk premium. The discount rate is used in conjunction with an exponential discounting formula.
• There are two common approaches to determining the discount rate: the ‘social opportunity cost of capital’ (SOC) approach and the ‘social rate of time preference’ (SRTP) approach. The former bases the public sector discount rate on the observed return on the next best alternative investment that has the same degree of risk. The latter is based on a social welfare function defined over present and future utilities.
• With exponential discounting, use of a 5% discount rate when evaluating a public sector project translates into an implicit decision to treat $1 of benefit today as worth more than $100 of benefit that occurs in a century’s time. Similarly, $9 of benefit today is worth more than a $100 of benefit that occurs in 50 years’ time.
• For projects in which all payoffs (costs and benefits) are valued in the market, government should use the same exponential discount rate (and hence the same discount factor) as does the private sector when undertaking competing activities (including the same risk premium for a similar project); otherwise, the choice of (a lower) discount rate would artificially bias production away from private towards public producers.
• It follows that the SRTP approach applies only to situations for which there are non-market payoffs. Returns to future generations, who are not represented in today’s market, can be considered as one form of non-market payoff.
• Hyperbolic (and quasi-hyperbolic) discounting applications often employ a lower discount factor (higher discount rate) for near-term payoffs and then have a higher discount factor for longer term payoffs than is the case with exponential discounting. The effect of hyperbolic discounting is to have a declining discount rate (DDR) over future years.
• Hyperbolic discounting in general leads to time inconsistent decisions. If hyperbolic discounting were to be adopted, it would need to be accompanied by an institutional framework that makes it difficult to reverse policy decisions, so building in time consistency for policymaking.
• Ramsey showed that under certain restrictive assumptions the SOC and SRTP discount rates are identical. The SRTP reflects three factors: the rate of pure time preference in the utility function (i.e. the degree to which the utility function exponentially discounts future consumption), the elasticity of utility with respect to consumption, and the per capita steady state growth rate of the economy. If future growth is higher, the SRTP discounts future consumption more highly so that some future consumption is brought forward to the present.
• The standard derivation of Ramsey’s result is based on intra-generational optimisation rather than inter-generational considerations, with the pure rate of time preference within and between generations assumed to be the same. Ethically, however, there is no basis to say that future generations should be discounted by a person today in the same way as that person might discount their own consumption in their old age. Hence the standard exponential discounting approach to the social discount rate does not have an ethical basis to underpin it.
• One formulation used to reflect inter-generational concerns is to adopt a DDR that converges to zero, implicitly increasing the weight placed on future generations’ utility as time evolves, so avoiding (or mitigating) one generation playing a dictatorial role over another.
• Private rates of return do not incorporate externalities, so in cases of negative externalities such as environmental degradation, the social rate of return will be less than the private return. In addition, the economy may not already be on the optimal consumption path. Each of these considerations imply that a discount rate determined by the SOC approach is not valid.
• Macroeconomic uncertainties relating to the future economic growth rate, and to the appropriate future discount rate, optimally result in the use of a DDR, similar to (but not the same as) use of hyperbolic discounting.
• Uncertainty about future consumption is especially relevant when dealing with tipping points, for example potential loss of biodiversity for a habitat. More generally, degradation of an environmental resource (and potentially also of a ‘resource’ such as social capital) should result in the payoff to that resource increasing as the resource becomes scarce. While, in some cases, this mathematically may be equivalent to adopting a stable payoff coupled with a DDR (an option referred to as ‘dual discounting’), it conceptually makes more sense to model this situation as one with a stable discount rate coupled with an increasing payoff as the resource (or amenity) becomes scarce, since that payoff represents the correct shadow price at the time.
• Another form of dual discounting mooted in this report for further investigation, is to drop the common assumption that all components of utility share the same rate of pure time discount and instead to assume that different components of utility are discounted by the individual (or society) at different rates. This approach is consistent with the treatment of goods in Debreu’s Theory of Value. The effects of including a lower discount rate on certain non-market outcomes (such as the environment) is to increase resources spent now to maintain resource stocks, so increasing the service flow from those stocks in future years. The approach does not necessarily lead to DDRs, so has a different rationale than does hyperbolic discounting, and the effects of the two approaches are different.
• Treasury’s default social discount rate includes the market average risk premium, based on the capital asset pricing model (CAPM). An alternative risk framework is the consumption CAPM (CCAPM) in which a project’s risk premium is determined by the correlation of its returns with the performance of the economy (rather than with the market investment portfolio). The CCAPM corresponds to the models underlying the SRTP approach within a risky environment.
• Use of the average risk premium (under either the CAPM or CCAPM approaches) is inappropriate for many government projects. Government projects are often chosen to address quite different features of society (e.g. public goods, combatting externalities and merit goods) than is the case for private sector projects. Many of these projects have low, zero, or even negative correlation with economic outcomes (or with market average returns). They may also be chosen to reflect the interests of future generations whose preferences are not represented in current market prices, and whose welfare is discounted by private sector decision-makers.
• The market return incorporates a liquidity component plus a component relating to project risk. The liquidity component should not be incorporated into the SDR as government incorporates such impacts already through its fiscal envelope for expenditure to protect its balance sheet.
• The component related to project risk comprises both diversifiable risk (represented by its covariance with the market return) and undiversifiable risk. The latter is relevant for irreversible projects in which a decision to invest foregoes the real option of waiting for more information prior to investment. This cost occurs only once, at the time the investment is begun, so should be reflected in a once-only discount rather than as a component of an ongoing discount rate.
• The preceding observations mean that for many government projects, it is inappropriate to apply the average market risk premium as incorporated in Treasury’s default discount rate.
• Treasury’s current assumed real risk-free rate is, however, set too low based on historical observation. Based on the decade preceding the pandemic, a real risk-free rate of between 0% and 1% is more appropriate than the current negative rate assumed by Treasury.
• Approaches used to set the SDR vary considerably across jurisdictions around the world, even amongst developed countries. Some countries use SOC, others use SRTP; some have DDRs, others do not; some have different discount rates for different sectors, others do not; amongst developed countries, default rates vary from a low of 1% p.a. (Germany) to 8% in Canada. Hence there is no consensus on the setting of the SDR across countries.
• One factor that is not clear in comparing cross-country practices is the extent to which government investment in each country is constrained by a broader fiscal envelope. Further investigation into the role that the SDR plays in determining the quantum, rather than the ranking, of investments across countries is warranted.
• On balance, the conceptual arguments indicate that the use in New Zealand of a 5% default discount rate for (non-commercial) public sector projects, coupled with exponential discounting, leads to an inappropriately high discounting of future returns for many projects.
• One avenue to explore is the use of a DDR. The use of DDRs may, however, lead to issues of time consistency; longer term reductions in the SDR, as used for instance in several countries including the UK, are unlikely to have major time consistency issues but are also unlikely to substantively change estimated present discounted values for projects with long-run payoffs.
• An alternative avenue that is recommended here is to attribute (potentially non-linearly) increasing returns to a resource as it becomes scarce. This approach may be supplemented by exploration of different rates of pure time preference for different goods reflecting societal preferences that value the preservation of certain resources more highly than the preservation of other resources. This approach more explicitly deals with both preferences and scarcity than does hyperbolic discounting or other DDR frameworks.
• The most important immediate action that Treasury can undertake to adopt an appropriate set of discount rates is to ascribe project-specific risk premia that reflect the distribution of a project’s returns relative to the state of the economy.