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.     

Measuring the Utility of Losses by Means of the Tradeoff Method

This paper investigates the shape of the utility function for losses. From a rational point of view it can be argued that utility should be concave. Empirically, measurements of the utility for losses show mixed results but most evidence supports convex rather than concave utilities. However, these measurements use methods that are either biased by the certainty effect or require complex parametrical estimations. This paper re-examines utility for losses, avoiding the mentioned pitfalls by using the tradeoff method. We find that utility for losses is convex. This is contrary to common assumption in the economics literature. Also, we investigate properties of the tradeoff method showing a new violation of procedure invariance. Our findings demonstrate that diminishing sensitivity is an important phenomenon for utility elicitation.     

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.     

Individual laboratory-measured discount rates predict field behavior

We estimate discount rates of 555 subjects using a laboratory task and find that these individual discount rates predict inter-individual variation in field behaviors (e.g., exercise, BMI, smoking). The correlation between the discount rate and each field behavior is small: none exceeds 0.28 and many are near 0. However, the discount rate has at least as much predictive power as any variable in our dataset (e.g., sex, age, education). The correlation between the discount rate and field behavior rises when field behaviors are aggregated: these correlations range from 0.09–0.38. We present a model that explains why specific intertemporal choice behaviors are only weakly correlated with discount rates, even though discount rates robustly predict aggregates of intertemporal decisions.     

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).

     

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.     

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.     

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.     

A tractable method to measure utility and loss aversion under prospect theory

This paper provides an efficient method to measure utility under prospect theory. Our method minimizes both the number of elicitations required to measure utility and the cognitive burden for subjects, being based on the elicitation of certainty equivalents for two-outcome prospects. We applied our method in an experiment and were able to replicate the main findings on prospect theory, suggesting that our method measures what it is intended to. Our data confirmed empirically that risk seeking and concave utility can coincide under prospect theory. Utility did not depend on the probability used in the elicitation, which offers support for the validity of prospect theory.

Evaluating Time Streams of Income: Discounting What?

For decisions whose consequences accrue over time, there are several possible techniques to compute total utility. One is to discount utilities of future consequences at some appropriate rate. The second is to discount per-period certainty equivalents. And the third is to compute net present values (NPVs) of various possible streams and to then apply the utility function to these net present values. We find that the best approach is to first compute NPVs of various possible income streams and then take the utility of such NPVs. We show the drawbacks of other alternative models of evaluating income streams. The article discusses the advantages of the power and logarithmic forms in the modeling of time preference. These are the only forms for which utility of income and utility of consumption are strategically equivalent. Further, these forms permit the flexibility in the choice of a time period (e.g., monthly or quarterly) without modifying the utility function, thus simplifying analysis.     

Risk-induced discounting

We establish a direct connection between time preference and risk about an attribute (health) of the instantaneous utility function. In doing so, we derive a risk-induced discount function that corresponds to a normalized expectation of that attribute. We provide several results characterizing this risk-induced discount function depending on the stochastic properties of the risk, which we model as a discrete Markov process. When it is well-defined, which we refer to as full approximation, the risk-induced discount function coincides with exponential discounting if the Markov process is stationary. However, a slight perturbation of the beliefs can trigger time-inconsistent discounting. When considering non-stationary Markov processes, time-inconsistency also emerges in situations where individuals’ beliefs change in a non-anticipated fashion over time, as exemplified by quasi-hyperbolic discounting. Results are illustrated via several applications.     

Intergenerational justice and the social discount rate

This paper applies the Harsanyi social welfare function to the problem of determining the social discount rate. It thus views the social discount question as one of justice between generations under conditions of individual uncertainty over position, rather than as one generation's paternalism or altruism for the next generation. Whether there is an accumulation of capital for future generations is shown to depend on the form of the individual (or collective) utility function. More importantly, the approach lends some insight into the kind of institutional structure which should be used to determine the social discount rate.This paper was written while the author was a postdoctoral fellow at the Center for Study of Public Choice at Virginia Polytechnic Institute and State University. Helpful comments were received on an earlier draft from James M. Buchanan, Pierre Pestieau, and Robert D. Tollison.     

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.     

Stochastic dominance in multicriterion analysis under risk

Traditionally, in the literature on the modelling of decision aids one notes the propensity to treat expected utility models and outranking relation models as rivals. It may be possible, however, to benefit from the use of both approaches in a risky decision context. Stochastic dominance conditions can be used to establish, for each criterion, the preferences of a decision maker and to characterise them by a concave or convex utility function.Two levels of complexity in preference elicitation, designated as clear and unclear, are distinguished. Only in the case of unclear preferences is it potentially interesting to attempt to estimate the value function of the decision maker, thus obtaining his (her) preferences with a reduced number of questions. The number of questions that must be asked of the decision maker depends upon the level of the concordance threshold that he(she) requires in the construction of the outranking relations using the ELECTRE method.     

Elicitation of Subjective Probabilities when the Initial Endowment is Unobservable

In the framework of subjective expected utility theory we develop two distinct procedures for the elicitation of a person's subjective probabilities when the initial endowment is random and unobservable. Procedures of the first kind rely on the boundedness of the utility function to elicit the person's subjective probabilities directly. Procedures of the second kind infer the person's initial endowment from his choice behavior prior to the application of probability elicitation.     

Models for estimating discount rates for long-term health risks using labor market data

This article utilizes evidence from job choices involving fatality risks to estimate individual discount rates for adverse health outcomes. The study compares the results from five distinct models for estimating discount rates from labor market data. The estimated discount rates range from 1% to 14% with confidence intervals that usually include financial market rates for the same period. This result, and consistent findings of significant compensating differentials for fatality risk, provide strong support for life-cycle models of individual rationality in the choice of job risks. Discounted value-of-life estimates are also developed and compared to the crosssection estimates that are more prevalent in the literature.     

Estimating Risk Attitudes using Lotteries: A Large Sample Approach

Attitudes towards risk play a major role in many economic decisions. In empirical studies it is quite often assumed that attitudes towards risk do not vary across individuals. This paper questions this assumption and analyses which factors influence an individual's risk attitude. Based on questions on lotteries in a large household survey we first semiparametrically estimate an index for risk aversion. We only make weak assumptions about the underlying decision process and our estimation method allows for generalisations of expected utility. We then estimate a structural model based on Cumulative Prospect Theory. Expected utility is strongly rejected and both the value function and the probability weighting function vary significantly with (among other things) age, income, and wealth of the individual.     

Investigating Risky Choices Over Losses Using Experimental Data

We conduct a battery of experiments in which agents make choices from several pairs of all-loss-lotteries. Using these choices, we estimate a representation of individual preferences over lotteries. We find statistically and economically significant departures from expected utility maximization for many subjects. We also estimate a preference representation based on summary statistics for behavior in the population of subjects, and again find departures from expected utility maximization. Our results suggest that public policies based on an expected utility approach could significantly underestimate preferences and willingness to pay for risk reduction.JEL Classification: C91, D81