scispace - formally typeset
Search or ask a question

Showing papers on "Revealed preference published in 2018"


Journal ArticleDOI
TL;DR: The article uses a tool from numerical linear algebra to measure the central tendency of worker flows, which is closely related to the ranking of firms revealed by workers' choices, to suggest that compensating differentials account for over half of the firm component of the variance of earnings.
Abstract: This article estimates workers' preferences for firms by studying the structure of employer-to-employer transitions in U.S. administrative data. The article uses a tool from numerical linear algebra to measure the central tendency of worker flows, which is closely related to the ranking of firms revealed by workers' choices. There is evidence for compensating differentials when workers systematically move to lower-paying firms in a way that cannot be accounted for by layoffs or differences in recruiting intensity. The estimates suggest that compensating differentials account for over half of the firm component of the variance of earnings.

168 citations


Journal ArticleDOI
TL;DR: In this paper, revealed preference theory for the equity premium around macroeconomic announcements is developed. But the authors focus on the stock market and do not consider the effect of macroeconomic news on the expected utility of stocks.
Abstract: This paper develops a revealed preference theory for the equity premium around macroeconomic announcements. Stock returns realized around pre‐scheduled macroeconomic announcements, such as the employment report and the FOMC statements, account for 55% of the market equity premium. We provide a characterization theorem for the set of intertemporal preferences that generates a nonnegative announcement premium. Our theory establishes that the announcement premium identifies a significant deviation from time‐separable expected utility and provides asset‐market‐based evidence for a large class of non‐expected utility models. We also provide conditions under which asset prices may rise prior to some macroeconomic announcements and exhibit a pre‐announcement drift.

109 citations


Journal ArticleDOI
Abstract: Many decisions of individuals involve a combination of internal preferences and mental processes related to cognitive ability. As Frederick (2005) argued in this journal, "there is no good reason for ignoring the possibility that general intelligence or various more specific cognitive abilities are important causal determinants of decision making." Since then, a number of empirical studies have focused on the relationship between cognitive ability and decision-making in different contexts. This paper will focus on the relationship between cognitive ability and decision-making under risk and uncertainty. Taken as a whole, this research indicates that cognitive ability is associated with risk-taking behavior in various contexts and life domains, including incentivized choices between lotteries in controlled environments, behavior in nonexperimental settings, and self-reported tendency to take risks. We begin by clarifying some important distinctions between concepts and measurement of risk preference and cognitive ability. In particular, complexity and possible confusions arise because observed measures of risk preference and cognitive ability are used to represent the latent characteristics of these concepts. We discuss the substantial (and somewhat implausible) range of assumptions that need to be satisfied in order to be able to interpret a correlation between measures of risk preference and cognitive ability as a relationship between latent risk preference and latent cognitive ability. Drawing causal inferences from such relationships raises additional challenges. We go on to argue that it is nevertheless important and valuable to study whether cognitive ability is related to measured risk preference (see also Dohmen, Falk, Huffman, and Sunde 2010). Risk preference is typically measured by risky behavior (actual or self-reported). If risky behavior varies systematically with cognitive ability, this may reinforce or counteract the impact of cognitive ability on life outcomes, depending on the nature of the correlation. If there is a relationship, it also becomes important to control for cognitive ability when relating life outcomes to standard revealed preference measures of risk preference. If cognitive ability has a causal impact on measured risk preference, it is important to understand the mechanism, and some intriguing policy implications arise. We then take stock of what is known empirically on the connections between cognitive ability and measured risk preferences, looking at studies using real-world risky behavior, experimental measures of risky choice, and self-reported measures of willingness to take risks. One pattern that emerges frequently in these studies is that cognitive ability tends to be positively correlated with avoidance of harmful risky situations, but it tends to be negatively correlated with risk aversion in advantageous situations. This suggests that the relationship between cognitive ability and risk taking has a reinforcing effect on economic outcomes. There is also intriguing emerging evidence that measured risk preference is particularly strongly related to certain facets of cognitive ability, those that facilitate quantitative problem solving, with implications for understanding mechanisms and possibly for better targeting policy interventions. We conclude by discussing perspectives for future research, in particular the scope for the development of richer sets of elicitation instruments and measurement across a wider range of concepts. We also consider progress in neuroscience, but conclude that at present that field still seems relatively far from allowing definitive conclusions about latent risk preference and cognitive ability. Nevertheless, the existing empirical evidence suggests that interventions to influence cognitive ability, should they be possible, might have spillovers on risky choice.

76 citations


Journal ArticleDOI
TL;DR: A recovery approach is advocated that is based on measures of the incompatibility between the revealed preference ranking implied by choices and the ranking induced by the considered parametric preferences and its applicability for misspecification measurement and model selection is demonstrated.
Abstract: Revealed preference theory is brought to bear on the problem of recovering approximate parametric preferences from consistent and inconsistent consumer choices. We propose measures of the incompati...

54 citations


Journal ArticleDOI
TL;DR: This article examined the income elasticity of the value of a statistical life based on international stated preference studies and found that the elasticity is between 0.94 and 1.05 for the more affluent countries and between 1.55 and 2.0 for lower income nations.
Abstract: Examination of estimates of the income elasticity of the value of a statistical life based on international stated preference studies yields an average between 0.94 and 1.05 overall and 0.65 and 0.80 after controlling for covariates. Quantile regression estimates indicate that the income elasticity is about 0.55 for more affluent countries and 1.0 for lower income nations, i.e., those countries that have estimates of the value of a statistical life below 3212. The estimates distinguish the values of the income elasticity across country either by income level or by the value of a statistical life. These elasticities are similar to those found in revealed preference labor market studies. The estimates are robust, controlling for possible sample selection bias and the influence of covariates, such as the type of risk.

42 citations


Journal ArticleDOI
05 Oct 2018-Science
TL;DR: The results suggest that education enhances the quality of economic decision-making as measured with decision problems and measures economic rationality 4 years after the intervention, which are derived from revealed preference theory.
Abstract: Schooling rewards people with labor market returns and nonpecuniary benefits in other realms of life. However, there is no experimental evidence showing that education interventions improve individual economic rationality. We examine this hypothesis by studying a randomized 1-year financial support program for education in Malawi that reduced absence and dropout rates and increased scores on a qualification exam of female secondary school students. We measure economic rationality 4 years after the intervention by using lab-in-the-field experiments to create scores of consistency with utility maximization that are derived from revealed preference theory. We find that students assigned to the intervention had higher scores of rationality. The results remain robust after controlling for changes in cognitive and noncognitive skills. Our results suggest that education enhances the quality of economic decision-making.

37 citations


Journal ArticleDOI
TL;DR: In this article, the authors compare two methods (contingent valuation and averting expenditures) to measure the demand for improved water reliability in urban Jordan, and develop a theoretical model to show that this relationship critically depends on household perceptions.

33 citations


Journal ArticleDOI
TL;DR: The authors provided a choice-theoretic explanation for each of these phenomena by means of three deferral-permitting models of decision making that are driven by preference incompleteness, undesirability and complexity constraints, respectively.
Abstract: Three reasons why decision makers may defer choice are *indecisiveness* between various feasible options, *unattractiveness* of these options, and *choice overload*. This paper provides a choice-theoretic explanation for each of these phenomena by means of three deferral-permitting models of decision making that are driven by preference incompleteness, undesirability and complexity constraints, respectively. These models feature *rational* choice deferral in the sense that whenever the individual does not defer, he chooses a most preferred feasible option. As a result, choices are always consistent with the Weak Axiom of Revealed Preference. The three models suggest novel ways in which observable data can be used to recover preferences as well as their indecisiveness, desirability and complexity components or thresholds. Several examples illustrate the relevance of these models in empirical and theoretical applications.

29 citations



Posted Content
TL;DR: In this paper, the authors develop a model of demand where consumers trade-off the utility of consumption against the disutility of expenditure, which is appropriate whenever a consumer's demand over a restricted subset of all available goods is being analyzed.
Abstract: We develop a model of demand where consumers trade-off the utility of consumption against the disutility of expenditure. This model is appropriate whenever a consumer's demand over a $\it{strict}$ subset of all available goods is being analyzed. Data sets consistent with this model are characterized by the absence of revealed preference cycles over prices. For the random utility extension of the model, we devise nonparametric statistical procedures for testing and welfare comparisons. The latter requires the development of novel tests of linear hypotheses for partially identified parameters. Our applications on national household expenditure data provide support for the model and yield informative bounds concerning welfare rankings across different prices.

20 citations


Journal ArticleDOI
TL;DR: The authors explored how changes in survey design influence the conclusions reached from discrete choice models, a topic which is of particular interest in the context of stated and revealed preference comparisons investigating potential hypothetical bias.
Abstract: This paper explores how changes in survey design influence the conclusions reached from discrete choice models, a topic which is of particular interest in the context of stated and revealed preference comparisons investigating potential hypothetical bias. We systematically test the WTP of a good with no related market value, using two standard, hypothetical stated preference data collections and an incentivized stated preference data collection, using a real donation mechanism. The investigations into the nature of hypothetical bias typically involve changes in more than just the elicitation format. Therefore, we explicitly test the importance of changes in bid range, payment vehicle, and elicitation format upon the estimated hypothetical bias, while keeping the survey context constant. Our results show that depending on the characteristics of the good in question, the choice of payment vehicle, bid range and elicitation format may affect the results. In many cases, the importance of payment vehicle itself is negligible – especially when the good in question is distant to people. The implication of our study is that caution should be applied when conducting stated and revealed preference comparisons in the context of public good with strong moral components, as even very small design decisions may influence the observed WTP disparities.

Journal ArticleDOI
TL;DR: These findings offer new insights into when pooling data sources may or may not be advisable for accurately estimating market preference parameters, including consideration of the conditions and context under which the data were generated as well as the relative balance of information between data sources.
Abstract: Pooled discrete choice models combine revealed preference (RP) data and stated preference (SP) data to exploit advantages of each. SP data is often treated with suspicion because consumers may respond differently in a hypothetical survey context than they do in the marketplace. However, models built on RP data can suffer from endogeneity bias when attributes that drive consumer choices are unobserved by the modeler and correlated with observed variables. Using a synthetic data experiment, we test the performance of pooled RP–SP models in recovering the preference parameters that generated the market data under conditions that choice modelers are likely to face, including (1) when there is potential for endogeneity problems in the RP data, such as omitted variable bias, and (2) when consumer willingness to pay for attributes may differ from the survey context to the market context. We identify situations where pooling RP and SP data does and does not mitigate each data source’s respective weaknesses. We also show that the likelihood ratio test, which has been widely used to determine whether pooling is statistically justifiable, (1) can fail to identify the case where SP context preference differences and RP endogeneity bias shift the parameter estimates of both models in the same direction and magnitude and (2) is unreliable when the product attributes are fixed within a small number of choice sets, which is typical of automotive RP data. Our findings offer new insights into when pooling data sources may or may not be advisable for accurately estimating market preference parameters, including consideration of the conditions and context under which the data were generated as well as the relative balance of information between data sources.

Journal ArticleDOI
TL;DR: The authors argue that time invariance and stationarity together imply time consistency, but the converse does not hold for non-dictatorial social preferences, and that revealed preference provides no guidance on whether social preferences should be time consistent or time invariant.

Journal ArticleDOI
TL;DR: In this paper, the feasibility of implementing high occupancy toll (HOT) lanes in a Middle Eastern country to obtain an improved understanding of such a policy and how it may affect the behavior of travelers in this region was examined.

Posted Content
TL;DR: In this article, a new statistical revealed preference (RP) framework for consumption panel data sets that allows for testing the utility maximization theory in the presence of measurement error is proposed, allowing for unrestricted heterogeneity in preferences and requiring only a centering condition on measurement error.
Abstract: A long-standing question about consumer behavior is whether individuals' observed purchase decisions satisfy the revealed preference (RP) axioms of the utility maximization theory (UMT). Researchers using survey or experimental panel data sets on prices and consumption to answer this question face the well-known problem of measurement error. We show that ignoring measurement error in the RP approach may lead to overrejection of the UMT. To solve this problem, we propose a new statistical RP framework for consumption panel data sets that allows for testing the UMT in the presence of measurement error. Our test is applicable to all consumer models that can be characterized by their first-order conditions. Our approach is nonparametric, allows for unrestricted heterogeneity in preferences, and requires only a centering condition on measurement error. We develop two applications that provide new evidence about the UMT. First, we find support in a survey data set for the dynamic and time-consistent UMT in single-individual households, in the presence of \emph{nonclassical} measurement error in consumption. In the second application, we cannot reject the static UMT in a widely used experimental data set in which measurement error in prices is assumed to be the result of price misperception due to the experimental design. The first finding stands in contrast to the conclusions drawn from the deterministic RP test of Browning (1989). The second finding reverses the conclusions drawn from the deterministic RP test of Afriat (1967) and Varian (1982).

Journal ArticleDOI
TL;DR: In this paper, a cross-nested logit (CNL) model was used to analyze the sensitivity of different policy scenarios per income level to the willingness to pay and to accept.
Abstract: This paper analyzes and compares different policy scenarios as well as discusses price elasticities and willingness to pay and to accept using revealed preference (RP) data from the French new-car market in 2014 by means of a cross-nested logit (CNL) model. We focus particularly on electric and hybrid vehicles. We use interactions between the cost (both fixed and running costs) and the household income to analyze the sensitivity towards different policy scenarios per income level. Results show that the willingness to pay and to accept obtained in our study is consistent with the real-market conditions. We also find that the most effective scenario to increase the market shares of new sold electric vehicles is that of a major technological advance such as a decrease in price due to cheaper manufacturing costs and an increase in driving range, rather than a policy-based scenario. In addition, the market segment that has more potential to increase the market shares of electric vehicle purchase is the middle-income level. In the paper, we discuss how to overcome the difficulties of working with revealed preference data, and propose multiple imputations to impute the attributes of the unchosen alternatives, by drawing from their empirical distributions.

Posted Content
TL;DR: It is argued that time invariant social preferences are often normatively and descriptively problematic, and cannot be stationary, although they may be time consistent if time invariance is abandoned.
Abstract: Recent work on collective intertemporal choice suggests that non-dictatorial social preferences are generically time inconsistent. We argue that this claim conflates time consistency with two distinct properties of preferences: stationarity and time invariance. While time invariance and stationarity together imply time consistency, the converse does not hold. Although non-dictatorial social preferences cannot be stationary, they may be time consistent if time invariance is abandoned. If individuals are discounted utilitarians, revealed preference provides no guidance on whether social preferences should be time consistent or time invariant. Nevertheless, we argue that time invariant social preferences are often normatively and descriptively problematic.

ReportDOI
TL;DR: This paper presents a two-step identification argument for a large class of quasilinear utility trading games, imputing agents' values using revealed preference based on their choices from a convex menu of expected outcomes available in equilibrium.
Abstract: This paper presents a two-step identification argument for a large class of quasilinear utility trading games, imputing agents' values using revealed preference based on their choices from a convex menu of expected outcomes available in equilibrium. This generalizes many existing two-step approaches in the auctions literature and applies to many cases for which there are no existing tools and where the econometrician may not know the precise rules of the game, such as incomplete-information bargaining settings. We also derive a methodology for settings in which agents' actions are not perfectly observed, bounding menus and agents' utilities based on features of the data that shift agents' imperfectly observed actions. We propose nonparametric value estimation procedures based on our identification results for general trading games. Our procedures can be combined with previously existing tools for handling unobserved heterogeneity and non-independent types. We apply our results to analyze efficiency and surplus division in the complex game played at wholesale used-car auctions, that of a secret reserve price auction followed by sequential bargaining between the seller and high bidder.

Journal ArticleDOI
TL;DR: This study aimed to investigate transit user mode choice in response to rapid transit service disruption in the City of Toronto, incorporating such factors as the type of disruption, stage of the passenger’s trip, weather conditions, and uncertainty of delay duration.
Abstract: Transit user behavioural response under disrupted service conditions, specifically how transit riders choose among available mode options to complete their trips, is not well understood. This study...

Journal ArticleDOI
TL;DR: In this article, the authors define the empirical conditions on prices and incomes under which transitivity of preferences has specific testable implications, and define necessary and sufficient requirements for budget sets under which consumption choices can violate SARP but not WARP.
Abstract: We define the empirical conditions on prices and incomes under which transitivityof preferences has specific testable implications. In particular, we set out necessaryand sufficient requirements for budget sets under which consumption choices canviolate SARP (Strong Axiom of Revealed Preferences) but not WARP (Weak Axiomof Revealed Preferences). As SARP extends WARP by additionally imposingtransitive preferences, this effectively defines the conditions under which transitivityis separately testable. Our findings have considerable practical relevance, as transitivityconditions are known to substantially aggravate the computational burden ofempirical revealed preference analysis. Our characterization takes the form of triangularconditions that must hold for all three-element subsets of normalized prices,and which are easy to verify in practice. We demonstrate their practical use throughtwo short empirical applications.

Posted ContentDOI
TL;DR: A new measure of deviations from expected utility, given data on economic choices under risk and uncertainty is proposed, and the correlation of the measure with demographics is also interesting, and provides new and intuitive findings on expected utility.
Abstract: We propose a new measure of deviations from expected utility, given data on economic choices under risk and uncertainty. In a revealed preference setup, and given a positive number e, we provide a characterization of the datasets whose deviation (in beliefs, utility, or perceived prices) is within e of expected utility theory. The number e can then be used as a distance to the theory. We apply our methodology to three recent large-scale experiments. Many subjects in those experiments are consistent with utility maximization, but not expected utility maximization. The correlation of our measure with demographics is also interesting, and provides new and intuitive findings on expected utility.

Journal ArticleDOI
TL;DR: The authors used both stated preference and revealed preference data to estimate willingness to pay (WTP) for shade-grown coffee as compared with conventionally grown coffee, and found that respondents with higher scores on measures of environmental attitudes and personal norms for pro-environmental behavior were willing to pay more for shade grown coffee.
Abstract: We used both stated preference and revealed preference data to estimate willingness to pay (WTP) for shade-grown coffee as compared with conventionally grown coffee. Stated preference data was collected using contingent valuation studies. Revealed preference data came from an experiment where all survey participants received a personally identifiable voucher redeemable for a free bakery item when the holder purchased a coffee. We compared estimates of mean and median WTP a price premium for shade-grown coffee from stated preference data with similar estimates from revealed preference data. We used a logit model to evaluate the effect of explanatory variables (measures of environmental attitudes, personal norms for pro-environmental behavior, and demographic variables) on respondents' WTP a price premium for shade grown coffee. Model parameters were estimated using the maximum likelihood approach. Respondents with higher scores on measures of environmental attitudes and personal norms for pro-environmental behavior were, on average, willing to pay more for shade-grown coffee. While this paper examined a specific case, purchase of shade-grown coffee, our results confirmed that stated environmental concern was a good predictor of pro-environmental behavior. We found that mean and median WTP estimates from stated preference methods were higher, but not significantly different than mean and median WTP estimates from actual purchases, indicating convergent validity between stated and realized preference methods. The majority of individuals both stated WTP a price premium and purchased shade-grown coffee at a price premium. We did, however notice some interesting behavior at the individual level where stated preferences under-predicted realized preferences at low price-premia and over-predicted realized preferences at high price premia. This article is protected by copyright. All rights reserved.

Journal ArticleDOI
TL;DR: In this article, a combined revealed preference (RP) and stated preference (SP) survey was conducted in Nanjing, China to obtain the observed attitudinal variables, including willingness to transfer, the sensitivity to time, the need for flexibility and the desire for comfort.
Abstract: Commuting by transfer in the public transit network is a green travel choice compared to private cars which should be encouraged when direct transit lines cannot take the commuters to their destinations. Therefore, transfer commuting attitudes are important for finding appropriate ways to attract more transfer commuters. Firstly, since attitudes are usually unobserved, a combined revealed preference (RP) and stated preference (SP) survey was conducted in Nanjing, China to obtain the observed attitudinal variables. Then the market segmentation approach including the factor analysis, the structural equation modelling (SEM) model and the K-means clustering method was used to identify the underlying attitudinal factors and variables and analyze the interrelationship between them. Six segments were identified by four key factors including the willingness to transfer, the sensitivity to time, the need for flexibility and the desire for comfort. The sensitivity to time is the most important factor for commuters influencing their willingness to transfer. The socio-economic features of each segment were also analyzed and compared. The result shows that socio-economic features have a great impact on the willingness to transfer. Corresponding policy and strategy implications to increase transfer commuting proportion were finally proposed.

Journal ArticleDOI
TL;DR: In this article, the impact of interdependencies created through multi-market entry on local market competition is studied, where the authors estimate a model of branch entry that explicitly allows for spillovers across markets, which include demand advantages in attracting more consumer deposits, cost advantages from economies of scale or density, or a diversication of risks.
Abstract: Local markets are often populated with multi-market rms rather than rms with no connections to outside markets. This paper studies the impact of interdependencies created through multi-market entry on local market competition. As a case study I examine the banking market, where deregulation in the early 1990s removed prior restrictions on where banks could open branches, thus encouraging banks to expand their branch networks into multiple markets. I estimate a model of branch entry that explicitly allows for spillovers across markets, which in banking include demand advantages in attracting more consumer deposits, cost advantages from economies of scale or density, or a diversication of risks. To do this I use a revealed preference approach that also deals with unobserved rm and market heterogeneity. I

Journal ArticleDOI
TL;DR: In this article, a decomposition into maximal domains of comparability is characterized and used to link optimization of incomplete preferences with maximization of local utility functions, and larger maximal domains correspond to more decisive preferences.
Abstract: I study incomplete preferences as a means to represent indecisiveness. A decomposition into maximal domains of comparability is characterized and used to link optimization of incomplete preferences with maximization of local utility functions. Larger maximal domains are shown to correspond to more decisive preferences. The decomposition can be uniquely recovered from choice data under standard assumptions. Applications to different models within decision theory are discussed.

Journal ArticleDOI
TL;DR: In this paper, the authors study the testable implications of normal demand in a two-goods setting and present the revealed preference conditions for normality of one or both goods.

Journal ArticleDOI
TL;DR: In this paper, the authors study the effect of the underlying preferences of the parents on the actual school choice decision and find that neither the husband's nor the wife's preferences prevail in the actual joint decision.

Posted Content
01 Feb 2018
TL;DR: In this article, a nonparametric revealed preference analysis of intertemporal consumption with risk is presented, where subjects allocate tokens over four commodities, consisting of consumption in two contingent states and at two time periods, subject to different budget constraints.
Abstract: This paper presents a nonparametric, revealed preference analysis of intertemporal consumption with risk. In an experimental setting, subjects allocate tokens over four commodities, consisting of consumption in two contingent states and at two time periods, subject to different budget constraints. With this data, one could test, using Afriat's Theorem and its generalizations, whether a subject's choices are consistent with utility maximization, and also utility maximization with various additional properties on the utility function. Our results broadly support a model where subjects maximize a utility function that is weakly separable across states but there is little support for weak separability across time. Our result sheds light on the source of the failure of the discounted expected utility model.

Journal ArticleDOI
TL;DR: In this paper, the authors developed a theoretical model and associated revealed preference conditions to analyze commodities with dierent degrees of diamondness, on the basis of real consumer data from the Russian Longitudinal Monitoring Survey.
Abstract: When consumers do not only care for the intrinsic consumption component of commodities but also for the value of a commodity, it can be rational to purchase products as they become more expensive. Standard revealed preference conditions are however unable to take diamond eects into account. We develop a theoretical model and the associated revealed preference conditions to analyze commodities with dierent degrees of diamondness. On the basis of real consumer data from the Russian Longitudinal Monitoring Survey, we test the empirical performance of dierent

Proceedings ArticleDOI
11 Jun 2018
TL;DR: This paper shows that EU and CEU have finite VC dimension, and are consequently learnable, and exhibits a close relationship between learnability and the underlying axioms which characterise the model.
Abstract: We study whether some of the most important models of decision-making under uncertainty are uniformly learnable, in the sense of PAC (probably approximately correct) learnability. Many studies in economics rely on Savage's model of (subjective) expected utility. The expected utility model is known to predict behavior that runs counter to how many agents actually make decisions (the contradiction usually takes the form of agents' choices in the Ellsberg paradox). As a consequence, economists have developed models of choice under uncertainty that seek to generalize the basic expected utility model. The resulting models are more general and therefore more flexible, and more prone to overfitting. The purpose of our paper is to understand this added flexibility better. We focus on the classical expected utility (EU) model, and its two most important generalizations: Choquet expected utility (CEU) and Max-min Expected Utility (MEU).Our setting involves an analyst whose task is to estimate or learn an agent's preference based on data available on the agent's choices. A model of preferences is PAC learnable if the analyst can construct a learning rule to precisely learn the agent's preference with enough data. When a model is not learnable we interpret it as the model being susceptible to overfitting. PAC learnability is known to be characterized by the model's VC dimension: thus our paper takes the form of a study of the VC dimension of economic models of choice under uncertainty. We show that EU and CEU have finite VC dimension, and are consequently learnable. Morever, the sample complexity of the former is linear, and of the latter is exponential, in the number of states of uncertainty. The MEU model is learnable when there are two states but is not learnable when there are at least three states, in which case the VC dimension is infinite. Our results also exhibit a close relationship between learnability and the underlying axioms which characterise the model.