Testing Distributional Dependence in the Becker-DeGroot-Marschak ...

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willingness to pay to avoid incurring a more painful loss. This phenomenon is called the attachment effect by Kőszegi and Rabin. If a subject with a moderate and certain valuation experienced asymmetric regret according to the model of Horowitz, her bids would be biased upward (downward) when facing distributions with the mass primarily below (above) her valuation. 6 That is, her bids would be expected to be higher when the mass of the distribution was lower and vice versa. 7 Note that the random selection of one round for resolution should theoretically remove any incentive for hedging across rounds; as long as the resolution of the chosen round were transparent and salient, there would still be ample scope for ex post regret of either type. Lusk, Alexander, and Rousu (2007) argue that when agents faced with the BDM mechanism experience some uncertainty about their true valuation they will have an incentive to deviate from the point estimate of their valuation in the direction of lower expected cost. If the distribution of random prices is locally asymmetric, an agent unsure of her exact valuation will tend to overstate it if there is less mass above her estimate of her valuation and understate it if there is less mass below this estimate. This explanation is similar to that of Horowitz: subjects minimize regret by choosing to err in the direction of lower expected cost. Both within and across subjects, the Lusk, et al. model implies that the triangular distributions should see more dramatic biasing effects than the other distributions, since they present subjects with far more possibilities for local asymmetry of mass around their point estimates of their valuations. 8 Like that of Horowitz, this model predicts that across subjects the 6 Insofar as these effects might intensify with respect to the extremity of a given valuation, slight adjustments still might be discernable even when the valuation is always on one side of the median of the various distributions. However, these would be second-order adjustments. Subjects with very low or very high valuations would not vary their bids dramatically across distributions in the model of Horowitz. 7 One important caveat: if the magnitude of any bias from asymmetric regret were too small relative to the level of discreteness of the distributions used in this experiment the last bids (at least) should be identical across all distributions (within subject). 8 For example, if a subject’s estimate of her valuation for the item in this experiment were $6 plus or minus $2, this model would predict that her last bids (at least) would be the same for two distributions that were flat from the entire support from $0 to $9.50, save for a spike at either $0 or $9.50 (i.e., distributions #3 and #4—see Table 1). 8
effect of varying distributions (apart from any effects from learning) should be to push elicitations away from mass. Kaas and Ruprecht (2006) also explain that distribution dependence may occur when agents experience uncertainty about their true valuations, which they conceptualize as “discriminal dispersion”: agents perceive value with a normal distribution of errors centered on their true valuation. 9 The implications of the Kaas and Ruprecht model are analogous to a specific case of the model of Horowitz in which agents nearly always place more weight on the potential regret of paying too much for an item. However, unlike Horowitz or Lusk et al., Kaas and Ruprecht come to the conclusion that due to the asymmetry of the potential for loss from overbidding, risk- averse agents will nearly always underbid when faced with a BDM elicitation task. The model of Kaas and Ruprecht, expects most subjects to underbid regardless of their estimate of their valuation or the distribution of random prices. The degree of underbidding is expected to increase in the amount of mass of the distribution to the right of the estimate of the valuation. 10 While direct measures of whether or not underbidding has occurred cannot be obtained from the BDM phase data alone, later survey questions asking about the subjects’ valuations for the item may provide some guidance on the matter (albeit admittedly imprecise). The model of Kaas and Ruprecht also predicts that across subjects underbidding will be reduced (or even reversed for high valuations) for those subjects who are less risk averse. In contrast, the standard model would predict that a rational expected-utility maximizer with a fully formed and certain personal valuation of the item from the beginning of the experiment However, triangular distributions (such as distributions #11, #12, #13, and #14—see Table 1) would yield differences even in the last bids. (That is, unless the subject’s estimates of her valuation were at the extremes or beyond the support of the distribution, or if her considered range of adjustment were smaller than the intervals between the mass points.) 9 A key limitation of Kaas and Ruprecht in the context of this study is that their analysis assumes a uniform distribution of random prices throughout. 10 Even if there were generally underbidding for most or all distributions the magnitude of the differential influences toward underbidding across distributions would be relatively small (similar in principle to the cases of extreme values in the Horowitz model). 9
Page 1 and 2: Testing Distributional Dependence i
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Page 29 and 30: 5 Discussion As seen in Sections 4.
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Page 43 and 44: Panel B. Round 2 WTP (Half of the s
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Panel B. Mass to the Left, High Sup
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#2 #2 #2 Panel D. Mass to the Right
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Appendix A Screenshots of the Exper
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[Second page of the instructions. T
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Figure A.3. Screenshot of the Holt-
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Survey Questions 1. What is your fi
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Appendix C Subject responses to the
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