Primary Outcomes (explanation)
We will construct these measures in the following way:
- For estimating discount factors from CTB responses we will follow the methodology from Andreoni et al. (2012), who outline the estimation of the per-period discount factor delta as well as the estimation of the present-bias parameter beta for each individual. For each individual we will use the point estimates obtained from this methodology, normalized such that delta is the “long-run discount factor” that measures the discounting between options in the future that are five weeks apart, while the “short-term discount factor” beta times delta measures the discounting between the present and five weeks later. We normalize to five weeks as this is the time horizon we use for the LTQ discount measurement.
- For assigning a discount factor for the LTQ method, we follow the method of multiple price lists as reviewed, e.g., in Anderson et al (2006), only that monetary rewards in that paper are replaced by the number of lottery tickets that individuals receive in our setup. In this methodology, for each time horizon, individuals answer several questions whether to take rewards earlier or later, where the amount of rewards for the later choice is increasing across questions. For individuals that switch only once from choosing current rewards to later rewards, the methodology establishes – at the individual level - a range for their short-run discount factor that rationalizes their switching point. This is backed out from questions involving today and five weeks later. The method also gives a range for their long-run discount factor that rationalizes their switching point for questions involving rewards 8 weeks from today and 13 weeks from today (i.e., also five weeks apart but in the future). We choose the mid-point of each interval to assign a short-run and a long-run discount factor. In cases an explicit value for present-bias (“beta”) is required, we take the ratio of this short-run discount factor over this long-run discount factor. For individuals with inconsistent answers (people switching “back and forth” between early and late choices involving the same time frame but increasing later rewards), we will consider the lower and upper bounds of the intervals that rationalize these switching points and choose the mid-point of that larger interval as measure of the discount factor.
- When we compare CTB with the LTQ method, it is important to take into account that LTQ assigns discount factors only at a few coarse values. It is of less interest in for our study whether these intervals were chosen optimally as this is easy to vary in later work, but rather whether the new LTQ method picks up the relevant discount factors correctly given these intervals. Therefore, for some of the comparisons it is useful to map the continuous measures of discount factors for the short run and the long run from the CTB method to the discrete points of the LTQ method. To do this, recall that LTQ assigns intervals of discount factors that would rationalize a single switching point in the answers in the LTQ elicitation. To convert a CTB point estimate, consider first into which LTQ interval the point estimate falls, and then assign the midpoint of that interval as the “coarse CTB discount factor”. This can be done both for the short-run and the long-run discount factor. To obtain the “coarse CTB present bias”, take the ratio of the coarse CTB short-run discount factor and divide by the coarse CTB long-run discount factor for the individual under consideration. We will only use these coarse values in the analysis where explicitly stated.