Public Sector Discount Rates: A Comparison of Alternative Approaches

Creedy, John; Passi, Hemant Working Paper Public Sector Discount Rates: A Comparison of Alternative Approaches New Zealand Treasury Working Paper, No. 17/02 Provided in Cooperation with: The Treasury, New Zealand Government Suggested Citation: Creedy, John; Passi, Hemant (2017) : Public Sector Discount Rates: A Comparison of Alternative Approaches, New Zealand Treasury Working Paper, No. 17/02, ISBN 978-1-988534-14-5, New Zealand Government, The Treasury, Wellington This Version is available at: https://hdl.handle.net/10419/205705 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Public Sector Discount Rates: A Comparison of Alternative Approaches John Creedy and Hemant Passi New Zealand Treasury Working Paper 17/02 2017 DISCLAIMER The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the author(s). They do not necessarily reflect the views of the New Zealand Treasury or the New Zealand Government. The New Zealand Treasury and the New Zealand Government take no responsibility for any errors or omissions in, or for the correctness of, the information contained in these working papers. The paper is presented not as policy, but with a view to inform and stimulate wider debate. NZ TREASURY WORKING PAPER 17/02 Public Sector Discount Rates: A Comparison of Alternative Approaches MONTH / YEAR June 2017 AUTHORS John Creedy Victoria University of Wellington 23 Lambton Street Wellington 6011 New Zealand Email Telephone [email protected] [+64 4 4637422] Hemant Passi New Zealand Treasury 1 The Terrace Wellington 6011 New Zealand Email Telephone Fax [email protected] +64 4 917 6305 +64 4 890 6686 ISBN (O NLINE ) 978-1-98-853414-5 URL Treasury website at June 2017: http://www.treasury.govt.nz/publications/research-policy/wp/2017/17-02 Persistent URL: http://purl.oclc.org/nzt/1962.txt ACKNOWLEDGEMENTS We should like to thank Girol Karacaoglu for supporting this work. We also benefited from helpful discussions with many colleagues in the New Zealand Treasury and a number of other government departments. In particular we should like to thank Kirsten Jensen, Dieter Katz, Joanne Leung, Chris Parker and John Yeabsley for their helpful comments on an earlier draft of this paper. NZ TREASURY New Zealand Treasury PO Box 3724 Wellington 6008 NEW ZEALAND Email Telephone Website [email protected] 64-4-472 2733 www.treasury.govt.nz WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES i Abstract This paper sets out the alternative approaches to the public sector discount rate and explains the assumptions involved. There are two main ways of thinking about the discount rate. First, the social opportunity cost of capital approach (SOC) defines the discount rate as the rate of return that a decision-maker could earn on a hypothetical ‘next best alternative’ to a public investment. Second, the social rate of time preference approach (SRTP) defines the discount rate as the rate of return that a decision-maker requires in order to divert resources from use in the present, to a public investment. In an ‘ideal’ market, these two rates are brought into alignment in equilibrium. However, as there are no markets for public investments, there are no market signals to equate preferences for investing in such projects with rates of return. There is no completely objective way of determining public sector discount rates. Essentially the discount rate reflects how the government values the future when making decisions on behalf of society: value judgements and assumptions are necessary. The paper aims to clarify these judgements. Elements of both approaches may be relevant to many policy and operational decisions that require discounting, in which case different approaches may be relevant for different contexts. The paper also briefly considers the use of hyperbolic discounting. JEL CLASSIFICATION H43; H50 KEYWORDS Public sector discount rate; social opportunity cost; social time preference rate. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES ii Executive Summary The public sector discount rate reflects how the government values outcomes that occur in the future relative to those that occur in the present. It is used across central and local government to ‘weight’ future costs and benefits when agencies carry out cost-benefit analysis (CBA), and to estimate the cost to the Crown of investing in public assets (the capital charge calculation). Despite many years of debate, there is no consensus on this topic, either in academic research or in policy guidance. This paper sets out the alternative approaches to discounting and explains the assumptions involved. The discount rate can be interpreted as the minimum rate of return that the government expects from its investments. This gives two ways of thinking about the discount rate. The social opportunity cost of capital approach (SOC) defines the discount rate as the rate of return that a decision-maker could earn on a hypothetical ‘next best alternative’ to a public investment The social rate of time preference approach (SRTP) defines the discount rate as the rate of return that a decision-maker requires in order to divert resources from use in the present, to a public investment. In theory, in an ‘ideal’ market, these two rates are brought into alignment in equilibrium. Rational decision-makers continue to invest as long as the rate of return that can be earned on public investments exceeds the rate demanded. However, as there are no markets for public investments, there are no market signals to equate preferences for investing in such projects with rates of return. This leaves the two alternative ways of approaching public sector discount rates introduced above. SOC is typically measured by reference to the rate of return on private-sector investments with similar risk characteristics to the public project under consideration. Under this approach, the discount rate is composed of a risk-free rate of return plus a risk-based premium which varies according to the riskiness of the project. This the basis for the NZ Treasury’s current advice. SRTP is a direct statement of the decision-maker’s preferences for valuing the future. Loosely speaking, it states that the discount rate depends on any intrinsic preference for trading-off the future relative to the present (so-called ‘pure time preference’), and the extent to which decision-makers may wish to prioritise the present, if there is an expectation that living standards are expected to grow in the future. There is no completely objective way of determining public sector discount rates. Essentially the discount rate reflects how the government values the future when making decisions on behalf of society. It is therefore natural to expect that value judgements and assumptions are necessary. First, a market-based SOC assumes that political decision-makers should trade-off the future for public investments in the same way that individuals and businesses do when making decisions about their own personal consumption and investment. However, it is possible that many individuals in their political roles as citizens might be more concerned about future social outcomes than is reflected in their decisions about their own personal consumption and investment. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES iii Second, a market-based SOC assumes that the government cares about the same types of risk, and demands the same risk-premiums, as private investors. Risk-premiums in financial markets are determined by the volatility of individual asset returns, and how those returns are expected to vary relative to the investor’s overall portfolio. This approach to measuring and pricing risk may not be meaningful in a public sector context. Furthermore, governments’ ability to manage risk is likely to be different to that of private sector firms. These considerations mean that the risk-premium component of public sector discount rates could, depending on how the government evaluates and prices risk, be different from those implied by private sector rates of return. Elements of both approaches may be relevant to many policy and operational decisions that require discounting, in which case a hybrid approach might be appropriate. Different approaches may be relevant for different contexts. The standard model of discounting involves discounting future amounts at a constant proportional rate, however long the time horizon under consideration. This is known as constant exponential discounting. One concern that has been raised with this approach is that, even with a low discount rate, the weights that a decision-maker attaches to future time periods eventually converge toward zero. An alternative approach is to apply a progressively lower rate to net benefits in more distant time periods. This is known as hyperbolic discounting, and has the effect of scaling-up the weight attached to the more distant future relative to exponential discounting. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES iv Table of Contents Abstract .................................................................................................................... i Executive Summary ................................................................................................ ii 1 Introduction .................................................................................................... 1 2 Discounting and Present Values .................................................................. 3 2.1 The need to discount ........................................................................................... 3 2.2 The Present Value of a Benefit Stream ............................................................... 3 2.3 Discounting over long periods ............................................................................. 4 3 Thinking About Discount Rates .................................................................... 5 3.1 Time preference ................................................................................................... 5 3.2 The optimal level of consumption and investment ............................................... 6 3.3 Market rates of return........................................................................................... 6 3.4 Public sector discount rates ................................................................................. 7 4 The social opportunity cost of capital .......................................................... 8 4.1 The rationale for a SOC approach ....................................................................... 8 4.2 Determination of SOC rate .................................................................................. 9 4.3 The definition of risk ........................................................................................... 10 4.4 Current public sector discount rates in New Zealand ........................................ 11 5 The social rate of time preference .............................................................. 12 5.1 Determination of the SRTP ................................................................................ 12 5.2 The social rate of time preference ..................................................................... 13 5.3 Specifying the parameters ................................................................................. 14 6 Comparison of alternative approaches ...................................................... 15 6.1 Reflecting opportunity cost ................................................................................ 16 6.2 Reflecting time preference ................................................................................. 17 6.3 Public sector risk ................................................................................................ 18 6.4 Measurement and parameter values ................................................................. 19 6.5 International approaches ................................................................................... 22 7 Time-varying discounting ........................................................................... 23 7.1 Discounting over the long term .......................................................................... 23 7.2 Hyperbolic discounting ....................................................................................... 23 7.3 Time inconsistency ............................................................................................ 24 8 Conclusions ................................................................................................. 25 References ............................................................................................................ 26 WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 1 Public Sector Discount Rates: A Comparison of Alternative Approaches 1 Introduction The public sector discount rate reflects how the government values outcomes that occur in the future relative to those that occur in the present. It is used to value the future costs and benefits of public projects and to estimate the cost of investing in public assets (the capital charge calculation).1 As a result, the discount rate plays an essential role in guiding public spending and investment decisions. The public sector discount rate can be interpreted as the minimum rate of return that the government expects from its investments. As a result, it represents the benchmark against which the returns from public sector investments should be assessed. Too high or too low a discount rate could cause the government to make the ‘wrong’ investments. In particular, setting the discount rate too high could lead to the rejection of public spending initiatives that would otherwise be regarded as valuable. Furthermore, a high discount rate, by lowering the weight that is attached to future outcomes, tilts decisions towards projects that deliver net benefits in the near term. Conversely, a low discount rate tilts decisions towards projects which deliver net benefits over the longer term. The recommended discount rate is, not surprisingly, highly controversial. Its choice involves both technical issues and a range of value judgements. This paper provides a comparison of alternative approaches. The aim is to clarify alternative viewpoints and so provide the basis for a balanced debate about advice regarding public sector discount rates. There are likely to be many competing opinions, many of which may ultimately boil down to value judgements which cannot be reconciled objectively. The paper aims to distinguish where objective considerations can be used to make recommendations and where value judgements are involved. Emphasis is given to the two main approaches to the public sector discount rate. These are the social rate of time preference approach and the social opportunity cost of capital approach. It also covers some other key considerations relevant to how public projects might be discounted, such as whether discount rates should be constant or whether they should gradually fall over the length of life of a project. It is of course recognised that the question of the public sector discount rate and the total amount of government expenditure are in principle intimately related. For example, a lower 1 In New Zealand, other discount rates are used across government, most notably, the risk-free rate for accounting valuations: see http://www.treasury.govt.nz/publications/guidance/reporting/accounting/discountrates. These are used as the basis for valuing a number of public sector assets and liabilities; for example, insurance liabilities (particularly ACC’s insurance claims liability), employee benefits (such as pensions), and the student loan book. These discount rates are outside the scope of this project. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 2 discount rate may be expected to be associated with higher planned levels of current expenditure. In practice however, current and planned spending levels are determined by a complex political process which involves many considerations other than the discount rate. These broader considerations are covered by New Zealand’s Fiscal Management Approach and are therefore not discussed here; see Lomax, McLoughlin and Udy (2016). The focus here is purely on the approaches taken to thinking about a public sector discount rate in the context of comparing cost-benefit profiles for the appraisal and ranking of public sector projects. Similarly the need to attach a monetary value to costs and benefits in each period during the life of a public project, where market prices are not available to provide a guide or markets are subject to distortions, presents a huge challenge that has also given rise to an extensive literature. The measurement of costs and benefits and the choice of public sector discount rate are often conflated, in particular in dealing with risk and uncertainty. Also, it sometimes argued that, where a discount rate is used that is lower than the market rate, the cost of a project should include an associated opportunity cost. Furthermore, it is often suggested that the ‘excess burden’ of taxation needed to finance the project should be taken into account. Sometimes the problems of measuring future benefits are simply assumed away when discussing discounting. Again, while recognising these issues, given the aims of this paper, focus is largely on the discount rate alone, although the questions of risk and opportunity costs are necessarily discussed. Finally, it is important to stress that the purpose of this paper is to clarify issues and provide a framework for discussion. It is not intended to propose any particular recommendations, or even reach unambiguous conclusions. As mentioned earlier, rational policy analysis requires clarification of the separate roles of value judgements and economic technicalities. Section 2 provides a brief introduction to the need for discounting, along with the basic mechanics of discounting and computing present values. Section 3 outlines the basic intuition behind approaches to discounting. Sections 4 and 5 go on to outline the two main approaches to thinking about public sector discount rates. These are, as mentioned above, the social opportunity cost of capital, and the social rate of time preference approaches. Section 6 compares these two approaches and so ‘sets the scene’ for debate. Section 7 introduces the issue of time-varying discount rates. Section 8 concludes. The public sector discount rate has been the subject of an extensive and often highly technical and controversial literature over a very long period.2 This paper makes no pretence to be comprehensive or to provide a review of the vast literature: references to this literature are therefore highly selective. As mentioned earlier, its aim is to set out the issues in a way that can stimulate rational debate. While it is not possible to avoid some technicalities, every attempt has been made to make the discussion clear and widely accessible. 2 A flavour of the controversy can be obtained from the debate following the Stern Report (2006) on climate change: see for example, Carter et al. (2006), Dasgupta (2006), Nordhaus (2006) and Varian (2006). For broader literature reviews, see Harrison (2010) and OECD (2015). WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 9 impacts. The benefits arising from public projects may also be, by their nature, very difficult to value in money terms compared with private investments. The assumption that they can all easily be incorporated in the calculation of a project’s benefits is a strong one. In addition, the next best use of the funds might, in the absence of a public project, be to take on less risk and a lower return than a comparable private sector investment. Therefore, taking the traditional SOC view that the next best use of the funds would be to invest in a private project with a given risk profile imposes a key assumption about individuals’ preferences for taking on risk in the absence of a government investment. A SOC-based view also assumes that the government is concerned about the same types of risk, and prices risk in the same way as markets. These assumptions may not be appropriate for all government projects. For example, the risks associated with public projects may not be strongly correlated with those in the market. As a result, a SOC-based approach is not, as is often assumed, a completely objective way of determining public sector discount rates. Rather, the decision to use a market-based SOC involves several implicit assumptions that need to be explicitly recognised. These issues are explored in further detail in section 6. 4.2 Determination of SOC rate At a high level, SOC-based approaches use asset-pricing models to estimate the expected rate of return from a public sector project. This is carried out by benchmarking or comparing the public project against private sector projects or companies considered to have similar risk characteristics. Given the choice to use a SOC-based approach, determining discount rates is then largely a technical exercise using well-established methods in the finance literature. A choice can be made between several different asset pricing models. These include the capital asset pricing model, arbitrage pricing theory, and multi-factor models. This is essentially the approach that private companies use to estimate their discount rates and cost of capital. This is also the basis for the NZ Treasury’s current approach to recommending public sector discount rates, using the Capital Asset Pricing Model (CAPM). The central insight of the CAPM is that, in a competitive market, the expected rate of return on any asset is equal to the risk-free rate of return, plus an equity premium that varies in direct proportion to the riskiness of that asset. This insight is captured by the basic CAPM formula: 𝑟𝑟=𝑟𝑟 𝑓𝑓+𝛽𝛽(𝑟𝑟 𝑚𝑚− 𝑟𝑟 𝑓𝑓) Where: • 𝑟𝑟 is the rate of return required, that is, the opportunity cost of investing in a public project. In other words, it is the required discount rate. • 𝑟𝑟 𝑓𝑓 is the risk-free rate of return. This is estimated by reference to the yields on long-term (10 year) government bonds. • 𝑟𝑟 𝑚𝑚− 𝑟𝑟 𝑓𝑓 is the equity-risk premium. This is the difference between the average rate of return available in the stock market (𝑟𝑟 𝑚𝑚) and the risk-free rate (𝑟𝑟 𝑓𝑓). WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 10 • 𝛽𝛽 is a measure of the riskiness of the private sector asset/company against which the government project is being benchmarked. It measures how sensitive the returns on the asset are (on average) to overall market returns. Therefore the CAPM formula can be used to estimate the discount rate as follows: 1. Select a set of private sector projects/companies that are considered to have similar risk characteristics to the public sector project under consideration 2. Estimate the average beta of these companies/projects (discussed further below) 3. Input this estimated beta, along with estimates of the risk-free rate and the equity premium, into the CAPM formula.10 The result can be interpreted as the expected rate of return on a market-based portfolio with similar risk characteristics to the public project under consideration. In other words, it is the ‘next best alternative’ rate of return available to the public for a given risk appetite. 4.3 The definition of risk It is important to stress that β measures risk in a precise sense. Usually, risk is understood to mean the variability of asset returns. However, if an investor chooses assets carefully, the portfolio can be balanced so as to offset at least some of the variability of individual assets while still yielding a positive expected rate of return on the portfolio overall. In other words, investors can diversify. If diversification is approximately costless, all investors seek to balance their portfolios so as to eliminate all diversifiable risk. In other words, investors hold well-diversified portfolios in equilibrium. This means that the only risk that investors bear is that part of an asset’s variability that cannot be diversified away by adding it to a well-balanced portfolio. This is referred to as ‘non-diversifiable’ risk. This is what is measured by β , and it is estimated by regressing the returns of an individual asset on market returns. It can be interpreted as the sensitivity of the returns of an individual asset to overall market movements.11 The key insight of the CAPM is that beta is the only notion of risk that is relevant to determining an asset’s risk premium. In particular, the CAPM predicts that this risk premium takes a particularly simple form: it is proportional to beta. However, this measure of risk does not automatically carry over well to public sector portfolios. It may not even be meaningful in a public sector context. A further issue is the way in which risks of public projects are correlated with the private market. This type of question is considered further in section 6. 10 In reality, some technical adjustments are made to the basic CAPM formula to account for the effects of taxation, inflation and the capital structure of the companies/projects being used for benchmarking. Further detail on the precise formula currently used to estimate public sector discount rates is available at: http://www.treasury.govt.nz/publications/guidance/planning/costbenefitanalysis/discountrates 11 For example, an asset with beta of 1.3 means that when the market rises or falls by an extra 1 per cent, on average the asset price will change by 1.3 per cent. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 11 4.4 Current public sector discount rates in New Zealand In New Zealand, the Treasury is responsible for advising central and local government agencies on the discount rate to be used for appraising public spending initiatives financed by general taxation. In addition to the default public sector discount rate (which is used to discount most government initiatives as well as for calculating departmental capital charge) Treasury also currently recommends specific discount rates for buildings, infrastructure and technology. These discount rates are set out in Table 1, and are specified in real pre-tax terms. Table 1 Recommended Public Sector Discount Rates in New Zealand12 Category Annual rate Default rate 6.0 General purpose office and accommodation buildings 4.0 Infrastructure and special purpose (single-use) buildings: • Water and energy • Prisons • Hospitals • Hospital energy plants • Road and other transport projects 6.0 Telecommunications, media and technology , IT and equipment, Knowledge economy (R&D) 7.0 They are set by reference to the rates of return that the government could hypothetically earn by investing public funds in a private sector project with similar risk characteristics to public investments. Treasury also allows for agencies to use project-specific discount rates, if these can be determined on clearly rationalised grounds for the case in hand. The 6 per cent default rate is the rate used to appraise initiatives in CBAx – Treasury’s costbenefit analysis tool. However, agencies can also conduct sensitivity testing using a 3 per cent discount rate, which reflects a risk-free rate of return set by reference to government bond yields.13 12 New Zealand Treasury (2016). 13 For further details of how Treasury determines public sector discount rates, see NZ Treasury (2008) and NZ Treasury (2016). WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 12 5 The social rate of time preference While the SOC attempts to specify the discount rate by trying to identify the rate of return on the next best alternative to a public project, the social rate of time preference (SRTP) takes the alternative route of attempting directly to specify preferences for trading-off the future when considering public projects.14 As mentioned above, there is no market for public projects, so there is no way of observing individual preferences for how to value the future in such cases. Nor is there any reliable way to survey and aggregate the preferences of individuals with regard to how time should be valued for public projects. As a result, the SRTP should not, despite the conventional language used, be interpreted as the preferences of ‘society’ in any aggregate sense. Rather, it is more appropriate to interpret the SRTP as reflecting the preferences of a decision-maker acting on behalf of society. The framework set out below can then be thought of as an attempt to formalise what considerations a rational decision-maker should take into account when setting the discount rate. 5.1 Determination of the SRTP The most common way of approaching the SRTP is to consider how a rational decisionmaker might optimise the consumption and investment path of the economy, supposing it could do so. Carrying out this thought experiment sheds light on what considerations such a decision-maker would take into account in setting a ‘socially optimal’ discount rate, and how those considerations depend on the preferences, or values, of the decision-maker. This approach can be formalised by supposing that the decision-maker can choose a consumption and investment path for the economy so as to maximise some function that evaluates different consumption paths; that is, it attaches a numerical value or ‘score’ to each path. Specifically, suppose that the decision-maker takes the following steps. • Assign a ‘welfare score’ to the level of consumption in each time period. This score reflects the decision-maker’s preferences for consumption within that period. In particular, it is generally assumed that the decision-maker has some preference for smoothing consumption over time.15 • Discount these welfare scores (as described in section 2) according to the decisionmaker’s own specific rate of time preference. This reflects the decision-maker’s own values about how future welfare should be valued relative to the present • Sum these discounted scores together to formulate an aggregate measure of ‘social welfare’ (that is, an abstract measure of the overall score that the decision-maker assigns to a given consumption path). This is often referred to as the decision-maker’s ‘social welfare function’. 14 For further discussion and references, see Creedy and Guest (2008). 15 More accurately, it is assumed that the decision-maker has a decreasing marginal valuation for consumption in any given period. That is, the greater is consumption, the less that additional increments to consumption add to the decision-maker’s score. This implies consumption smoothing, as the more a decision-maker reallocates from one year to another, the more unwilling they are to do so further. Thus the decision-maker is somewhat averse to unequal consumption streams over time. The degree of this aversion depends on the specification of preferences. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 13 This evaluation or social welfare function is therefore considered to be additive (the marginal benefit from increasing consumption in one period does not depend on consumption in other periods). It can be written formally as follows: 𝑊𝑊(𝐶𝐶)=𝑈𝑈(𝑐𝑐0)+𝑈𝑈(𝑐𝑐1) 1 + 𝜌𝜌+𝑈𝑈(𝑐𝑐2) (1 + 𝜌𝜌)2+⋯+𝑈𝑈(𝑐𝑐𝑇𝑇) (1 + 𝜌𝜌)𝑇𝑇 Where: • 𝑊𝑊(𝐶𝐶) represents the aggregate ‘social welfare’ that the decision-maker seeks to maximise by choosing the consumption profile 𝐶𝐶= (𝑐𝑐0,𝑐𝑐1, … , 𝑐𝑐𝑇𝑇). • 𝑈𝑈(𝑐𝑐𝑡𝑡) is the function that the decision-maker uses to assign a ‘welfare score’ to the level of consumption (𝑐𝑐𝑡𝑡) in any given year t.16 • 𝜌𝜌 represents the decision-maker’s pure rate of time preference. It is important to stress that this parameter is different from the discount rate that we are seeking to specify. Namely this parameter 𝜌𝜌 is used to discount welfare scores, whereas the discount rate that we are seeking to specify is used to discount cash flows. Nonetheless, 𝜌𝜌 is a key determinant of the overall discount rate. • 𝑇𝑇 is the length of the decision-maker’s evaluation horizon. Importantly, the above expression differs from the present value formula given above. The term W(C) is the present value of the stream of U(c) values, discounted at the pure time preference rate. The term, 𝜌𝜌, in particular attracts a great deal of controversy, as it implies that the decisionmaker values future generations less than the present. As this is a crucial value judgement, it is not surprising that views differ regarding the value of 𝜌𝜌 that ‘should’ be imposed for public projects, and that these views are often expressed in strong terms. This parameter is discussed further in section 6 (particularly box 1). 5.2 The social rate of time preference Given the form of objective – the welfare function given above - the decision-maker is then assumed to choose a consumption and investment path for the economy so as to maximise the value of 𝑊𝑊(𝐶𝐶) subject to the constraints of available resources, productivity, and so on. A further important assumption is made about the weighting function U(ct): this is considered to be ‘iso-elastic’. That is, the elasticity of U with respect to c is assumed to take the constant value, say θ . The maximisation problem can be solved to show that money values, that is the consumption values, c, rather than the ‘welfare’ values, U, are discounted at the rate, r, where: 𝑟𝑟=𝜌𝜌+𝜃𝜃𝜃𝜃 and: • 𝜌𝜌 is the decision-maker’s pure rate of time preference (as defined above) 16 In the context of individual multi-period optimisation, U represents a utility function. In the present context it is instead a cardinal weighting function. In the individual context, the term , 𝜌𝜌, is referred to as a ‘utility discount rate’. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 14 • g is the annual growth rate of per capita consumption, generally assumed to be constant. • 𝜃𝜃 is a term that reflects the nature of the decision maker’s preferences with respect to consumption smoothing. As mentioned above it represents the (assumed to be) constant elasticity of U with respect to variations in c. It is a parameter of the welfare scoring function, 𝑈𝑈. Loosely speaking, it captures how averse the decision maker is to unequal consumption streams across time, or its ‘aversion to intertemporal inequality’. Then r is the social rate of time preference. In cost-benefit analyses, the present value (in money terms) of a stream of annual net benefits (interpreted here as the stream, ct) is evaluated using this social time preference rate, r.17 The equation above is known as the ‘Ramsey equation’, following Ramsey (1928).18 In the last two decades, a number of countries have moved to using this equation as the basis for setting public sector discount rates according to a social rate of time preference approach: see section 6 for a summary of international approaches. The equation states that the socially efficient consumption discount rate is equal to: • the decision-maker’s rate of pure time preference, 𝜌𝜌, • plus a ‘wealth effect’. This reflects the reasoning that if the decision-maker cares about equalising consumption over time, and per capita consumption is expected to grow over time, future outcomes should be discounted due to the fact that people in the future enjoy higher living standards. The size of this wealth discount effect depends on the decision-maker’s aversion to intertemporal inequality, as captured by 𝜃𝜃. This implies that even if the decision-maker chooses to value the welfare of all time-periods and generations equally (that is, chooses a rate of pure time preference equal to zero) there are nevertheless other reasons to discount cash flows of consumption in the future because of the wealth effect.19 5.3 Specifying the parameters The SRTP approach involves a number of assumptions and value judgements, particularly in relation to the choice of variables in the Ramsey equation. These value judgements need to be made as explicit as possible. Many commentators attempt to set the values of 𝜌𝜌 and 𝜃𝜃 by reference to observed individual behaviour. However, these approaches involve a number of strong assumptions, and also make the implicit assumption that what is, is an appropriate signal of what the relevant values should be. Therefore it is more appropriate to understand the implications of different choices, and treat these decisions as value judgements that have to be made openly. How this might be possible is considered in section 6. Table 2 illustrates some of the parameter choices that have been used internationally. 17 It is tempting to think that discounting U using 𝜌𝜌 is equivalent to discounting c using r. However, the two are not necessarily equivalent. 18 It plays an important part in optimal growth models involving a ‘representative agent’: see, for example, Blanchard and Fischer (1989) and Barro and Sala-i-Martin (1995). 19 Some economists argue for the inclusion of an additional term in the Ramsey equation to account for the chance that there will be some catastrophe event so devastating that the outcomes of the policy become irrelevant. In reality, this term is difficult to quantify, and is likely to be small enough to ignore. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 15 Table 2 Percentage Discount Rates used with the Ramsey Equation Country 𝝆𝝆 𝜽𝜽 𝒈𝒈 SRTP UK baseline public sector discount rate 1.5 1 2 3.5 France baseline public sector discount rate20 1 2 1.5 4 Stern climate change review 0.1 1 1.3 1.4 Nordhaus critique of the Stern review 1.5 2 2 5.5 Harmonised European Approaches for Transport Costing 1.5 1 1.5 3 Sources: HM Treasury (2003), Cropper et al (2014), Stern (2007), Nordhaus (2007), HEATCO (2006) 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’ decisionmaker 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. 20 The French guidance does not explicitly state the values used to derive its public sector discount rate: the 4 per cent baseline discount rate was chosen as a central value. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 16 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 21 It is often set by reference to some measure of government bond yields as a proxy for a risk-free rate of saving. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 17 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 costbenefit 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. 6.2 Reflecting time preference The SRTP approach to determining discount rates is a direct way of trying to think about the considerations that are relevant to determining a decision-maker’s time preference. However, actually specifying these considerations requires subjective decisions about somewhat abstract concepts. These issues are discussed below when looking at the measurability of the two approaches. Furthermore, although the underlying theory used to formulate the version of SRTP presented above is widely used and cited, it involves a number of assumptions which need to be scrutinised. On the other hand, using a market-based SOC to determine public sector discount rates (whether this is based on share market returns or risk-free rates, or a combination of the two) assumes that market rates of return contain all relevant preferences about how the future should be traded-off versus the present in all cases. That is, a market-based SOC imposes the value judgement that political decision makers should trade-off the future for public investments in the same way that individuals or businesses do when making decisions about their own personal consumption and investment. This might be appropriate for some government investments whose principal purpose is to earn a financial rate of return for society, for example the New Zealand Superannuation 22 See for example Boardman et al. (2006), Boardman et al. (2008), Lind (1990) and Parker (2011) WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 18 Fund, and some investments by state-owned enterprises. However, the relevant question to ask is whether individuals would trade-off the future for, say, publicly-funded health, education, arts and community projects in the same way that they do for decisions about their own personal consumption and investment. That is, would individuals demand the same rate of return in order to sacrifice a unit of present consumption for a social investment, as that which they demand for a private investment? 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. Specifically, people may care about the wellbeing of current and future generations from both a financial and social justice perspective (involving intra-generational and inter-generational equity). These preferences are unlikely to be reflected in market-based instruments, the primary purpose of which is to shift private consumption through time. If this were the case, it would mean that individuals would be more willing to invest in public sector projects than is implied by market rates of return. That is, individuals would be willing to invest in public projects up to a point where the rates of return on public investments are lower than those observed in financial markets. 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. A separate issue is whether government agencies are able to value all relevant costs and benefits, including social costs and benefits, when carrying out cost-benefit analyses (CBA) of policy initiatives. The current New Zealand Treasury approach assumes that this is the case.23 As mentioned earlier, the question of whether all costs and benefits can be measured in money terms is outside the main focus of this project. However it is recognised that this is likely to be a strong assumption, and that if some of these benefits cannot be valued, or are otherwise systematically undervalued in CBA, then a dollar yield on a public sector project is not equivalent to a dollar yield on a private sector investment. Under these circumstances it is sometimes argued that it is appropriate to trade-off the future for social sector projects differently than for private sector projects. In other words, it is argued that the required rate of return for some public investments might be lower than that implied by a market-based SOC. It is certainly important to know whether some types of cost and benefit might be systematically under- or over-estimated in CBA. However, it is not usually advisable to try to correct for these biases through the discount rate. The wrong assessment of costs and/or benefits could go in either direction, and they are likely to vary widely from project to project. 6.3 Public sector risk Section 4 highlighted the point that private sector measures of risk may not automatically carry over to the public sector. In particular, the CAPM (and other market-based models of risk-premiums) assume that the decision-maker is willing to freely substitute between different assets in order to balance the risk and return of the overall portfolio in accordance with the decision-maker’s appetite for risk. For example, this definition of risk means that governments are comfortable offsetting the risk of say a health intervention ‘failing’ with an 23 The New Zealand Treasury’s CBA guidance states, ‘assuming all benefits have been valued correctly, we should be indifferent between one kind of benefit and another if their value is the same’. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 25 Time inconsistency raises an interesting question, as it effectively introduces two ‘versions’ of the decision maker. One is a forward-looking version who discounts more distant outcomes at a low rate, and the second is a more present-focussed person who discounts the immediate future at a high rate. This comes into conflict when the more distant future becomes the immediate future. 8 Conclusions The purpose of this paper has been to explain the alternative ways of thinking about public sector discount rates, and thereby provide the basis for a rational debate. It has been shown that there are two main ways of thinking about public sector discount rates. These depend largely on the assumption regarding the way the resources would otherwise be used in the absence of the public project being considered. They are as follows. • The social opportunity cost of capital approach – the rate of return that a decision-maker could earn on a hypothetical next best available alternative (or the opportunity cost of a public project) • The social rate of time preference – the rate of return that a decision-maker requires to sacrifice a unit of present consumption in order to invest in a public project. It has been stressed that neither approach offers an objective way of determining public sector discount rates. Value judgements are inevitable. SOC-based approaches are traditionally regarded as being more objective, based as they are on observable market returns. However, the very decision to select a SOC-based approach carries a number of implicit assumptions. These include assumptions that marketbased counterfactuals provide an appropriate counterfactual for public projects, public projects fully crowd-out private sector projects of equal magnitude, political decision-makers should trade-off the future in the same way that individuals and businesses do when making decisions about their own personal consumption and investment – or all relevant preferences are measurable and accounted for in CBA cash flows. Also it is assumed that the way markets evaluate and price risk are also how governments evaluate and price risk. Furthermore, SRTP-based approaches require explicit statements of the decision-maker’s value judgements. Indeed, the necessity to specify these aspects explicitly, rather than concealing them, may be considered a strength of the approach. Only very limited information can be drawn from financial markets to help calibrate SRTP. Nevertheless, the determination of the appropriate discount rate involves complex concepts that are not easy to specify precisely. It has been seen that there is no unambiguously clear answer to the question of what public sector discount rate to use. The choice depends on a complex range of technical judgements as well as value judgements, so it is not surprising that widespread agreement about the rate is very difficult, if not impossible, to achieve. After first making a decision regarding the general approach to be taken, many further questions remain involving orders of magnitude of crucial variables. It is hoped that the present paper can contribute to rational policy analysis by clarifying the essential features of alternative approaches and highlighting the central role of value judgements. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 26 References Atkinson, A.B. (1970) On the measurement of inequality. Journal of Economic Theory, 2, 244–63. Barro, R.J. and Sala-i-Martin, X. (1995) Economic Growth. New York: McGraw-Hill. Blanchard, O.J. and Fischer, S. (1989) Lectures on Macroeconomics. MIT Press, Cambridge, MA. Boardman, A., Greenberg, D., Vining, A. and Weimer, D. (2006) Cost-benefit analysis: concepts and practice. Prentice-Hall, New Jersey. Boardman, A., Moore, M. and Vining, A. (2008) Social Discount Rates for Canada. Available from Jdilegacy.econ.queensu.ca/Files/Conferences/PPPpapers/Moore%20conference% 20paper.pdf Caplin, A. and Leahy, J.V. (2000) The social discount rate. National Bureau of Economic Research Working Paper, No. W7983. Cambridge, MA. Carter, R.M., de Freitas, C.R., Goklany, I.M., Holland, D., Lindzen, R.S., Byatt, I., Castles, I., Henderson, D., Lawson, N., McKitrick, R., Morris, J., Peacock, A., Robinson, C. and Skidelsky, R. (2006) The Stern Review: A dual critique. World Economics, 7, 165–232. Chichilnisky, G. (1997) What is sustainable development? Land Economics, 73, 467–91. Creedy, J. (2007) Policy evaluation, welfare weights and value judgements: a reminder. Australian Journal of Economics, 10, 1-15. Creedy, J. and Guest, R. (2008) Discounting and the time preference rate, Economic Record, 84, 109-127. Cropper, M.L., Freeman, M.C., Groom, B. and Pizer, W.A. (2014) Declining discount rates. American Economic Review, 104, 538-43 Dasgupta, P. (2006) Comments on the Stern Review of Climate Change. University of Cambridge, Cambridge, UK. Gollier, C. and Hammitt, J.K. (2014) The long-run discount rate controversy. Annual Review of Resource Economics, 6, 273-295. Harrison, M. (2010) Valuing the Future: the social discount rate in cost-benefit analysis. Available from http://www.pc.gov.au/research/supporting/cost-benefit-discount Heal, G. (1998), Valuing the Future: Economic Theory and Sustainability. Columbia University Press, New York. HEATCO (2006) Developing Harmonised Approaches for Transport Costing and Project Assessment – Proposal for Harmonised Guidelines. Available from http://www.transport-research.info/project/developing-harmonised-european- approaches-transport-costing-and-project-assessment WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 27 H.M. Treasury (2003) The Green Book. Available from https://www.gov.uk/government/publications/the-green-book-appraisal-and- evaluation-in-central-governent Johansson, P.O. and Kristrom, B. (2015) Cost-Benefit Analysis for Project Appraisal. Cambridge: Cambridge University Press. Koopmans, T.C. (1960) Stationary ordinal utility and impatience. Econometrica, 28, 287– 309. Laibson, D. (1996) Hyperbolic discount functions, undersaving, and savings policy. National Bureau of Economic Research Working Paper No. 5635. NBER, Cambridge, MA. Mouter, N. (2015) Why do discount rates differ? Analyzing the differences between discounting policies for transport Cost-Benefit Analysis in five countries. MKBA working paper. Available from http://www.mkba-informatie.nl/mkba-voor- gevorderden/working-papers/mouter-why-do-discount-rates-differ-anayzling- differences-fi/ Li, C.-Z. and Lofgren, K.-G. (2000) Renewable resources and economic sustainability: a dynamic analysis with heterogenous time preferences. Journal of Environmental Economics and Management, 40, 236–50. Lind, R. (1990) Reassessing the government’s discount rate policy in light of new theory and data ina world economy with a high degree of capital mobility. Journal of Environmental Economics and Management, 18, S8-S28. Lomax, N., McLoughlin, S. and Udy, B. (2016) The New Zealand Fiscal Management Approach. Available from http://www.nzae.org.nz/wp-content/uploads/2016/10/3228152_FINAL-Conference- Paper-Guide-to-NZs-FMA.pdf Nordhaus, W.D. (2006) The stern review on the economics of climate change. National Bureau of Economic Research Working Paper No. 12741. Cambridge, MA. Nordhaus , W.D. (2007) A review of the Stern Review on the Economics of Climate Change. Journal of Economic Literature, 45, 686-702. NZ Treasury (2008) Public Sector Discount Rates for Cost Benefit Analysis. Available from http://www.treasury.govt.nz/publications/guidance/planning/costbenefitanalysis/dis countrates NZ Treasury (2016) Current Discount Rates. Available from http://www.treasury.govt.nz/publications/guidance/planning/costbenefitanalysis/cur rentdiscountrates OECD (2015) Adapting Transport Policy to Climate Change: Carbon Valuation, Risk and Uncertainty. Available from http://www.oecd.org/publications/adapting-transport- policy-to-climate-change-9789282107928-en.htm Office of Management and Budget (2003) Circular A-4. Available from https://www.transportation.gov/regulations/omb-circular-no-4 Okun, A.M. (1975) Equality and Efficiency: The Big Trade-Off. The Brookings Institution, Washington, DC. WP 17/02 | PUBLIC SECTOR DISCOUNT RATES: A COMPARISON OF ALTERNATIVE APPROACHES 28 Parker, C. (2011) Valuing the future appropriately: Case for using the shadow price of capital in social discount rate policy. NZIER report for Auckland Council. Available from: http://www.aucklandcouncil.govt.nz/SiteCollectionDocuments/aboutcouncil/commit tees/economicdevelopmentforum/meetings/economicfmag20111011.pdf Ramsey, F.P. (1928) A mathematical theory of saving. Economic Journal, 38, 543–59. Stern, N. (2006) The Economics of Climate Change. Available from http://www.hmtreasury.gov.uk/independent_reviews/stern_review_economics_climate_change/st ernreview_index.cfm. Stern, N. (2007) The Economics of Climate Change: The Stern Review.. Cambridge University Press, Cambridge and New York. Treasury Board of Canada (2007) Canadian Cost-Benefit Analysis Guide: Regulatory Proposals. Available from http://publications.gc.ca/site/eng/456648/publication.html Varian, H.L. (2006) Recalculating the costs of global climate change. New York Times, 14 December. Weitzman, M.L. (2007) Subjective expectations and asset-return puzzles. American Economic Review, 97, 1102-1130.