http://repub.eur.nl/res/aut/14109/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/32664/ 2012-04-26T00:00:00Z As societies are increasingly concerned with social risks, it is important to evaluate risks not only from an individual perspective, but also from a societal one. Many increases in social risk involve a simultaneous increase in risk and inequality. This paper presents an experiment which disentangles concerns for risk and inequality in a social risk context. Subjects choose between different types of allocations of risks over 10 other participants. The allocations differ only in terms of dispersion. We disentangle four types of dispersion: ex ante inequality, ex post inequality, individual risk, and collective risk. The results show that people are averse towards ex ante inequality and individual risk, whereas they are ex post inequality and collective risk seeking. 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/21327/ 2010-12-01T00:00:00Z Abstract: 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 preference reversals in intertemporal choice are consistent with constant discounting and can alternatively be explained by decreasing absolute risk aversion together with the individual's risk perception. 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. We show how relative degrees of changes in risk over time can determine choices. 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/26884/ 2010-07-13T00:00:00Z 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. 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/19990/ 2009-12-01T00:00:00Z Prelec (2004) showed that the Arrow–Pratt degree of convexity of the logarithm of the discount function can serve as a measure of decreasing impatience and of the corresponding time-inconsistency. In decision under risk and uncertainty the convexity of the utility function itself, not of its logarithm, has empirical meaning in terms of risk attitude. This paper introduces decreasing relative impatience, which is directly related to the degree of convexity of the discount function. By giving empirical meaning to the convexity of the discount function this paper clarifies the relations between several concepts in intertemporal choice. This paper also introduces a concept of spread seeking. Spread seeking and decreasing relative impatience are likely to have distinct underlying psychological motives, but are shown to be equivalent under discounted utility. http://repub.eur.nl/res/pub/17490/ 2009-11-17T00:00:00Z Many empirical studies on intertemporal choice report preference reversals in the sense that a preference between a small reward to be received soon and a larger reward to be received later reverses as both rewards are equally delayed. Such preference reversals are commonly interpreted as contradicting constant discounting. We show that this interpretation is correct only if baseline consumption to which the outcomes are added, remains constant over time. The difficulty with measuring discounting when baseline consumption changes over time, is that delaying an outcome has two simultaneous effects: (1) due to the change in baseline consumption, it changes the increase in utility from receiving the outcome, and (2) it changes the discount factor applied to this increase in utility. In order to draw conclusions about discounting one needs to disentangle these two effects which seems impossible at first sight (Noor, 2009). Yet, in this paper we propose a way to disentangle the two effects. 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/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/15929/ 2008-11-01T00:00:00Z We reconsider the allocational invariance of equilibria to different formulations of market completeness. We identify the so-far neglected assumption of sophisticated behavior as being crucial. First, the Arrow-Debreu setting is considered, where markets do not reopen in the future. Second, sequentially complete markets are analyzed, where goods on the spot markets and all contingent one-period ahead commodities can be traded in every state. Finally, complete markets are analyzed, where all possible contingent commodities can be traded at every state. Preferences may be time-consistent or time-inconsistent. A distinction is made between naïve and sophisticated behavior. 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/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/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.