Kirsten I. M. Rohde

Non-hyperbolic time inconsistency

The commonly used hyperbolic and quasi-hyperbolic discount functions have been developed to accommodate decreasing impatience, which is the prevailing empirical finding in intertemporal choice, in particular for aggregate behavior. However, these discount functions do not have the flexibility to accommodate increasing impatience or strongly decreasing impatience. This lack of flexibility is particularly disconcerting for fitting data at the individual level, where various patterns of increasing impatience and strongly decreasing impatience will occur for a significant fraction of subjects. This paper presents discount functions with constant absolute (CADI) or constant relative (CRDI) decreasing impatience that can accommodate any degree of decreasing or increasing impatience. In particular, they are sufficiently flexible for analyses at the individual level. The CADI and CRDI discount functions are the analogs of the well-known CARA and CRRA utility functions for decision under risk.

Time-Tradeoff Sequences for Analyzing Discounting and Time Inconsistency

textabstractABSTRACT. This paper introduces time-tradeoff (TTO) sequences as a new tool to analyze time inconsistency and intertemporal choice. TTO sequences simplify the measurement of discount functions, requiring no assumption about utility. They also simplify the qualitative testing of time inconsistencies, and allow for quantitative measurements thereof. TTO sequences can easily be administered using only pencil and paper. They readily show which subjects are most prone to time inconsistencies. We further use them to axiomatically analyze and empirically test (quasi-)hyperbolic discount functions. An experiment demonstrates the feasibility of measuring TTO sequences. Our data falsify (quasi-)hyperbolic discount functions and call for the development of models that can accommodate increasing impatience.

A preference foundation for Fehr and Schmidt's model of inequity aversion

Fehr and Schmidt (FS) introduced an influential social utility function for individuals in interpersonal contexts that captures self-centered inequity aversion. The value of this social utility function lies in its exceptionally good balance between parsimony and fit. This paper provides a preference foundation for exactly the model of FS with preference conditions that exactly capture the exceptionally good balance of FS. Remarkably, FS is a special case of Schmeidler’s rank-dependent utility for decision under uncertainty.

An experimental test of the concentration index

The concentration index is widely used to measure income-related inequality in health. No insight exists, however, whether the concentration index connects with peoples preferences about distributions of income and health and whether a reduction in the concentration index reflects an increase in social welfare. We explored this question by testing the central assumption underlying the concentration index and found that it was systematically violated. We also tested the validity of alternative health inequality measures that have been proposed in the literature. Our data showed that decreases in the spread of income and health were considered socially desirable, but decreases in the correlation between income and health not necessarily. Support for a condition implying that the inequality in the distribution of income and in the distribution of health can be considered separately was mixed.

Managing social risks – tradeoffs between risks and inequalities

As societies are increasingly concerned with risks, it is important to evaluate risks not only from an individual but also from a societal perspective. Two essential dimensions of public or social risks are the inequality concerning the distribution of risks over various groups and members of society and the level of risk faced by individuals and by the society as a whole. This paper disentangles these two essential dimensions and studies people’s preferences concerning different types of allocations of risks over groups of people. We do so in a laboratory experiment with real incentives, where subjects are placed in the role of a social planner and choose between different types of allocations of risks over 10 other participants. The allocations differ only in terms of dispersion, i.e. they differ only in terms of inequality and risk. The majority of our subjects exhibit clear preferences over different types of allocations consistent with ex ante inequality and individual risk aversion, and ex post inequality and collective risk seeking behavior. These results are consistent with the literature on public risk and can be reconciled with responsibility aversion.

Are all health gains equally important? An exploration of acceptable health as a reference point in health care priority setting.

BackgroundAccumulating evidence suggests that members of society prefer some QALY gains over others. In this paper, we explore the notion of acceptable health as a reference point in assessing the value of health gains. The value of health benefits may be assessed in terms of their position relative to this reference level, benefits above the level of acceptable health being valued differently from benefits below this level. In this paper we focus on assessing the level of acceptable health at different ages and associations with background variables.MethodsWe recruited a sample of the adult population from the Netherlands (n = 1067) to investigate which level of health problems they consider to be acceptable for people aged 40 to 90, using 10-year intervals. We constructed acceptable health curves and associated acceptable health with background characteristics using linear regressions.ResultsThe results of this study indicate that the level of health problems considered acceptable increases with age. This level was associated with respondents’ age, age of death of next of kin, health and health behaviour.ConclusionsOur results suggest that people are capable of indicating acceptable levels of health at different ages, implying that a reference point of acceptable health may exist. While more investigation into the measurement of acceptable health remains necessary, future studies may also focus on how health gains may be valued relative to this reference level. Gains below the reference point may receive higher weight than those above this level since the former improve unacceptable health states while the latter improve acceptable health states.

Weighted Temporal Utility

We propose a utility representation for preferences over risky timed outcomes, the weighted temporal utility model. It separates subjective evaluations of outcomes from attitudes towards psychological distance induced by risks and delays. Subjective evaluations of outcomes may depend on the time of receipt. A natural special case of our model arises when decision makers evaluate an outcome according to the extra utility it generates on top of expected baseline consumption, which can be interpreted as the status quo. Thus, deviations from stationarity can be driven by expected changes in baseline consumption, and need not be irrational. Moreover, a decision maker with a weighted temporal utility function can have time-consistent yet non-stationary preferences or stationary yet time-inconsistent preferences. We provide a characterization of our model and propose a non-parametric approach to elicit a weighted temporal utility function.

Discounted Utility and Present Value—A Close Relation

We introduce a new type of preference condition for intertemporal choice, which requires present values to be independent of various other variables. The new conditions are more concise and more transparent than traditional ones. They are directly related to applications because present values are widely used tools in intertemporal choice. Our conditions give more general behavioral axiomatizations, which facilitate normative debates and empirical tests of time inconsistencies and related phenomena. Like other preference conditions, our conditions can be tested qualitatively. Unlike other preference conditions, our conditions can also be directly tested quantitatively, and we can verify the required independence of present values from predictors in regressions. We show how similar types of preference conditions, imposing independence conditions between directly observable quantities, can be developed for decision contexts other than intertemporal choice and can simplify behavioral axiomatizations there. Our preference conditions are especially efficient if several types of aggregation are relevant because we can handle them in one stroke. We thus give an efficient axiomatization of a market pricing system that is (i) arbitrage-free for hedging uncertainties and (ii) time consistent.

Anomalies in Intertemporal Choice

This paper argues that observations of non-stationary choice behavior need not necessarily imply specific properties of the individual’s discount function. As we show, the observed “anomalies” in intertemporal choice can alternatively be explained by an individual’s perception of the risk that is involved whenever an outcome is to be received in the future. This risk may concern the size of the actual outcome or the endowment consumption stream to which the outcome is added. Both types of uncertainty naturally appear in the context of intertemporal choice and both are difficult to control in experiments. We show how relative degrees of changes in risk over time can predict choices.

Measuring Decreasing and Increasing Impatience

Many studies show that time preference data from experiments and surveys are related to field behavior. Time preference measures in these studies typically depend simultaneously on utility curvature, the level of impatience, and the change in the level of impatience. Thus, these studies do not allow one to establish which of these three components drive(s) the field behavior of interest. Of these components, the change in the level of impatience is theoretically thought to be the main driver of time inconsistencies and self-control problems. To test this theoretical presumption, one has to measure the change in the level of impatience independently from utilities and levels of impatience. This paper introduces a measure of the degree of decreasing impatience, the DI-index. It measures the change of impatience independently from the level of impatience and independently from utility. It can also be used to test various discounting models. An experiment finds no correlation between the degree of decreasing impatience and self-reported self-control problems in daily life, suggesting that changing impatience is not the sole driver of self-control problems.