Experimental Design
The experimental design follows a within-subject structure. The decision problem resembles that of Choi, Fisman, Gale, and Kariv (2007), where subjects allocate money between two accounts, termed Account X and Account Y, according to a budget line constraint. Subjects will make 48 decisions of this form, and one randomly selected decision will determine their final earnings. For this randomly selected decision, a die will be rolled to determine which account balance determines payment at the end of the experiment. Final earnings consist of a baseline payment of 15 SGD, plus the earnings from the selected budgetary choice.
The primary innovation in this design lies in the mapping between subjects’ choices and the resulting lottery. Each decision problem features a Fixed Payment F, which remains unaffected by choices on the budget line. The payment mechanism is as follows:
- If the die lands on 1 or 2, the subject receives the balance in Account X.
- If the die lands on 3, 4, or 5, the subject receives Fixed Payment F.
- If the die lands on 6, the subject receives the balance in Account Y.
Subjects will complete 48 decision problems, divided into three parts.
- Within each part, the Fixed Payment F remains constant but changes across parts.
- The possible values of F are 3, 11, and 33, with their order randomized. The primary consideration for these values is ensuring sufficient variation in fixed payments.
- Each part contains 16 budget line problems, where subjects allocate money between Account X and Account Y.
- The budget lines remain the same across parts, but the order in which they appear is randomized for each part and subject.
The trade-offs between Account X and Account Y are defined by the following budget constraints. The primary consideration here is to ensure sufficient variation and intersection across different budget lines, so that the CCEI index (for models of interest) remains sufficiently low in a randomly generated dataset (Bronars test).
#1 Y = 30 - 1.5X
#2 Y = 36 - 2X
#3 Y = 38.4 - 2.2X
#4 Y = 42 - 2.5X
#5 Y = 45.6 - 2.8X
#6 Y = 48 - 3X
#7 Y = 50.4 - 3.2X
#8 Y = 54 - 3.5X
#9 Y = 31.5 - 0.625X
#10 Y = 33 - 0.75X
#11 Y = 34.5 - 0.875X
#12 Y = 36 - X
#13 Y = 42 - 1.5X
#14 Y = 48 - 2X
#15 Y = 50.4 - 2.2X
#16 Y = 54 - 2.5X
Below is a list of candidate reference points. Each reference point is a numerical value unless explicitly defined in the xOy coordinate system or specified according to existing theoretical models (in which case, the authors’ names are provided).
[I] Choice-Dependent Reference Point
1. Payment in X Account
2. Payment in Y Account
[II] Budget Set-Dependent Reference Points (these points are defined in the xOy coordinate system)
3. (In xOy coordinates) The allocation where the X Account balance is equal to the Y Account balance
4. (In xOy coordinates) The allocation where (probability of X × X Account balance) = (probability of Y × Y Account balance)
5. (In xOy coordinates) The midpoint of the budget line
6. (In xOy coordinates) The point where the horizontal coordinate is the maximal balance achievable in Account X, and the vertical coordinate is the maximal balance achievable in Account Y.
[III] Choice-Irrelevant Reference Point
7. Fixed Payment F
[IV] Hybrid of Choice-Dependent and Choice-Irrelevant Reference Points
8. Kőszegi-Rabin CPE
9. Bell-Loomes-Sugden Disappointment Aversion, or the expected value of the chosen lottery
10. Minimum Payment
11. Median Payment
12. Maximum Payment
[V] Hybrid of Budget-Dependent and Choice-Irrelevant Reference Point
13. (In xOy coordinates) Allocation where the X Account balance is equal to the Fixed Payment balance F
14. (In xOy coordinates) Allocation where the Y Account balance is equal to the Fixed Payment balance F
15. (In xOy coordinates) A budget-set reference point (3, 4, 5, 6, 7, 13, 14) if at least one of these reference points dominates the Fixed Payment F; otherwise, the reference point is set to zero.
16. (In xOy coordinates) A budget-set reference point (3, 4, 5, 6, 7, 13, 14) if at least one of these reference points is dominated by the Fixed Payment F; otherwise, the reference point is set to zero.
17. Minimax Criterion
18. Maximin Criterion