Utility of gambling I: entropy modified linear weighted utility

Behavioral axioms about preference orderings among gambles and their joint receipt lead to numerical representations consisting of a subjective utility term plus a term depending upon the events and the subjective weights. The results here are for uncertain alternatives, in much the same sense as Savage’s usage. Several open problems are described. Results for the risky case are in a second article.      

Risk Attitudes of Children and Adults: Choices Over Small and Large Probability Gains and Losses

In this paper we examine how risk attitudes change with age. We present participants from age 5 to 64 with choices between simple gambles and the expected value of the gambles. The gambles are over both gains and losses, and vary in the probability of the non-zero payoff. Surprisingly, we find that many participants are risk seeking when faced with high-probability prospects over gains and risk averse when faced with small-probability prospects. Over losses we find the exact opposite. Children's choices are consistent with the underweighting of low-probability events and the overweighting of high-probability ones. This tendency diminishes with age, and on average adults appear to use the objective probability when evaluating risky prospects.     

Consumer Capital as the Source of Happiness: The Missing Economic Theory Underlying the Income-Happiness Paradox

Self-reported happiness does not generally increase with rising income, as established by Richard Easterlin. We argue that the current debate in economics about the income-happiness paradox has paid too little attention to the theoretical foundation of the expected positive relation between income and happiness, seeking an empirical resolution through better data and more elaborate estimating equations instead. We return to the history of economics and revisit the contributions of Irving Fisher and Kenneth Boulding for the missing economic theory that underlies the income-happiness paradox. According to both Fisher and Boulding, “consumer capital” is the ultimate source of welfare, whereby consumer capital is defined as an accumulated stock of tangible and intangible instruments that yield a stream of services over their useful life. In the view of Fisher and Boulding, it is the utilization of this capital stock that renders happiness to individuals. Moreover, income that pays for the goods of consumption can be a “bad,” reflecting the cost of maintaining the consumer capital stock. Therefore, Fisher and Boulding’s insights bring a new perspective to the Easterlin paradox, showing that the empirical finding that rising income contributes only little, if anything, to levels of happiness has been overemphasized at the expense of the theoretically more relevant relation between consumer capital and happiness, and the exact role of income therein.     

Forecasting risk attitudes: An experimental study using actual and forecast gamble choices

We develop and evaluate a simple gamble-choice task to measure attitudes toward risk, and apply this measure to examine differences in risk attitudes of male and female university students. In addition, we examine stereotyping by asking whether a person's sex is read as a signal of risk preference. Subjects choose which of five 50/50 gambles they wish to play. The gambles include one sure thing; the remaining four increase (linearly) in expected payoff and risk. Each subject also is asked to guess which of the five gambles each of the other subjects chose, and is paid for correct guesses. The experiment is conducted under three different frames: an abstract frame where the two highest-payoff gambles carry the possibility of losses, an abstract frame with no losses, and an investment frame that mirrors the payoff structure of the former. We find that women are significantly more risk averse than men in all three settings, and predictions of both women and men tend to confirm this difference. While average guesses reflect the average difference in choices, only 27 percent of guesses are accurate, which is slightly higher than chance.     

Giffen behavior independent of the wealth level

We demonstrate that a well-behaved utility function can generate Giffen behavior, where “well-behaved” means that its indifference curves are smooth, convex, and closed in a commodity space; the resulting demand function of each good is differentiable with respect to prices and income. Moreover, we show that Giffen behavior is compatible with any level of utility and an arbitrarily low share of income spent on the inferior good. This contrasts sharply with the common view that the Giffen paradox tends to occur when households’ wealth levels are low. Comments from Murray C. Kemp, Binh Tran-Nam, Ngo Van Long, Masao Oda, Noritsugu Nakanishi, and Chiaki Hara have greatly improved the paper. We have also benefited from discussions with Koichi Hamada, Satya Das, Takashi Kamihigashi, Tomoyuki Kamo, Toru Kikuchi, Katsufumi Fukuda, Yu-chin Chen, Fahad Khalil, Takeshi Nakatani, Kazuo Nishimura, Ken-Ichi Shimomura, and Stephen J. Turnovsky. We thank the anonymous referee for his/her helpful comments. Iwasa would like to acknowledge financial support from Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. Professor Koji Shimomura passed away on February 24, 2007. This paper was completed after his untimely death.     

The outsourcing productivity paradox: total outsourcing, organisational innovation, and long run productivity growth

A growing number of empirical studies find a relationship between the outsourcing of activities and a long term loss of firm productivity growth. The paper addresses this outsourcing productivity paradox by examining the connection between total outsourcing and organisational innovation. We present a model of organisational innovation in which managers raise productive efficiency by identifying organisational architectures that more effectively integrate value-adding activities and administrative routines. As part of this process, managers can internally or externally source an activity. Simulations of the model show that large scale outsourcing restricts the scope for future organisational innovation, leading to lower productivity growth. The findings accord with the empirical data and provide a salutary warning for managers and policy-makers about the long term implications of total outsourcing.

Deregulation,news releases,and price discovery

We hypothesize that the firm’s regulatory environment influences the sensitivity of its equity value to information. Using intraday stock price data of utilities operating in differing regulatory environments we test for systematic differences between the responsiveness of stock prices of utility firms operating in deregulated and regulated environments to a common information set. Our findings reveal sharp differences in responses, with those of utilities operating in deregulated environments the strongest, and the responses of utilities in highly regulated environments the weakest. While the evidence supports our hypothesis, in a broader sense, the evidence suggests that deregulation aids in the process of price discovery. We also find evidence that suggests that deregulation, per se, does not lead to higher stock price volatility.      

有限理性与自我主体意识

经济学界至今还没有对有限理性的成因找到一个公认的正确答案.通过实验,本文证明了经济主体的有限理性不是由于人脑计算能力的约束,也不是由于道德或社会规范的约束,而是因为受到其不愿尊重客体的自我主体意识的影响.本文还证实,自我主体意识是禀赋效应、现状偏爱现象、沉没成本谬误、占便宜悖论、Ellsberg悖论和分离效应等异常现象产生的真正原因.     

Choice proliferation,simplicity seeking,and asset allocation

In settings such as investing for retirement or choosing a drug plan, individuals typically face a large number of options. In this paper, we analyze how the size of the choice set influences which alternative is selected. We present both laboratory experiments and field data that suggest larger choice sets induce a stronger preference for simple, easy-to-understand options. The first experiment demonstrates that, in seeming violation of the weak axiom of revealed preference, subjects are more likely to select a given sure bet over non-degenerate gambles when choosing from a set of 11 options than when choosing from a subset of 3. The second experiment clarifies that large choice sets induce a preference for simpler, rather than less risky, options. Lastly, using records of more than 500,000 employees from 638 institutions, we demonstrate that the presence of more funds in an individual's 401(k) plan is associated with a greater allocation to money market and bond funds at the expense of equity funds.     

Differentiable von Neumann-Morgenstern utility

Summary. Differentiability is a convenient property of von Neumann-Morgenstern utility functions which is almost always imposed but has not been translated into behavioral terms. In applications, expected utility is usually maximized subject to a constraint, and the maximization is carried out by differentiating the utility function. This paper presents two sets of necessary and sufficient conditions for a risk averse von Neumann-Morgenstern utility function to be differentiable. The first of them is formulated in terms of the equivalent risk premia of small gambles. It says, in brief, that the equivalent risk premium is of a smaller order of magnitude than the risk itself, as measured by the expectation of the absolute value of the risk. The second set of necessary and sufficient conditions is formulated in terms of the probability premium of small lotteries. It says, essentially, that the probability premium for small binary lotteries goes to zero as the size of the lottery goes to zero. Received: May 11, 1997; revised version: May 14, 1998     

GAMBLING WITH TAX DOLLARS

Municipalities often spend money in the hopes of generating new tax revenue. Because the estimated increase in tax revenues is uncertain, these policies are essentially gambles with tax dollars. This paper shows that it is possible for a welfare-maximizing government to exhibit risk-loving behavior even though individual taxpayers are risk-averse. This risk-loving behavior may occur when the government has the option to provide an indivisible public good, such as a park. Interestingly, the poorest and wealthiest municipalities do not find gambles optimal. For communities that find gambles optimal, both the provision of the public good and tax rates are affected.     

Playing the wrong game: An experimental analysis of relational complexity and strategic misrepresentation

It has been suggested that players often produce simplified and/or misspecified mental models of strategic decisions [Kreps, D., 1990. Game Theory and Economic Modeling. Oxford Univ. Press, Oxford]. We submit that the relational structure of players' preferences in a game is a source of cognitive complexity, and may be an important driver of such simplifications. We provide a classification of order structures in two-person games based on the properties of monotonicity and projectivity, and present experiments in which subjects construct representations of games of different relational complexity and subsequently play the games according to these representations. Experimental results suggest that relational complexity matters. More complex games are harder to represent, and this difficulty seems correlated with short term memory capacity. In addition, most erroneous representations are simpler than the correct ones. Finally, subjects who misrepresent the games behave consistently with such representations, suggesting that in many strategic settings individuals may act optimally on the ground of simplified and mistaken premises.     

Strength of preference and cardinal utility

Summary. This paper provides simpler and more general preference foundations for difference representations than known before and shows how to obtain cardinal utility from those difference representations. In addition, this paper unifies all earlier derivations of cardinal utility by showing that they are implied as direct corollaries.Received: 9 November 2002, Revised: 27 December 2004, JEL Classification Numbers: C6.The author particularly thanks Peter P. Wakker and an anonymous referee for many helpful comments and suggestions. The author also thanks Han Bleichrodt and Horst Zank. The paper was partly written during a visit at the Kellogg School of Management, Northwestern University. The author thanks the Dutch Science Foundation NWO for financial support under grant 425-11-003.     

Ambiguity aversion among student subjects: the role of probability interval and emotional parameters

In the literature on decision-making under uncertainty, it has been shown that decision-makers tend to prefer taking gambles with known-risk probabilities (pure risk) over equivalent gambles with ambiguous probabilities. This article contributes to the ongoing discussion in the literature on cognitive and non-cognitive covariates of ambiguity aversion. Through a series of experiments, it finds that subjects are more ambiguity-averse to prospects with wide probability intervals than to an equivalent prospect with narrow intervals, and that subjects’ inherent trust, happiness and level of optimism affect the level of ambiguity aversion.     

Riskiness for sets of gambles

Aumann–Serrano (J Polit Econ 116:810–836, 2008) and Foster–Hart (J Polit Econ 117:785–814, 2009) suggest two new riskiness measures, each of which enables one to elicit a complete and objective ranking of gambles according to their riskiness. These riskiness measures were created with a risky world in mind, but not an uncertain one. We apply similar arguments to models of decision under uncertainty and develop complete and objective rankings of sets of gambles, which arise naturally in many such models. Clearly, these results extend the previous riskiness measures, and they have a natural interpretation in terms of those measures even when uncertainty does play a significant role.     

Non-linear adjustment of real wages,employment and output in the UK

We employ the Brock, Dechert and Scheinkman statistic to investigate non-linearity in conditional mean in UK real wages, employment and output, and to fit threshould regression models to the series. The latter porvide reasonable representations for thenon-lineraity in real wages and output but the residuals from the threshold autoregressive model for employment still contain a non-linear component. In a forecast comparison the TAR models performed better than simple autoregressions. Using the lagged share of wages as an error-correction term we find evidence that all three series respond asymmetrically to lagged changes in wage share and other variables. Fore-casts of real wages and employment derived from these models were superior to those derived from standard, symmetric, ECMs.     

Trade distance functions and the derivation of inverse demand for imports

This article introduces a new representation of trade preferences termed as the trade distance function, which measures the maximum amount by which import quantities must be deflated or inflated to reach the indifference surface. The properties of this function are discussed and employed to derive systems of inverse demand for imported goods. We illustrate its usefulness by proposing two new parametric forms of trade distance functions. While the trade distance function directly yields Hicksian inverse demand functions of imports, they usually lack closed-form representations in terms of observable variables. This problem, however, need not hinder estimation and could be solved by using the numerical inversion estimation method. Results generally indicate that the suggested modelling and estimation methods are operationally, implying that the trade distance function approach is a promising tool of the empirical analysis of import demands subjected to tight theoretical conditions.     

The Endowment Effect and Expected Utility

The endowment effect, which is well documented in the contingent valuation literature, alters people's preferences according to a reference point established in an elicitation question. In particular, the utility that people place on a bundle is both a positive function of the quantities of the goods comprising the bundle, and a negative function of any loss (real or hypothetical) that the elicitation question asks them to incur. Biases such as this have lead some to reject the contingent valuation method as a means of quantifying costs and benefits in favour of other methods of preference elicitation such as standard gambles. But, most preference elicitation methods used by economists require people to express their preferences for one good in terms of their willingness to forego some of another good. Consequently, it is reasonable to expect that, and prudent to check whether, an endowment effect is also evident in other methods of preference elicitation such as von Neumann-Morgenstern's standard gambles. Internal inconsistencies in the standard gamble method from the experimental economics literature and from a study into the value of non-fatal road injuries are shown to be evidence that an endowment effect is also at work in standard gambles.     

Marginal risk aversion and preferences in a betting market

An individual's behavioural attitudes toward variance and non-symmetry in the payoff distributions of pari-mutuel gambles are empirically examined using the von Neumann - Morgenstern expected utility of wealth paradigm. Preferences over payoff distributions for a representative bettor are estimated from observed payoffs at a greyhound racetrack. The results indicate that the representative bettor exhibits increasing absolute risk aversion and, given that the representative bettor is locally non-satiated with regard to wealth, exhibits preference for variance and aversion to positive skewness in the payoff distributions of the gambles examined.     

Experienced versus decision utility: large-scale comparison for income–leisure preferences*

Subjective well-being (SWB) data are increasingly used to perform welfare analysis. Interpreted as “experienced utility”, it has recently been compared to “decision utility” using small-scale experiments most often based on stated preferences. We transpose this comparison to the framework of non-experimental and large-scale data commonly used for policy analysis, focusing on the income–leisure domain where redistributive policies operate. Using the British Household Panel Survey, we suggest a “deviation” measure, which is simply the difference between actual working hours and SWB-maximizing hours. We show that about three-quarters of individuals make decisions that are not inconsistent with maximizing their SWB. We discuss the potential channels that explain the lack of optimization when deviations are significantly large. We find proxies for a number of individual and external constraints, and show that constraints alone can explain more than half of the deviations. In our context, deviations partly reflect the inability of the revealed preference approach to account for labor market rigidities, so the actual and SWB-maximizing hours should be used in a complementary manner. The suggested approach based on our deviation metric could help identify labor market frictions.