Empirical and public choice evidence for hyperbolic social discount rates and the implications for intergenerational discounting

The derivation of the correct discount rate for intergenerational projects in Cost Benefit Analysis is particularly contentious. Public choice has resulted in lower discretionary exponential discount rates for many intergenerational projects in Britain and the USA. This is shown to be strong indirect evidence that the true social discount rate may be a hyperbolic (rather than an exponential) function. There is also empirical evidence for this hypothesis. The hyperbolic nature of discounting is also a standard finding in the behavioural sciences. For intergenerational time frames hyperbolic discount rates should be employed together with exponential discount rates in cost-benefit sensitivity analyses.Sincere thanks to Maureen Cropper and Paul Portney for supplying their survey results and to Elaine Barrow and Phillip Judge for graphics assistance. Two anonymous referees also provided valuable comments.     

Declining Discount Rates: The Long and the Short of it

The last few years have witnessed important advances in our understanding of time preference and social discounting. In particular, several rationales for the use of time-varying social discount rates have emerged. These rationales range from the ad hoc to the formal, with some founded solely in economic theory while others reflect principles of intergenerational equity. While these advances are to be applauded, the practitioner is left with a confusing array of rationales and the sense that almost any discount rate can be justified. This paper draws together these different strands and provides a critical review of past and present contributions to this literature. In addition to this we highlight some of the problems with employing DDRs in the decision-making process, the most pressing of which may be time inconsistency. We clarify their practical implications, and potential pitfalls, of the more credible rationales and argue that some approaches popular in environmental economics literature are ill-conceived. Finally, we illustrate the impact of different approaches by examining global warming and nuclear power investment. This includes an application and extension of Newell and Pizer [‘Discounting the benefits of climate change mitigation : how much do uncertain rates increase valuations?’ Journal of Environmental Economics and Management 46 (2003) 52] to UK interest rate data.     

Valuation and management of wetland ecosystems

We recently completed a study of wetland values in coastal Louisiana that employed both willingness-to-pay and energy analysis-based methodologies and were able to bracket a range of values within which we feel fairly confident the true value lies. However, a large amount of uncertainty remains. Our current estimates of the total prsent value of an average acre of natural wetlands in Louisiana are US$2429–6400 per acre (assuming an 8% discount rate) to $8977–17000 per acre (assuming a 3% discount rate). At the lowest value, the current annual rate of loss of Louisiana wetlands (50 sq miles per year) is worth about $77 million. At the largest value it is worth about $544 million.In this paper we (a) discuss the fundamental theoretical and practical problems underlying natural resources valuation; (b) summarize our methods and findings for Louisiana wetlands; and (c) elaborate on some of the more recalcitrant problems attending applied natural resource valuation, including discounting and dealing with uncertainty and imprecision.The discount rate makes more difference in the final result than any other one factor, and yet there is much disagreement about the appropriate approach to discounting natural resources. We discuss the discounting problem as applied to natural resources and argue for lower discount rates for valuing renewable natural resources than apply for other aspects of the economy.It now seems clear that no reasonable amount of effort will produce very precise estimates of wetland values, and we suspect this is also the case for several other classes of natural resources. We elaborate a Wetlands Asurance Bonding System to address these problems.     

Justifying social discounting: The rank-discounted utilitarian approach

The discounted utilitarian criterion for infinite horizon social choice has been criticized for treating generations unequally. We propose an extended rank-discounted utilitarian (ERDU) criterion instead. The criterion amounts to discounted utilitarianism on non-decreasing streams, but it treats all generations impartially: discounting becomes the mere expression of intergenerational inequality aversion. We show that more inequality averse ERDU societies have higher social discount rates when future generations are better off. We apply the ERDU approach in two benchmark economic growth models and prove that it promotes sustainable policies that maximize discounted utilitarian welfare.     

CLIMATE CHANGE AND OVERLAPPING GENERATIONS

This paper examines the interplay between discounting and the distribution of welfare between generations in formulating climate change response strategies. The analysis shows that one can understand Nordhaus's (1994) standard representative agent model for climate policy analysis as a reduced form of an overlapping generations model that embodies more realistic demographic assumptions. In this setting, alternative Pareto efficient allocations may be supported as competitive equilibria given appropriate sets of income transfers between generations. Numerical simulations establish that increased intergenerational transfers entail reduced monetary discount rates and increased rates of greenhouse gas emissions abatement. Short-run policy choices are highly sensitive to normative judgments concerning the relative weight attached to the welfare of future generations.     

Spatial discounting of ecosystem services

The impact of conservation efforts targeted at preserving ecosystem services largely depend on the welfare implications associated with spatial variations in the provision of ecosystem services. While there is ample empirical evidence of spatial discounting or decay of the valuation of ecosystem services, there are still few underpinnings based on welfare economic theory. We establish a theory of spatial discounting that closely follows the concept of time discounting pertaining to climate change, and show spatial discount rates in the consumption, ecosystem service, and willingness to pay (WTP) numeraires. We consider the role of key parameters such as pure rate of spatial preference, consumption change, ecosystem services change, population density, and elasticity of marginal utility. We find that the spatial discount rate of WTP for ecosystem services that frequently appears in the empirical literature is the difference between the ecosystem service discount rate and consumption discount rate, where the ecosystem service discount rate includes both physical distance decay and welfare effects. Finally, we use numerical simulations to illustrate how the three different spatial discount rates vary with the spatial distance from the source of ecosystem services and with consumption patterns, implying many more possible spatial variations of WTP.     

How Much is Transfer and How Much is Insurance in a Pay‐as‐you‐go System? The German Case

Pay-as-you-go pension systems provide insurance against longevity-related old-age poverty and related risks. They are commonly also used as instruments for redistribution. This paper provides several estimates of the insurance and transfer share of the German public pension system. Estimating these shares is important because they are indicative of taxation-related deadweight losses and influence public acceptance of the pension system. We also disentangle intragenerational from intergenerational transfers. Although our estimate of intragenerational transfers is smaller than recent semi-official estimations, such transfers create substantial deadweight losses. Intergenerational transfers are much larger, thereby contributing to strong negative participation incentives for the younger generation.
JEL classification : H 55; J 26     

Convex Time Budgets and Individual Discount Rates in the Long Run

The purpose of this study is to use experimental data to estimate individual discount rates and test for hyperbolic discounting over a long time horizon. To do this, we employ the convex time budget experimental approach with cash payments over a 20 year time horizon. To date, there are few experimental studies that explore discount rates beyond a 1 year time horizon. Previous experimental studies that focus on short time horizons find high discount rates, which may not be applicable to decisions that affect outcomes in the distant future. Our findings are quite similar to the average rate of 4.9% found by Grijalva et al. (Environ Resour Econ 59:39–63, 2014), who similarly use a 20 year time horizon, but use the multiple price list elicitation method along with payment via government savings bonds. We find annual discounts rates in the range of 1.9–5.5%, depending on the specific model used. We also find evidence for declining discount rates, and that this hyperbolic pattern of behavior is related to the confidence subjects have in receiving distant-future payments.     

Family linkages,social interactions,and investment in human capital: A theoretical analysis

This paper introduces parent–child interactions into the Beckerian model of human capital. The acquisition of human capital, jointly determined by parental investment and child effort, is an equilibrium outcome of the intergenerational interactions, which is Pareto efficient within the family. We show that the equilibrium output of human capital is not affected by the parental authority over child behavior, but it is usually lower than the level that maximizes the instantaneous aggregate family welfare. In a family with more than one child, siblings not only compete for parental investments but also directly interact with each other in their effort choices. Exploring intragenerational connections and their interplay with intergenerational forces, we present a more complete theory of family linkages in human development and its implications for the rise and fall of families. Social interactions among children from different families induce intragenerational feedback effects that are further amplified by intrafamily interactions and accelerate regression toward the mean in the economic status of families.     

Reconciling sustainability and discounting in Cost–Benefit Analysis: A methodological proposal

The incorporation of the intergenerational equity objective has rendered the traditional Cost–Benefit Analysis (CBA) approach obsolete for the evaluation of projects presenting an important number of environmental externalities and for those whose impacts extend throughout a long period of time.Based on the assumption that applying a discount rate rewards current consumption and, therefore, that it is only possible to introduce a certain intergenerational equity in a Cost–Benefit Analysis, in this work we propose an approach to discounting based on a different rationale for tangible and intangible effects. We designed two indicators of environmental profitability: a) the Intergenerational Transfer Amount (ITA), which quantifies in monetary units what the current generation is willing to pass on future generations when an environmental restoration project is carried out, and b) the Critical Environmental Rate (CER), measures the implicit environmental profitability.These concepts were tested through an empirical case study pertaining to the assessment of an Erosion Control Project in the southeast of Spain. The results yield traditional profitability indicators that are higher — and probably closer — to the real values set by the contemporary society. The information provided by the environmental profitability indicators proposed renders more transparency to the quantification of the levels of intergenerational equity applied, thereby facilitating the difficult reconciliation of the CBA technique with the objective of sustainability.     

Ramsey discounting calls for subtracting climate damages from economic growth rates

The Ramsey equation ties the utility discount rate and the elasticity of marginal utility of consumption together with per capita consumption growth rates to calculate consumption discount rates. For many applications, per capita consumption growth rates can be approximated with per capita output growth rates. That approximation does not work for climate change, which drives an ever-increasing and increasingly uncertain wedge between output and consumption growth. NAS (2017), in a central recommendation and illustrative example, conflates the two. The correct, consumption-based discounting method generally decreases consumption discount rates and, thus, increases the resulting Social Cost of Carbon Dioxide (SC-CO₂).     

Hyperbolic discounting and the time-consistent solution of three canonical environmental problems

In this paper I propose a time-consistent method of discounting hyperbolically and apply it to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, and (iii) economic growth and pollution. I show that, irrespective of potentially high initial discount rates, time-consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time-consistent hyperbolic discounting. This result is also confirmed for open-access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the modified Green Golden Rule.     

The Ethics of Intertemporal Distribution in a Warming Planet

This paper evaluates, from the ethical viewpoint, current work by economists on intergenerational resource allocation in the presence of global warming. We begin by attempting to elucidate the debate that has recently occurred on the appropriate choice of the discount rate. We offer three justifications for maximizing the discounted sum of generational utilities, and find only one of these to be a satisfactory justification of that practice: the possibility that the human species may become extinct. This implies that a very small discount rate (large discount factor) should be used. We argue that the justification for discounting, inherent in the approaches taken by many economists, is that of ‘the present generation of hegemon,’ which is unacceptable. The role of the Ramsey equation in deducing the discount rate in these theories is explained. As an alternative to discounted utilitarianism, we propose a principle of sustainability; we describe optimal paths that have been calculated for the sustainabilitiarian (Rawlsian) objective function, and paths that will sustain growth in welfare, at a positive rate. We report results concerning optimal paths when the uncertainty of existence of future generations is taken into account. In sharp contrast to the utilitarian model, it turns out that under some conditions, the ‘sustainabilitarian’ can ignore the uncertainty regarding the date at which humans become extinct. There is a striking difference between the solutions of the discounted utilitarian program and the sustainabilitarian program under uncertainty.     

Patience auctions: the impact of time vs. money bidding on elicited discount rates

We introduce, test, and compare two auction-based methods for eliciting discount rates. In these “patience auctions”, participants bid the smallest future sum they would prefer -or- the longest time they would wait for a reward, rather than receive a smaller, immediate payoff. The most patient bidder receives the delayed reward; all others receive the immediate payoff. These auctions allow us to compare discounting when participants’ attention is focused on the temporal versus monetary dimension of delayed rewards. We find that the estimated parameters in the three most commonly used discount functions (exponential, hyperbolic, and quasi-hyperbolic) differ across these two bidding methods (time-bids vs. money-bids). Specifically, our participants tend to show more impatience under time-bids. Furthermore, we find that people are more likely to exhibit exponential (as opposed to hyperbolic) discounting and exhibit less present bias under time-bids, compared to money-bids. To our knowledge, this paper is the first to directly compare time versus money preference elicitations, within the same subjects, using an incentive-compatible mechanism.     

Discounting and altruism to future decision-makers

Is discounting of future decision-makers’ consumption utilities consistent with “pure” altruism toward those decision-makers, that is, a concern that they are better off according to their own, likewise forward-looking, preferences? It turns out that the answer is positive for many but not all discount functions used in the economics literature. In particular, “hyperbolic” discounting of the form used by Phelps and Pollak (Rev. Econ. Studies 35 (1968) 201) and Laibson (Quart. J. Econ. 112 (1997) 443) is consistent with exponential altruism towards future generations. More generally, we establish a one-to-one relationship between discount functions and altruism weight systems, and provide sufficient, as well as necessary, conditions for discount functions to be consistent with pure altruism.     

Discounting in a world of limited growth

This paper explores the consequences fordiscounting of assuming limits to growth. One of the main determinants of the discount rate is the rate of economic growth. If growth rates decline in the future then the discount rate should not be constant but also decline over time. In fact, we would then need not a single discount rate but rather a variable discount schedule. This would imply higher present values for the distant future. The paper analyses how discount rates would vary with different assumptions about the patterns of growth and the pure rate of time preference.An earlier version of this paper was presented at the conference ECOLOGICAL ECONOMICS, Stockholm, August 1992. I am grateful for valuable comments from Partha Dasgupta, Gunnar Köhlin, Karl-Göran Mäler, Mike Young and two anonymous referees.     

Capital markets integration, growth and income distribution

The paper considers a two-country model of overlapping generation heterogenous economies with intergenerational transfers carried out in the form of bequest and investment in human capital. We examine in competitive equilibrium the transitory and long-run effects of capital markets integration. First, we explore how the regime of public education affects the dynamics of the integrated economy. Second, we study the effects of capital markets integration, in equilibrium, on the intragenerational income distribution in both the host and investing country.     

Developments in discounting: With special reference to future health events

Research on time preferences and discounting has two main motivations: to inform decision making by providing a basis for the comparison of future costs and benefits; to explain the influence of the future on current behaviour. This paper introduces the wide range of discount functions which have been advocated in addition to the standard constant rate exponential model. The different approaches taken to estimating the parameters of the discount function are reviewed. The issues raised by discounting in the longer term are discussed. Particular attention is given to time preferences with respect to future health events which have for a number of reasons been a fruitful area for research on time preferences. Specifically the paper examines: the distinctive issues raised when discounting future health events; the methods which have been used to discount health events; the relationship between time preferences and health-affecting behaviour.     

Saving behavior in stationary equilibrium with random discounting

Summary. We study the implications of random discount rates of future generations for saving behavior and capital holdings in a steady state competitive equilibrium with heterogeneous population. A well-known difficulty in deterministic economies with heterogeneous households is that in steady state only the most patient households hold capital. In this paper we state conditions under which this random discounting is sufficient for households other than the most patient ones to save. We thus provide a simple and natural way of overcoming the aforementioned difficulty. Received: December 28, 1998; revised version: May 19, 1999