Bibliography
§4.3 uses a nice version of power utility. %}
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| §4.3 uses a nice version of power utility. %}
Vendrik, Maarten & Geert Woltjer (2007) “Happiness and Loss Aversion: Is Utility Concave or Convex in Relative Income?,” Journal of Public Economics 91, 1423–1448. {% Seems to describe the rule of succession: when you observe m successes in n trials of a further unknown event, (m+1)/(n+1) is a good estimate of probability. %} Venn, John (1866) “The Logic of Chance.” MacMillan, New York. {% crowding-out: government subsidies seem to crowd-out private donations and charitable contributions. %} Venti, Steven F. & David A. Wise (1990) “Have IRAs Increased U.S. Saving? Evidence from Consumer Expenditure Surveys,” Quarterly Journal of Economics 105, 661–698. {% foundations of statistics: msunderstandings in health economics. %} Verdam, Mathilde G. E., Frans J. Oort, & Mirjam A. G. Sprangers (2014) “Significance, Truth and Proof of p Values: Reminders about Common Misconceptions Regarding Null Hypothesis Significance Testing,” Quality of Life Research 3, 257–265. {% %} Verhoef, Lia C.G. (1994) “The Measurement of Individual Preferences for Treatment Outcomes in Breast Cancer,” Ph.D. dissertation, Medical Department, University of Nijmegen, the Netherlands. {% utility elicitation %} Verhoef, Lia C.G., Anton F.J. de Haan, & Willem A.J. van Daal (1994) “Risk Attitude in Gambles with Years of Life: Empirical Support for Prospect Theory,” Medical Decision Making 14, 194–200. {% %} Verhoef, Lia C.G., Anton F.J. de Haan, Arne Maas, André L.M. Verbeek, & Willem A.J. van Daal (1994) “Utility Assessment for Breast Cancer Treatment Selection: Reliability and Internal Consistency of the Time Tradeoff Test and the Certainty Equivalent Method,” Institute of Radiotherapy, University of Nijmegen, Nijmegen, the Netherlands. {% utility elicitation %} Verhoef, Lia C.G., Arne Maas, Lucas J.A. Stalpers, André L.M. Verbeek, & Willem A.J. van Daal (1993) “Utility Assessment in Decision Support for Individual Patients: A Tradeoff between Feasibility and Validity,” Health Policy 17, 39–50. {% utility elicitation %} Verhoef, Lia C.G., Arne Maas, Lucas J.A. Stalpers, André L.M. Verbeek, Theo Wobbes, & Willem A.J. van Daal (1991) “The Feasibility of Additive Conjoint Measurement in Measuring Utilities in Breast Cancer Patients,” Health Policy 17, 39–50. {% utility elicitation; %} Verhoef, Lia C.G., Lucas J.A. Stalpers, André L.M. Verbeek, Theo Wobbes, & Willem A.J. van Daal (1991) “Breast-Conserving Treatment or Mastectomy in Early Breast Cancer: A Clinical Decision Analysis with Special Reference to the Risk of Local Recurrence,” Eur. J. Cancer 27, 1132–1137. {% utility elicitation %} Verhoef, Lia C.G., André L.M. Verbeek, Lucas J.A. Stalpers, & Willem A.J. van Daal (1990) “Utiliteitsmeting bij the Klinische Besluitvorming,” Nederlands Tijdschrift voor de Geneeskunde 134, 2195–2200. {% real incentives/hypothetical choice: for social preferences, it does not matter for a Krupka-Weber coordination game. %} Veselý, Štěpán (2015) “Elicitation of Normative and Fairness Judgments: Do Incentives Matter?,” Judgement and Decision Making 10, 191–197. {% %} Vesely, William E. & Dale M. Rasmuson (1984) “Uncertainties in Nuclear Probabilistic Risk Analyses,” Risk Analysis 4, 313–322. {% foundations of probability; reviewed by James Cussens (1990), in History and Philosophy of Logic 11, 116–117. %} Vickers, John M. (1988) “Chance and Structure: An Essay on the Logical Foundations of Probability.” Clarendon Press, Oxford. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value): p. 327/328 seem to write: “Furthermore, there is abundant evidence that individual decisions in situations involving risk are not always made in ways that are compatible with the assumption that the decisions are made rationally with a view to maximizing the mathematical expectation of a utility function. The purchase of tickets in lotteries, sweepstakes, and ‘numbers’ pools would imply, on such a basis, that the marginal utility of money is an increasing rather than a decreasing function of income. Such a conclusion is obviously unacceptable as a guide to social policy.” P. 328, “utilities derived in the process rather than from the end result;” P. 329 states the veil of ignorance, preceding Harsanyi and Rawls. %} Vickrey, William (1945) “Measuring Marginal Utility by Reactions to Risk,” Econometrica 13, 319–333. {% %} Vieider, Ferdinand M. (2009) “The Effect of Accountability on Loss Aversion,” Acta Psychologica 132, 96–101. {% %} Vieider, Ferdinand M. (2010) “Preference Reversals: The Impact of Truth-Revealing Monetary Incentives. A Methodological Note,” Ludwig-Maximilians-University Munich, Germany, Climate Policy Initiative, DIW Berlin, Germany. {% %} Vieider, Ferdinand M. (2011) “Separating Real Incentives and Accountability,” Experimental Economics 14, 507–518. {% %} Vieider, Ferdinand M. (2012) “Moderate Stake Variations for Risk and Uncertainty, Gains and Losses: Methodological Implications for Comparative Studies,” Economics Letters 117, 718–721. {% Use choice lists to determine CEs (certainty equivalents) of two-outcome prospects. Use RIS for real payment. Study within- and between-country differences, by doing two cities in China (Shanghai & Bejing) and two in Egypt. Find no within-country difference, but clear between-country difference. They point out that this suggests that randomization within a country, often difficult to do in intercultural studies, may not be a big problem. %} Vieider, Ferdinand M., Thorsten Chmura, Tyler Fisher, Takao Kusakawa, Peter Martinsson, Frauke M. Thompson, & Adewara Sunday (2015) “Within- versus between-Country Differences in Risk Attitudes: Implications for Cultural Comparisons,” Theory and Decision 78, 209–218. {% %} Vieider, Ferdinand M., Thorsten Chmura, & Martinsson (2014) “Risk Attitudes, Development, and Growth Macroeconomic Evidence from Experiments in 30 Countries,” working paper. {% losses from prior endowment mechanism: did this. The prior endowment, conditional on a loss question implemented for real, was equal to the maximum loss, being €20c (p. 426). Used RIS. Collected data of 2,939 subjects from 30 countries from all continents except Antarctica. They always take students. This makes the sample less representative for the world population as a whole, but makes between-country comparisons more reliable because for this purpose it is good to have little within-country heterogeneity. Various teams and the main organizer, Vieider, wrote a number of papers on it. This paper verifies construct and convergence validity (my terms) of the measurements, by studying correlations between different ways to measure things. For each subject, 44 CEs of lotteries with gains, losses, mixed, and risk and uncertainty. (I did not find if/how they control for suspicion.) They analyze the CEs of the uncertain options, capturing general uncertainty attitude. To capture ambiguity attitude, which is the difference between uncertainty and risk, they could inspect differences of CEs under uncertainty and risk. Further intospective questions about general risk attitude and other things. They find that corresponding measures, both behaviorally and introspectively, are always positively related, though sometimes not strongly. This also holds between countries (taking each country as an individual). Section 3.1, p. 428: they take unnormalized risk premium as index of risk aversion, and mention that normalizing by dividing by expected value (I: what if that is 0?; better divide by standard deviation) would not affect the results. As they will explain later (p. 446 last para of paper), this is not suited to test likelihood insensitivity (which they, unfortunately, call likelihood dependence), because to get that right you need different parameters. inverse-S: is found (p. 430 top); Section 3.3, p. 439, end of 1st para: the uncertainty attitudes are more related to introspective questions than the risk attitudes. Section 3.4, Table 3, gives correlations between the preference-based indexes, taking all countries together. It also considers many introspection-based indexes. Risk and uncertainty aversion for gains are strongly related (0.68), which is no surprise because uncertainty aversion comprises risk aversion (correlation risk & ambiguity attitude). reflection at individual level for risk: they find a positive relation between risk aversion for gains and for losses. They also find that, stronger, for uncertainty aversion (p. 440; uncertainty amplifies risk). gender differences in risk attitude: p. 443 reports more risk aversion for women and gains, but no significant result for losses. P. 443 reports more uncertainty aversion (note that this comprises risk + ambiguity) for RICH countries. P. 445 last para will state the same for risk aversion. P. 444 2nd para has nice discussion of context dependence being popular among psychologists. The finding of correlations of this paper shows that not everything is completely context dependent, but still to some degree. P. 444 3rd para has nice discussion of constructive view of preference and writes: “We thus conclude that preferences are indeed discovered and derived from an underlying preference, rather than constructed ex nihilo.” P. 445 2nd para has an, again nice, discussion of the drawback of introspective measures that they are not clearly related to decision-theory components. P. 445 last para: risk aversion is decreasing in wealth between individuals, but increasing in wealth between countries. This is a risk-income paradox. They cite preceding papers on it. %} Vieider, Ferdinand M., Mathieu Lefebvre, Ranoua Bouchouicha, Thorsten Chmura, Rustamdjan Hakimov, Michal Krawczyk, & Peter Martinsson (2015) “Common Components of Risk and Uncertainty Attitudes across Contexts and Domains: Evidence from 30 Countries,” Journal of the European Economic Association 13, 421–452. {% Comments here are on version of March 29 2012. ambiguity seeking for unlikely & ambiguity seeking for loses: they find both. N = 157 subjects from Ethiopia, students from Addis Ababa University. Measure certainty equivalents (CEs) for binary prospects, both risky and Ellsberg ambiguous, using choice lists. For gains and losses (losses from prior endowment mechanism). First risky gains, then ambiguous gains, then risky losses, then ambiguous losses. The authors prefer order effects to the cognitive difficulties for subjects if losses precede gains. The authors find the best fit for CE/X = c + s EV/X with X the maximum amount of the prospect and EV being expected value. With c > 0 and 0 < s c this means that for small EV/X, so small probabilities, CE > EV with risk/uncertainty seeking, and for large EV/X risk/uncertainty aversion. This measure relates to proportional risk/uncertainty aversion. Then from c and s they derive sensitivity (through s) and optimism (through c + s/2) the usual way. This agrees with measures in Abdellaoui et al. (2011 AER) for weighting functions under linear utility, as the authors point out in footnote 2 (version of March 29 2012). Concave utility will push c and s down for big gains as opposed to small gains. The paper, unusually, finds prevailing risk aversion, and no prevailing uncertainty aversion. It finds that increasing stakes increases ambiguity seeking for small-probability gains and large-probability losses, and more ambiguity averse for large-probability gains and small-probability losses. That is, a-insensitivity is increased. The text suggests that for gains mostly uncertainty aversion for high probabilities is increased. reflection at individual level for risk: the authors consider it, but it is hard to interpret with prevailing risk seeking for gains. The authors also consider it for ambiguity and losses, and many correlations between the various variables. decreasing ARA/increasing RRA: the authors study relative risk aversion, and find that it increases, rather than decreases, with stakes, over the whole probability range. %} Vieider, Ferdinand M., Peter Martinsson, & Haileselassie Medhin (2012) “Stake Effects on Ambiguity Attitudes for Gains and Losses,” working paper. {% Use Anscombe-Aumann model, but to each state of nature not one lottery is assigned, but a set of lotteries. This set is evaluated by a convex combination of its best and worst element. The mixture weight is an index of pessimism. It reminded me much of Jaffray (1989), although it does not refer to this. The axioms used are as usual to characterize -maxmin, dominance and independence of adding-removing intermediate ones. Considers both where is set-dependent and where it is constant. %} Vierø, Marie-Louise (2009) “Exactly what Happens after the Anscombe–Aumann Race?; Representing Preferences in Vague Environments,” Economic Theory 41, 175–212. {% %} Vierø, Marie-Louise (2012) “Contracting in Vague Environments,” American Economic Journal: Microeconomics 4, 104–130. {% %} Vijn, Pieter & Ivo W. Molenaar (1981) “Robustness Regions for Dichotomous Decisions,” Journal of Educational Statistics 6, 205–235. {% Seems to criticize/correct ideas of von Mises. %} Ville, Jean A. (1939) “Etude Critique de la Notion de Collectif.” Gauthiers-Villars, Paris. {% revealed preference %} Ville, Jean A. (1946) “Sur les Conditions d’Existence d’une Ophélimité Totale et d’un Indice du Niveau des Prix,” Annales de l’Université de Lyon, 9, Sec. A(3) 32–39. Translated into English by Peter K. Newman (1952) “The Existence-Conditions of a Total Utility Function,” Review of Economic Studies 19, 123–128. {% %} Villegas, Cesáreo (1964) “On Quantitative Probability -Algebras,” Annals of Mathematical Statistics 35, 1787–1796. {% ordering of subsets %} Villegas, Cesáreo (1967) “On Qualitative Probability,” American Mathematical Monthly 74, 661–669. {% Shows that Gorman’s (1968) famous theorem only needs connectedness and not arc-connectedness. %} Vind, Karl (1971) “The Structure of Utility Functions” and “Comment,” Review of Economic Studies 38, 113 and 115. {% %} Vind, Karl (1974) “A Note on a Four-Flagged Lemma,” Review of Economic Studies 41, 571. Vind, Karl (1990) “Additive Utility Functions and Other Special Functions in Economic Theory,” (with contributions by Birgit Grodal), Discussion paper 90–21, Institute of Economics, University of Copenhagen, Denmark. {% %} Vind, Karl (1991) “Independent Preferences,” Journal of Mathematical Economics 20, 119–135. {% %} Vind, Karl (1992) “Uncertainty,” Institute of Economics, University of Copenhagen, Copenhagen. {% A very abstract and general, so not-very-specific, extension of vNM EU, dropping transitivity and completeness. Theorems give sufficient, but apparently not necessary, conditions. %} Vind, Karl (2000) “von Neumann Morgenstern Preferences,” Journal of Mathematical Economics 33, 109–122. {% %} Vind, Karl (2003) “Independence, Additivity, Uncertainty.” With contributions by Birgit Grodal. Springer, Berlin. First version 1969. {% In personal communication I (Peter Wakker) told Ghirardato, Maccheroni, Marinacci, Siniscalchi, and Vind, shortly after appearance of the Econometrica paper of the former 4 authors in 2003, that Karl Vind had found an alternative endogenous midpoint operation before. Karl then put this into writing, shortly before he died. %} Vind, Karl (2004) “Midpoints and Biseparable Preferences,” working paper. {% Dutch book; P. 186: “The consequence of suffering a sure loss at the hands of a clever bookie is sometimes the best alernative in the long run” %} Vineberg, Susan (1997) “Dutch Books, Dutch Strategies and What They Show About Rationality,” Philosophical Studies: An International Journal for Philosophy in the Analytical Tradition 86, 185–202. {% real incentives/hypothetical choice: argue that instead of real incentives, other motives such as altruism and curiosity can be just as effective. Support it by a web experiment with no real incentives. Subjects who drop out before the end are taken to be badly motivated, and those who finish are taken to be well motivated. Then there is a usual control group of students with real incentives. They find that the well-motivated hypothetical students are not different from the incentivized, but the poorly-motivated are. To implement this idea, problem is how to get intrinsically motivated subjects. they write p. 307 2nd column 2nd para: “Our main hypothesis is that non-monetary factors like curiosity and altruism provide adequate and non-distortionary incentives.” The particular test where they show the above things is the standard Ellsberg urn, where they find things as usual. A weak point is that the study is thin, basically having a one-point observation. %} Vinogradov, Dmitri & Elena Shadrina (2013) “Non-Monetary Incentives in Online Experiments,” Economics Letters 119, 306–310. {% %} Viscusi, W. Kip (1979) “Employment Hazards: An Investigation of Market Performance.” Harvard University Press, Cambridge, MA. {% inverse-S; we perceive probability distributions as a convex mix of what the probabilities really are, and the uniform distribution. Reminiscent of Parducci’s range-frequency theory. biseparable utility %} Viscusi, W. Kip (1989) “Prospective Reference Theory: Toward an Explanantion of the Paradoxes,” Journal of Risk and Uncertainty 2, 235–264. {% paternalism/Humean-view-of-preference: last paragraph of paper (p. 108) is relevant, not only to insurance but to the whole decision theory. It points out that not only the existence of biases and deviations from rationality should be signaled but a better sense of the magnitudes of these is needed so as to mitigate these inadequacies: “These results suggest that examination of theoretical characteristics of biases in decisions resulting from irrational choices of various kinds should not be restricted to the theoretical explorations alone. We need to obtain a better sense of the magnitudes of the biases that result from flaws in decision making and to identify which biases appear to have the greatest effect in distorting individual decisions. Assessing the incidence of the market failures resulting from irrational choices under uncertainty will also identify the locus of the market failure and assist in targeting government interventions intended to alleviate these inadequacies.” Also argues (p. 107, conclusion, first phrase) that most aspects of insurance are based on probability perception: “Most aspects of risk taking and insurance-related decisions hinge on the relationship between the perceived probability by the individual and the actual risk.” %} Viscusi, W. Kip (1995) “Government Action, Biases in Risk Perception, and Insurance Decisions,” Geneva Papers in Risk and Insurance Theory 20, 93–110. {% Z&Z Finds that in aggregating different sources of info about risk, participants overweight the worst case prediction. P. 1667 calls participants “informationally risk-averse” and writes “This phenomenon is, however, independent of the shape of individual preferences and the presence of risk aversion for changes of wealth.” %} Viscusi, W. Kip (1997) “Alarmist Decisions with Divergent Risk Information,” Economic Journal 107, 1657–1670. {% inverse-S; ambiguity seeking for losses: finds ambiguity seeking for “likely” ambiguous losses, ambiguity aversion for unlikely ambiguous losses. The crossover point is at approximately .5. Complication is here that it is risk per time unit, risks per 10 years were given. Coastal North Carolina 266 business owners and managers, for risks of storm damages (risk per 10 years was given). Ambiguous probabilities were generated by conflicting expert estimates of a risk. For example, one expert estimates p = .5 and the other p = .1, etc. P. 158 points out that this way of generating ambiguity is more ‘real-world’ than urn games etc. (natural sources of ambiguity). P. 175 states explicitly that ambiguity aversion/seeking is irrational: “The findings presented in this paper suggest that the presentation of the risk as a mean will lead to more rational risk perceptions …more closely accord with a rational Bayesian learning process.” [my italics] reflection at individual level for ambiguity: only losses, so they do not consider it. %} Viscusi, W. Kip & Harrell W. Chesson (1999) “Hopes and Fears: The Conflicting Effects of Risk Ambiguity,” Theory and Decision 47, 153–178. {% %} Viscusi, W. Kip & William N. Evans (1990) “Utility Functions that Depend on Health Status: Estimates and Economic Implications,” American Economic Review 80, 353–374. {% natural sources of ambiguity: inverse-S: reanalyze data of their 1990 paper on chemical workers’ risk perceptions and decisions. Analyzed judged probabilities but also decision weights derived from decisions (so the two-stage model), finding that the decision weights depended on the stated probabilities through the usual inverse-S relationship. Their curve fit found decision weights never below 0.10 and never above 0.49, so that the inverse-S is very strong. They jointly fit decision weights and utility, with utility results being plausible. They seem to find that neo-additive weighting function fits well. %} Viscusi, W. Kip & William N. Evans (2006) “Behavioral Probabilities,” Journal of Risk and Uncertainty 32, 5–15. {% Study WTP-WTA discrepancy. Consider not only the case where an outcome changes and one pays/is paid for that change, but also the case where a probability (of health risk) changes and one pays/is paid for that change. Propose a model where loss aversion as well applies to probability level, with an increase in probability (which is unfavorable and is a loss) weighted more than the corresponding decrease. Standard reference dependence as in prospect theory cannot model the latter because they only concern changes in outcome. I think that standard reference dependence can handle it if we take a two-stage probability model with backward induction (certainty equivalent substitution), where first-stage probabilities may be 1. They find that reference dependence for outcomes is stronger than for probabilities. For adversarial probabilities it is only if they decrease, not it they increase. That is, there is an interaction. The authors can nicely rule out income effects in their large 2008-2009 national sample. %} Viscusi, W. Kip & Joel Huber (2012) “Reference-Dependent Valuations of Risk: Why Willingness-to-Accept Exceeds Willingness-to-Pay,” Journal of Risk and Uncertainty 44, 19–44. {% Participants are ambiguity averse to low probability losses. People are asked, hypothetically, if they rather move to area A or B. The areas are the same as where they live now, only due to a particular polution one kind of disease has different likelihood. About area A they receive two conflicting pieces of evidence, next the objective probability in area B that gives equivalence is established; i.e., the matching probability. There is between-subject income dependence, in that it is different for rich than for poor people. The authors consider both event-based and outcome-based (unfortunately, the authors often call the latter preference-based) ambiguity models (ambiguous outcomes vs. ambiguous probabilities), but, as they indicate in several places (e.g. p. 385 top) their data cannot distinguish between the two. P. 376 Eq. 7: take difference between a-neutral probability (my term) and matching probability as index of ambiguity aversion. Was also done by Kahn & Sarin (1988). P. 383 4th para indicates cognitive limitations underlying deviation from ambiguity neutrality, something about people paying more attention to investigation presented first without rational reason. (cognitive ability related to risk/ambiguity aversion) suspicion under ambiguity: p. 380 indicates that Ellsberg urn may reflect that subjects think that the unknown urn is manipulated against them, rather than ambiguity attitude. reflection at individual level for ambiguity: only losses, so they do not consider it. natural sources of ambiguity: several places, e.g. p. 385 last para of main text, points out that they deal with natural events, although they do not strongly plea for the importance of doing this. %} Viscusi, W. Kip & Wesley A. Magat (1992) “Bayesian Decisions with Ambiguous Belief Aversion,” Journal of Risk and Uncertainty 5, 371–387. {% If probabilistic information coming from Environmental Protection Agency is stated more vaguely then subjects get more suspicious and estimate risks higher. %} Viscusi, W. Kip, Wess A. Magat & Joel Huber (1991) “Pricing Environmental Health Risks: Survey Assessments of Risk-Risk and Risk-Dollar Trade-Offs for Chronic Bronchitis,” Journal of Environmental Economics and Management 21, 32–51. {% %} Viscusi, W. Kip, Wesley A. Magat, Alan Carlin, & Mark K. Dreyfus (1994) “Environmentally Responsible Energy Pricing,” The Energy Journal 15, 23–42. {% Estimates biases in estimates of statistical values of lifes in big international data sets and then corrects for those. %} Viscusi, W. Kip & Clayton Masterman (2017) “Anchoring Biases in International Estimates of the Value of a Statistical Life,” Journal of Risk and Uncertainty 54, 103–128. {% %} Viscusi, W. Kip & Mike J. Moore (1989) “Rates of Time Preference and Valuations of the Duration of Life,” Journal of Public Economics 38, 297–317. {% Seem to indicate a situation where ambiguous risks are preferable, however, in a complex situation with learning etc. involved. %} Viscusi, W. Kip & Charles O’Connor (1984) “Adaptive Responses to Chemical Labeling: Are Workers Bayesian Decision Makers?,” American Economic Review 74, 942–956. {% If individuals take individual risky decisions but they are in a group, then the decisions taken by the others greatly influence those decisions. gender differences in risk attitudes: no differences %} Viscusi, W. Kip, Owen R. Phillips, & Stephan Kroll (2011) “Risky Investment Decisions: How Are Individuals Influenced by Their Groups?,” Journal of Risk and Uncertainty 43, 81–106. {% Ask a sample from the general public how they think about uncertainties regarding climate change, described as: (1) imprecision and uncertainty in theories and measurement instruments; (2) disagreement between experts; (3) unknown consequences due to complexity of climate models (p. 46 2nd column 2nd para). In several places, e.g. p. 44 §1.1, the authors seem to equate ambiguity with low level of info, reflecting a common misunderstanding. Ambiguity is the distance of state of information to a probabilized state of information, and not a general index of quality of information. A state of known probability can, by increase of information, turn into a state of ambiguity. %} Visschers, Vivianne H.M. (2018) “Public Perception of Uncertainties within Climate Change Science,” Risk Analysis 38, 43–55. {% probability communication: this is exactly the survey that I searched for for many years. Although the paper focuses on communicating risk to the general public, rather than on how to explain probabilities in experiments (my main interest), it nevertheless covers studies on the latter also. The paper focusses on risks on health or technological accidents that could harm health. %} Visschers, Vivianne H.M., Ree M. Meertens, Wim W.F. Passchier, & Nanne N.K. de Vries (2009) “Probability Information in Risk Communication: A Review of the Research Literature,” Risk Analysis 29, 267–287. {% Z&Z; report data summarized from the 1987 National Medical Expenditure Survey that reveal that 26% of Medicare beneficiaries bought supplementary insurance to obtain complete coverage P. 316: “beneficiaries in good or fair health are seven percentage points more likely to purchase insurance than those in poor health.” ??? Isn’t this the opposite of adverse selection??? %} Vistnes, Jessica P. & Jessica S. Banthin (1997/98) “The Demand for Medicare Supplemental Insurance Benefits: The Role of Attitudes toward Medical Care and Risk,” Inquiry 34, 311–324. {% Marinacci wrote to me: about the article that in the 1920s dealt with nonadditive integration, the author is the famous analyst (the same who came up with the first nonmeasurable set, the Vitali lemma, the Vitali-Hahn-Saks theorem, etc.). He considered the special case of inner and outer measure on the real line, and defined a notion of integral relative to them that looked to me close to that of Choquet for general nonadditive measures. %} Vitali, Giuseppe (1925) “Sulla Definizione di Integrale delle Funzioni di una Variabile,” Annali di Matematica Pura ed Applicata 4, 111–121. {% DOI: http://dx.doi.org/10.1111/j.1539-6924.2010.01433.x. P. 7, nicely, mentions that people’s recent experience with risk “leaks” into their current pereption of objective risks. P. 7 2nd column also points out that same objective probabilities in different contexts generate different behavior, which violates the fundamental assumption of decision under risk and suggests a source preference idea, be it that the literature on source preference usually assumes that risk is one source. (violation of objective probability = one source) P. 8 l. 1, on possible applications of their work: “These issues are likely to be of central importance in the development of the next generation of financial services.” [italics added] Conclusion writes that the goal of our cognitive system is to flexibly adapt to dynamic environments, with many positive adjectives added, and then suddenly targets on classical approaches with context-independence and transitivity (apparently transitivity is also a target of their criticisms). To end with psychologists’ favorite conclusion: context-dependence (i.e., everything depends on everything). gender differences in risk: no difference %} Vlaev, Ivo, Petko Kusev, Neil Stewart, Silvio Aldrovandi, & Nick Chater (2010) “Domain Effects and Financial Risk Attitudes,” Risk Analysis 30, no. {% %} Vlek, Charles A.J. (1987) “Towards a Dynamic Structural Theory of Decision Behavior?,” Acta Psychologica 66, 225–230. {% Seems to be: decision under stress: chapter about risk management and acceptance, with sections about “protection motivation theory” and “emotional significance of risk”. %} Vlek, Charles A.J. (2004) “Environmental versus Individual Risk Taking: Perception, Decision, Behavior.” In Charles D. Spielberger (ed.) Encyclopedia of Applied Psychology, Volume 1, 825–840, Elsevier, Amsterdam. {% Many countries, the Netherlands and the UK primarily, have national risk assessment programs, for assessing risks of natural and other catastrophes. %} Vlek, Charles (2013) “How Solid Is the Dutch (and the British) National Risk Assessment? Overview and Decision-Theoretic Evaluation,” Risk Analysis 33, 948–971. {% %} Vlek, Charles A.J. & Lauri Hendrickx (1988) “Statistical Risk versus Personal Control as Conceptual Bases for Evaluating (Traffic) Safety.” In Talib Rothengatter & Rudie A. de Bruin (eds.) Road user Behavior: Theory and Research. Van Gorcum, Assen. {% Do priming experiments such as letting subjects wait with screen saver either displaying money or other things. Then let supposedly unrelated person (but in fact experimenter; there is deception everywhere in these experiments) supposedly by accident drop pencils, and measure to what extent the primed subjects help pick up the pencils; or donate supposedly to some good purpose. People primed with money less help other people and more like to stay on their own. %} Vohs, Kathleen D., Nicole L. Mead, & Miranda R. Goode (2006) “The Psychological Consequences of Money,” Science 314, 17 Nov, 1154–156. {% dynamic consistency, distinguishes preference from choice and considers what happens if there are indifferences. %} von Auer, Ludwig (1999) “Dynamic Choice Mechanisms,” Theory and Decision 46, 291–308. {% discounting normative: Strotz refers to p. 253–255 for zero discounting %} von Böhm-Bawerk, Eugen (1889) “Positive Theorie des Kapitals, Vol. II.;” 4th edn.; translated by George D. Huncke & Hans F. Sennholz (1959) “Capital and Interest, Vol. II, Positive Theory of Capital, Book IV, §I, pp. 257–289, Libertarian Press, South Holland, IL. {% %} Völckner, Franziska (2006) “An Empirical Comparison of Methods for Measuring Consumers' Willingness to Pay,” Marketing Letters 17, 137–149. {% dynamic consistency: shows that, given dynamic consistency and one of consequentialism and reduction of compound lotteries, the other is equivalent to independence. %} Volij, Oscar (1994) “Dynamic Consistency, Consequentialism and Reduction of Compound Lotteries,” Economic Letters 46, 121–129. {% bisection > matching: seems that this later Nobel-prize winner introduced bisection, called the staircase method (also sometimes called the simple-up down method), in psychophysics, so as to avoid biases in top-down or -bottom-up methods such as choice lists. The latter methods are called limiting methods, and were already used by Fechner (1860). %} von Békésy, Georg (1947) “A New Audiometer,” Acta Otolaryngology 35, 411–422. {% foundations of probability %} von Furstenberg, George M. (1990, ed.) “Acting under Uncertainty: Multidisciplinary Conceptions.” Kluwer Academic Publishers, Dordrecht. {% It uses the choice list to find indifferences between two-outcome gain prospects. 1. MAIN FINDING Uses the representative Dutch LISS panel with N=1422 subjects. It nicely tests Kreps & Porteus (1978), by having payment in three months, but resolving the uncertainty immediately or in three months. Will not find serious differences here (source-dependent utility: not found). The further main findings presented are that there are no clear predictions from demographics or otherwise because of unobserved heterogeneity of risk attitude. 2. SOME KEY WORDS real incentives/hypothetical choice & between-random incentive system: one group did hypothetical choice, and one group had real incentives, with one of every 10 subjects paid. (There was also a group with small real incentives.) No differences are found, also not in choice errors (p. 681). losses from prior endowment mechanism: this they do. P. 677: they use the good econometric technique of Conte, Hey, & Moffatt (2011). between-random incentive system: pays one choice for one of every 10- subjects. concave utility for gains, convex utility for losses: this paper does not provide evidence on this topic (see below). 3. THEORETICAL ANALYSIS AND ITS LIMITATIONS The authors consider risky choices with payments in 3 months, and two treatments (within-subject): either the uncertainty is resolved immediately (treatment 1) or in 3 months (treatment 2). They assume PT without probability weighting and with a fixed reference point 0. That is, they assume expected utility with a kink of utility at 0 (loss aversion). Then they test whether utility in one treatment is more or less conave than in the other, to test Kreps & Porteus. For treatment 2, late resolution, they assume exponential utility ez, with the same for gains and losses (discussed below), and loss aversion added by multiplying loss utility by (adding the appropriate constant to have continuity at 0); see their Eq. 2. (Their function h in the second line of Eq. 3 can be dropped.) For treatment 1, early resolution, they also assume, in my notation, exponential utility e´z. Then ´ > gives more concave utility, and thus less preference, for early resolution. The authors use ´/ as an index. Because of this division by , effects depend on the sign of . Thus for > 0, a large ratio means preference for late resolution, and for < 0 it is the other way around. Hence the authors impose the following restrictions: (1) They do not allow a sign-change between and ´. In particular, for = 0 (linear utility) they allow no difference between early and late resolution. (2) They assume the same loss aversion in both treatments. (Loss aversion is a substantial part of utility curvature and in general Kreps-Porteus comparisons would have to be incorporated in the comparison.) (3) For positive and ´ they take the ratio ´/ = as index of preference for late resolution (Eq. 8, p. 691). (4) For negative and ´ they take the ratio /´ = (so here is different than, reciproke to, the one for positive , ´) as index of preference for late resolution (Eq. 8, p. 691). The particular way of comparing concavity of utility chosen by the authors imposes a further restriction, the most serious one, being (5) Utility must have the same for gains as for losses (mentioned above), and also the same ´ for gains and for losses. Hence it must either be concave for both gains and losses, or convex for both, and the majority pattern of utility, concave for gains and convex for losses, cannot be considered. Especially this last restriction imposes a limitation on the empirical relevance of the findings of this paper, and they should be taken only within this modeling assumption. P. 665 end of 1st para: for further studies measuring loss aversion by measuring utility and then a kink at 0, see Abdellaoui, Bleichrodt, & Paraschiv (2007) and their references. 4. THE FINDINGS GIVEN THE THEORETICAL MODEL P. 666 end of penultimate para & p. 683: demographic variables do not explain much variance in risk attitudes; pp. 684-685 discusses relations found. P. 684: “The individual choices thus contain much more information than what is captured by sociodemographic goups.” gender differences in risk attitudes: pp. 684-685: women are more loss averse. It finds utility -exp(-0.032) where the unit if money is, I guess, euro (given the Dutch population). It means that the risk tolerance is €30. Risk tolerance means, for instance, that a gamble (0.5:2, 0.5: ) is neutral (equivalent to not gambling), giving a nice and well known interpretation to the utility parameters. The authors do not use this interpretation (p. 680 beginning of 3rd para; p. 682 l. 3), but instead use risk premiums that, of course, depend on the prospects chosen. Loss aversion is = 2.38. They find 8% inconsistency (p. 680), which is less than usual. Maybe the choice list method enhances consistent choice. It, nicely, finds that loss aversion is most volatile (p. 681), and utility is less volatile (p. 686 middle). 5. TOPIC FOR FUTURE RESEARCH An obvious topic for future research is modifications of the above utility restrictions, for example by comparing differences rather than ratios of the Pratt-Arrow indexes and ´, or even better, differences of their reciprokes, being risk tolerances, or by using other concave transformations such as exponential (leading to expexp utility for early resolution) to relate the utilities of the two treatments to more easily handle sign-dependence, or by separate comparisons for gains and for losses, preferably by also allowing for different loss aversion and then comparisons between those. 6. ALTERNATIVE UTILITY SPECIFICATIONS ANALYZED IN THE WEB APPENDIX The web appendix pp. 4 ff. discusses alternative utilities. Unlike what was suggested in the main text, they do not really consider the utility function common in PT (see their Eqs. 11 & 12). Common in PT, if taking only one parameter for basic utility (= utility without the loss aversion parameter), is to take reflected utility, with: for x < 0, u(x) = -u(-x) (*) The authors use this formula only if utility is concave for gains. If utility for gains is convex then they add a flip, and let utility for losses be convex rather than concave by multiplying the exponential parameter by -1 for losses. (Their claim that prospect theory is silent on convex functions for gains, on p. 4 l. -5 of the web appendix, I did not understand.) Thus, for losses, gamma and -gamma give the same utility function, and for losses no concave utility is possible. This is an unconventional model of utility that I haven’t seen before. This paper finds that it does not perform well. P. 669 seems to point out that their adaptive measurement is not incentive compatible. P. 681: more noise for LISS panel than for students. %} von Gaudecker, Hans-Martin, Arthur van Soest, & Erik Wengström (2011) “Heterogeneity in Risky Choice Behavior in a Broad Population,” American Economic Review 101, 664–694. {% losses from prior endowment mechanism; between-random incentive system (paid 1 of every 10 subjects in the real incentive treatment) Measure risk attitudes in usual ways, using choice lists and a variation of Binswanger (1981), with a student sample and a CentER panel data set representative of the general population. There are considerable differences between the students and the population, showing that the external validity of student experiments is questionable. Self-selection is less of a problem. Risk aversion and loss aversion is much larger in the general population than with students. They use usual PT parameter estimations as in their 2011 AER paper, but do not report their results here; for that see AER. %} von Gaudecker, Hans-Martin, Arthur van Soest, & Erik Wengström (2012) “Experts in Experiments: How Selection Matters for Estimated Distributions of Risk Preferences,” Journal of Risk and Uncertainty 45, 159–190. {% P. 18 seems to write: “Human action is necessarily always rational. The term “rational action” is therefore pleonastic and must be rejected as such. When applied to the ultimate ends of action, the terms rational and irrational are inappropriate and meaningless. The ultimate end of action is always the satisfaction of some desires of the acting man.” %} von Mises, Ludwig (1949) “Human Action.” Ludwig von Mises Institute, Auburn, Alabama. {% %} von Mises, Richard (1928) “Wahrscheinlichkeit, Statistik, und Wahrheit.” Springer, Berlin. (Translated into English in 1939 as “Probability, Statistics and Truth,” Hodge, London. Republished in 1957 by Allen & Unwin.) {% %} von Mises, Richard (1957) “Probability, Statistics, and Truth.” Allen & Unwin, London. {% Seems to have shown that mixed Nash-equilibrium already exists in noncooperative game theory if preferences are quasi-concave w.r.t. probabilistic mixing. See also Debreu (1952 §4). %} von Neumann, John (1928) “Zur Theorie der Gesellschaftsspiele,” Mathematische Annalen 100, 295–320. {% Citaat overgenomen van Nau: p. 8 (on unit of exchange between players): “substitutable, freely transferable and identical, even in the quantitative sense, with whatever ‘satisfaction’ or ‘utility’ is desired by each participant.” Pp. 8-9 seems to write, about utility being a theoretical construct but then becoming as real as energy: “It is sometimes claimed in the economic literature that discussions of the notions of utility and preference are altogether unnecessary, since these are purely verbal definitions with no empirically observable consequences, i.e., entirely tautological. It does not seem to us that these notions are qualitatively inferior to certain well established and indispensable notions in physics, like force, mass, charge, etc. That is, while they are in their immediate form merely definitions, they become subject to empirical control through the theories which are built upon them—and in no other way.” Citaat overgenomen van Nau: p. 11 (that no probabilities should be assigned to strategy choices of others): “One would be mistaken to believe that it can be obviated, like the difficulty in the Crusoe case ... by a mere recourse to the devices of the theory of probability. Every participant can determine the variables which affect his own interest but not those of the others. Nevertheless those “alien” variables cannot, from his point of view, be described by statistical assumptions. This is because the others are guided, just as he himself, by rational principles-whatever that may mean-and no modus procedendi can be correct which does not attempt to understand those principles and the interactions of the conflicting interests of all participants.” Download 7.23 Mb. Share with your friends:
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