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We review the experimental evidence on risk aversion in controlled laboratory settings. We review the strengths and weaknesses of alternative elicitation procedures, the strengths and weaknesses of alternative estimation procedures, and finally the effect of controlling for risk attitudes on inferences in experiments.

Hypothesis tests for dominance in income distributions has received considerable attention in recent literature. See, for example, Barrett and Donald (2003a, b), Davidson and Duclos (2000) and references therein. Such tests are useful for assessing progress towards eliminating poverty and for evaluating the effectiveness of various policy initiatives directed towards welfare improvement. To date the focus in the literature has been on sampling theory tests. Such tests can be set up in various ways, with dominance as the null or alternative hypothesis, and with dominance in either direction (X dominates Y or Y dominates X). The result of a test is expressed as rejection of, or failure to reject, a null hypothesis. In this paper, we develop and apply Bayesian methods of inference to problems of Lorenz and stochastic dominance. The result from a comparison of two income distributions is reported in terms of the posterior probabilities for each of the three possible outcomes: (a) X dominates Y, (b) Y dominates X, and (c) neither X nor Y is dominant. Reporting results about uncertain outcomes in terms of probabilities has the advantage of being more informative than a simple reject/do-not-reject outcome. Whether a probability is sufficiently high or low for a policy maker to take a particular action is then a decision for that policy maker.

The methodology is applied to data for Canada from the Family Expenditure Survey for the years 1978 and 1986. We assess the likelihood of dominance from one time period to the next. Two alternative assumptions are made about the income distributions – Dagum and Singh-Maddala – and in each case the posterior probability of dominance is given by the proportion of times a relevant parameter inequality is satisfied by the posterior observations generated by Markov chain Monte Carlo.

This study empirically investigates the difference in employment status between marriage immigrants and native women in Taiwan based on a combined dataset from the 2003 Survey of Foreign and Mainland Spouses’ Life Status and 2003 Women’s Marriage, Fertility and Employment Survey. The conceptual framework is based on the family labor supply model, the human and social capital theories, and the immigrant assimilation theory. From the Probit model of the employment probability, our findings indicate that family background variables, including the presence of small children and husbands’ characteristics, play fairly significant roles in determining the employment probability of marriage immigrants. As for native women, human capital variables such as schooling and age are the most significant factors affecting their employment probability, while husbands’ characteristics play a less important role in this respect. The finding that the employment probability of foreign spouses rises rapidly with the number of years that have elapsed since migration may confirm the employment assimilation for marriage immigrants. This study further applies the nonlinear decomposition analysis developed in the work of Yun (2004) to examine the gap in employment probability between native women and foreign spouses in Taiwan. Our findings show that the employment probability differentials are mostly due to the difference in coefficients and that the effects of the two age variables play dominant roles. The difference in coefficients, in sum, contributes to increasing the gap of employment probability, while the difference in characteristics, in sum, tends to reduce the employment probability differentials.

This chapter documents an exchange between Leonard Savage, founder of the subjective probability approach to decision-making, and Karl Popper, advocate of the so-called propensity approach to probability, of which there is no knowledge in the literature on probability theory. Early in 1958, just after being informally tested by Daniel Ellsberg with a test of consistency in decision-making processes that originated the so-called Ellsberg Paradox, Savage was made aware that a similar argument had been put forward by Popper. Popper found it paradoxical that two apparently similar events should be attributed the same subjective probability even though evidence supporting judgment in one case was different than in the other case. On this ground, Popper rejected the subjective probability approach. Inspection of the Savage Papers archived at Yale University Library makes it possible to document Savage’s reaction to Popper, of which there is no evidence in his published writings. Savage wrote to Popper denying that his criticism had paradoxical content and a brief exchange followed. The chapter shows that while Savage was unconvinced by Popper’s argument he was not hostile to an axiomatically founded generalization of his theory.

The author presents new estimates of the probability weighting functions found in rank-dependent theories of choice under risk. These estimates are unusual in two senses. First, they are free of functional form assumptions about both utility and weighting functions, and they are entirely based on binary discrete choices and not on matching or valuation tasks, though they depend on assumptions concerning the nature of probabilistic choice under risk. Second, estimated weighting functions contradict widely held priors of an inverse-s shape with fixed point well in the interior of the (0,1) interval: Instead the author usually finds populations dominated by “optimists” who uniformly overweight best outcomes in risky options. The choice pairs used here mostly do not provoke similarity-based simplifications. In a third experiment, the author shows that the presence of choice pairs that provoke similarity-based computational shortcuts does indeed flatten estimated probability weighting functions.

In this study, we ask whether economic factors that can be directly manipulated by public policy have important effects on the probability that women experience long-lasting unions. Using data from the 1979 National Longitudinal Survey of Youth, we estimate a five-stage sequential choice model for women's transitions between single with no prior unions, cohabiting, first-married, re-single (divorced or separated), and remarried. We control for expected income tax burdens, Aid to Families with Dependent Children (AFDC) or Temporary Assistance for Needy Families (TANF) benefits, Medicaid expenditures, and parameters of state divorce laws, along with an array of demographic, family background, and market factors. We simulate women's sequences of transitions from age 18 to 48 and use the simulated outcomes to predict the probability that a woman with given characteristics (a) forms a first union by age 24 and maintains the union for at least 12 years, and (b) forms a second union by age 36 and maintains it for at least 12 years. While non-policy factors such as race and schooling prove to have important effects on the predicted probabilities of long-term unions, the policy factors have small and/or imprecisely estimated effects; in short, we fail to identify policy mechanisms that could potentially be used to incentivize long-term unions.

The Austrian economist Ludwig Lachmann claimed that Keynes was a lifelong subjectivist. To evaluate this, we start by distinguishing Keynes’ writings on probability theory from his writings on economics. In the General Theory (1936), Keynes’ treatment of expectations provides the basis for Lachmann’s view that Keynes was a subjectivist at heart. In his Treatise on Probability (1921), Keynes refers explicitly to the subjectivism–objectivism divide in probability theory and pins his colors to the objectivist mast. In this essay, we present the objectivist slant in Keynes’ earlier writings on probability theory. Thereafter, we evaluate the criteria Lachmann employed to cast Keynes as a subjectivist.