Experimental Design Details
We will collect data on participants’ choices in a session of decisions about lotteries and certainty equivalents. Each session will consist of six rounds of a chance-based game to understand participants' attitudes towards risk and uncertainty. In each round, each participant will ultimately draw a ball from a bag of red and blue balls to determine their payout for the round, which we refer to as the 'lottery'.
In each of the first four rounds, drawing a blue ball will be worth 30 GHS and drawing a red ball will be worth 10 GHS. In the fifth and sixth rounds the payout will be the sum of two draws, where each blue ball is worth 15 GHS and each red ball is worth 5 GHS. After six rounds, we will randomly choose one round and award the payout earned in that round. Participants will be informed of the way their payout is determined before the game begins.
At various points in each round, participants will have the option to forego the lottery and receive a certain (fixed) payout for the round instead. We refer to the minimum fixed payout a participant would accept as the 'certainty equivalent'. To elicit the certainty equivalent, will ask each participant whether they would prefer a fixed value over the lottery for a range of values between 30 GHS and 10 GHS. We will then randomly select one of those values for the round and honor the participant's request to either participate in the lottery or receive the amount selected for that round.
In the first four rounds, the lottery is a single draw so the certainty equivalent will be the option to forego that single draw. In the fifth and sixth rounds the lottery is the sum of two draws. In these rounds, we will vary how the certainty equivalent is computed across sessions. In half the sessions, we will elicit a single certainty equivalent to forego both lottery draws. In the other half of sessions, we will elicit two certainty equivalents corresponding to each of the two lottery draws.
We will elicit certainty equivalents for each participant at multiple points in each round. However, for each round, only one of the elicitations (randomly selected) will be implemented, and it will only be implemented for one participant (randomly selected). Every other participant will earn a payoff from the lottery for that round regardless of their certainty equivalent. Participants will be aware of this in advance, so they will know that most of the certainty equivalent elicitations are hypothetical but will not know whether any given elicitation will be hypothetical or for real stakes.
The order of activities in each round will be:
1) Announce the order of ball drawings for the round.
2) Elicit certainty equivalents for each participant.
3) Alternate between drawing balls and eliciting certainty equivalents as described below until the penultimate balls are drawn.
4) Randomly select one of the elicited certainty equivalents to offer, one participant to offer it to, and one value to offer that participant.
5) Honor that participant's choice to either participate in the lottery or accept the randomly drawn value as previously stated. At this time, the participant will not have the opportunity to change their decision on accepting that value instead of the lottery outcome.
6) Let participants draw the final ball(s) to determine payouts.
After six rounds we will randomly select one round and pay money based on performance in that round. Each participant will earn at least a minimum of 10 GHS, which can be thought of as a participation fee, and may earn more depending on their performance. The expected payout in each round is 20 GHS as there is ultimately a 50/50 chance of drawing either color.
The exact sequence of ball draws and certainty equivalent elicitation for each round (Step 3 above) after the initial elicitation are as follows. There will be a black bag with 50/50 red and blue balls, a red bag with 75/25 red and blue balls, and a blue bag with 25/75 red and blue balls out of which participants may draw.
Round 1: Each participant draws a ball from the black bag to determine their payout.
Rounds 2 and 3 (identical): The enumerator draws a ball from the black bag for each participant. After having seen all the draws, certainty equivalents are elicited once again. Then, each participant who was assigned a blue ball draws a ball from the blue bag, and each who was assigned a red ball draws from the red bag to determine their payout.
Round 4: The enumerator draws a single ball from the black bag. After seeing the draw, certainty equivalents are elicited once again. Then every participant draws from the same color bag as the enumerator's draw (red or blue) to determine their payout.
Round 5: The enumerator draws a ball from the black bag for each participant. After having seen all the draws, certainty equivalents are elicited once again. Then, each participant first draws a ball from their assigned color bag to determine the first half of their payout, and then draws a ball from the same color bag for the second half of their payout.
Round 6: The enumerator draws a ball from the black bag for each participant. After having seen all the draws, certainty equivalents are elicited once again. Then, each participant first draws a ball from their assigned color bag to determine the first half of their payout, and then draws a ball from the bag with the opposite color of their first draw for the second half of their payout. For example, if the participant's first draw was blue, then the first half of their payout would be 15 GHS and their second draw would be from the red bag.
We will treat rounds 1 and 2 as practice rounds to help participants internalize the structure and stakes of the game, and then use rounds 3--6 for analysis. Primary analysis will use participants’ decisions from the certainty equivalent elicitation that takes place after the black bag draw. For each participant in each round, the certainty equivalent will be defined as the midpoint of the lowest certain payment the participant is willing to accept and the highest certain payment the participant rejects.