TIME PREFERENCES USING A MULTIPLE LOTTERY LIST: Validation

We aim to induce experimentally a perceived variation in background consumption that generates changes in measured present-bias in the convex budget set (CBS) elicitation method of Andreoni and Sprenger (2012). We aim to test that this does not induce variations in measured discount factors elicited via multiple lottery lists proposed by Belot et al (2021).

2023-07-10

2023-08-26

Individual discount factors elicited with the method of Convex Budget Sets (CBS) proposed by Andreoni and Sprenger (2012): especially the individual "beta" for each participant and treatment status

Individual discount factors elicited with the method of Multiple Lottery Lists (MLL) proposed by Belot et al (2021): especially the individual "beta" for each participant and treatment status

The variable for CBS will be computed for each individual and treatment status through the regression proposed in Andreoni and Sprenger (2012), applied to the choices of participants across a number of CBS questions that ask the individual to allocate tokens to early and late outcomes.

The variable for MLL is constructed from the answers to questions about receiving a lottery ticket earlier or later. The switching point from earlier to later identifies their discount factor over a particular time horizon. The present bias will be elicited by dividing the discount factor for payment within three days and payment in 2 months by the discount factor between payment in 2 month and 4 month. Both have similar waiting times, but one has immediate rewards. We will apply the same methodology to delays of 4 months, and average. Please see the full uploaded pre-analysis plan for details.

Please see longer pre-analysis plan for the exact construction of variables.

Individuals will be randomly allocated to one of four treatment arms with 100 participants each:
(1) CBS no prompting / MLL no prompting / CBS prompting
(2) MLL no prompting / CBS no prompting / MLL prompting
(3) CBS prompting / MLL prompting
(4) MLL prompting / CBS prompting

We will test for differences between groups 1+2 and 3+4 for the first two questions. We will also test for differences between the first and third question for groups 1 and 2. We expect differences when these are measured with CBS, and not if they are measured with MLL.

The experimental design relies on our intervention to successfully alter expenditure expectations. See the full pre-analysis plan for details.

Individuals in treatments 3 and 4 will first answer detailed questions about their near-term expenditures along a number of categories. They will then be asked to answer a series of elicitation questions for discount factors according to MLL and CBS, where the order depends on treatment

Individuals in treatments 1 and 2 are first asked asked elicitation questions for CBS and MLL methods without being prompted.

The difference between answers of those in treatment 1 and 2 vs those in treatments 3 and 4 is used for between-individual comparison.

After answering to CBS and MLL questions, individuals in treatments 1 and 2 are also asked detailed "prompting" questions about their near-term expenditures. They are then asked again a set of questions about time preferences, in treatment 1 via CBS and in treatment 2 via MLL.

In a within-individual design, the difference between present-bias elicited via early CBS answers before prompting and via late CBS answers after prompting for individuals in treatment 1 is used to study the effects of prompting on measured present-bias under CBS.

In a within-individual design, the difference between present-bias elicited via early MLL answers before prompting and via late MLL answers after prompting for individuals in treatment 2 is used to study the effects of prompting on measured present-bias under MLL.

Individuals are informed that one of the questions they answered will be randomly selected for payment, which also includes one question about risk aversion.

We expect treatments to be balanced. We also expect individuals to report higher expected expenditures after prompting than before. In particular, for the between-individual variation we expect individuals in treatments 3 and 4 to report on average higher expenditures after the prompting then individuals in treatment 1 and 2 before prompting. For within-individual variation we expect individuals in treatments 1 and 2 to report higher expected expenditures after prompting than before. These are necessary for the subsequent hypothesis.

Our core hypothesis is a joint hypothsis test:

The average beta measured under MLL for individuals in treatments 3 and 4 (after prompting) is not significantly difference from that of individuals in treatments 1 and 2 (before prompting).
AND
The difference between the beta elicited with MLL after prompting and the beta measured before prompting for individuals in treatment 2 is not significantly different from zero.
AND
at least one of the following holds:
[The average beta measured under CBS for individuals in treatments 3 and 4 (after prompting) is significantly lower that of individuals in treatments 1 and 2 (before prompting). OR The difference between the beta elicited with CBS after prompting and the beta measured before prompting for individuals in treatment 1 is significantly negative. OR BOTH]

The first two tests about MLL are at the heart of our investigation. The last part about CBS is there only to illustrate that we are operating in a setting that would be challenging for other monetary methods. If the part about CBS fails, the experimental variation in background consumption would not be sufficient to significantly alter standard discount factor measurement, and therefore we would not have managed to create an environment in which a new method is warranted. If at least one of the measures for CBS reveals significant differences, this indicates that standard methods might have an issue, and the tests for MLL become more meaningful.

Please see the detailed pre-analysis plan for secondary hypothesis and more details.

Randomization to one of the treatment arms is done via Prolific.

Sample size: 400

We will recruit participants using the on-line research platform Prolific.

Eligibility criteria:
● currently residing in New York State
● with a household income below 99,999 US dollars

No

There are no clusters. Each unit is one independent observation.

400 individuals

100 per treatment arm, across 4 arms

Power calculation for detecting differences in the cross-section comparison (one-sided t-test) From Belot et al (2021), we use the following parameter values: Mean estimate for β without prompting: μ_(β-CBS-NP)=0.992 Standard deviation estimates for β: σ_(β-CBS-NP)=σ_(β-CBS-P)=0.236 Significance level (type-1 error): α=0.05 Sample size: n_(CBS-NP)=n_(CBS-P)=200 Power (1-Type II error): 80% Given these parameters the minimum detectable effect size is -0.059, meaning that β_(i,CBS-P) should be at most 0.933. This is for CBS measurement. For MLL we do not expect to detect differences. If differences were of the size of CBS, this also indicates our ability to detect such (unexpected) differences. Power calculation for detecting difference in the within-individual design (one-sided paired t-test) Standard deviation for the difference (β_(i,CBS-P)-β_(i,CBS-NP)): 0.15 Significance level (type-1 error): 0.05 Sample size: 100 Power (1-Type II error): 80% Given these parameters the minimum detectable effect size is -0.038. This is for CBS measurement. For MLL we do not expect to detect differences. If differences were of the size of CBS, this also indicates our ability to detect such (unexpected) differences.