Kontek, Krzysztof (2015): Continuous or Discontinuous? Estimating Indifference Curves Inside the MarschakMachina Triangle using Certainty Equivalents.
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Abstract
This paper presents results of a study, which shed new light on the shape of indifference curves in the MarschakMachina triangle. The most important observation concerns (possibly discontinuous) jumps in indifference curves at the triangle legs towards the triangle origin. Such jumps, however, do not appear at the triangle hypotenuse. This points out to discontinuity in the lottery valuation when the range of the lottery outcomes changes. This observation is confirmed by an econometric analysis of six decisionmaking models: those models, which correctly predict jumps at the triangle legs, offer the best fit of the data collected. Focusing attention to the range of lottery outcomes appears thus one of the most important factors driving decisions under risk. The study has been made using a novel method of estimating indifference curves, which is based on linear interpolation of certainty equivalent values between adjacent points representing the lotteries under consideration.
Item Type:  MPRA Paper 

Original Title:  Continuous or Discontinuous? Estimating Indifference Curves Inside the MarschakMachina Triangle using Certainty Equivalents. 
Language:  English 
Keywords:  MarschakMachina triangle, indifference curves, fanningout, fanningin, models of decisionmaking under risk, certainty equivalents 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology ; Computer Programs > C81  Methodology for Collecting, Estimating, and Organizing Microeconomic Data ; Data Access C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology ; Computer Programs > C88  Other Computer Software C  Mathematical and Quantitative Methods > C9  Design of Experiments > C91  Laboratory, Individual Behavior D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty 
Item ID:  64408 
Depositing User:  Krzysztof Kontek 
Date Deposited:  17 May 2015 19:40 
Last Modified:  26 Sep 2019 10:46 
References:  Abdellaoui, M., Munier, B. (1998). “The Riskstructure Dependence Effect: Experimenting with an Eye to Decisionaiding”, Annals of Operations Research 80 (1998), 237252. Bardsley, N., Cubbit, R., Loomes, G., Moffat P., Starmer C., Sugden R. (2010). “Experimental Economics: Rethinking the Rules”. Princeton University Press. Becker, J. L., Sarin, R. K. (1987). “Lottery Dependent Utility”. Management Science, 33(11) 13671382). Birnbaum, M. H. (1997). “Violations of monotonicity in judgment and decision making”. In A. A. J. Marley (Ed.) “Choice, Decision, and Measurement: Essays in Honor of R. Duncan Luce (73100). Mahwah, NJ: Erlbaum. Blavatskyy, P. (2006). “Axiomatization of a Preference for Most Probable Winner”. Theory and Decision, 60: 1733. Bordalo, P., Gennaioli, N., Schleifer, A. (2012). “Salience Theory of Choice under Risk”. The Quarterly Journal of Economics. 127, 3, p. 12431285. Camerer, Colin, (1989). “An Experimental Test of Several Generalized Utility Theories”, Journal of Risk and Uncertainty, 2: 61104. Carbone, E., Hey, J. D. (1994). “Estimation of Expected Utility and NonExpected Utility Preference Functionals Using Complete Ranking Data” in Munier B., Machina M. J. (Eds.) “Models and Experiments in Risk and Rationality”, Kluwer Academic Publishers. Cavagnaro, D., Gonzales, R., Myung, J. I., Pitt, M. A. (2013). “Optimal Decision Stimuli for Risky Choice Experiments: An Adaptive Approach”. Management Science, 59 (2), 358–375. Chew, S. H. (1983). “A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox”. Econometrica, 51(4), 10651092. Cohen, M. (1992). “Security Level, Potential Level, Expected Utility: A Three Criteria Decision Model under Risk”, Theory and Decision, 33:2, 101134. Conlisk, John, (1989). “Three Variants on the Allais Example”, American Economic Review, vol. 79(3), 392407. Dekel, E. (1986). “An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom”. Journal of Economic Theory, 40, 304318. Gonzales, R., Wu, G. (1999). “On the Shape of the Probability Weighting Function”. Cognitive Psychology, 38, 129166. Gul, F. (1991). A Theory of Disappointment Aversion”. Econometrica, 59, 667686. Harless, D. (1992). “Predictions about Indifference Curves Inside the Unit Triangle”. Journal of Economic Behavior and Organization, 18, 391414. Harless, W., Camerer, C. (1994). “The Predictive Utility of Generalized Expected Utility Theories”. Econometrica, 62(6), 12511289. Hey, J. D., Strazzera E., (1989). “Estimation of Indifference Curves in the MarschakMachina Triangle”, Journal of Behavioral Decision Making, Vol. 2. 239260. Hey, J., D., Di Cagno, D. (1990). “Circles and Triangles: An Experimental Estimation of Indifference Lines in the MarschakMachina Triangle”, Journal of Behavioral Decision Making, Vol. 3, 279306. Hey, J. D., Orme, C. (1994). “Investigating Generalizations of Expected Utility Theory Using Experimental Data”. Econometrica, 62(6), 12911326. Jia, J., Dyer, J. S., Butler, J. C. (2001). “Generalized Disappointment Models”. Journal of Risk and Uncertainty, 22(1), 5978. Kahneman, D., Tversky, A. (1979). “Prospect Theory: An Analysis of Decision under Risk”. Econometrica, 47(2) 263291. Kontek, K., Lewandowski, M. (2013). “RangeDependent Decision Utility”. ssrn.com/abstract=2307858. Machina, M. (1982). “Expected Utility Analysis without the Independence Axiom”. Econometrica, 50, 277323. Machina, M. (1987). "Choice Under Uncertainty: Problems Solved and Unsolved", Journal of Economic Perspectives, Vol. 1, No. 1. Marschak, J. (1950). “Rational Behavior, Uncertain Prospects, and Measurable Utility”. Econometrica, Vol. 18(2), 111141. Neilson, W. S. (1992). “Some mixed results on boundary effects”, Economics Letters, Vol. 39, 275278. Sopher, B., Gigliotti, G. (1993). “A Test of Generalized Expected Utility Theory”. Theory and Decision, 35, 75106. Tversky, A., Kahneman, D. (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty”. Journal of Risk and Uncertainty, 5: 297323. Viscusi, K. (1989). “Prospective Reference Theory: Toward an Explanation of the Paradoxes”. Journal of Risk and Uncertainty, 2, 235264. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/64408 
Available Versions of this Item

FanningOut or FanningIn? Continuous or Discontinuous? Estimating Indifference Curves Inside the MarschakMachina Triangle using Certainty Equivalents. (deposited 29 Apr 2015 06:34)
 Continuous or Discontinuous? Estimating Indifference Curves Inside the MarschakMachina Triangle using Certainty Equivalents. (deposited 17 May 2015 19:40) [Currently Displayed]