Table 2
PAYOFFS OF THE GAMBLES IN THE ALTERNATIVE SET
(a) Treatment R-R and A-A
w-b
w-b
4-6
10-2
5-6
11-2
6-6
12-2
7-6
13-2
8-6
14-2
9-6
15-2
10-6
16-2
17-2
(b) Treatment R-A
w-b
w-b
5-6
12-2
6-6
13-2
7-6
14-2
8-6
15-2
9-6
16-2
10-6
17-2
18-2
19-2
20-2
(c) Treatment A-R
w-b
w-b
4-6
8-2
5-6
9-2
6-6
10-2
7-6
11-2
8-6
12-2
9-6
13-2
14-2
15-2
16-2
NOTES: The table lists the payoffs of the gambles offered as alternatives to the status quo in each treatment.
Each pair of numbers w − b reports the payoff in US dollars of, respectively, a draw of a white chip and a
black chip.
In part 2 each subject receives a card with a description of the (10, 4) gamble on the
known bag and is explicitly told he owns it. Subsequently, the subjects answer 24 questions.
In each question they are asked whether they would like to keep their (10, 4) gamble or
switch to the alternative gamble to be performed on the unknown bag. Thus we explicitly
induce a frame of maintaining the endowment or giving it up for the alternative. Of the
24 alternatives which appear sequentially, 15 coincide with the gambles presented in part 1
which are listed in Table 2(b). Thus, subjects compare the (10, 4) gamble with the gambles
in the alternative set twice, first under a neutral frame and then under a status quo frame.
The Gambles in the Alternative Set. The alternative gambles presented in Table 2(b)
are divided into two columns (or subsets): Gambles that pay $6 if a black chip is drawn
and gambles that pay $2 if a black chip is drawn. In each of these subsets the gambles are
ordered in terms of first order stochastic dominance (determined by the varying prize of
10
the white chip) and each subset contains both “attractive” gambles (high expected payoffs)
and “non-attractive” gambles (low expected payoffs). As a result, most subjects choose
the (10, 4) gamble over the low expected payoff alternatives and switch at some threshold
to choosing from the alternative set. The threshold at which the switch occurs depends
on the individual’s preferences. The presence of such a switching point in the interior of
the range of available alternatives ensures that the magnitude of the status quo bias is
correctly assessed. Subjects who do not exhibit an interior switching point are discussed
in detail in Appendix C.
We chose to present the questions in random order and sequentially on separate cards,
rather than in an ordered list so as to allow subjects to treat each question and each part
of the experiment in isolation. Presenting questions in this manner also allows us to mix in
the 9 additional questions which were crucial for reducing the salience of the fixed (10, 4)
gamble in part 1. In pilot rounds, we validated our assumption that participants viewed
the two parts as completely separate and that indeed, once they reached the second part
of the experiment, did not think about the decisions they made in part 1.
A consequence of our approach compared to the list procedure is that more subjects
switch back and forth between the (10, 4) gamble and the alternative set, violating the
combination of the assumptions of monotonicity and transitivity. These are most likely
mistakes which arise when answering multiple questions of similar nature. However, of the
143 subjects, roughly 75 percent exhibit a single switching point or at most one “mistake”
(i.e., changing their answer to one question leads to a single switching point). In analyzing
the data we run a probit regression where the error term absorbs mistakes of this sort.
Payment. Subjects are paid according to one randomly selected question among the 48
they answer during the experiment. At the payment stage we invite a volunteer who assists
11
in constructing the unknown bag using the Dow Jones Index. Next, he flips a coin that
determines according to which part (1 or 2) subjects will be compensated. We then ask the
volunteer to roll a 24-sided fair die which sets the exact question used for payoff. Finally,
the volunteer draws a chip from each bag and subjects are paid according to their choices
in that question.
The Dow Jones Index. The choice of the Dow Jones Index to determine the composition
of the unknown bag was made to clarify to the subjects that the experimenters do not
know and have no control over the distribution of chips in the unknown bag. It also
ensures subjects do not alter their beliefs regarding the composition of the unknown bag
throughout the experiment and allows for a ceteris paribus comparison of the two choice
frames.
12
At the end of the experiment a non-incentivized questionnaire was distributed
in which we asked whether the beliefs regarding the composition of the unknown bag
changed throughout the experiment (and if so why and at which stage).
13
All but one
subject answered that their beliefs did not change.
14
We were concerned that subjects may perceive the distribution of the decimals of the
Dow Jones as uniform and not view the unknown bag as genuinely ambiguous. Rather,
they may view gambles performed on this bag as compound lotteries where at the first
stage the bag’s composition is determined and at the second stage a chip is drawn. We
investigate this hypothesis in our questionnaire, where we ask: Did you have any belief
regarding how many white chips will be placed in the unknown bag? Some typical answers
12
Beliefs regarding the proportions of white and black chips could change when, in the second part,
subjects receive a specific endowment whose value depends on the bag’s composition.
13
The questionnaire and a categorical distribution of the answers are available in the online Appendix.
14
In a pilot session we used a typical two color Ellsberg Bag in which the bag was set up before the
experiment and the composition left completely unspecified to subjects. This attempt was unsuccessful in
maintaining the ceteris paribus requirement. From the questionnaire following the experiment we concluded
that a significant percent of the subjects made inferences regarding the bag’s composition based on the stakes
of the gambles they faced during the experiment.
12