ToAD is a discount rate elicitation procedure developed as a part of journal manuscript “A Closer Look at the Yardstick: a new discount rate measure with precision and range“. ToAD is implemented on Qualtrics to facilitate collaborations with other researchers.

Click here to run ToAD Demo. This demo is also accessible via mobile phones. (Firefox or Chrome are recommended to run ToAD)

How to use ToAD in your study

Before you elicit discount rates from participants, there are four things (parameters) that you need to decide.

  • Domain: Gain domain (gldomain=1) or Loss domain (gldomain=2)
  • Magnitude (e.g., magnitude=1000): This will show around $1,000 range questions
  • Delay range (e.g., delay=180): The delay of the longest option will be generated with the mean of 180 and sd=.3 (The delay variation can be adjusted in the coding).
  • Annual Percentage Rate (APR) feedback on (feedback = 1) or feedback off (feedback=0)

Option 1. If you have access to Qualtrics, download qsf file for Qualtrics here and upload to your account. Modify the embedded field as needed.

Option 2. If you don’t have access to Qualtrics, modify the link below to generate the desired ToAD questions. The example link will generate questions for $1,000 magnitude (magnitude=1000), in about 180 days of delay range (delay=180), gain domain (gldomain=1), and will show feedback at the end (feedback=1). Participant ID is attached to retrieve the result (serial=x1234). Of course, the participant ID should be unique to each participant. If you send me your Participant ID, I can retrieve the results and send it back to you.

Interpreting results from ToAD (Please read carefully)

  • If you want to use the analysis code, replace ‘k_lg’ column in ‘ToAD_Results.csv’ with ‘k_lg’ column in your Qualtrics output file, and save it as csv file format, and run the code. You can also include PID, the participant identification number in the csv file. When you run the code, ‘ToAD_out.csv’ will be created. This is the output after exclusions (details described in the output file and below).
  • One of the benefits of ToAD is that, once you finished the ToAD procedure, you do not need to go through complex post-experiment calculations to get participants’ discount rates after the survey. Participants’ elicited discount rates will be available on Qualtrics results data (e.g., one that you download from Qualtrics) as soon as when participants finish answering ten ToAD questions. “k_lg” shows log-transformed daily hyperbolic discount rate with log base 10. “k_apr” indicates Annual Percentage Rate (APR) which is converted from k_lg. For example, k_apr = 10 implies 10% APR. In the paper, I found that log-transformed value (k_lg) is normally distributed. So I encourage to use k_lg for parametric statistical analysis (e.g., t-test or ANOVA), instead of using k_apr.
  • Occasionally, k_lg are k_apr marked with Null or blank. This indicates that ToAD detected unusual discounting pattern from participants. Unusual discounting implies negative discounting (e.g., $9 tomorrow is better than $10 today) or zero discounting (e.g., $10 today and $10 tomorrow are the same). These are not “wrong” responses, but qualitatively different discounting behavior that need to be separated normal, positive discounting that ToAD elicits.
  • ToAD does not prohibit participants to express their extremely high or low discount rates. However, it was designed to estimate discount rates from .035% APR to 350000% APR, which is -6 < k_lg < 1 in log scale (base 10). And the analysis code follows this range. It is up to researcher’s discretion, but I would be cautious about anything beyond -7 <k_lg < 2 (which is .00365% APR ~ 3,650,000% APR). I don’t think there will be any doubt among researchers that anything beyond these numbers can be considered as very unusual cases, which can be caused by participant’s misunderstanding of the task.

ToAD is designed to measure a discount rate using the hyperbolic discounting function by Mazur (1987). As long as the target discounting model has one free parameter for the discount rate (e.g., exponential model by Hull, 1943), results from ToAD can be used interchangeably. ToAD is not designed to test model selection problem (e.g., hyperbolic vs. exponential model). The model selection problem is largely different from parameter estimation. iPRP focuses on the model selection problem in intertemporal choice.

Yoon, H., & Chapman, G. B. (2016). A Closer Look at the Yardstick: A New Discount Rate Measure with Precision and Range. Journal of Behavioral Decision Making, 29(5), 470-480. doi:10.1002/bdm.1890

This material is based upon work supported by the National Science Foundation under Grant No. 1156072.