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

nearly a quarter more of them reporting that they strongly liked cookies (23.5%). More subjects
reported a downward trend in their valuations over the course of the experiment than an upward
trend (19 versus 10), but the modal response was that their valuation remained about the same
(32 out of the 68 respondents). 27
Descriptive statistics for the average last elicitations of WTP for each of the 14 distributions
appear in Table 4.
4.1 Results on Dependence
Exactly three of the 69 subjects submitted a constant elicitation for all 20 rounds, consistent
with the standard model with a certain valuation (see the charts for subjects 41, 52, and 56 in
Appendix B). Six more subjects had zero variance in their last elicitations for each round,
meaning that at some point they went back to revise one or more submissions so that they would
be perfectly consistent across rounds—consistent with the standard model with learning (see the
charts for subjects 13, 18, 29, 44, 50, 64). Nevertheless, Figure 1 and the bulk of Appendix B
show that the vast majority of subjects exhibited positive variance in their elicitations to a
greater or lesser degree, even over their last elicitations.
The visual suggestions of widespread distributional dependence in Appendix B are backed up
by regressions on the within-subjects data. Under the simple model ��� = � � + � � ∙ ������ + �
(where Median is the median of the distribution displayed in a given round) the coefficient � �
should be zero in the absence of distributional dependence. Running this regression specification
separately for each of the 69 subjects, � � is found to be significantly different from zero at a 5%
level for 36 subjects and at a 1% level for 33 (see Table 5). 28 That is, roughly half of the subjects
gave responses that were sensitive to the distributions of random prices they faced each round.
summarizes the numbers of subjects for whom the coefficient � � is significantly different from
27 Collectively, the individual patterns of the subjects’ reported valuations over the course of the 20 BDM rounds
roughly match their respective reports on the trend of their valuations given in the survey.
28 The sample for each of these regressions was restricted to the subjects’ last submissions for each round.
18