IDEAS home Printed from https://ideas.repec.org/p/rut/rutres/201301.html
   My bibliography  Save this paper

Consistency and Aggregation in Individual Choice Under Uncertainty

Author

Listed:
  • Jeff Birchby

    () (Rutgers University)

  • Gary Gigliotti

    () (Rutgers University)

  • Barry Sopher

    () (Rutgers University)

Abstract

It is common in studies of individual choice behavior to report averages of the behavior under consideration. In the social sciences the mean is, indeed, often the quantity of interest, but at times focusing on the mean can be misleading. For example, it is well known in labor economics that failure to account for individual differences may lead to incorrect inference about the nature of hazard functions for unemployment duration. If all workers have constant hazard functions independent of duration, simple aggregation will nonetheless lead to the inference that the hazard function is state-dependent, with the hazard of leaving unemployment declining with duration of unemployment. Similarly, a recent study in psychology has shown that the “learning curve,” a monotonically increasing function of response to a stimuli, is better understood as an average representation of individual response functions that are, in fact, more step-function-like. As such, the learning curve as commonly understood is a misleading representation of the behavior of any one individual. These observations motivate us to consider the question of possible aggregation bias in the realm of choice under uncertainty. In particular, Cumulative Prospect Theory posits a weighting function through which probabilities are transformed into decision weights. An inverted S-shaped weighting function is commonly taken to be “the” appropriate weighting function, based on quite a number of experimental studies. This particular version of the weighting function implies, in simple two outcome lotteries, that an individual will tend to overweight small (near 0) probabilities and to underweight large (near 1) probabilities. A natural question to ask, suggested by both the hazard function and the learning curve examples, is whether this weighting function is not, similarly, an artifact of aggregation. Of course, no one believes that every individual’s behavior can be accounted for by a single weighting function. Studies have shown that there can be considerable variation in estimated weighting functions across individuals. But no one, to our knowledge, has systematically addresses the question of whether, in fact, one can meaningfully use a single weighting function, even as a rhetorical device, to accurately discuss individual choice behavior. If most individuals indeed do have an inverted S-shaped weighting function, then this representation of choice behavior is not misleading, provided it is clear that one is discussing the behavior of “most,” not all, individuals. We focus on the reliability of estimated weighting functions. We study the problem of determining the parameters of the cumulative prospect theory function. Using responses to paired sets of choice questions, it is possible to derive estimates for a two-parameter version of the Cumulative Prospect Theory choice function (using a power function for the value function and Prelec’s one parameter version of the weighting function). By analyzing multiple such pairs of choice questions, we are able to also investigate the consistency of these estimates. Our main finding is that there is, in general, considerable variation at the individual level in the choice parameters implied by the responses to the different pairs of choice questions. The modal choice pattern observed is one consistent with expected value maximization, and there is considerably less variation (again, at the individual level) in the parameters implied by those who appear to be maximizing expected value on one pair of choice questions than for those who never choose in this way. But these individuals account for only about one-fifth to one-sixth of subjects. For the rest of the subjects, it is rare that any two pairs of estimates are the same, and often the implied parameters

Suggested Citation

  • Jeff Birchby & Gary Gigliotti & Barry Sopher, 2013. "Consistency and Aggregation in Individual Choice Under Uncertainty," Departmental Working Papers 201301, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:201301
    as

    Download full text from publisher

    File URL: http://www.sas.rutgers.edu/virtual/snde/wp/2013-01.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Tomomi Tanaka & Colin F Camerer & Quang Nguyen, 2006. "Poverty, politics, and preferences: Field Experiments and survey data from Vietnam," Levine's Bibliography 122247000000001099, UCLA Department of Economics.
    2. Kiefer, Nicholas M, 1988. "Economic Duration Data and Hazard Functions," Journal of Economic Literature, American Economic Association, vol. 26(2), pages 646-679, June.
    3. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    uncertainty; prospect theory; aggregation; consistency;

    JEL classification:

    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rut:rutres:201301. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://edirc.repec.org/data/derutus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.