http://repub.eur.nl/res/aut/14025/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/38379/ 2013-01-01T00:00:00Z Quality-Adjusted Life Years (QALYs) are the most widely used measure of health in economic evaluations of health care. Within a welfarist framework QALYs are consistent with people's preferences under stringent assumptions. Several authors have argued that QALYs are a valid measure of health within an extra-welfarist framework. This paper studies the applicability of QALYs within the best-known extra-welfarist framework, Sen's capability approach. We propose a procedure to value capability sets and provide a foundation for QALYs within Sen's capability approach. We show that, under appropriate conditions, the ranking of capabilities can be represented locally by a QALY measure and that a willingness to pay for QALYs can be defined. The validity of QALYs as a general measure of health requires the same stringent conditions as in a welfarist framework. http://repub.eur.nl/res/pub/34700/ 2012-06-15T00:00:00Z Time discounting and quality of life are two important factors in evaluations of medical interventions. The measurement of these two factors is complicated because they interact. Existing methods either simply assume one factor given, based on heuristic assumptions, or invoke complicating extraneous factors, such as risk, that generate extra biases. The authors introduce a method for measuring discounting (and then quality of life) that involves no extraneous factors and that avoids distorting interactions. Their method is considerably simpler and more realistic for subjects than existing methods. It is entirely choice based and thus can be founded on economic rationality requirements. An experiment demonstrates the feasibility of this method and its advantages over classical methods. http://repub.eur.nl/res/pub/38326/ 2012-01-01T00:00:00Z The concentration index is widely used to measure income-related inequality in health. No insight exists, however, whether the concentration index connects with people's 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. http://repub.eur.nl/res/pub/37327/ 2012-01-01T00:00:00Z The concentration index is widely used to measure income-related inequality in health. No insight exists, however, whether the concentration index connects with people's 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. http://repub.eur.nl/res/pub/26324/ 2011-09-28T00:00:00Z Utility independence is a central condition in multiattribute utility theory, where attributes of outcomes are aggregated in the context of risk. The aggregation of attributes in the absence of risk is studied in conjoint measurement. In conjoint measurement, standard sequences have been widely used to empirically measure and test utility functions, and to theoretically analyze them. This paper shows that utility independence and standard sequences are closely related: utility independence is equivalent to a standard sequence invariance condition when applied to risk. This simple relation between two widely used conditions in adjacent fields of research is surprising and useful. It facilitates the testing of utility independence because standard sequences are flexible and can avoid cancelation biases that affect direct tests of utility independence. Extensions of our results to nonexpected utility models can now be provided easily. We discuss applications to the measurement of quality-adjusted life-years (QALY) in the health domain. http://repub.eur.nl/res/pub/21094/ 2010-11-01T00:00:00Z This paper introduces time-tradeoff (TTO) sequences as a general tool to analyze intertemporal choice. We give several applications. For empirical purposes, we can measure discount functions without requiring any measurement of or assumption about utility. We can quantitatively measure time inconsistencies and simplify their qualitative tests. TTO sequences can be administered and analyzed very easily, using only pencil and paper. For theoretical purposes, we use TTO sequences to axiomatize (quasi-)hyperbolic discount functions. We demonstrate the feasibility of measuring TTO sequences in an experiment, in which we tested the axiomatizations. Our findings suggest rejections of several currently popular discount functions and call for the development of new ones. It is especially desirable that such discount functions can accommodate increasing impatience. http://repub.eur.nl/res/pub/20349/ 2010-06-01T00:00:00Z This article provides a parameter-free measurement of utility in intertemporal choice and presents new and more robust evidence on the discounting of money outcomes. Intertemporal utility was concave for gains and convex for losses, consistent with a hypothesis put forward by Loewenstein and Prelec (1992). Discount rates declined over time but less so than previously observed under the assumption of linear utility. For approximately 40% of our subjects constant discounting provided the best fit. The remaining 60% were most consistent with Harvey's (1986) power discounting. Our data provide little support for the popular quasi-hyperbolic model, which is widely used in economics today. We observed an asymmetry in the discounting of gains and losses that, unlike earlier findings, cannot be explained by a framing effect. http://repub.eur.nl/res/pub/21096/ 2010-04-01T00:00:00Z ABSTRACT. 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. http://repub.eur.nl/res/pub/23745/ 2010-03-01T00:00:00Z Gandjour and Gafni (2010) criticize our paper on two counts. Their first point of criticism is ill-founded and results from many mathematical mistakes that they make. The second is due to a lack of understanding of the general principles of empirical research. http://repub.eur.nl/res/pub/23746/ 2010-02-01T00:00:00Z A common assertion is that rating scale (RS) values are lower than both standard gamble (SG) and time tradeoff (TTO) values. However, differences among these methods may be due to method specific bias. Although SG and TTOs suffer systematic bias, RS responses are known to depend on the range and frequency of other health states being evaluated. Over many diverse studies this effect is predicted to diminish. Thus, a systematic review and data synthesis of RS-TTO and RS-SG difference scores may better reveal persistent dissimilarities. Purpose. The purpose of this study was to establish through systematic review and meta-analysis the net effect of biases that endure over many studies of utilities. Methods. A total of 2206 RS and TTO and 1318 RS and SG respondents in 27 studies of utilities participated. MEDLINE was searched for data from 1976 to 2004, complemented by a hand search of full-length articles and conference abstracts for 9 journals known to publish utility studies, as well as review of results and additional recommendations by 5 outside experts in the field. Two investigators abstracted the articles. We contacted the investigators of the original if required information was not available. Results. No significant effect for RS and TTO difference scores was observed: effect size (95% confidence interval [CI]) = 0.04 (−0.02, 0.09). In contrast, RS scores were significantly lower than SG scores: effect size (95% CI ) =−0.23 (−0.28, −0.19). Correcting SG scores for 3 known biases (loss aversion, framing, and probability weighting) eliminated differences between RS and SG scores: effect size (95% CI ) = 0.01 (−0.03, 0.05). Systematic bias in the RS method may exist but be heretofore unknown. Bias correction formulas were applied to mean not individual utilities. Conclusions. The results of this study do not support the common view that RS values are lower than TTO values, may suggest that TTO biases largely cancel, and support the validity of formulas for correcting SG bias. http://repub.eur.nl/res/pub/20300/ 2010-01-01T00:00:00Z This paper introduces a method to measure regret theory, a popular theory of decision under uncertainty. Regret theory allows for violations of transitivity, and it may seem paradoxical to quantitatively measure an intransitive theory. We adopt the trade-off method and show that it is robust to violations of transitivity. Our method makes no assumptions about the shape of the functions reflecting utility and regret. It can be performed at the individual level, taking account of preference heterogeneity. Our data support the main assumption of regret theory, that people are disproportionately averse to large regrets, even when event-splitting effects are controlled for. The findings are robust: similar results were obtained in two measurements using different stimuli. The data support the reliability of the trade-off method: its measurements could be replicated using different stimuli and were not susceptible to strategic responding. http://repub.eur.nl/res/pub/19626/ 2009-12-01T00:00:00Z Most health care evaluations today still assume expected utility even though the descriptive deficiencies of expected utility are well known. Prospect theory is the dominant descriptive alternative for expected utility. This paper tests whether prospect theory leads to better health evaluations than expected utility. The approach is purely descriptive: we explore how simple measurements together with prospect theory and expected utility predict choices and rankings between more complex stimuli. For decisions involving risk prospect theory is significantly more consistent with rankings and choices than expected utility. This conclusion no longer holds when we use prospect theory utilities and expected utilities to predict intertemporal decisions. The latter finding cautions against the common assumption in health economics that health state utilities are transferable across decision contexts. Our results suggest that the standard gamble and algorithms based on, should not be used to value health. http://repub.eur.nl/res/pub/16976/ 2009-09-21T00:00:00Z A central assumption in health utility measurement is that preferences are invariant to the elicitation method used. This assumption is challenged by preference reversals. Previous studies have observed preference reversals between choice and matching tasks and between choice and ranking tasks. We present a preference reversal that is entirely derived from choices, the basic primitive of economics and utility theory. The preference reversal was observed in two studies regarding health states after stroke. Both studies involved large representative samples from the Spanish population, interviewed professionally, and face-to-face. Possible explanations for the preference reversal are the anticipation of disappointment and elation in risky choice and the impact of ethical considerations about the value of life. http://repub.eur.nl/res/pub/17855/ 2009-09-01T00:00:00Z The person tradeoff (PTO) is commonly used in health economic applications. However, to date it has no theoretical basis. The purpose of this paper is to provide this basis from a set of assumptions that together justify the most common applications of the PTO method. Our analysis identifies the central assumptions in PTO measurements. We test these assumptions in an experiment, but find only limited support for the validity of the PTO. http://repub.eur.nl/res/pub/16048/ 2009-05-01T00:00:00Z 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. http://repub.eur.nl/res/pub/26889/ 2009-05-01T00:00:00Z Prospect theory is currently the main descriptive theory of decision under uncertainty. It generalizes expected utility by introducing nonlinear decision weighting and loss aversion. A difficulty in the study of multiattribute utility under prospect theory is to determine when an attribute yields a gain or a loss. One possibility, adopted in the theoretical literature on multiattribute utility under prospect theory, is to assume that a decision maker determines whether the complete outcome is a gain or a loss. In this holistic evaluation, decision weighting and loss aversion are general and attribute-independent. Another possibility, more common in the empirical literature, is to assume that a decision maker has a reference point for each attribute. We give preference foundations for this attribute-specific evaluation where decision weighting and loss aversion are depending on the attributes. http://repub.eur.nl/res/pub/14145/ 2008-12-01T00:00:00Z Koopmans provided a well-known preference axiomatization for discounted utility, the most widely used model for maximizing intertemporal choice. There were, however, some technical problems in his analysis. For example, there was an unforeseen implication of bounded utility. Some partial solutions have been advanced in various fields in the literature. The technical problems in Koopmans' analysis obscure the appeal of his intuitive axioms. This paper completely resolves Koopmans' technical problems. In particular, it obtains complete flexibility concerning the utility functions that can be used. This paper, thus, provides a clean and complete preference axiomatization of discounted utility, clarifying the appeal of Koopmans' intuitive axioms. http://repub.eur.nl/res/pub/14347/ 2008-12-01T00:00:00Z Traditionally aversion to health inequality is modelled through a concave utility function over health outcomes. Bleichrodt et al. [Bleichrodt, H., Diecidue E., Quiggin J., 2004. Equity weights in the allocation of health care: the rank-dependent QALY model. Journal of Health Economics 23, 157-171] have suggested a "dual" approach based on the introduction of explicit equity weights. The purpose of this paper is to analyze how priorities in health care are determined in the framework of these two models. It turns out that policy implications are highly sensitive to the choice of the model that will represent aversion to health inequality. http://repub.eur.nl/res/pub/14619/ 2008-10-01T00:00:00Z Many traditional conjoint representations of binary preferences are additively decomposable, or additive for short. An important generalization arises under rank-dependence, when additivity is restricted to cones with a fixed ranking of components from best to worst (comonotonicity), leading to configural weighting, rank-dependent utility, and rank- and sign-dependent utility (prospect theory). This paper provides a general result showing how additive representations on an arbitrary collection of comonotonic cones can be combined into one overall representation that applies to the union of all cones considered. The result is applied to a new paradigm for decision under uncertainty developed by Duncan Luce and others, which allows for violations of basic rationality properties such as the coalescing of events and other framing conditions. Through our result, a complete preference foundation of a number of new models by Luce and others can be obtained. We also show how additive representations on different full product sets can be combined into a representation on the union of these different product sets. http://repub.eur.nl/res/pub/13282/ 2008-09-19T00:00:00Z Economic evaluations of health care can help to make better medical decisions. Decisions about life and death. Our current methods are wrong. Reality is different from what we did believe. Policy decisions based on our current tools are not at all in the best interests of patients. We, scientists, have the responsibility to bridge the gap between theory and reality. Prospect theory respects reality. Now, we have all the opportunity to reliably value health. And, these values can even be obtained free of charge: we do not have to collect additional data. We can apply prospect theory immediately. What remains is to spread the word. http://repub.eur.nl/res/pub/15960/ 2008-09-01T00:00:00Z This paper performs new tests of the QALY model when health varies over time. Our tests do not involve confounding assumptions and are robust to violations of expected utility. The results support the use of QALYs at the aggregate level, i.e. in economic evaluations of health care. At the individual level, there is less support for QALYs. The individual data are, however, largely consistent with a more general QALY-type model that remains tractable for applications. http://repub.eur.nl/res/pub/26890/ 2008-06-01T00:00:00Z 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. http://repub.eur.nl/res/pub/29218/ 2007-10-01T00:00:00Z A growing body of qualitative evidence shows that loss aversion, a phenomenon formalized in prospect theory, can explain a variety of field and experimental data. Quantifications of loss aversion are, however, hindered by the absence of a general preference-based method to elicit the utility for gains and losses simultaneously. This paper proposes such a method and uses it to measure loss aversion in an experimental study without making any parametric assumptions. Thus, it is the first to obtain a parameter-free elicitation of prospect theory's utility function on the whole domain. Our method also provides an efficient way to elicit utility midpoints, which are important in axiomatizations of utility. Several definitions of loss aversion have been put forward in the literature. According to most definitions we find strong evidence of loss aversion, at both the aggregate and the individual level. The degree of loss aversion varies with the definition used, which underlines the need for a commonly accepted definition of loss aversion. http://repub.eur.nl/res/pub/10952/ 2007-08-01T00:00:00Z Many empirical studies have shown that people’s preferences are reference-dependent. Previous theoretical studies of referencedependence assumed that the reference point was fixed and then imposed the usual assumptions of decision theory, in particular completeness of preferences. This paper gives preference foundations for additive reference-dependent utility when the reference point varies across decisions and is one of the options in the decision maker’s opportunity set. This decision situation is common, for example because usually the retention of the status quo is an available option, but is difficult to handle axiomatically because it implies incompleteness of preferences. The results of this paper provide tools to extend existing theories of reference-dependent preferences, such as prospect theory, to new and empirically important decision contexts. r 2007 Elsevier Inc. All rights reserved. http://repub.eur.nl/res/pub/10953/ 2007-03-01T00:00:00Z This paper explores inconsistencies that occur in utility measurement under risk when expected utility theory is assumed and the contribution that prospect theory and some other generalizations of expected utility can make to the resolution of these inconsistencies. We used five methods to measure utilities under risk and found clear violations of expected utility. Of the theories studied, prospect theory was the most consistent with our data. The main improvement of prospect theory over expected utility was in comparisons between a riskless and a risky prospect (riskless-risk methods). We observed no improvement over expected utility in comparisons between two risky prospects (risk-risk methods). An explanation for the latter observation may be that there was less distortion in probability weighting in the interval [0.10, 0.20] than has commonly been observed. http://repub.eur.nl/res/pub/10949/ 2007-01-01T00:00:00Z A common assertion is that rating scale (RS) values are lower than both standard gamble (SG) and time tradeoff (TTO) values. However, differences among these methods may be due to method specific bias. While SG and TTO suffer systematic bias, RS responses are known to depend on the range and frequency of other health states being evaluated. Over many diverse studies this effect is predicted to diminish. Thus, a systematic review and data synthesis of RS-TTO and RS-SG difference scores may better reveal persistent dissimilarities. PURPOSE: To establish through systematic review and meta-analysis the net effect of biases that endure over many studies of utilities. http://repub.eur.nl/res/pub/10950/ 2007-01-01T00:00:00Z Gul’s (1991) theory of disappointment aversion (DA) has several attractive features, being intuitive, analytically tractable, and parsimonious. In spite of this, the DA model has received little attention in practical applications, which may be partly due to the absence of a procedure to elicit the model. We show how the trade-off method, developed by Wakker and Deneffe (1996), can be used to elicit DA. Our elicitation method is parameter-free: it requires no assumption about utility and/or disappointment aversion. Quantitative tests of DA in three outcome domains, monetary gains, monetary losses, and life-years, suggest that the DA model is too parsimonious. Of the other models of disappointment aversion that have been proposed in the literature, our data are most consistent with the model of Loomes and Sugden (1986). http://repub.eur.nl/res/pub/10951/ 2007-01-01T00:00:00Z A growing body of qualitative evidence shows that loss aversion, a phenomenon formalized in prospect theory, can explain a variety of field and experimental data. Quantifications of loss aversion are, however, hindered by the absence of a general preference-based method to elicit the utility for gains and losses simultaneously. This paper proposes such a method and uses it to measure loss aversion in an experimental study without making any parametric assumptions. Thus, it is the first to obtain a parameterfree elicitation of prospect theory’s utility function on the whole domain. Our method also provides an efficient way to elicit utility midpoints, which are important in axiomatizations of utility. Several definitions of loss aversion have been put forward in the literature. According to most definitions we find strong evidence of loss aversion, at both the aggregate and the individual level. The degree of loss aversion varies with the definition used, which underlines the need for a commonly accepted definition of loss aversion. http://repub.eur.nl/res/pub/11069/ 2007-01-01T00:00:00Z A central assumption in health utility measurement is that preferences are invariant to the elicitation method that is used. This assumption is challenged by preference reversals. Previous studies have observed preference reversals between choice and matching tasks and between choice and ranking tasks. We present a new preference reversal that is entirely choice-based. Because choice is the basic primitive of economics and utility theory, this preference reversal is more fundamental and troubling. The preference reversal was observed in two studies regarding health states after stroke. Both studies involved large representative samples from the Spanish population, interviewed professionally and face-to-face. Possible explanations for the preference reversal are the anticipation of disappointment and elation in risky choice and the impact of ethical considerations about the value of life. http://repub.eur.nl/res/pub/11072/ 2007-01-01T00:00:00Z This paper introduces a choice-based method that for the first time makes it possible to quantitatively measure regret theory, one of the most popular models of decision under uncertainty. Our measurement is parameter-free in the sense that it requires no assumptions about the shape of the functions reflecting utility and regret. The choice of stimuli was such that event-splitting effects could not confound our results. Our findings were largely consistent with the assumptions of regret theory although some deviations were observed. These deviations can be explained by psychological heuristics and referencedependence of preferences. http://repub.eur.nl/res/pub/11073/ 2007-01-01T00:00:00Z Koopmans provided a well-known preference foundation for discounted utility, the most widely used model for intertemporal optimization. There were, however, some problems in his analysis. For example, there was an unforeseen implication of bounded utility. For some domains solutions have been advanced in the literature, primarily when particular production processes impose time-dependent restrictions on consumption. This paper completely resolves the problems mentioned, irrespective of what the restrictions on consumption are. It obtains complete flexibility concerningt he utility functions that can be used and concerning the conceivable economic growth. This paper, thus, provides a complete preference foundation of discounted utility, and clarifies the appeal of Koopmans’ intuitive axioms. http://repub.eur.nl/res/pub/11074/ 2007-01-01T00:00:00Z Traditionally aversion to health inequality is modelled through a concave utility function over health outcomes. Bleichrodt et al. (2004) have suggested a "dual" approach based on the introduction of explicit equity weights. The purpose of this paper is to analyze how priorities in health care are determined in the framework of these two models. It turns out that policy implications are highly sensitive to the choice of the model that will represent aversion to health inequality. http://repub.eur.nl/res/pub/11075/ 2007-01-01T00:00:00Z This paper provides an efficient method to measure utility under prospect theory, the most important descriptive theory of decision under uncertainty today. Our method is based on the elicitation of certainty equivalents for two-outcome prospects, a common way to measure utility. We applied our method in an experiment and found that most subjects were risk averse for gains and risk seeking for losses but had concave utility both for gains and for losses. This finding illustrates empirically that risk seeking and concave utility can coincide under prospect theory, a result that was derived theoretically by Chateauneuf and Cohen (1994). Utility was steeper for losses than for gains, which is consistent with loss aversion. Utility did not depend on the probability used in the elicitation, which offers support for prospect theory. http://repub.eur.nl/res/pub/11076/ 2007-01-01T00:00:00Z http://repub.eur.nl/res/pub/11077/ 2007-01-01T00:00:00Z The commonly used hyperbolic and quasi-hyperbolic discount functions imply decreasing impatience, which is the prevailing empirical phenomenon in intertemporal choice, in particular for aggregate behavior. At the individual level there is much variation, however, and there will always be some individuals who exhibit increasing impatience. Hence, to fit data at the individual level, new discount functions are needed. This paper introduces such functions, with constant absolute (CADI) or constant relative (CRDI) decreasing impatience. These functions can accommodate any degree of decreasing or increasing impatience, which makes them 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. http://repub.eur.nl/res/pub/10954/ 2006-09-01T00:00:00Z The empirical literature on the measurement of health inequalities is vast and rapidly expanding. To date, however, no foundation in welfare economics exists for the proposed measures of health inequality. This paper provides such a foundation for commonly used measures like the health concentration index, the Gini index, and the extended concentration index. Our results indicate that these measures require assumptions that appear restrictive. One way forward may be the development of multi-dimensional extensions. http://repub.eur.nl/res/pub/10987/ 2006-04-07T00:00:00Z This paper explores how to evaluate changes in survival probabilities when people do not process probabilities linearly, as is commonly assumed in the literature, but distort probabilities. We show that the valuation of risks to life depends critically on two parameters: the elasticity of the probability weighting function and the elasticity of the utility function with respect to future consumption. Using estimates from the empirical literature we derive that the bias of erroneously ignoring probability distortion in general leads to cost–benefit ratios that are too high and that generate too much priority for programs that save young lives. http://repub.eur.nl/res/pub/10988/ 2006-02-01T00:00:00Z We study the willingness to pay for reductions in health risks when people do not evaluate probabilities linearly, as is commonly assumed in elicitations of willingness to pay, but weight probabilities, as is commonly observed in empirical studies of decision under risk. We show that for the levels of baseline risk typically considered, probability weighting strongly affects willingness to pay estimates and may lead to unstable monetary valuations of health. http://repub.eur.nl/res/pub/11070/ 2006-01-01T00:00:00Z This paper is the first to measure utility in intertemporal choice and presents new and more robust evidence on the discounting of money outcomes. Our measurement method is parameterfree in the sense that it requires no assumptions about utility or discounting. We found that intertemporal utility was concave for gains and convex for losses, consistent with a hypothesis put forward by Loewenstein and Prelec (1992). Utility in intertemporal choice was close to utility in decision under risk and uncertainty, suggesting that there may be one unifying concept of utility that applies to all of economics. The existence of one concept of utility is important for applied economics, because it largely reduces data requirements. Discount rates declined over time, but less so than has been observed in previous studies that assumed linear utility. Of the main discounted utility models, Loewenstein and Prelec’s (1992) generalized hyperbolic discounting model best fitted our data. The widely-used quasi-hyperbolic model fitted the data only slightly better than constant discounting. Finally, we obtained evidence of an asymmetry in discounting between gains and losses, which, in contrast with earlier findings, cannot be explained by a framing effect. http://repub.eur.nl/res/pub/11071/ 2006-01-01T00:00:00Z Many empirical studies have shown that preferences are reference-dependent, implying loss aversion. Because reference-dependence is a relatively new concept, there exists little theory on it. The theories that are available generally take the reference point as given and then impose the traditional assumptions such as completeness of preferences. Reference-dependence raises, however, new problems that do not occur in reference-independent theories. This paper argues that in the empirically realistic case where the reference point is always an element of the decision maker’s opportunity set, reference-dependent preferences are, according to the principles of revealed preference, necessarily incomplete. A new model of decision under uncertainty is presented that extends prospect theory to cover this case. The paper also gives preference foundations for two special cases: one in which utility is decomposed into a normative and a psychological component and one in which loss aversion is constant. The latter case has frequently been used in empirical research and in applied decision analysis. http://repub.eur.nl/res/pub/10990/ 2005-07-01T00:00:00Z We performed an empirical elicitation of the equity-efficiency trade-off in cost-utility analysis using the rank-dependent quality-adjusted life-year (QALY) model, a model that includes as special cases many of the social welfare functions that have been proposed in the literature. Our elicitation method corrects for utility curvature and, therefore, our estimated equity weights are not affected by diminishing marginal utility. We observed a preference for equality in the allocation of health. The data suggest that the elicited equity weights were jointly determined by preferences for equality and by insensitivity to group size. A procedure is proposed to correct the equity weights for insensitivity to group size. Finally, we give an illustration how our method can be implemented in health policy. http://repub.eur.nl/res/pub/10991/ 2005-04-01T00:00:00Z We provide a new test of the feasibility of using contingent valuation to value informal care. We start with a theoretical model of informal caregiving and derive that willingness to pay depends positively on wealth and negatively on own health, whereas the effect of other's health is sign-ambiguous. These predictions are tested in two new data sets on patients' and caregivers' willingness to pay (WTP) and willingness to accept (WTA) for informal care. The data are generally consistent with the theoretical predictions: wealth generally has a positive impact and own health a negative impact. Other's health has a mixed effect. We find only small differences between WTP and WTA. Our findings suggest that contingent valuation may be a useful technique to value informal care in economic evaluations of health care. http://repub.eur.nl/res/pub/10992/ 2005-02-01T00:00:00Z In this note we use the rank-dependent utility (RDU) model to analyze saving decisions. The RDU model enables us to separate the effects of pessimism and optimism on saving from that of concavity of the utility function. While pessimism induces more saving, the importance of this effect is shown to depend upon properties of the utility function such as prudence and temperance. http://repub.eur.nl/res/pub/10989/ 2005-01-01T00:00:00Z This paper examines applications of non-expected utility in the health domain. The most widely used utility model in health economics, the time-linear QALY model, assumes (i) separability of quality of life and life duration, and (ii) linearity of the utility for life duration. We perform new tests, which are robust to violations of expected utility, of these two assumptions. The data support separability, but show that the utility for life duration is concave rather than linear. The finding of concave utility may not be surprising in itself. The contribution of this paper is to demonstrate this empirically without being invalidated by violations of expected utility. http://repub.eur.nl/res/pub/10994/ 2004-03-01T00:00:00Z Previous empirical tests of quality-adjusted life-years (QALYs), the most widely used outcome measure in economic evaluations of health care, generally yielded negative results. These tests were, however, for the most part based on expected utility, which is now widely acknowledged to be descriptively inaccurate. The observed violations might, therefore, have been caused by violations of expected utility. We performed a new test of QALYs, which is valid under expected utility and under the two most influential non-expected utility theories, rank-dependent utility and prospect theory, and found considerable support for the QALY model. Our findings suggest that QALYs may be valid if nonexpected utility formulas are used to compute health state utilities. http://repub.eur.nl/res/pub/10993/ 2004-01-01T00:00:00Z This paper introduces the rank-dependent quality-adjusted life-years (QALY) model, a new method to aggregate QALYs in economic evaluations of health care. The rank-dependent QALY model permits the formalization of influential concepts of equity in the allocation of health care, such as the fair innings approach, and it includes as special cases many of the social welfare functions that have been proposed in the literature. An important advantage of the rank-dependent QALY model is that it offers a straightforward procedure to estimate equity weights for QALYs. We characterize the rank-dependent QALY model and argue that its central condition has normative appeal. http://repub.eur.nl/res/pub/10998/ 2003-11-01T00:00:00Z This paper tests the internal consistency of time trade-off utilities. We find significant violations of consistency in the direction predicted by loss aversion. The violations disappear for higher gauge durations. We show that loss aversion can also explain that for short gauge durations time trade-off utilities exceed standard gamble utilities. Our results suggest that time trade-off measurements that use relatively short gauge durations, like the widely used EuroQol algorithm, are affected by loss aversion and lead to utilities that are too high. http://repub.eur.nl/res/pub/10997/ 2003-10-01T00:00:00Z We show that the willingness to pay for health improvements increases with the severity and probability of occurrence of comorbidities. This result, which is obtained under mild restrictions on the shape of the utility function, has important implications for cost benefit studies applied to health care. In particular it implies that the discrimination of the elderly, believed to be implicit in cost benefit analysis, is less of a problem than commonly thought. http://repub.eur.nl/res/pub/10996/ 2003-09-01T00:00:00Z Medical decision analyses typically focus on one disease, that is, on one source of risk. In many medical decisions multiple sources of risk co-exist, however. This paper analyzes the effect of such comorbidities on treatment decisions. The effect of comorbidities on treatment decisions depends primarily on the way in which the patient’s attitude to health status risks varies with duration. In the QALY model comorbidities do not affect treatment decisions. This property of the QALY model can be used as a diagnostic test of its descriptive and prescriptive validity. http://repub.eur.nl/res/pub/10995/ 2003-01-01T00:00:00Z Quality-adjusted life-years (QALYs) are the most common utility measure in medical decision analysis and economic evaluations of health care. This paper presents an axiomatization of QALYs under cumulative prospect theory (CPT), currently the most influential model for decision under uncertainty. Because the set of health states need not be endowed with a natural topology that is connected, we first show how existing CPT characterizations can be extended to a class of outcome sets for which no connected natural topology is given. We then characterize QALY models with linear, power, and exponential utility for duration. Finally, we define loss aversion for multiattribute utility theory and characterize the QALY models under general and constant loss aversion. The measurement of QALYs belongs to the general field of multiattribute utility theory. Hence, our results can be generalized to other multiattribute decision contexts and they thereby contribute to the development of multiattribute utility theory under cumulative prospect theory. http://repub.eur.nl/res/pub/10999/ 2002-07-23T00:00:00Z This paper studies two important explanations of why people violate procedure invariance: loss aversion and scale compatibility. The paper extends previous research by studying loss aversion and scale compatibility simultaneously and in a quantitative manner, by looking at a new decision domain, medical decision making, and by using an experimental design that is less conducive to violations of procedure invariance. We find significant evidence both of loss aversion and of scale compatibility. The effects of loss aversion and scale compatibility are not constant but vary over trade-offs and most participants do not behave consistently according to loss aversion or scale compatibility. In particular, the effect of loss aversion in medical trade-offs decreases with life duration. The rejection of constant loss aversion and constant scale compatibility is discouraging for attempts to model loss aversion and scale compatibility. The findings are encouraging for utility measurement and prescriptive decision analysis that seeks to avoid the effects of loss aversion and scale compatibility. The data suggest that there exist decision contexts in which the effects of loss aversion and scale compatibility can be minimized and that utilities can be measured that are unaffected by their impact. http://repub.eur.nl/res/pub/11000/ 2002-07-22T00:00:00Z This paper gives a new explanation for the systematic disparity between standard gamble (SG) utilities and time trade-off (TTO) utilities. The common explanation, which is based on expected utility, is that the disparity is caused by curvature of the utility function for duration. This explanation is, however, incomplete. People violate expected utility and these violations lead to biases in SG and TTO utilities. The paper analyzes the impact on SG and TTO utilities of three main reasons why people violate expected utility: probability weighting, loss aversion, and scale compatibility. In the SG, the combined effect of utility curvature, probability weighting, loss aversion, and scale compatibility is an upward bias. In the TTO these factors lead both to upward and to downward biases. This analysis can also explain the tentative empirical finding that the TTO better describes people's preferences for health than the SG. http://repub.eur.nl/res/pub/11078/ 2002-04-15T00:00:00Z In cost-utility analysis it is assumed that health state valuations are directly comparable across individuals. Instead, health state valuations may be relative and related to people’s expectations and abilities. Then health state valuations are not fully comparable across people and, consequently, cost utility analysis cannot be applied in full. The present paper analyzes this comparability problem and proposes a method to solve it. http://repub.eur.nl/res/pub/11008/ 2002-02-05T00:00:00Z http://repub.eur.nl/res/pub/11033/ 2002-01-01T00:00:00Z A two-person game is formulated for a queuing situation involving a pair of exponential servers competing for arriving customers. The servers have identical characteristics except for their service rates. Each server is free to select its own service rate. The objective of each server is to select a service rate that will maximize its own profit. Arrivals are Poison. The probability that an arriving customer enters the queue is allowed to depend on the queue length at the time of arrival. The proportion of arrivals to a given server is shown to be strictly concave in the server's own service rate and decreasing in the other service rate. Furthermore, we show that when the cost function is convex and increasing, there exists a unique pure strategy Nash equilibrium point for the resulting game. http://repub.eur.nl/res/pub/11034/ 2001-11-01T00:00:00Z This paper proposes a quantitative modification of standard utility elicitation procedures, such as the probability and certainty equivalence methods, to correct for commonly observed violations of expected utility. Traditionally, decision analysis assumes expected utility not only for the prescriptive purpose of calculating optimal decisions but also for the descriptive purpose of eliciting utilities. However, descriptive violations of expected utility bias utility elicitations. That such biases are effective became clear when systematic discrepancies were found between different utility elicitation methods that, under expected utility, should have yielded identical utilities. As it is not clear how to correct for these biases without further knowledge of their size or nature, most utility elicitations still calculate utilities by means of the expected utility formula. This paper speculates on the biases and their sizes by using the quantitative assessments of probability transformation and loss aversion suggested by prospect theory. It presents quantitative corrections for the probability and certainty equivalence methods. If interactive sessions to correct for biases are not possible, then the authors propose to use the corrected utilities rather than the uncorrected ones in prescriptions of optimal decisions. In an experiment, the discrepancies between the probability and certainty equivalence methods are removed by the authors' proposal. http://repub.eur.nl/res/pub/11016/ 2001-04-01T00:00:00Z This paper provides a new and more robust test of the descriptive validity of the constant rate discounted utility model in medical decision analysis. The constant rate discounted utility model is compared with two competing theories, Harvey's (1986) proportional discounting model and Loewenstein and Prelec's (1992) hyperbolic discounting model. To compare the various intertemporal models, previous studies on intertemporal preferences for health assumed a specific parametric form of the utility function for life-years and no discounting within the time periods that health states are experienced. The present study avoids such confounding assumptions by focusing on the axiomatic structure of the discounting models. The present study further differs by using choices instead of matching to elicit intertemporal preferences. The experimental results provide support for decreasing timing aversion, the condition underlying the proportional and the hyperbolic discounting model, but they violate stationarity, the central condition of the constant rate discounted utility model. There is some ambiguity whether the violations of stationarity are primarily caused by an immediacy effect. The results confirm violations of stationarity in choice-based elicitations tasks, in contrast with the results from Ahlbrecht and Weber (1997) which supported stationarity in choices over monetary outcomes. http://repub.eur.nl/res/pub/11017/ 2001-01-01T00:00:00Z This paper reports a violation of rank-dependent utility with inverse S-shaped probability weighting for binary gambles. The paper starts with a violation of expected utility theory: one-stage gambles elicit systematically different utilities than theoretically equivalent two-stage gambles. This systematic disparity does not disappear, but becomes more pronounced after correction for inverse S-shaped probability weighting. The data are also inconsistent with configural weight theory and Machina''s fanning out hypothesis. Possible explanations for the data are loss aversion and anchoring and insufficient adjustment. http://repub.eur.nl/res/pub/11031/ 2001-01-01T00:00:00Z Reviews the book "Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches," by R. Duncan Luce. http://repub.eur.nl/res/pub/11032/ 2001-01-01T00:00:00Z Editors and authors should be complimented for their impressive attempt to provide a fair account of the state-of-the-art in health economics. To review such an extensive work in a short time span, we decided to select certain chapters for more in depth study. This selection was based on our areas of expertise under the restriction that all major research areas distinguished in the handbook should be covered. Before turning to the review of the separate chapters, let us first make some general comments about the handbook. An important first question is whether all relevant research areas are covered and whether this has been done in a balanced way. Of course, exhaustive coverage in one book is unattainable for a large area like health economics. Rather the question is that regarding balance and possible lack of bias. In that respect, the book focuses on the US literature and health care system with 24 chapters written by US authors and only 11 by European and Canadian authors. The more traditional economic areas are generally covered by the US authors, emphasising a neo-classical rather than an institutional paradigm, and boundary topics like ‘equity’ and the ‘measurement of health’ are covered by the non-US authors. This structure both reflects the contributions in the health economics literature and the large variation in US health care institutions, and is only troublesome in some chapters as suggested below. http://repub.eur.nl/res/pub/11030/ 2000-01-01T00:00:00Z In his first presidential candidate debate with Senator Robert Dole, President Clinton cited hazardous waste cleanup among his administration's important environmental efforts. W. Kip Viscusi's most recent book deals with the rationality of these and other efforts addressed at reducing risk and compensating risk victims. Unfortunately for President Clinton, the book's main conclusion about government efforts in general and hazardous waste cleanup in particular is negative: government regulations often mirror the irrationalities present in individual decisions leading to costly and relatively ineffective policies. http://repub.eur.nl/res/pub/11035/ 2000-01-01T00:00:00Z An important reason why people violate expected utility theory is probability weighting. Previous studies on the probability weighting function typically assume a specific parametric form, exclude heterogeneity in individual preferences, and exclusively consider monetary decision making. This study presents a method to elicit the probability weighting function in rank-dependent expected utility theory that makes no prior assumptions about the functional form of the probability weighting function. We use both aggregate and individual subject data, thereby allowing for heterogeneity of individual preferences, and we examine probability weighting in a new domain, medical decision making. There is significant evidence of probability weighting both at the aggregate and at the individual subject level. The modal probability weighting function is inverse S-shaped, displaying both lower subadditivity and upper subadditivity. Probability weighting is in particular relevant at the boundaries of the unit interval. Compared to studies involving monetary outcomes, we generally find more elevation of the probability weighting function. The robustness of the empirical findings on probability weighting indicates its importance. Ignoring probability weighting in modeling decision under risk and in utility measurement is likely to lead to descriptively invalid theories and distorted elicitations. http://repub.eur.nl/res/pub/11019/ 1999-12-01T00:00:00Z This paper studies life-cycle preferences over consumption and health status. We show that cost-effectiveness analysis is consistent with cost–benefit analysis if the lifetime utility function is additive over time, multiplicative in the utility of consumption and the utility of health status, and if the utility of consumption is constant over time. We derive the conditions under which the lifetime utility function takes this form, both under expected utility theory and under rank-dependent utility theory, which is currently the most important nonexpected utility theory. If cost-effectiveness analysis is consistent with cost–benefit analysis, it is possible to derive tractable expressions for the willingness to pay for quality-adjusted life-years (QALYs). The willingness to pay for QALYs depends on wealth, remaining life expectancy, health status, and the possibilities for intertemporal substitution of consumption. http://repub.eur.nl/res/pub/11018/ 1999-01-01T00:00:00Z Quality-Adjusted Life-Years (QALYs) are currently the most important utility model in medical decision making. QALYs are calculated by adjusting years of life for the utility of the health state in which these years are spent. For normative reasons the standard gamble is the preferred method to measure health state utilities, but concern exists about its descriptive properties. Recent theoretical work has suggested that probability weighting can explain anomalies in standard gamble measurement. This paper shows that applying probability weighting in standard gamble measurement increases the consistency of QALYs with individual preferences. The consistency of QALYs with individual preferences is not significantly increased further if utility curvature is also taken into account. http://repub.eur.nl/res/pub/11055/ 1998-01-01T00:00:00Z This paper studies the implications of the "zero-condition" for multiattribute utility theory. The zero-condition simplifies the measurement and derivation of the Quality Adjusted Life Year (QALY) measure commonly used in medical decision analysis. For general multiattribute utility theory, no simple condition has heretofore been found to characterize multiplicatively decomposable forms. When the zero-condition is satisfied, however, such a simple condition, "standard gamble invariance," becomes available. http://repub.eur.nl/res/pub/11024/ 1997-04-01T00:00:00Z This paper compares the relative performance of quality adjusted life years (QALYs) based on quality weights elicited by rating scale (RS), time trade-off (TTO) and standard gamble (SG). The standard against which relative performance is assessed is individual preference elicited by direct ranking. The correlation between predicted and direct ranking is significantly higher for TTO-QALYs than for RS-QALYs and SG-QALYs. This holds both based on mean Spearman rank correlation coefficients calculated per individual and based on two social choice rules: the method of majority voting and the Borda rule. Undiscounted TTO-QALYs are more consistent with direct ranking than discounted TTO-QALYs http://repub.eur.nl/res/pub/11020/ 1997-02-01T00:00:00Z The aim of this paper is to propose methods that incorporate equity concerns into cost utility analysis. The focus of the paper is on QALYs, but the results apply to health utility indices in general. Two interpretations of QALYs are considered: QALYs as (von Neumann Morgenstern) utilities and QALYs as measures of health. A justification is provided for aggregating consistently scaled “QALYs as utilities” over individuals. The conditions underlying unweighted aggregation of QALYs are identified. These conditions exclude two common types of equity concern. Algorithms are proposed that take into account equity concerns and that are relatively easy to apply. http://repub.eur.nl/res/pub/11021/ 1997-02-01T00:00:00Z This paper presents evidence on income-related inequalities in self-assessed health in nine industrialized countries. Health interview survey data were used to construct concentration curves of self-assessed health, measured as a latent variable. Inequalities in health favoured the higher income groups and were statistically significant in all countries. Inequalities were particularly high in the United States and the United Kingdom. Amongst other European countries, Sweden, Finland and the former East Germany had the lowest inequality. Across countries, a strong association was found between inequalities in health and inequalities in income. http://repub.eur.nl/res/pub/11026/ 1997-01-01T00:00:00Z This paper shows that QALYs can be derived from more elementary conditions than thought hitherto in the literature: it suffices to impose risk neutrality for life years in every health state. This derivation of QALYs is appealing because it does not require knowledge of concepts from utility theory such as utility independence. Therefore our axiomatization greatly facilitates the assessment of the normative (non)validity of QALYs in medical decision making. Moreover, risk neutrality can easily be tested in experimental designs, which makes it straightforward to assess the descriptive (non)validity of QALYs. http://repub.eur.nl/res/pub/11027/ 1997-01-01T00:00:00Z This paper provides a characterization of QALYs, the most important outcome measure in medical decision making, in the context of a general rank dependent utility model. We show that both for chronic and for nonchronic health states the characterization of QALYs depends on intuitive conditions. This facilitates the assessment of the validity of QALYs in rank dependent non-expected utility theories and a comparison with other utility based measures of health. http://repub.eur.nl/res/pub/11028/ 1996-02-01T00:00:00Z The constant rate discounted utility model is commonly used to represent intertemporal preferences in health care program evaluations. This paper examines the appropriateness of this model, and argues that the model fails both normatively and descriptively as a representation of individual intertemporal preferences for health outcomes. Variable rate discounted utility models are more flexible, but still require restrictive assumptions and may lead to dynamically inconsistent behaviour. The paper concludes by considering two ways of incorporating individual intertemporal preferences in health care program evaluations that allow for complementarity of health outcomes in different time periods. http://repub.eur.nl/res/pub/22305/ 1996-01-18T00:00:00Z This thesis studies the applicability of quality-adjusted life years (QALYs) and other utility based outcome measures in medical decision making and health economics. The main conclusion will be that utility based measures are more useful to model health related behaviour than has commonly been thought. http://repub.eur.nl/res/pub/11029/ 1995-06-14T00:00:00Z The paper examines what restrictions have to be imposed on the individual's preference structure for QALYs and HYEs to yield identical results. It is shown that using QALYs involves imposing three additional restrictions. Empirical evidence suggests that these restrictions cannot be expected to hold in all applications. The main problem in using HYEs appears to be practical. An alternative index is proposed, that may help to bridge the gap between QALYs and HYEs by combining to some extent the advantages of the two measures.