A new test of convexity–concavity of discount function

Discounted utility theory and its generalizations (e.g., quasihyperbolic discounting, generalized hyperbolic discounting) use discount functions for weighting utilities of outcomes received in different time periods. We propose a new simple test of convexity–concavity of discount function. This test can be used with any utility function (which can be linear or not) and any preferences over risky lotteries (expected utility theory or not). The data from a controlled laboratory experiment show that about one third of experimental subjects reveal a concave discount function and another one third of subjects reveal a convex discount function (for delays up to two month).

     

Estimating discount rates for environmental quality from utility-based choice experiments

We estimate rates of time preference using a utility-based choice experiment administered to a nationally representative sample of 2,914 respondents. For the full sample, the rate of time preference is very high for immediate benefits and drops off substantially thereafter, which is inconsistent with exponential discounting but consistent with hyperbolic discounting. Estimates of the hyperbolic discounting parameter range from 0.48 to 0.61. Visitors to water bodies have low rates of discount but exhibit hyperbolic discounting, whereas those who do not visit have consistently high rates of discount and low valuations of water quality.     

Temporal discounting of gains and losses of time: An experimental investigation

This paper investigates “asymmetries” between non-monetary gains and losses in intertemporal choice. We considered gains and losses of spare/working time with respect to a reference duration defined in a working contract. Specifically, we elicited a behavioral model of intertemporal choice that accounts for a gain/loss-dependent discounting function and a reference-dependent utility. Additionally, we did not impose preference for the present (positive discounting) and allowed for both decreasing and increasing impatience. While our results are standard regarding the discount of money (our baseline treatment), our subjects heavily discounted gains of time. More patience was observed for losses of time and a sizable portion of subjects even exhibited negative discounting, i.e. they preferred to expedite losses of time. Our econometric estimations also reveal a much larger heterogeneity of behavior in terms of both utility and discounting for gains and losses of spare time as compared to money.     

Discounting health and money: New evidence using a more robust method

This study compares discounting for money and health in a field study. We applied the direct method, which measures discounting independent of utility, in a representative French sample, interviewed at home by professional interviewers. We found more discounting for money than for health. The median discount rates (6.5% for money and 2.2% for health) were close to market interest rates, suggesting that at the aggregate level the direct method solves the puzzle of unrealistically high discount rates typically observed in applied economics. Constant discounting fitted the data better than the hyperbolic discounting models that we considered. The substantial individual heterogeneity in discounting was correlated with age and occupation.     

Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting

A large body of experimental research has demonstrated that, on average, people violate the axioms of expected utility theory as well as of discounted utility theory. In particular, aggregate behavior is best characterized by probability distortions and hyperbolic discounting. But is it the same people who are prone to these behaviors? Based on an experiment with salient monetary incentives we demonstrate that there is a strong and significant relationship between greater departures from linear probability weighting and the degree of decreasing discount rates at the level of individual behavior. We argue that this relationship can be rationalized by the uncertainty inherent in any future event, linking discounting behavior directly to risk preferences. Consequently, decreasing discount rates may be generated by people’s proneness to probability distortions.     

Avoiding the curves: Direct elicitation of time preferences

We propose and test a new method for eliciting curvature-controlled discount rates that are invariant to the form of the utility function. Our method uses a single elicitation task and obtains individual discount rates without knowledge of risk attitude or parametric assumptions about the form of the utility function. We compare our method to a double elicitation technique in which the utility function and discount rate are jointly estimated. Our experiment shows that these methods yield consistent estimates of the discount rate, which is reassuring given the wide range of estimates in the literature. We find little evidence of probability weighting, but in a second experiment, we observe that discount rates are sensitive to the length of the front-end delay, suggesting present bias. When the front-end delay is at least two weeks, we estimate average discount rates to be 11.3 and 12.2% in the two experiments.     

Is Time-Discounting Hyperbolic or Subadditive?

Subadditive time discounting means that discounting over a delay is greater when the delay is divided into subintervals than when it is left undivided. This may produce the most important result usually attributed to hyperbolic discounting: declining impatience, or the inverse relationship between the discount rate and the magnitude of the delay. Three choice experiments were conducted to test for subadditive discounting, and to determine whether it is sufficient to explain declining impatience. All three experiments showed strong evidence of subadditive discounting, but there was no evidence of declining impatience. I conclude by questioning whether hyperbolic discounting is a plausible account of time preference.     

On the functional form of temporal discounting: An optimized adaptive test

The tendency to discount the value of future rewards has become one of the best-studied constructs in the behavioral sciences. Although hyperbolic discounting remains the dominant quantitative characterization of this phenomenon, a variety of models have been proposed and consensus around the one that most accurately describes behavior has been elusive. To help bring some clarity to this issue, we propose an Adaptive Design Optimization (ADO) method for fitting and comparing models of temporal discounting. We then conduct an ADO experiment aimed at discriminating among six popular models of temporal discounting. Rather than supporting a single underlying model, our results show that each model is inadequate in some way to describe the full range of behavior exhibited across subjects. The precision of results provided by ADO further identify specific properties of models, such as accommodating both increasing and decreasing impatience, that are mandatory to describe temporal discounting broadly.     

Choosing monetary sequences: theory and experimental evidence

We formulate and investigate experimentally a model of how individuals choose between time sequences of monetary outcomes. The model assumes that a decision maker uses, sequentially, two criteria to screen options. Each criterion only permits a decision between some pairs of options, while the other options are incomparable according to that criterion. When the first criterion is not decisive, the decision maker resorts to the second criterion to select an alternative. We find that: (1) traditional economic models based on discounting alone cannot explain a significant (almost 30%) proportion of the data no matter how much variability in the discount functions is allowed; (2) our model, despite considering only a specific (exponential) form of discounting, can explain the data much better solely thanks to the use of the secondary criterion; (3) our model explains certain specific patterns in the choices of the “irrational” people. We reject the hypothesis that anomalous behavior is due simply to random “mistakes” around the basic predictions of discounting theories: deviations are not random and there are clear systematic patterns of association between “irrational” choices.     

Measures of Mortality Risks

Different risks of death are not equivalent because of differences in timing. This paper develops measures of mortality risks that recognize the probability of death, the duration of life lost, and the role of discounting. These adjustments lead to a substantial reordering of the major causes of death. Recognition of duration-related issues explains much of the public's misperception of mortality risk probabilities, which may reflect duration-related concerns rather than biases in risk beliefs. Our estimates suggest that in forming their risk beliefs the public discounts years of life lost at a rate from 3.3–12.4 percent. Standardization of lifetimes at risk also alters the relative efficacy of regulatory policies for which we provide a variety of cost-effectiveness measures.     

Discounting statistical lives

Benefit-cost analysis of government projects that reduce health risks over an extended period of time requires an estimate of the value of a future life. This in turn requires a discount rate. We suggest and carry out a method to estimate the discount rate using observations on discrete choices between projects with different time horizons. This method is implemented in a survey context. For our primary example, the estimated median discount rate is close to the market rate. A substantial proportion of the sample is estimated to have quite low discount rates. We provide some evidence that discount rates may differ for different types of risks.This research was supported in part by the U.S. Environmental Protection Agency under Cooperative Agreement in Environmental Economics Research CR-813557-01-0. The opinions expressed do not necessarily reflect the views of the U.S. Environmental Protection Agency. We would like to thank Paul Portney for bringing the importance of discounting statistical lives to our attention, and John Conlisk, Maureen Cropper, Mark Machina, Robert Mitchell, Peter Navarro, and Walter Oi for helpful comments.     

Coping With Ethnic Stereotypes in the Academic Domain: Perceived Injustice and Psychological Disengagement

Psychological disengagement is the defensive detachment of self-esteem from a particular domain. In the academic arena, disengagement can result from devaluing academic success or discounting the validity of academic outcomes. We review evidence for ethnic differences in these two processes of psychological disengagement and present results of a multiethnic study examining perceived ethnic injustice and academic performance as predictors of devaluing and discounting. Among African American students, beliefs about ethnic injustice (but not academic performance) predicted greater discounting and devaluing. Among European American students, poor academic performance (but not beliefs about ethnic injustice) predicted greater devaluing and discounting. Among Latino/a students, beliefs about ethnic injustice were associated with greater discounting, whereas poorer academic performance was associated with increased devaluing.     

Pure hyperbolic discount curves predict “eyes open” self-control

The models of internal self-control that have recently been proposed by behavioral economists do not depict motivational interaction that occurs while temptation is present. Those models that include willpower at all either envision a faculty with a motivation (??strength??) different from the motives that are weighed in the marketplace of choice, or rely on incompatible goals among diverse brain centers. Both assumptions are questionable, but these models?? biggest problem is that they do not let resolutions withstand re-examination while being challenged by impulsive alternatives. The economists?? models all attempt to make a single equilibrium preference predictable from a person??s prior incentives. This was the original purpose of these models?? hyperboloid (???¨C????) delay discount functions, which have been widely justified by the assumption that a person??s intertemporal inconsistency (impulsiveness) can be accounted for by the arousal of appetite for visceral rewards. Although arousal is clearly a factor in some cases of intertemporal inconsistency, it cannot be blamed for others, and furthermore does not necessarily imply hyperboloid discounting. The inadequacy of ?¨C?? functions is particularly evident in models of internal self-control. I have reviewed several of these models, and have argued for a return to pure hyperbolic discount function as originally proposed, the relatively high tails of which can motivate a recursive process of self-prediction and thereby the formation of self-enforcing intertemporal contracts. Such a process does not require a separately motivated faculty of will, or incompatible goals among brain centers; but it also does not permit the prediction of unique preferences from prior incentives.     

Common ratio using delay

We present an experiment in which we add a common delay in a choice between two risky prospects. The results show that delay produces the same change in preferences as in the well-documented common ratio effect in risky lotteries. The added common delay acts as if the probabilities were divided by some common ratio. Moreover, we show that there is a strong magnitude effect, in the sense that the effect of delay depends on the magnitude of the outcome. The results are consistent with the recently introduced probability time trade-off (PTT) model by Baucells and Heukamp. We present a parameterization of the model based on the experimental results, showing that the value function exhibits increasing relative risk aversion, the weighting function is s-shaped, and the intrinsic discount rate is decreasing.     

Heterogeneous risk and time preferences

Assessing individuals’ time and risk preferences is crucial in domains such as health-related decisions (e.g., dieting, addictions), environmentally-friendly practices, and saving opportunities. We propose a new method to jointly elicit and estimate risk attitudes and intertemporal choices. We use a novel individual level estimation procedure based on a hierarchical Bayes methodology, which can integrate different functional forms for discounting and risk attitudes. This method provides individual level estimates, and allows us to explore the heterogeneity in the data. In addition, we report a negative correlation between risk and time preferences, implying that risk-seeking individuals are less patient and less willing to defer consumption.     

Asymmetric discounting of gains <Emphasis Type="Italic">and</Emphasis> losses: A query theory account

People discount delayed gains (where the default is to receive a smaller gain sooner) more than accelerated gains (where the default is to receive a larger gain later). For losses, the pattern reverses—people discount delayed losses less than accelerated losses. In Study 1, confirming a Query Theory process account, this sign by direction interaction is mediated by the prominence of thoughts in favor of the default. Thoughts in favor of the smaller, sooner amount are more prominent in delay scenarios than acceleration scenarios, and this increases discounting for gains and decreases discounting for losses. Study 2 confirms the causal role of the order of option consideration. Participants considering thoughts in the natural order (pro-default thoughts first) replicate the sign by direction interaction, whereas participants considering thoughts in the opposite, unnatural order (pro-alternative thoughts first) do not. Reversing the order of option consideration eliminates the sign by direction interaction.     

Judgmental Discounting and Environmental Risk Perception: Dimensional Similarities, Domain Differences, and Implications for Sustainability

Environmental risks constitute a special category of risks because they often involve consequences that are highly uncertain, strongly delayed, occurring at distant places, and—therefore—mostly borne by others. Economic, decision–theoretic, and psychological research about the way people deal with such consequences is reviewed. Two major findings are presented: first, there is evidence that discounting mechanisms are stable across different preference dimensions (uncertainty, temporal, spatial, and social distance). Second, discount rates tend to vary across different problem domains (e.g., environmental vs. health vs. financial risks). In particular, it appears that temporal discounting is less pronounced for environmental risks than in other domains. Several factors are identified that affect the nature of the risk evaluation process, and it is argued that environmental risks differ from other risks on such factors. These environmental-risk characteristics may have important implications for policy strategies to promote environmental sustainability. Contrary to other domains, appealing to the public's long-term preferences may be successful. Also in policy making, insights from standard economic decision theory to environmental decision making should be applied with caution.