Extended present bias: a direct experimental test

Abstract

This study experimentally tests our proposed extended present bias hypothesis—discount factor increases over the proximate future and eventually approaches constancy, but remains distinct from unity in the remote future. Using front-end delay and a post-dated check for payment, discount factors are elicited for three seven-day durations: between 2 and 9 days later (proximate), between 31 and 38 days later (intermediate), and between 301 versus 308 days later (remote). We find support for diminishing discounting between the proximate and intermediate comparisons, but not between the intermediate and the remote comparisons. The findings validate our extended present bias hypothesis.

Appendices

Appendices

1.1 Appendix 1: Experimental instruction

Welcome to our study on decision making. The descriptions of the study contained in this experimental instrument will be implemented fully and faithfully. The overall compensation includes a $50 show up fee in addition to earnings based on how you make decisions. All information provided will be kept CONFIDENTIAL. Information in the study including your personal information as well as your decisions will be used for research purposes only. You are not to discuss with anyone any aspect of the specific tasks during or after the study.

• 1. The set of decision making tasks and the instructions for each task are the same for all participants.

• 2. It is important to read the instructions CAREFULLY so that you understand the tasks and make better decisions.

• 3. If you have any questions, please raise your hand to ask our experimenters at ANY TIME.

• 4. PLEASE DO NOT communicate with others during the experiment.

• 5. Please take the time to go through the instructions carefully and make your decisions.

• 6. Cell phones and other electronic devices (with the exception of calculator functions), are not allowed.

• 7. Today’s session will last about half an hour.

This task involves your choosing between receiving a sum of money on a specific day and another sum of money on another specific day. There are 30 choices to make. The first ten pairs of choices are about receiving $100 2 days later versus receiving a larger amount 9 days later; the second ten pairs of choices are about receiving $100 in 31 days versus receiving a larger amount of money in 38 days; the third ten pairs of choices are about receiving $100 in 301 days versus receiving a larger amount of money in 308 days.

We will pay you according to one randomly selected choice out of the 30 choices. Specifically, we will give you cheques with the specified date at the end of today’s experiment. Under Hong Kong banking practices, a cheque can be deposited on or after the date of the cheque. Since it will take one day to clear the cheque, to make sure you may cash the cheque on the date specified in your choice, the date on the cheque will be one day before the specified date.

Please indicate your choices in the next page.

Decision: For each of the 30 rows, please indicate your decision with a tick ($\surd )$

	A	B
	2 days later	9 days later
$1$	$100	$101
$2$	$100	$104
$3$	$100	$107
$4$	$100	$110
$5$	$100	$113
$6$	$100	$116
$7$	$100	$119
$8$	$100	$122
$9$	$100	$125
$10$	$100	$128

	A	B
	31 days later	38 days later
$11$	$100	$101
$12$	$100	$104
$13$	$100	$107
$14$	$100	$110
$15$	$100	$113
$16$	$100	$116
$17$	$100	$119
$18$	$100	$122
$19$	$100	$125
$20$	$100	$128
	301 days later	308 days later
$21$	$100	$101
$22$	$100	$104
$23$	$100	$107
$24$	$100	$110
$25$	$100	$113
$26$	$100	$116
$27$	$100	$119
$28$	$100	$122
$29$	$100	$125
$30$	$100	$128

1.2 Appendix 2: Raw data

Switch points in Menu 1 and Menu 2. The columns (rows) represent the switch points in the 2 vs. 9 days (31 vs. 38 days) menu. Choices on the diagonal correspond to exponential/quasi-hyperbolic discounters ($n = 39$) who have the same switch points in the two menus. Choices in the upper right correspond to hyperbolic discounters ($n = 18$) who switch later in the later menu. Choices in the lower left correspond to counter-hyperbolic discounters ($n = 7$) who switch earlier in the later menu.

Switch points in Menu 1 and Menu 3. The columns (rows) represent the switch points in the 2 vs. 9 days (301 vs. 308 days) menu. Choices on the diagonal correspond to exponential/quasi-hyperbolic discounters ($n = 35$) who have the same switch points in the two menus. Choices in the upper right correspond to hyperbolic discounters ($n = 23$) who switch later in the later menu. Choices in the lower left correspond to counter-hyperbolic discounters ($n = 6$) who switch earlier in the later menu.

Switch points in Menu 2 and Menu 3. The columns (rows) represent the switch points in the 31 vs. 38 days (301 vs. 308 days) menu. Choices on the diagonal correspond to exponential/quasi-hyperbolic discounters ($n = 47$) who have the same switch points in the two menus. Choices in the upper right correspond to hyperbolic discounters ($n = 13$) who switch later in the later menu. Choices in the lower left correspond to counter-hyperbolic discounters ($n = 4$) who switch earlier in the later menu.