Intersecting Lorenz Curves, the Degree of Downside Inequality Aversion, and Tax Reforms

This paper clarifies the conceptual distinction of downside inequality aversion (or transfer sensitivity) as a normative criterion for judging income distributions from the Pigou-Dalton principle of transfers. We show that when the Lorenz curves of two income distributions intersect, how the change from one distribution to the other is judged by an inequality index exhibiting downside inequality aversion often depends on the relative strengths of its downside inequality aversion and inequality aversion. For additive inequality indices or their monotonic transformations, a measure characterizing the strength of an index’s downside inequality aversion against its inequality aversion is shown to determine the ranking by the index of two distributions whose Lorenz curves cross once. The precise condition under which the same result generalizes to the case of multiple-crossing Lorenz curves is also identified. The results are particularly useful in understanding the distributional impact of tax reforms. I received exceptionally helpful comments from Mike Hoy, Peter Lambert, the Editor, Buhong Zheng, and an anonymous referee. The remaining errors and shortcomings are my own – W.H. Chiu     

Expected subjective utility: Is the Neumann-Morgenstern utility the same as the Neoclassical's?

Using axioms no stronger than those for the Neumann-Morgenstern expected utility hypothesis, with the recognition of finite sensibility, it is shown that the utility function derived by the N-M method is a neoclassical subjective utility function, contrary to the belief otherwise by prominent economists. This result is relevant for issues of utility measurability, social choice, etc. since it is subjective utility that is relevant for social choice. The relevance of individual risk aversion to the form of social welfare functions and the rationality of pure risk aversion are also discussed.     

Time-based versus money-based decision making under risk: An experimental investigation

This paper investigates whether individuals make similar decisions under risk when the outcomes are expressed in time versus monetary units. We address this issue in two studies measuring individual risk preferences and prospect theory parameters (i.e., utility curvature, probability weighting, and loss aversion) for both time and money. In the first (resp., second) study we consider relatively small (resp., large) time and monetary outcomes. We find that individuals hold similar risk preferences for time and money; we also find evidence that “time is money” with regard to the utility curvature for gains, loss aversion, and decision weighting. However, individuals have different valuations of losing time and money. The utility function for small losses of money is more concave and variable than the utility function for small losses of time (Study 1), but the utility function for large losses of time is more concave and variable than that for large losses of money (Study 2). We argue that these results reflect a difference in the perceived slack of the respective resource.     

Cultural capital or relative risk aversion? Two mechanisms for educational inequality compared1

In this paper we empirically examined two explanatory mechanisms for educational inequality: cultural reproduction and relative risk aversion, using survey data taken from secondary school pupils in Amsterdam. Cultural reproduction theory seeks to explain class variations in schooling by cultural differences between social classes. Relative risk aversion theory argues that educational inequalities can be understood by between-class variation in the necessity of pursuing education at branching points in order to avoid downward mobility. We showed that class variations in early demonstrated ability are for a substantial part cultural: cultural capital - measured by parental involvement in highbrow culture - affected school performance at the primary and secondary level. However, relative risk aversion - operationalized by being concerned with downward mobility - strongly affects schooling ambitions, whereas cultural capital had no effect. Thus, we conclude that 'primary effects' of social origin on schooling outcomes are manifested through cultural capital and not through relative risk aversion (in addition to other potential sources of class variations such as genetics). Relative risk aversion, and not cultural capital, affects schooling ambitions, which is relevant for our understanding of secondary effects.     

The measurement of transient poverty: Theory and application to Pakistan

The present paper investigates the measurement of transient poverty when each person's welfare level fluctuates due to exogenous risk. The paper namely characterizes the sensitivity of transient/chronic poverty decomposition with respect to the poverty line and to the expected welfare level so that the decomposition analysis will be based on solid theoretical foundations and be robust empirically. Theoretical results show that poverty measures associated with prudent risk preferences perform better than other measures in assuring that the value of transient poverty increases with the depth of chronic poverty and that the decomposition is not highly sensitive to the poverty line. Poverty measures such as those associated with constant relative risk aversion are thus superior to popular Foster–Greer–Thorbecke (FGT) measures such as headcount, poverty gap, and squared poverty gap indices. These theoretical arguments are confirmed empirically by the application of the decomposition to a two-period household panel dataset from rural Pakistan. The relative magnitudes of transient versus chronic poverty are more robust to changes in the poverty line when poverty measures associated with constant relative risk aversion are used than when FGT poverty measures are used.     

Anticipated Regret,Risk Perception,or Both: Which is Most Likely Responsible for Our Intention to Gamble?

The current study investigated whether risk aversion or regret aversion could be related to a lower intention to gamble, and whether the type of gambling was a moderator of this relationship. The study took place in Macau, often called “the Las Vegas of East Asia.” A total of 373 Macau residents completed a questionnaire survey dealing with thirteen types of gambling. The results showed that risk perception and anticipated regret had a significant negative effect on the intention to gamble. This negative effect was domain-specific, varying with the type of gambling. Our findings indicated that neither risk aversion nor regret aversion can uniquely explain an individual’s risk-taking tendency consistently. Instead, which factor plays a greater role in lowering the intention to gamble—regret aversion, risk aversion, or both—is itself dependent on the type of gambling involved. The finding that not all gambles are created equal could be useful in gambling prevention and advertising appeal by providing a basis for understanding the role that cognitive and emotional factors play in different types of gambling.     

RISK PREFERENCES AND EXPECTED UTILITY: EVIDENCE FROM LABOR SUPPLY DATA

This paper adds to the growing body of evidence that observed risk preferences are not consistent with expected‐utility theory. Using the link between labor supply decisions and utility as outlined by Chetty (“A Bound on Risk Aversion Using Labor Supply Elasticities.” The American Economic Review, 96(5), 2006, 1821–34), I compute the curvature of utility over wealth for 3,900 individuals in the 1996 Panel Study of Income Dynamics. I then compare this estimate to a measure of relative risk aversion based on the respondents' answers to hypothetical gambling questions and find virtually zero correlation. Finally, I investigate how the two measures and their correlations change by demographic groups and risky behavior. (JEL C81, D80, J22)     

Ranking profiles of capability sets

In this paper, we present an innovative approach for ranking profiles of capability sets on the basis of equity. An interesting way of capturing the notion of equity is to take into account the extent to which each of the different functioning vectors is shared by the population under consideration (of size n). This is done by defining the ‘common capability sets’ enjoyed by k individuals as the set of functioning vectors simultaneously available to at least k individuals (1 ≤ k ≤ n). These sets are closely related to the original capability sets and have some interesting properties that are examined throughout the paper. We define and axiomatically characterize a capability profile ranking that lexicographically compares the different common capability sets. We would like to thank for helpful discussion and comments to Jorge Alcalde-Unzu, Ritxar Arlegi, Miguel A. Ballester, Jose Enrique Galdón, Antonio Nicolò, Jorge Nieto, Prasanta Pattanaik, John Weymark and the anonymous referees of this paper. The project is supported by Spanish’ Comision Interministerial de Ciencia y Technologia (SEC2003-08105) and by the European Commission (MRTN-CT-2003-504796).     

Is India better off today than 15 years ago? A robust multidimensional answer

This paper provides a robust multidimensional normative evaluation of the growth episode that India has experienced in the last 15 years. Specifically, the paper compares the evolution, between 1987, 1995 and 2002, of the distribution of several individual attributes on the basis of ethically robust dominance criteria. The individual attributes considered are real consumption (measured at the individual level), literacy rate, under 5 mortality and violent crime rates (all measured at the district levels). District level variables are interpreted as (local) public goods which, along with consumption, contribute to individual well-being. The robust criteria used are generalizations, to more than two attributes, of the first and second order dominance criteria of Atkinson and Bourguignon (Rev Econ Stud 49:183–201, 1982) and coincide with the unanimity of utilitarian value judgements taken over a specific class of individual utility functions. The main result of the empirical analysis is that all utilitarian rankings of distributions of the four attributes that assume that individual utility functions satisfy the assumptions of second order dominance agree that India is better off in 2002 than in 1987 or 1995 but that these rankings disagree as to how to rank 1987 and 1995. Furthermore, if one removes crime from the list of attributes, the dominance is shown to apply steadily over the whole period.     

Characterizing uncertainty aversion through preference for mixtures

Uncertainty aversion is often modelled as (strict) quasi-concavity of preferences over uncertain acts. A theory of uncertainty aversion may be characterized by the pairs of acts for which strict preference for a mixture between them is permitted. This paper provides such a characterization for two leading representations of uncertainty averse preferences; those of Schmeidler [24] (Choquet expected utility or CEU) and of Gilboa and Schmeidler [16] (maxmin expected utility with a non-unique prior or MMEU). This characterization clarifies the relation between the two theories. Received: 20 February 1998/Accepted: 25 March 1999     

Aggregation of individuals' preference intensities into social preference intensity

A result of John Harsanyi concerns the aggregation of individuals' preferences into social preferences. The result states that if the individuals in a society and the society as a whole have preference relations that compare probability distributions on a set of outcomes, and the preference relations satisfy expected-utility conditions and Pareto conditions, then a utility function for the social preference relation is a positive affine function of utility functions for the individuals' preference relations. This paper presents an analogous result for preference relations that denote intensity of preference, i.e., preference relations that compare exchanges of outcomes. This approach avoids the difficulties of requiring that the individuals in the society have common beliefs regarding uncertainty. Received: 14 October 1996 / Accepted: 4 September 1997     

A FINANCE APPROACH TO ESTIMATING CONSUMPTION PARAMETERS

This paper relates consumption economics more closely to an aggregate financial variable than in any previous research. We compile the net real rate of return on a synthetic mutual fund (SMF) encompassing all major classes of financial assets and residential real estate. Return on the SMF better represents the market return of financial portfolio theory than any measure in use today and we demonstrate its merit in an expected utility model to estimate consumption parameters, the coefficient of relative risk aversion (CRRA), and intertemporal elasticity of substitution (IES). The estimates are stable across varying time periods and alternative measures of consumption. (JEL E21, D91, G11, C13)     

Social welfare functions with a reference income

A foundation of social welfare functions is considered with a given reference income (or utility): relative and absolute invariance of the underlying welfare ordering are defined to hold for societies with either all members having incomes below the reference income or all members having incomes above the reference income. These conditions, alongside standard properties of a social preference relation, provide reference income dependent extensions of traditional classes of welfare functions. Dalton’s principle of positive transfers is incorporated, under which relative invariance leads to a class of piecewise (rank-)linear welfare functions, including the class of generalized Gini social welfare functions as a special case. To ensure quasi-concavity a new preference condition is proposed, which has the interpretation of aversion to income dropping below the reference income.     

RISK PREFERENCE AND THE WORK-LEISURE TRADE-OFF

The paper investigates the interrelationships between the wage rate, period of employment, work-leisure choice and the attitude toward risk. The model makes risk preference endogenous given external forces acting on individual choice. Beginning with assumptions normally considered consistent with risk aversion –––namely concave utility with respect to leisure and wealth along with perfect markets–––rational behavior consistent with the "insurance buying gambler" is shown to be a reasonable possibility. The theory also provides an explanation for the "repeating gambler paradox."     

Progress and conservation under Rawls's maximin principle

I argue the compatibility of progress with Rawls's maximin principle when applied to individual utility functions which are “nonaltruistic” in the sense that any transfer of consumption goods from old to young (resp. from young to old) lowers (resp. increases) old people's utility. The paper shows that necessary conditions for that compatibility are: (A) a bound on the feasible transfers from young to old, and (B) a positive intergenerational stock externality. The analysis implies that the maximin principle has the drawback of making, under mild assumptions, conservation incompatible with progress. Received: 15 December 1999/Accepted: 17 April 2000     

Twofold optimality of the relative utilitarian bargaining solution

Given a bargaining problem, the relative utilitarian (RU) solution maximizes the sum total of the bargainer’s utilities, after having first renormalized each utility function to range from zero to one. We show that RU is “optimal” in two very different senses. First, RU is the maximal element (over the set of all bargaining solutions) under any partial ordering which satisfies certain axioms of fairness and consistency; this result is closely analogous to the result of Segal (J Polit Econ 108(3):569–589, 2000). Second, RU offers each person the maximum expected utility amongst all rescaling-invariant solutions, when it is applied to a random sequence of future bargaining problems generated using a certain class of distributions; this is recalls the results of Harsanyi (J Polit Econ 61:434–435, 1953) and Karni (Econometrica 66(6):1405–1415, 1998).     

Strategy-proof Cardinal Decision Schemes

This paper analyses strategy-proof mechanisms or decision schemes which map profiles of cardinal utility functions to lotteries over a finite set of outcomes. We provide a new proof of Hylland’s theorem which shows that the only strategy-proof cardinal decision scheme satisfying a weak unanimity property is the random dictatorship. Our proof technique assumes a framework where individuals can discern utility differences only if the difference is at least some fixed number which we call the grid size. We also prove a limit random dictatorship result which shows that any sequence of strategy-proof and unanimous decision schemes defined on a sequence of decreasing grid sizes approaching zero must converge to a random dictatorship. We are most grateful to an Associate Editor and two referees for very helpful comments on an earlier version of the paper. An erratum to this article can be found at     

RISK PREFERENCE ESTIMATION IN THE NONLINEAR MEAN STANDARD DEVIATION APPROACH

Risk preferences and technology are jointly estimated in the nonlinear mean-standard deviation framework for a competitive firm model under price risk. A utility function is proposed that nests various risk preference structures and risk neutrality as empirically refutable special cases. The empirical application using firm-level data finds evidence of decreasing absolute risk aversion, differences in the nature of relative risk aversion by firm size, and little support for the widely used linear mean-variance framework. The estimation results also show that ignoring risk and risk preferences can substantially overestimate output supply and input demand elasticities.     

Heterogeneity of Loss Aversion in Pathological Gambling

Pathological gambling (PG) is characterized by continual repeated gambling behavior despite negative consequences. PG is considered to be a disorder of altered decision-making under risk, and behavioral economics tools were utilized by studies on decision-making under risk. At the same time, PG was suggested to be a heterogeneous disorder in terms of personality traits as well as risk attitude. We aimed to examine the heterogeneity of PG in terms of loss aversion, which means that a loss is subjectively felt to be larger than the same amount of gain. Thirty-one male PG subjects and 26 male healthy control (HC) subjects underwent a behavioral economics task for estimation of loss aversion and personality traits assessment. Although loss aversion in PG subjects was not significantly different from that in HC subjects, distributions of loss aversion differed between PG and HC subjects. HC subjects were uniformly classified into three levels (low, middle, high) of loss aversion, whereas PG subjects were mostly classified into the two extremes, and few PG subjects were classified into the middle range. PG subjects with low and high loss aversion showed a significant difference in anxiety, excitement-seeking and craving intensity. Our study suggested that PG was a heterogeneous disorder in terms of loss aversion. This result might be useful for understanding cognitive and neurobiological mechanisms and the establishment of treatment strategies for PG.