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.     

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.     

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.     

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.     

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.     

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.     

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.     

A Deeper Look at Hyperbolic Discounting

We conduct an experiment to investigate the degree to which deviations from exponential discounting can be accounted for by the hypothesis of hyperbolic discounting. Subjects are asked to choose between an earlier or later payoff in a series of 40 choice questions. Each question consists of a pair of monetary amounts determined by compounding a given base amount at a constant rate per period. Two bases (8 and 20 dollars), three compounding rates (low, medium and high) and three delays (2, 4, and 6 weeks) are each used. There are also 2 initial periods (Today and 2 weeks) and there are two separate questionnaires, one with lower “realistic” compounding rates and the other with higher compounding rates, typical of those used in previous studies. We analyze the detailed patterns of choice in 6 groups of 6 related questions each (in which the base and rate is fixed but the initial period and delay varies), documenting the frequency of patterns consistent with exponential discounting and with hyperbolic discounting. We find that exponential discounting is the clear modal choice pattern in virtually all cases. Hyperbolic discounting is never the modal pattern (except in the sense that constant discounting is a special case of hyperbolic discounting). We also estimate a linear probability model that takes account of individual heterogeneity. The estimates show substantial increases in the probability of choosing the later option when the compounding rate increases, as one would expect. There are small, sometimes significant, increases in this probability when the delay is increased or the initial period is in the future. Such behavior is consistent with hyperbolic discounting, but can account for only a small proportion of choices. Overall, deviations from exponential discounting appear to be due to error, or to other effects not accounted for by hyperbolic discounting. Principal among these is an increase in later choices when the base is larger.     

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...     

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.     

Does nurture matter: Theory and experimental investigation on the effect of working environment on risk and time preferences

Building upon the reference dependent preferences model, we develop a theoretical framework to examine the relationship between environment and preferences. To verify the model’s prediction, we use a combined artefactual field experiment and household survey data in Vietnam to investigate whether involvement is risky and has long-run targeted benefits, thereby causing fishermen to exhibit different risk and time preferences than workers in other occupations. Using a structural model approach, we integrate prospect theory and hyperbolic time discounting into a single framework, to simultaneously estimate and correlate the parameters of both risk and time preferences with other demographic variables. The key finding that fishermen are found to be less risk-averse and more patient than others asserts the theoretical prediction about the influence of the working environment on preferences.     

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.     

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).

     

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.     

Performance of procrastinators: on the value of deadlines

Earlier study has shown that procrastination can be explained by quasi-hyperbolic discounting. We present a model of effort choice over time that shifts the focus from completion of to performance on a single task. We find that being aware of the own self-control problems may reduce a person??s performance as well as his or her overall well-being, which is in contrast to the existing literature on procrastination. Extending this framework to a multi-task model, we show that interim deadlines help a quasi-hyperbolic discounter to structure his or her workload more efficiently, which in turn leads to better performance. Moreover, being restricted by deadlines increases a quasi-hyperbolic discounter??s well-being. Thus, we provide a theoretical underpinning for recent empirical evidence and numerous casual observations.     

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.     

Non-linear mixed logit

We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discounting functions to characterize impatience. There are several unexpected benefits of this extension, apart from the ability to directly estimate structural parameters of theoretical interest.