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.     

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.     

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.     

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.     

Estimating representations of time preferences and models of probabilistic intertemporal choice on experimental data

We here estimate a number of alternatives to discounted-utility theory, such as quasi-hyperbolic discounting, generalized hyperbolic discounting, and rank-dependent discounted utility with three different models of probabilistic choice. The data come from a controlled laboratory experiment designed to reveal individual time preferences in two rounds of 100 binary-choice problems. Rank-dependent discounted utility and its special case—the maximization of present discounted value—turn out to be the best-fitting theory (for about two-thirds of all subjects). For a great majority of subjects (72%), the representation of time preferences in Luce’s choice model provides the best fit.     

Bounded awareness and anomalies in intertemporal choice: Zooming in Google Earth as both metaphor and model

This paper draws on recent developments in the theory of choice under uncertainty to model anomalies in intertemporal choice. Cognitive limitations leading to hyperbolic discounting and magnitude effects in intertemporal choice may be described in terms of bounded awareness, and represented by phenomena familiar from visualization software such as Google Earth. Cognitive limits on visualization impose constraints on both the area being viewed and the level of detail of the view, with a trade-off between the two. Increasing detail at the expense of limiting the area viewed may be described as zooming. Data from a field experiment were used to assess the theory with an incentive-compatible multiple price list approach involving magnitude levels of 5x, 10x and 20x the basic magnitude level with time horizons of one, three, six and 12 months. Without zooming adjustments in base consumption, very strong hyperbolic and magnitude effects were found, and present bias could not explain the hyperbolic effects. The zooming model provides an explanation of what appear to be significant intertemporal anomalies in the data.     

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.     

The hyperbolic factor: A measure of time inconsistency

Many studies have found that discounting is hyperbolic rather than constant. Hyperbolic discounting induces time-inconsistent behavior and is becoming increasingly popular in economic applications. Most studies that provide evidence in favor of hyperbolic discounting either are merely qualitative or they depend on assumptions about, or parametric fittings of, utility functions. This paper provides a quantitative measure for the degree of deviation from stationarity and the induced time-inconsistency that can overcome the problems mentioned. This measure, the hyperbolic factor, also provides simple preference foundations of the most popular discount functions. Moreover, it can easily be calculated from data and does not require knowledge of utility. Thus, the hyperbolic factor provides an easy tool for theoretical preference foundations, critical empirical tests, and quantitative measurements of hyperbolic discounting.     

Empirical tests of stochastic binary choice models

This paper provides an experimental test of stochastic choice models of decisions. Models that admit Fechnerian structure are tested through the repeated pairwise choice problems. Results refute the Fechner hypothesis that characterizing the probability of selecting a given prospect increases in how strongly it is preferred to alternative choices. However, the experimental data lend support to characterizing an individual’s binary choice probability as some scalable functions of the von Neumann–Morgenstern utilities in the risky context.

     

Justice in an uncertain world: Evidence on donations to cancer research

The paper uses information on actual and hypothetical charitable contributions to cancer research in the United Kingdom to elicit information on justice principles endorsed by donors. They face a choice between fund-raising contributions for several hereditary and lifestyle-related cancers. Donors’ choices of how much to donate to different cancers reveal how they view luck vis-a-vis risky individual choices. The estimation results reveal that donations are smaller for cancers with higher prevention rates, which is the probability that the potential cancer victim can avoid the cancer in question by some choice. We also find that provision of information on lifestyle-related causes of cancer adversely affects contributions. In contrast, information on hereditary causes has a positive effect on donations. Furthermore, a large share of donors indicated in their feedback that they chose donations to a hereditary over a lifestyle-related cancer to “punish” poor individual choices. These findings suggest that many donors lean toward choice egalitarianism, which conditions donations on the potential beneficiaries’ choices.

     

Discounting and the evaluation of lifesaving programs

The evaluation of lifesaving programs whose benefits extend into the future involves two discounting issues. The intragenerational discounting problem is how to express, in age-j dollars, reductions in an individual's conditional probability of dying at some future age k. Having discounted future lifesaving benefits to the beginning of each individual's life, one is faced with the problem of discounting these benefits to the present—the intergenerational discounting problem. We discuss both problems from the perspectives of cost-benefit and costeffectiveness analyses. These principles are then applied to lifesaving programs that involve a latency period.The authors are, respectively, Associate Professor of Economics, Univesity of Maryland and Senior Fellow, Resources for the Future; and Senior Fellow and Vice President, Resources for the Future. We thank the National Science Foundation for their support under grant DIR-8711083.     

The Use of Base Rate Information as a Function of Experienced Consistency

Three experiments examine the effect of base rate consistency under direct experience. Base rate consistency was manipulated by blocking trials and setting base rate choice reinforcement to be either consistent or inconsistent across trial blocks. Experiment 1 shows that, contrary to the usual finding, participants use base rate information more than individuating information when it is consistent, but less when it is inconsistent. In Experiment 2, this effect was replicated, and transferred in verbal questions posed subsequently. Despite experience with consistent base rates increasing sensitivity to base rates in word problems, verbal responses were far from normative. In Experiment 3, participants’ use of base rates was once again moderated by its consistency, but this effect was itself moderated by the diagnosticity of base rate information. Participants were highly accurate in estimating experienced base rates. These studies demonstrate that base rate usage is complex and a function of how base rates are presented (experienced versus summary statistics) and response format (choice proportions versus probability estimates). Knowledge of base rates was insufficient for proper usage in verbal word problems. Although choice proportions showed a sophisticated sensitivity to experienced base rate information, participants seemed unable to demonstrate a similar sophistication when given typical word problems indicating that base rate neglect is a function of information representation and not an inherent processing bias.     

Looking ahead: Subjective time perception and individual discounting

Journal of Risk and Uncertainty - We disentangle hyperbolic discounting from subjective time perception using experimental data from incentive-compatible tests to measure time preferences, and a...     

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.     

The Collapsing Choice Theory: Dissociating Choice and Judgment in Decision Making

Decision making theory in general, and mental models in particular, associate judgment and choice. Decision choice follows probability estimates and errors in choice derive mainly from errors in judgment. In the studies reported here we use the Monty Hall dilemma to illustrate that judgment and choice do not always go together, and that such a dissociation can lead to better decision-making. Specifically, we demonstrate that in certain decision problems, exceeding working memory limitations can actually improve decision choice. We show across four experiments that increasing the number of choice alternatives forces people to collapse choices together, resulting in better decision-making. While choice performance improves, probability judgments do not change, thus demonstrating an important dissociation between choice and probability judgments. We propose the Collapsing Choice Theory (CCT) which explains how working memory capacity, probability estimation, choice alternatives, judgment, and regret all interact and effect decision quality.      

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.     

Behavioral patterns and reduction of sub-optimality: an experimental choice analysis

This paper attempts to identify behavioral patterns and compare their average success considering several criteria of bounded rationality. Experimentally observed choice behavior in various decision tasks is used to assess heterogeneity in how individual participants respond to 15 randomly ordered portfolio choices, each of which is experienced twice. Treatments differ in (not) granting probability information and in (not) eliciting aspirations. Since in our setting neither other regarding concerns nor risk attitude matter and probability of the binary chance move is (optimal) choice irrelevant, categorizing decision types relies on parameter dependence and choice adaptations. We find that most participants reduce systematically sub-optimality when following the identified criteria.