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.     

Is there a daily discount rate? Evidence from the food stamp nutrition cycle

Quasi-hyperbolic discounting predicts impatience over short-run tradeoffs. I present a direct non-laboratory test of this implication using data on the nutritional intake of food stamp recipients. Caloric intake declines by 10 to 15 percent over the food stamp month, implying a significant preference for immediate consumption. These findings constitute a rejection of the permanent income hypothesis and are extremely difficult to reconcile with exponential discounting. The data support an explanation based on time preference and reject several alternative explanations, including highly elastic intertemporal substitution. I explore implications for the optimal timing of transfer payments under alternative assumptions about preferences.     

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.     

Government size and economic growth in an endogenous growth model with rent‐seeking

We explore the relationship between government size and economic growth in an endogenous growth model with human capital and an unproductive capital which facilitates rent‐seeking. With exogenous as well as endogenous time discounting, we find a non‐monotonic relationship between the size of government and economic growth. We find that with very high (low) discounting, there is a unique low (high) growth equilibrium, regardless of the size of government. For the intermediate range of discounting, there are multiple equilibria and the growth outcome depends on the size of government. With endogenous time discounting, the growth outcome is path dependent and depends on the level of inherited human capital. However, there is only one stable growth regime and the economy endogenously switches to it. When the institutional constraints on rent‐seeking are not extremely high, the stable regime is the one in which there is a high‐growth equilibrium for a smaller size of the government and for larger size, both the high‐growth and the low‐growth equilibrium coexist. When the institutional constraints on rent‐seeking are extremely high, there exists only a unique high‐growth equilibrium irrespective of the size of government. Furthermore, economies with bigger size of the government and/or with poor quality institutions will take longer to endogenously switch to this stable growth regime.     

Present bias and the inefficiency of the centralized economy: The role of the elasticity of intertemporal substitution

We analyze an endogenous growth model considering agents with an isoelastic utility. Preferences are characterized by a utility affected by a negative externality, and a level of impatience which decays with the time distance from the present. Agents who cannot commit the actions of their future selves, play a game against them. The stationary equilibrium of this game defines a balanced growth path with a slower growth when played by subsequent central planners than when played by decision makers in the market economy. First, we prove that the fast growing market economy implies higher welfare if the negative externality is small, while the centralized economy is welfare improving above a given threshold for the externality (obtained for a specific family of non-constant discount functions). Secondly, we observe that this threshold increases with the elasticity of intertemporal substitution in consumption. Therefore, the greater this elasticity the more likely it is that the externality lies below this threshold, where policy interventions would not be adequate. Finally, as one would expect, the range of values of the externality for which the market equilibrium provides higher welfare widens the more different from constant discounting time preferences are, due either to a wider range of variation for the instantaneous discount rates or because these decay more slowly.     

An economic reappraisal of the Melamchi water supply project - Kathmandu,Nepal

This paper examines whether the benefits of the Melamchi water supply project in Nepal are likely to exceed its costs, assuming that high-quality municipal water services can be delivered to households and firms in the urbanized part of the Kathmandu Valley. Monte Carlo simulations are used to explore the sensitivity of the net present value and economic internal rate of return calculations to a wide range of assumptions and input parameters. We find that extreme assumptions are not required to generate large differences in economic feasibility; quite plausible differences in the values of some key parameters can lead to large differences in the economic attractiveness of the project. The results reveal that the three most important influences on net present value and economic internal rate of return are: (i) the discount rate and discounting procedure; (ii) the magnitude of monthly benefits for households connected to the new water system; and (iii) the annual growth rate in monthly benefits of connected households after the project comes on line. Our contribution lies in illustrating, with an actual case study in a developing country, the degree to which cost-benefit calculations of large infrastructure projects are influenced by key economic modeling assumptions and input parameters.JEL Classification: H42, H43, H54, Q25, Q56 Correspondence to: Dale WhittingtonWe would especially like to thank Keiichi Tamaki (ADB) and Ian Hill (Acres International) for their guidance and assistance with this project. We would also like to thank the following individuals for their help during our mission to Kathmandu in May, 2003: Richard W. A. Vokes, Kathie M. Julian, Raj Kumar Malla, Madan Shankar Shrestha, Suman Prasad Sharma and Noor Kumar Tamrakar.     

An Experimental Study of Influences of Performance-Related Payments on Timing of Delegated Stock Purchases

Performance-related bonuses are important tools for investment organizations to incentivize stock traders. Yet, two experiments indicate that bonuses rewarding short-term performance may lead to worse timing of purchases. The authors propose that hyperbolic time discounting makes participants set lower aspired purchase prices for short-term (decreasing percentage) bonuses than for long-term (increasing percentage) bonuses. For this reason purchases are made earlier for decreasing than increasing percentage bonuses, earlier for decreasing than random prices, and earlier for high price volatility than for low price volatility. Neither purchases at the lowest price or highest bonus are attained. Hyperbolic time discounting may account for bubbles observed in experimental double-auction markets.     

Behavioral New Keynesian Models: An empirical assessment

This paper uncovers the fact that cognitive discounting modeled à la Gabaix (2020) is highly generalizable to alternative models and expectational assumptions by offering a mathematically tractable way of introducing behavioral elements in linearized models. This is not the case for other models of bounded rationality, as most derivations, if not all among those proposed up to today, are algebraically too cumbersome to be of general applicability.This finding is used to introduce cognitive discounting into the Smets and Wouters (2007) model, hence building and estimating the first micro-founded behavioral medium scale DSGE model, to my knowledge. The empirical estimation shows that the data prefers a substantial degree of bounded rationality even in a model with as many frictions as the Smets and Wouters model.     

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     

On Impatience, Economic Growth and the Environmental Kuznets Curve: A Dynamic Analysis of Resource Management

The paper presents a dynamic analysis of natural resource management and investigates some key factors that affect optimal management and resource conservation.Using a recursive specification of time preferences, we show how endogenous discounting and impatience can affect the motivation for both capital investments and environmental preservation. We examine the relationships between economic growth and environmental quality. Endogenous discounting provides new insights in the economic dynamics underlying the environmental Kuznets curve. By treating growth as endogenous, we examine how externalities and economic growth interact with each other. We investigate how economic development can contribute to an increased demand for environmental preservation. As an important new result, we also show how poverty can contribute to environmental degradation.     

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.     

Economics training and hyperbolic discounting: training versus selection effects

This paper contributes to the literature on the effects of economics training on behavior by examining the link between hyperbolic discounting and the number of economics classes taken by a sample of 1310 college graduates at Ohio University. A strong negative correlation is found between economics training and hyperbolic discounting behavior. Regression analysis shows that dynamic consistency is a determinant of taking economics classes. Once the endogeneity of these variables is accounted for, economics training is no longer a statistically significant determinant of hyperbolic discounting. Thus, the selection effect of studying economics outweighs the training effect. Behavioral variables are found to be more important in explaining hyperbolic discounting than demographic variables. The study suggests the importance of controlling for both the selection effect and the training effect for all studies that examine the role of economic training on behavior.     

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.     

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.     

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.     

A simple explanation of some key time preference anomalies

Abstract Individual time discounting behaviour experimentally exhibits important anomalies that are inconsistent with the standard discounted utility model. These include the time preference reversal characteristic of hyperbolic discounting, the magnitude effect and the extreme sign effect. I propose a simple explanation of discounting that accounts for these three anomalies simultaneously, within the context of the expected utility model with uncertainty, risk aversion, and preference for precautionary saving.     

Exponential discounting bias

We address intertemporal utility maximization under a general discount function that nests the exponential discounting and the quasi-hyperbolic discounting cases as particular specifications. Under the suggested framework, the representative agent adopts, at some initial date, an optimal behavior that shapes her consumption trajectory over time. This agent desires to take a constant discount rate to approach the optimization problem, but bounded rationality, under the form of a present bias, deviates the individual from the intended goal. As a result, decreasing impatience will end up dominating the agent’s behavior. The individual will not be aware of her own time inconsistency and, therefore, she will not revise her plans as time elapses, what makes the problem relatively simple to address from a computational point of view. The general discounting framework is used to approach a standard optimal growth model in discrete time. Transitional dynamics and stability properties of the corresponding dynamic setup are studied. An extension of the standard utility maximization model to the case of habit persistence is also considered.     

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.     

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.     

Individual discount rates forecast county-level unemployment change

We use a national survey to estimate individuals’ discount rates for job creation in the community and test whether impatience for jobs is associated county-level unemployment change outcomes in subsequent years. Our results suggest that impatience for jobs is a possible forecast variable for future modelling efforts. To explore whether the impatience effect is general or simply limited to attitudes about local job creation, the same survey asked about discount rates for local amenity development and personal financial windfall. We find that job growth discount rates perform best for forecasting.