Ambiguity aversion and the propensities for self-insurance and self-protection

Two models of ambiguity preferences that permit comparative statics analysis of greater ambiguity aversion yield definite predictions concerning propensities for self-insurance and self-protection: The levels of both activities that are optimal for an ambiguity-averse decision maker are higher in the presence of ambiguity than in its absence, and demands for both activities increase with greater ambiguity aversion. The reason is that, at levels optimal for one decision maker, an increase in either activity results in a mean-preserving contraction in the distribution of expected utility in the presence of ambiguity, which is valuable to anyone with the same risk preferences who is more ambiguity averse.     

Ross' measure of risk aversion and portfolio selection

This article shows that if Ross' definition of riskier is replaced by a more traditional definition, such as a mean-preserving spread or second-degree stochastic dominance, then the application of Ross's stronger measure of risk aversion to the portfolio problem may no longer produce the desired result. It is also shown that the stronger measure may not perform satisfactorily when applied to exponential utility functions.The authors are grateful to John Pratt for his helpful comments.     

Changes in multiplicative background risk and risk-taking behavior

This article analyzes the conditions under which any change in a multiplicative background risk induces a more cautious behavior. We give necessary and sufficient conditions under which any change in the multiplicative background risk with respect to the Nth-degree stochastic dominance raises local risk aversion. Surprisingly, decreasing relative risk aversion of any order up to N in the sense of Pratt (Econometrica 32:122–136, 1964) coupled with decreasing relative risk aversion in the sense of Ross (Econometrica 49:631–638, 1981) are sufficient to guarantee an increase in local risk aversion after any deterioration of the multiplicative background risk thanks to the Nth-degree stochastic dominance. We link our results concerning second-order stochastic dominance with the concept of multiplicative risk vulnerability.     

Observing different orders of risk aversion

A decision maker's attitude towards risk is said to be of orderi, i=1, 2, if for every given riskē with expected value zero, the risk premium the decision maker is willing to pay to avoid the risktē goes witht to zero at the same order ast ⁱ. This article presents an experiment testing the order of decision makers' attitudes toward risk. Its major result is that both attitudes exist, each in significant proportions. Moreover, two classes of first-order behavior are defined. The rank-dependent model (Quiggin, 1982) belongs to one, the disappointment aversion model (Gul, 1991) to the other. We show that only the first of these two classes appears among our subjects.     

Risk seeking with diminishing marginal utility in a non-expected utility model

The present work takes place in the framework of a non-expected utility model under risk: the RDEU theory (Rank Dependent Expected Utility, first initiated by Quiggin under the denomination of Anticipated Utility), where the decision maker's behavior is characterized by two functionsu andf. Our first result gives a condition under which the functionu characterizes the decision maker's attitude towards wealth. Then, defining a decision maker as risk averter (respectively risk seeker) when he always prefers to any random variable its expected value (weak definition of risk aversion), the second result states that a decision maker who has an increasing marginal utility of wealth (a convex functionu) can be risk averse, if his functionf issufficiently below his functionu, hence if he is sufficientlypessimistic. Obviously, he can also be risk seeking with a diminishing marginal utility of wealth. This result is noteworthy because with a stronger definition of risk aversion/risk seeking, based on mean-preserving spreads, Chew, Karni, and Safra have shown that the only way to be risk averse (in their sense) in RDEU theory is to have, simultaneously, a concave functionu and a convex functionf.     

Pareto utility

In searching for an appropriate utility function in the expected utility framework, we formulate four properties that we want the utility function to satisfy. We conduct a search for such a function, and we identify Pareto utility as a function satisfying all four desired properties. Pareto utility is a flexible yet simple and parsimonious two-parameter family. It exhibits decreasing absolute risk aversion and increasing but bounded relative risk aversion. It is applicable irrespective of the probability distribution relevant to the prospect to be evaluated. Pareto utility is therefore particularly suited for catastrophic risk analysis. A new and related class of generalized exponential (gexpo) utility functions is also studied. This class is particularly relevant in situations where absolute risk tolerance is thought to be concave rather than linear.     

An experimental investigation of risk sharing and adverse selection

Does adverse selection hamper the effectiveness of voluntary risk sharing? How do differences in risk profiles affect adverse selection? We experimentally investigate individuals’ willingness to share risks with others. Across treatments we vary how risk profiles differ between individuals. We find strong evidence for adverse selection if individuals’ risk profiles can be ranked according to first-order stochastic dominance and only little evidence for adverse selection if risk profiles can only be ranked according to mean-preserving spreads. We observe the same pattern also for anticipated adverse selection. These results suggest that the degree to which adverse selection erodes voluntary risk sharing arrangements crucially depends on the form of risk heterogeneity.     

Dimensions of Structural Disadvantage: A Latent Class Analysis of a Neighborhood Measure in Child Welfare Data

ABSTRACT

Contextual constructs, such as neighborhood structure, may contribute to child welfare involvement. Secondary data analysis is used with the nationally representative, longitudinal National Survey of Child and Adolescent Well-Being-II (N = 5,872). This study employs latent class analysis (LCA) to identify the number of classes needed to explain the distribution of caregiver responses on the Community Environment Scale. LCA is ideal for this study to identify meaningful groups of caregivers involved with child welfare using neighborhood risk factors. Three latent classes are identified: high social order/medium social capital; high social order/low social capital; low social order/low social capital. Multinomial logistic regression tests whether there are significant differences across the classes, partially validating the LCA that poor, minority caregivers live in neighborhoods with lower social order and capital. Understanding neighborhoods as “high” versus “low” risk may not fully illuminate contextual risk factors in order to develop neighborhood-based interventions. This study reveals that there is a third group of caregivers who reside in places with higher social order but lower social capital. Social capital might be an important factor in preventing child maltreatment. Future work is needed to understand additional individual and neighborhood characteristics that predict membership in each class.     

Is diversity in capabilities desirable when adding decision makers?

When the benefit of making a correct decision is sufficiently high, even a slight increase in the probability of making such a decision justifies an increase in the number of decision makers. Applying a standard uncertain dichotomous choice benchmark setting, this study focuses on the relative desirability of two alternatives: adding individuals with capabilities identical to the existing ones and adding identical individuals with mean-preserving capabilities that depend on the states of nature. Our main result establishes that when the group applies the simple majority rule, variability in the capabilities of the new decision makers under the two states of nature, which is commonly observed in various decision-making settings, is less desirable in terms of the probability of making the correct decision.     

On the definition of risk aversion

Two definitions of risk aversion have recently been proposed for non-expected utility theories of choice under uncertainty: the former refers the measure of risk aversion (Montesano 1985, 1986 and 1988) directly to the risk premium (i.e. to the difference between the expected value of the action under consideration and its certainty equivalent); the latter defines risk aversion as a decreasing preference for an increasing risk (introduced as mean preserving spreads) (Chew, Karni and Safra 1987, Machina 1987, Röell 1987, Yaari 1987).When the von Neumann-Morgenstern utility function exists both these definitions indicate an agent as a risk averter if his or her utility function is concave. Consequently, the two definitions are equivalent. However, they are no longer equivalent when the von Neumann-Morgenstern utility function does not exist and a non-expected utility theory is assumed. Examples can be given which show how the risk aversion of the one definition can coexist with the risk attraction of the other. Indeed the two definitions consider two different questions: the risk premium definition specifically concerns risk aversion, while the mean preserving spreads definition concerns the increasing (with risk) risk aversion.The mean preserving spreads definition of risk aversion, i.e. the increasing (with risk) risk aversion, requires a special kind of concavity for the preference function (that the derivatives with respect to probabilities are concave in the respective consequences). The risk premium definition of local risk aversion requires that the probability distribution dominates on the average the distribution of the derivatives of the preference function with respect to consequences. Besides, when the local measure of the first order is zero, there is risk aversion according to the measure of the second order if the preference function is concave with respect to consequences.Yaari's (1969) measure of risk aversion is closely linked to the r.p. measure of the second order. Its sign does not indicate risk aversion (if positive) or attraction (if negative) when the measure of the first order is not zero (i.e., in Yaari's language, when subjective odds differ from the market odds).     

Increasing Risk: Some Direct Constructions

This article extends the classic RothschildNStiglitz characterization of comparative risk ("increasing risk") in two directions. By adopting a more general definition of "mean preserving spread" (MPS), it provides a direct construction of a sequence of MPS's linking any pair of distributions that are ranked in terms of comparative risk. It also provides a direct, explicit construction of a zero-conditional-mean "noise" variable for any such pair of distributions. Both results are extended to the case of second order stochastic dominance.     

Mean-preserving changes in risk with tail-dominance

In this paper, we consider a class of mean preserving increases in risk such that all risk-averse decision makers respond to an increase in risk by reducing the level of their risky activities. The type of increase in risk that we consider is based on the notion of tail dominance which generalizes other cases previously discussed in the literature.L. Eeckhoudt is Professor of Economics at the Catholic Faculties of Mons (Belgium) and Lille (France). P. Hansen is Professor of Operations Research at Ecole des Hautes Etudes Commerciales, Montréal. Both authors have benefited from comments by P. Caperaa, G. Dionne, J. Meyer and H. Varian. They also thank A. Coopman who carefully reviewed and improved the English style.     

A Diamond-Stiglitz approach to the demand for self-protection

The existing research concerning the relationship between risk aversion and prudence and the demand for self-protection assumes that the loss variable follows a Bernoulli distribution, and that changes in the level of self-protection are mean preserving. The analysis here replaces these two very strong conditions with ones which are more general. When doing this, the method of analysis is also significantly modified. This modification includes representing a change in the level of self-protection using the procedure developed by Diamond and Stiglitz (Journal of Economic Theory 8:337-360, 1974) for representing a change in risk. This alternate representation allows the existing findings to be generalized considerably, and also simplifies the analysis.     

Combining expert probabilities using the product of odds

We resolve a useful formulation of the question how a statistician can coherently incorporate the information in a consulted expert??s probability assessment for an event into a personal posterior probability assertion. Using a framework that recognises the total information available as composed of units available only to each of them along with units available to both, we show: that a sufficient statistic for all the information available to both the expert and the statistician is the product of their odds ratios in favour of the event; that the geometric mean of their two probabilities specifies a contour of pairs of assertions in the unit-square that yield the same posterior probability; that the information-combining function is parameterised by an unknown probability for the event conditioned only on the unspecified information common to both the statistician and the expert; and that an assessable mixing distribution over this unspecified probability allows an integrable mixture distribution to represent a computable posterior probability. The exact results allow the identification of the subclass of coherent probabilities that are externally Bayesian operators. This subclass is equivalent to the class of combining functions that honour the principles of uniformity and compromise.     

Preferences for information on probabilities versus prizes: The role of risk-taking attitudes

Many real-world decisions entail choices between information on either probabilities or payoffs (i.e., prizes). Simplified versions of such decisions are examined to gain insight into preferences for different types of information as a function of risk-attitudes. General and simple decision rules are derived for cases where the utility function is concave (or convex) over the relevant payoff interval.The article further describes several experiments to test business students' intuitions concerning these optimal decision rules. In general, risk-taking attitudes did not correlate significantly with subjects' preferences for information, in violation of theorems regarding mean-preserving spreads of risk. Other tests, e.g., narrowing certain probability ranges, also resulted in preferences contrary to expected utility (EU) theory.     

The bipolar Choquet integral representation

Cumulative Prospect Theory is the modern version of Prospect Theory and it is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e., the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assumption of the theory, proposing new paradoxes where the Gain-Loss Separability is violated. We present a generalization of Cumulative Prospect Theory which does not imply Gain-Loss Separability and is able to explain the cited paradoxes. On the other hand, the new model, which we call the bipolar Cumulative Prospect Theory, genuinely generalizes the original Prospect Theory of Kahneman and Tversky, preserving the main features of the theory. We present also a characterization of the bipolar Choquet Integral with respect to a bi-capacity in a discrete setting.     

Measuring risk aversion with lists: a new bias

Various experimental procedures aimed at measuring individual risk aversion involve a list of pairs of alternative prospects. We first study the widely used method by Holt and Laury (Am Econ Rev 92(5):1644–1655, 2002), for which we find that the removal of some items from the lists yields a systematic decrease in risk aversion and scrambles the ranking of individuals by risk aversion. This bias, that we call embedding bias, is quite distinct from other confounds that have been previously observed in the use of the HL method. It may be related to empirical phenomena and theoretical developments where better prospects increase risk aversion. Nevertheless, we also find that the more recent elicitation method due to Abdellaoui et al. (Theory Decis 71:63–80, 2011), also based on lists but using only one and the same probability in the list, does not display any statistically significant bias when the corresponding items of the list are removed. Our results suggest that methods other than the popular HL one may be preferable for the measurement of risk aversion.     

A new challenge to economic science: Global model simulation

The FUGI (Futures of Global Interdependence) global modeling system has been developed as a scientific policy modeling and future simulation tool of providing global information to the human society and finding out possibilities of policy co-ordination among countries in order to achieve sustainable development of the global economy co-existing on the planet Earth in the ever changing universe. The FUGI global model M200 classifies the world into 200 countries/regions where each national/regional model is globally interdependent. Each national/regional model has nine subsystems as population, foods, energy, environment, economic development, peace and security, human right, healthcare and quality of life (IT revolution). This is a super complex dynamic system model using integrated multidisciplinary systems analysis where number of structural equations is over 170,000. Economic model as a core includes major economic variables such as production of GDP, employment, expenditures of GDP, income distribution, prices, money, interest rates and financial assets, government finance, international balance of payments, international finance, foreign exchange rates and development indicators.The purpose of this article is twofold, namely to provide information on a new frontier science of economics: global model simulation as well as appropriate policy exercise for sustainable development of the interdependent global economy. The world economy is facing “green” energy revolution to change from fossil to create alternative energy and energy saving technology against sky rocketing higher oil prices. Japan takes a lead in this field of technology innovation. Under such circumstances, Japan should take an initiative to create a new peaceful world through not only harmonized adjustments of Japanese economic policy but also wise cosmic mind to promote human solidarity with the ever changing nature will be desirable to adjust orbit of the fluctuated global economy. Japan should challenge for a new strategy to accelerate economic growth rates by “CO₂ reducing environment investment” based on technology innovations.     

Adverse selection and equilibrium in liability insurance markets

Models of asymmetric information in insurance markets typically consider insurance buyers with Bernoulli loss distributions differing in expected loss. This article analyzes markets where buyer loss distributions are characterized by mean-preserving spreads and insurers can classify applicants in terms of expected values but not by risk. Because liability losses are characterized by skewed continuous probability distributions, both discrete and continuous loss distributions are considered. In contrast to the single separating equilibrium in the classic Rothschild-Stiglitz insurance market, multiple separating equilibria are identified in this article: three in the discrete case and four in the continuous case. The possibility of extreme discontinuities in insurer policy offers provides a new explanation for crises in liability insurance markets.The support of the National Association of Insurance Commissioners is gratefully acknowledged.