Hello,
I conduct an inter temporal choice experiment where each trial consists of two different reward options with different time points. Subjects need to decide for one of the two options per trial. For instance, participants either choose the reward option 10 euros today versus 30 euros in 2 months. My aim is to get the discount rate resulting from the indifference points.
To analyze the data I worked with the scientific article: A Tutorial on the Use of Excel 2010 and Excel for Mac 2011 for conducting delay-discounting analyses by D. D. Reed, B. A. Kaplan & A. T. Brewer (2012). Please find the article attached. However, they only show how to calculate the discount rate for sooner options involving immediate rewards (today, 30 euros) and not for delayed sooner rewards (in 3 months, 30 euros).
Also having delayed sooner rewards in my inter temporal choice experiment, my question is how I can best include them in the analysis in order to get the discount rate involving a hyperbolic delay discounting function.
I would highly appreciate if someone has any suggestions regarding this question.
Thanks a lot in advance!
Mi Marco,
I suggest you go look at Andersen et al (2008) 'Eliciting time preferences' in Econometrica or http://excen.gsu.edu/fur2012/fullpapers/gharrison2.pdf.
These will show you how to econometrically examine these aspects and give you some ideas on approaches to considering hyperbolic time preferences.
If you only have delayed sooner and delayed later rewards (same delay for the sooner and same delay for the later) then i doubt you can consider hyperbolic preferences - these are indicated by a decreasing marginal (across time) rate of discount when you represent preferences using the exponential form. If you have immediate reward data too you could compare the implied discount rate (exponential form) for the immediate reward data against the delayed sooner data - hyperbolic time preferences would be suggested by a higher rate of exponential discount in the former than the latter. If a hyperbolic representation for both leads to the same discount factor then you could possibly suggest that this is evidence of hyperbolic discounting. Alternatively use an econometric model and test which form better represents the data.
Econometric analysis is not so difficult for these simple types of experiments - you just need to replace the linear utility representation in the Logit (or Probit) with a non-linear one. If you have included uncertainty then you will run into some identification issues which can be dealt with if you have included a risk-preferences only experiment as well (see the above references for that again).
Hope that helps, follow up the literature cited in the two articles provided above to find out more.
Cheers,
Daniel
p.s. as always i am happy to be corrected, early morning here - need more coffee to think clearly.
Hi Daniel,
Thanks very much.
I think your suggestions and ideas are very clear.
Best wishes,
Marco
Use difference differential equations to model the motion in the choice over time. See my Economerical paper: Optimal grow with time lags. Available on my Research Gate page. Let me know if you have questions
Daniel Gregg gave you the perfect answer, much more so than I am able to give you.
Dear Marco,
In line with the first answer, you may also try to look at this paper:
Wileyto, E. P., Audrain-Mcgovern, J., Epstein, L. H., & Lerman, C. (2004). Using logistic regression to estimate delay-discounting functions. Behavior Research Methods, Instruments, & Computers, 36(1), 41-51.
They use a logistic regression (with no intercept) to estimate the discount factor.
Best,
Rodica
Just curious, has anyone actually tried producing the excel file outlined in Reed et al 2012?
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