Discounting and divergence of opinion

Agents impatience rate and their anticipations about the future of the economy, are two essential determinants of the equilibrium discount rate, as illustrated by the Ramsey formula. Heterogeneity in time preference rates and in anticipations is widely acknowledged. Our objective is to determine the equilibrium discount rate when this heterogeneity is taken into account. Among others we tackle the following questions: As an additional risk or uncertainty, can dispersion in agents' characteristics lead to lower discount rates? What is the asymptotic behavior of the discount rate in such a setting? More generally, what is the shape of the yield curve?     

Endogenous Discounting and Climate Policy

Under risk of abrupt climate change, the occurrence hazard is added to the social discount rate. As a result, the social discount rate (1) increases and (2) turns endogenous to the global warming policy. The second effect bears profound policy implications that are magnified by economic growth. In particular, we find that greenhouse gases (GHG) emission should be terminated at a finite time so that the ensuing occurrence risk will vanish in the long run. Due to the public bad nature of the catastrophic risk, the second effect is ignored in a competitive allocation and unregulated economic growth will give rise to excessive emissions. In the long term, the GHG emission paths under the optimal and competitive growth regimes lie at the extreme ends of the range of feasible emissions.     

Discounting and Bayesian spectral analysis

In this paper an example of Bayesian time series analysis is given. A spectral analysis model is applied to the problem how expectations regarding periodic regularities of a series of capital values differ from expectations regarding periodic regularities of the original payment series. The result of the analysis is, that there is a systematic difference in such a way that capital values are expected to have longer periodic regularities than the original payments.     

Discounting and welfare evaluation of policies

We start with the premise that if policy discounting is to have any welfare relevance, one has to accept it being a derivative of a social welfare function (SWF). We show that if that derivative is to have a net present value (NPV) form, then the baseline allocation must be stationary. In addition, we show that at a stationary baseline in an overlapping generations growth economy, the intergenerationally fair discount rate equals the growth rate of per‐capita consumption, which is, roughly, 2% for the United States. This differs from the interest rate, even in the golden rule equilibrium, unless population growth is null. The last result is based on the main theorem in Mertens and Rubinchik (2012) and is demonstrated for a policy space that might naturally arise in applications.     

Decreasing Impatience: A Criterion for Non‐stationary Time Preference and "Hyperbolic" Discounting

Despite recent interest in hyperbolic discounting, there has been little discussion of exactly what property of time preferences is instantiated by hyperbolic or quasi‐hyperbolic functional forms. The paper revives an earlier proposal in Prelec (1989) that the key property is Pratt–Arrow convexity of the log of the discount function, which corresponds to decreasing impatience(DI) at the level of preferences. DI provides a natural criterion for assessing the severity of departure from stationarity in that greater DI is equivalent to more choices of dominated options in two‐stage decision problems, as well as greater convexity of the log of the discount function. Inefficient choices may arise as intentional precommitments, or as unintended reversals of preference by “naïve” agents.     

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.     

贴现因子、偏好和行为经济学

本文讨论了影响人们跨时选择的重要因素--贴现因子的最新进展以及他们在经济学和金融中的重要应用,给出了目前关于改变贴现因子的模型.     

Discounting the Distant Future: An Experimental Investigation

We use a laboratory experiment to elicit discount rates over a 20-year time horizon using government savings bonds as a payment vehicle. When using a constant (exponential) discount rate function, we find an implied average discount rate of 4.9 %, which is much lower than has been found in previous experimental studies that used time horizons of days or months. However, we also find strong support for non-constant, declining discount rates for longer time horizons, with an extrapolated implied annual discount rate approaching 0.5 % in 100 years. There is heterogeneity in discount rates and risk preferences in that people with more optimistic beliefs about technological progress have higher discount rates. These findings contribute to the debate over the appropriate discount rate to use in comparing the long-term benefits of climate change mitigation to the more immediate costs.     

Hyperbolic Discounting,Borrowing Aversion and Debt Holding

Analysis of an original Internet‐based survey reveals that debt holding is related to time discounting through: (i) present bias, measured by the degree of declining impatience in the generalized hyperbolic discount function; (ii) borrowing aversion, captured by a sign effect in that future losses are discounted at lower rates than future gains; and (iii) impatience, measured by the overall discount rate. Hyperbolic respondents are classified naïve if their answers reveal them to be time‐inconsistent procrastinators, and otherwise sophisticated. Naïve respondents with more steeply declining impatience are more likely to be debtors. The sign effect relates negatively to borrowing. Survey responses indicative of high or declining impatience are associated with credit card borrowing and other overborrowing indicators.     

Behavioural Economics,Hyperbolic Discounting and Environmental Policy

This paper reviews some recent research in “behavioural economics” with an application to environmental issues. Empirical results from behavioural economics provide a reminder that human behaviour is context-dependent, implying that policy may go awry if based upon models of behaviour which are inappropriate to the contexts in which decisions are made. Recognizing that agents may, in some contexts, systematically make mistakes raises challenging questions about the role of “paternalism” in government policy. The paper considers the research into hyperbolic discounting, and examines the implications for environmental policy. We develop a model of resource management under hyperbolic discounting, which shows that if a planner is unable to commit to a policy, the temptation to re-evaluate the policy in future could lead to an inadvertent collapse in the stocks of a natural resource.     

Equilibrium Welfare and Government Policy with Quasi-geometric Discounting

We consider a representative-agent equilibrium model where the consumer has quasi-geometric discounting and cannot commit to future actions. We restrict attention to a parametric class for preferences and technology and solve for time-consistent competitive equilibria globally and explicitly. We then characterize the welfare properties of competitive equilibria and compare them to that of a planning problem. The planner is a consumer representative who, without commitment but in a time-consistent way, maximizes his or her present-value utility subject to resource constraints. The competitive equilibrium results in strictly higher welfare than the planning problem whenever the discounting is not geometric. Journal of Economic Literature Classification Numbers: E21, E61, E91.     

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.     

What really matters: Discounting, technological change and sustainable climate

This paper discusses the interplay between the choice of the discount rate, greenhouse gas mitigation and endogenous technological change. Neglecting the issue of uncertainty it is shown that the Green Golden Rule stock of atmospheric carbon is uniquely determined, but is not affected by technological change. More generally it is shown analytically within the framework of a reduced model of integrated assessment that the optimal stationary stocks of atmospheric carbon depend on the choice of the discount rate, but are independent of the stock of technological knowledge. These results are then reinforced numerically in a fully specified integrated assessment analysis.     

Environmental Liability Law and Induced Technical Change – The Role of Discounting

We analyse the incentives of environmental liability law for inducing progress to emission abatement technology. We consider three liability rules: strict liability, a negligence rule with an emission norm as the due care standard, and a double negligence rule which combines the emission standard with an abatement technology norm. In the case of distortive discounting, i.e. where the private discount rate deviates from the social one, we show, how the level of distortion influences the ranking of liability rules, according to the criterion of generated social cost.     

Testing the Influence of Substitute Sites in Nature Valuation by Using Spatial Discounting Factors

This paper investigates the effect of nearby nature substitute sites on preferences for nature restoration. Contrary to prior studies, we use a respondent-centric approach to control for substitute sites. We assess each respondent-specific spatial context by computing densities of nature substitute sites within various ranges from each respondent’s home. This approach considers the use and non-use values of nature together. Data from three similar discrete choice experiments carried out in Flanders (Belgium) are compared. Different spatial discounting factors are tested to explore how the substitution effect behaves with regard to distance. Latent class analyses are performed to account for preference heterogeneity among respondents. We observe divergent behaviours across groups of respondents. The “distance-to-substitutes” affects how respondents gauge substitute sites. We find a significant influence of the squared average buffer distance but this effect varies in sign across case studies and classes of respondents. Our results demonstrate that individual-specific GIS data can significantly improve the representation of the spatial context and the transferability of value functions. However, the roles played by preference heterogeneity and nature perception on respondents’ capacity to value nature still deserves further attention in future research.     

Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems

This paper is concerned with the relationship between the discount rate and the nature of long-run behavior in dynamic optimization models. The theory is developed under two conditions. The first is history independence, which rules out multiple limit sets. The second is a condition that avoids the reversion to a stable steady state, as the discount factor is lowered, once cycles have emerged. These conditions appear to be the minimal restrictions that would allow analysis by a bifurcation diagram. The results are illustrated by two well-known examples in this literature, due to Sutherland and Weitzman–Samuelson. Journal of Economic Literature Classification Numbers: C61, D90, 041.     

Limits to Substitution Between Ecosystem Services and Manufactured Goods and Implications for Social Discounting

This paper examines implications of limits to substitution for estimating substitutability between ecosystem services and manufactured goods and for social discounting. Based on a model that accounts for a subsistence requirement in the consumption of ecosystem services, we provide empirical evidence on substitution elasticities. We find an initial mean elasticity of substitution of two, which declines over time towards complementarity. We subsequently extend the theory of dual discounting by introducing a subsistence requirement. The relative price of ecosystem services is non-constant and grows without bound as the consumption of ecosystem services declines towards the subsistence level. An application suggests that the initial discount rate for ecosystem services is more than a percentage-point lower as compared to manufactured goods. This difference increases by a further half percentage-point over a 300-year time horizon. The results underscore the importance of considering limited substitutability in long-term public project appraisal.     

Discounting,Distribution and Disaggregation: Discount Rates for the Rich and the Poor with Climate as a Source of Utility

To consider the implications of disaggregated consumption and discounting in the context of climate change, we study discounting in a world composed of the rich and the poor; a standard setting in the literature of cost–benefit analysis with distributional considerations. We derive several discount rates for different numéraires, which allow us to discuss intergenerational and intragenerational equity in common terms. In the example of CES‐CRRA utility, we also show that disaggregated discount rates may vary owing to several factors. One important parameter, inequality aversion, can be determined in the weighting of intergenerational and intragenerational concerns.