speculation under unawareness no trade theorems establish that in various trading environments investors who share a common prior will not engage in speculation as long as expected utility bayesian updating and full awareness are imposed we relax the last assumption by allowing for asymmetric unawareness and examine under which conditions speculative behaviour emerges we find that if common knowledge is assumed as in the settings of aumann 1976 and milgrom and stokey 1982 unawareness cannot generate speculation this is not true however in settings where no common knowledge is assumed such as speculation in equilibrium geanakoplos 1989 and betting that is always beneficial morris 1994 unless stronger conditions on awareness are imposed

uncertainty and risk in financial markets this paper considers a general equilibrium model in which the distinction between uncertainty and risk is formalized by assuming agents have incomplete preferences over statecontingent consumption bundles as in bewley 1986 without completeness individual decision making depends on a set of probability distributions over the state space a bundle is preferred to another if and only if it has larger expected utility for all probabilities in this set when preferences are complete this set is a singleton and the model reduces to standard expected utility in this setting we characterize pareto optima and equilibria and show that the presence of uncertainty generates robust indeterminacies in equilibrium prices and allocations for any specification of initial endowments we derive comparative statics results linking the degree of uncertainty with changes in equilibria despite the presence of robust indeterminacies we show that equilibrium prices and allocations vary continuously with underlying fundamentals equilibria in a standard risk economy are thus robust to adding small degrees of uncertainty finally we give conditions under which some assets are not traded due to uncertainty aversion

knightian uncertainty and moral hazard abstract this paper presents a principal agent model in which the agent has imprecise beliefs we model this situation formally by assuming the agent s preferences are incomplete as in bewley 1986 2 in this setting incentives must be robust to knightian uncertainty we study the implications of robustness for the form of the resulting optimal contracts we give conditions under which there is a unique optimal contract and show that it must have a simple flat payment plus bonus structure that is output levels are divided into two sets and the optimal contract pays the same wage for all output levels in each set we derive this result for the case in which the agent s utility function is linear and then show it also holds if this utility function has some limited curvature

financial complexity and trade what are the implications on trading activity if investors are not sophisticated enough to understand and evaluate trades that have a complex payoff structure can frictions generated by this type of financial complexity be so severe that they lead to a complete market freeze like that of the recent financial crisis starting from an allocation that is not pareto optimal we find that whether complexity impedes trade depends on how investors perceive risk and uncertainty for smooth convex preferences such as subjective expected utility complexity cannot halt trade even in the extreme case where each investor is so unsophisticated that he can only trade up to one arrow debreu security without being able to combine two or more in order to construct a complex trade however for non smooth preferences which allow for kinked indifference curves such as maxmin expected utility complexity can completely shut down trade

first order and second order ambiguity aversion different models of uncertainty aversion imply strikingly different economic behavior the key to understanding these differences lies in the dichotomy between first order and second order ambiguity aversion which i define here my definition and its characterization are independent of specific representations of decisions under uncertainty i show that with second order ambiguity aversion a positive exposure to ambiguity is optimal if and only if there is a subjective belief such that the act s expected outcome is positive with first order ambiguity aversion zero exposure to ambiguity can be optimal examples in finance insurance and contracting demonstrate the economic relevance of this dichotomy this paper was accepted by han bleichrodt decision analysis

pareto optima and equilibria when preferences are incompletely known an exchange economy in which agents have convex incomplete preferences defined by families of concave utility functions is considered sufficient conditions for the set of efficient allocations and equilibria to coincide with the set of efficient allocations and equilibria that result when each agent has a utility in her family are provided welfare theorems in an incomplete preferences framework therefore hold under these conditions and efficient allocations and equilibria are characterized by first order conditions

learning and earning do multiple training events pay a decade of evidence from a cohort of young british men this paper estimates the impact of work related training on wage growth over the period 1981 91 using longitudinal data from the national child development study a cohort of young men aged 23 in 1981 a hurdle negbin model is used to control for training endogeneity we find that training incidence has a significant positive effect on wage growth we also find that young men with a higher level of education are not only more likely to be trained but are also more likely to experience substantially higher wage growth as a result

intertemporal equilibria with knightian uncertainty we study a dynamic and infinite dimensional model with incomplete multiple prior preferences in interior efficient allocations agents share a common risk adjusted prior and subjective interest rate interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents multiple prior sets a specific model with neither risk nor uncertainty at the aggregate level is considered risk is always fully insured for small levels of ambiguity there exists an equilibrium with inertia where agents also insure fully against knightian uncertainty when the level of ambiguity exceeds a critical threshold full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all we also show that equilibria with inertia are indeterminate

interim efficient allocations under uncertainty abstract this paper considers an exchange economy under uncertainty with asymmetric information uncertainty is represented by multiple priors and posteriors of agents who have either bewley s incomplete preferences or gilboa schmeidler s maximin expected utility preferences the main results characterize interim efficient allocations under uncertainty that is they provide conditions on the sets of posteriors thus implicitly on the way how agents update the sets of priors for non existence of a trade which makes all agents better off at any realization of private information for agents with the incomplete preferences the condition is necessary and sufficient but for agents with the maximin expected utility preferences the condition is sufficient only a couple of necessary conditions for the latter case are provided

private sector training and graduate earnings this paper uses a survey of british graduates to estimate the impact of employer provided training on the earnings of men and women graduates the results indicate that although the training impact is reduced after controlling for endogeneity some forms of training have a considerable impact however there are substantial gender differences in the earnings impact of various typ es of training moreover men graduates are more likely to receive training than otherwise identical women

a theory of subjective compound lotteries abstract we develop a savage type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries our theory permits issue preference that is agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues hence we establish subjective foundations for the anscombe aumann framework and other models with two different types of probabilities we define second order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second order risk which implies issue preference and behavior consistent with the ellsberg paradox

voluntary export restraints and rationing u k leather footwear imports from eastern europe following the imposition of a quantitative import restriction someone somewhere must be quantity rationed concentrating on demand we develop methods to test and allow for the presence of rationing in the estimation of demand equations and in the calculation of the welfare effects of quantitative restrictions using a ces model we analyse the voluntary export restraints on u k imports of two types of leather footwear from comecon countries the results suggest that even if prices did not rise to clear the market u k consumers could have lost up to 60 million in 1986 from these restrictions

sharing risk and ambiguity we study the market implications of ambiguity in common models we show that generic determinacy is a robust feature in general equilibrium models that allow a distinction between ambiguity and risk

overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short selling the theory of existence of equilibrium with short selling is reconsidered under risk and ambiguity modelled by risk averse variational preferences no arbitrage conditions are given in terms of risk adjusted priors a sufficient condition for existence of efficient allocations is the overlapping of the interiors of the risk adjusted sets of priors or the inexistence of mutually compatible trades with non negative expectation with respect to any risk adjusted prior these conditions are necessary when agents are not risk neutral at extreme levels of wealths it is shown that the more uncertainty averse or risk averse the agents the more likely are efficient allocations and equilibria to exist

uncertainty risk neutral measures and security price booms and crashes abstract this paper provides a general analysis of intertemporal utility based on the multiple priors model of aversion to knightian uncertainty then the existence of equilibrium is proven for a representative agent security market model it is shown that uncertainty aversion can invalidate the existence of a risk neutral measure representation for prices in addition an example suggests an intriguing link between uncertainty aversion and the possibility of abrupt changes in security prices the analysis relies heavily on a fubini type theorem for analytic functions due to dellacherie and meyer probabilities and potential c north holland new york 1988 journal of economic literature classification numbers g12 d81 d90

a theory of anticipated utility abstract a new theory of cardinal utility with an associated set of axioms is presented it is a generalization of the von neumann morgenstern expected utility theory which permits the analysis of phenomena associated with the distortion of subjective probability

incomplete preferences and equilibrium in contingent markets this paper shows that betting or speculative trading between agents with incomplete preferences is likely to occur if agents have access to convex choice sets this contrasts sharply with endowment economy models where preference incompleteness often hinders betting speculative trading or mutually beneficial insurance arrangements our results imply that decision makers with identical tastes and identical feasible sets will potentially gain from speculative trade for generic status quo allocations we also develop a framework for endogenizing the status quo allocations of decision makers that are treated exogenously in the existing literature finally we provide a tractable differential representation of status quo allocations equilibria and conditions where speculative trade may or may not emerge

asset demands without the independence axiom an important application of the theory of choice under uncertainty is to asset markets and an important property in these markets is a preference for portfolio diversification if an investor is an expected utility maximizer then s he is risk averse if and only if s he exhibits a preference for diversification this paper examines the relationship between risk aversion and portfolio diversification when preferences over probability distributions of wealth do not have an expected utility representation

dual approaches to the analysis of risk aversion we present a dual formulation of choice under uncertainty based on a few simple assumptions about preferences it is shown that the additive separability restriction on preferences key to expected utility theory can be dropped with little loss of analytic power for a broad class of choice problems dual risk premiums are characterized and it is shown that placing various invariance restrictions on them leads naturally to generalizations of the concepts of cara crra and lrt familiar from expected utility theory each of these generalizations conforms to a notion of homotheticity

interim efficiency with meu preferences abstract recently kajii and ui 2009 17 proposed to characterize interim efficient allocations in an exchange economy under asymmetric information when uncertainty is represented by multiple posteriors when agents have bewley s incomplete preferences kajii and ui 2009 17 proposed a necessary and sufficient condition on the set of posteriors however when agents have gilboa schmeidler s maxmin expected utility preferences they only propose a sufficient condition the objective of this paper is to complete kajii and ui s work by proposing a necessary and sufficient condition for interim efficiency for various models of ambiguity aversion and in particular maxmin expected utility our proof is based on a direct application of some results proposed by rigotti shannon and stralecki 2008 24

food scares in an uncertain world we develop a model that explains the stylized facts of food scares an immediate and sharp decline in consumption of the product followed by a slow and frequently partial recovery of demand after the scare passes the model is used in conjunction with the natural experiment afforded by the mad cow crisis to elicit empirical information on decision makers perception of uncertainty our theoretical and quantitative results suggest that observed behavior is consistent with sharp changes in beliefs and the presence of knightian uncertainty as measured by the degree of imprecision in our model

survival with ambiguity we analyze a market populated by expected utility maximizers and smooth ambiguity averse consumers we study conditions under which ambiguity averse consumers survive and affect prices in the limit if ambiguity vanishes with time or if the economy exhibits no aggregate risk ambiguity averse consumers survive but have no long run impact on prices in both scenarios ambiguity averse consumers are fully insured against ambiguity in equilibrium and thus behave as expected utility maximizers with correct beliefs if ambiguity averse consumers are not fully insured against ambiguity their behavior mimics expected utility maximizers with wrong beliefs and a stochastic discount factor which might be consistently higher or lower than their actual discount factor we use this insight to analyze a markov economy with large persistent ambiguity consumers with decreasing absolute ambiguity aversion whose prudence with respect to ambiguity exceeds twice their absolute ambiguity aversion a s survive in the presence of expected utility maximizers with correct beliefs if the economy further exhibits aggregate risk they drive the expected utility maximizers out of the market and determine prices in the limit in contrast consumers with increasing or constant absolute ambiguity aversion only survive in the absence of aggregate risk and have no impact on limit prices

a more robust definition of subjective probability the goal of choice theoretic derivations of subjective probability is to separate a decisionmaker s underlying beliefs subjective probabilities of events from their preferences attitudes toward risk classical derivations have all relied upon some form of the marschak samuelson independence axiom or the savage sure thing principle which imply that preferences over lotteries conform to the expected utility hypothesis this paper presents a choice theoretic derivation of subjective probability in a savage type setting of purely subjective uncertainty which neither assumes nor implies that the decisionmaker s preferences over lotteries necessarily conform to the expected utility hypothesis copyright 1992 by the econometric society

risk aversion in the theory of expected utility with rank dependent probabilities expected utility with rank dependent probability theory is a model of decision making under risk where the preference relations on the set of probability distributions is represented by the mathematical expectation of a utility function with respect to a transformation of the probability distributions on the set of outcomes this paper defines based on g teaux differentiability measures of risk aversion for such preferences which characterize the relation more risk averse and applies these measures to the analysis of unconditional and conditional portfolio choice problems

uncertainty efficiency and incentive compatibility ambiguity solves the conflict between efficiency and incentive compatibility abstract a fundamental result of modern economics is the conflict between efficiency and incentive compatibility that is the fact that some pareto optimal efficient allocations are not incentive compatible this conflict has generated a huge literature which almost always assumes that individuals are expected utility maximizers what happens if they have other kind of preferences is there any preference where this conflict does not exist can we characterize those preferences we show that in an economy where individuals have complete transitive continuous and monotonic preferences every efficient allocation is incentive compatible if and only if individuals have maximin preferences

time to change what to sow risk preferences and technology adoption decisions of cotton farmers in china this paper examines the role of individual risk attitudes in the decision to adopt a new form of agricultural biotechnology in china i conducted a survey and a field experiment to elicit the risk preferences of chinese farmers who faced the decision of whether to adopt genetically modified bt cotton a decade ago in my analysis i expand the measurement of risk preferences beyond expected utility theory to incorporate prospect theory i find that farmers who are more risk averse or more loss averse adopt bt cotton later farmers who overweight small probabilities adopt bt cotton earlier

why do low educated workers invest less in further training several studies document that low educated workers participate less often in further training than high educated workers this article investigates two possible explanations low educated workers invest less in training because of 1 the lower economic returns to these investments or 2 their lower willingness to participate in training controlling for unobserved heterogeneity we find that the economic returns to training for low educated workers are positive and not significantly different from those for high educated workers however low educated workers are significantly less willing to participate in training we show that this lesser willingness to train is driven by economic preferences and personality traits

optimism and pessimism in games this paper considers the impact of ambiguity in strategic situations it extends the earlier literature by allowing for optimistic responses to ambiguity ambiguity is modelled by ceu preferences we propose a new solution concept for players who may express ambiguitypreference then we study comparative statics of changes in ambiguity attitude in games with strategic complements this gives a precise statement of the impact of ambiguity on economic behaviour

risk sharing in the small and in the large abstract this paper analyzes risk sharing in economies with no aggregate uncertainty when agents have non convex preferences in particular agents need not be globally risk averse or uncertainty averse in the sense of schmeidler 1989 we identify a behavioral condition under which betting is inefficient i e every pareto efficient allocation provides full insurance and conversely if and only if agents supporting probabilities defined as in rigotti et al 2008 have a non empty intersection our condition is consistent with empirical and experimental evidence documenting violations of convexity in either outcomes or utilities our results show that the connection between speculative betting and inconsistent beliefs does not depend upon global notions of risk or ambiguity aversion

decision theory under ambiguity we review recent advances in the field of decision making under uncertainty or ambiguity we start with a presentation of the general approach to a decision problem under uncertainty as well as the standard bayesian treatment and issues with this treatment we present more general approaches choquet expected utility maximin expected utility smooth ambiguity and so forth that have been developed in the literature under the name of models of ambiguity sensitive preferences we draw a distinction between fully subjective models and models incorporating explicitly some information we review definitions and characterizations of ambiguity aversion in these models we mention the challenges posed by some of the models presented we end with a review of part of the experimental literature and applications of these models to economic settings

subjective beliefs and ex ante trade we study a definition of subjective beliefs applicable to preferences that allow for the perception of ambiguity and provide a characterization of such beliefs in terms of market behavior using this definition we derive necessary and sufficient conditions for the efficiency of ex ante trade and show that these conditions follow from the fundamental welfare theorems when aggregate uncertainty is absent our results show that full insurance is efficient if and only if agents share some common subjective beliefs our results hold for a general class of convex preferences which contains many functional forms used in applications involving ambiguity and ambiguity aversion we show how our results can be articulated in the language of these functional forms confirming results existing in the literature generating new results and providing a useful tool for applications

ambiguity aversion in the long run to disagree we must also agree abstract we consider an economy populated by smooth ambiguity averse agents with complete markets of securities contingent to economic scenarios where bankruptcy is permitted but there is a penalty for it we show that if agents posterior belief reductions given by their average probabilistic beliefs do not become homogeneous then an equilibrium does not exist it is worth noting that our main result does not imply any convergence of ambiguity perception or even the attitudes towards it in this way complete markets with default and punishment allow for ambiguity aversion in the long run and the agents can disagree on their ambiguity perception but they must agree on their expected beliefs

a definition of uncertainty aversion a definition of uncertainty or ambiguity aversion is proposed it is argued that the definition is well suited to modelling within the savage as opposed to anscombe and aumann domain of acts the defined property of uncertainty aversion has intuitive empirical content behaves well in specific models of preference multiple priors and choquet expected utility and is tractable tractability is established through use of a novel notion of differentiability for utility functions called eventwise differentiability

when does aggregation reduce risk aversion we study the problem of risk sharing within a household or syndicate a household shares risky prospects using a social welfare functional we characterize the social welfare functionals such that the household is collectively less risk averse than each member and satisfies the pareto principle and an invariance axiom we single out the sum of certainty equivalents as the unique member of this family which is quasiconcave over riskless allocations

policy appraisal and the structure of protection in a low income developing country problems of measurement and evaluation in burundi the article provides estimates of the structure of nominal and effective tariffs and the tariff equivalents of a set of quantitative import restrictions for burundi a low income data deficient developing country it carefully indicates the assumptions and limitations of the analysis the overall conclusion of the article is that not much significance can be attached to the estimates in a cardinal sense nevertheless recommendations about altering the structure of relative incentives can be justified where these are directed at increasing transparency and uniformity

financial market structures revealed by pricing rules efficient complete markets are prevalent abstract it is well known that when an arbitrage free financial market is incomplete or has tradable financial assets with frictions there must be multiple risk neutral probability measures the main motivation for the present study is to elucidate what type of market structure usually emerges from pricing rules first we obtain that finitely generated pricing rules characterized by polytopes of probabilities capture the class of all finite arbitrage free financial markets that are potentially incomplete or subject to frictions affecting tradable assets next we provide a novel characterization of efficient securities and introduce related notions of market completeness that underlies pricing rules our main result shows that the class of efficient complete markets with bid ask spreads is the prevalent case revealed by finitely generated pricing rules

efficient allocations under ambiguity abstract important implications of the expected utility hypothesis and risk aversion are that if agents have the same probability belief then consumption plans in every efficient allocation of resources under uncertainty are comonotone with the aggregate endowment and if their beliefs are concordant then the consumption plans are measurable with respect to the aggregate endowment we study these two properties of efficient allocations for models of preferences that exhibit ambiguity aversion using the concept of conditional beliefs which we introduce in this paper we provide characterizations of such conditional beliefs for the standard models of preferences used in applications

estimating the welfare effects of voluntary export restraints and tariffs an application to nonleather footwear in the uk 1986 estimating the welfare effects of voluntary export restraints and tariffs an application to nonleather footwear in the uk applied economics vol 18 no 10 pp 1065 1083