Minimum detectable effect size for main outcomes (accounting for sample design and clustering)

1. Do parents discount their own future consumption and that of their children differently?
Hypothesis 1a: Parents discount their own future consumption more than that of their children.
We are testing whether parents allocate a larger share of peanuts for their child to consume at t=2 than at t=3, when making the decision at t=1.
We will pool the observations from all our subsamples except “Child’s participation (imposed)” to conduct this analysis. This would allow us to detect a 0.0886 s.d. diﬀerence in the share of peanuts allocated to the child at t = 2 and t = 3, which is 2.55% of the mean of the outcome variable, as measured in the pilot.
For consistency with the rest of our analyses, we will also conduct the same regression in the “Probabilistic commitment device × Baseline” sample, which would allow us to detect a 0.1402 s.d. diﬀerence, which represents 4.21% of the pilot mean of the outcome variable
2. Does this diﬀerential discounting give rise to within-household inconsistencies (parent-bias)?
Hypothesis 2a: Parents exhibit parent-bias.
We are testing whether parents allocate a smaller share of peanuts for their children to consume at t=2 when making the decision at t=2 rather than t=1. We will conduct this regression in the “Probabilistic commitment device × Baseline” sample, which would allow us to detect a 0.1402 s.d. diﬀerence, which is 3.46% of the pilot value of the mean outcome variable.
Hypothesis 2b: Parents exhibit Within-household Present-Bias.
We are testing whether the gap between the planned t=2 and t=3 allocations is larger when parents make the decision at t=2 than t=1. We will conduct this regression in the “Probabilistic commitment device × Baseline” sample, which would allow us to detect a 0.1402 s.d. diﬀerence between both gaps (90% of the mean outcome variable, as measured in the pilot).
3. Is there demand for commitment devices to help mitigate parent-bias, above and beyond demand for commitment devices that help mitigate present-bias?
Hypothesis 3a: Parents demand commitment devices to help them stick to their within-household allocation plans.
2,000 respondents in our sample are oﬀered a probabilistic commitment device to help them stick to their planned within-household allocation. They are oﬀered this probabilistic commitment device at 3 diﬀerent prices: 0.5/1/1.5 packets of peanuts. We will plot the demand curve for this commitment device, at diﬀerent level of prices.
Hypothesis 3b: The demand for commitment devices to help parents stick to their within-household allocation plans is smaller than the demand for commitment devices to help them stick to their inter-temporal allocations. The respondents are also oﬀered a probabilistic commitment device to help them stick to their inter-temporal allocation.
We will pool the observations from all our “Probabilistic commitment devices” subsamples except “Child’s participation (chosen)” to conduct this analysis. This would allow us to detect a 0.0991 s.d. diﬀerence between the take-up of both types of commitment devices (2.4% of the mean value of the outcome variable, as measured in the pilot).
For consistency with the rest of our analyses, we will also conduct the same regression in the “Probabilistic commitment device×Baseline” sample, which would allow us to detect a 0.1402 s.d. diﬀerence (3.4% of the mean outcome variable).
6. Can labeling mitigate time-inconsistencies?
Hypothesis 6: Reminding parents of their past choices will decrease time inconsistencies.
-Pooling samples from the “Baseline” and “Labeling” treatment arms, we will measure whether labeling help mitigate time-inconsistencies. This sample size enables us to detect a 0.1717 standard deviation decrease in the change of the share of peanuts allocated to be consumed by the child at t=2 following the introduction of labeling (160% of the mean of the outcome variable in the Baseline treatment arm, as measured in the pilot).
Distinguishing between the role of labeling and anchoring
We will distinguish between the role played by labeling and anchoring, by polling the “Labeling” and “Anchoring” samples. This sample size enables us to detect a 0.1983 standard deviation diﬀerence in the distance between the amount of peanuts allocated to the child by the parents at t = 2 and in the allocation presented to them.
7. Can encouraging children to participate in household decisions increase investments in children and mitigate parent-bias?
Hypothesis 7a: Making children participate in household decisions increases investments in children We will test this hypothesis by pooling the “Baseline” and “Child’s decision (imposed)” samples. This sample size enables us to detect a 0.1717 standard deviation increase in the share of peanuts allocated to the child following the increase in child{'}s bargaining power (3.55% of the mean outcome variable in the baseline treatment arm, as measured in the pilot).
Hypothesis 7b: Making children participate in household decisions decreases reallocation towards parents
We will test this hypothesis by pooling the “Control” and “Child’s decision (imposed)” samples. This sample size enables us to detect a 0.1717 standard deviation decrease in the change in the share of peanuts allocated to the child following the increase in child{'}s bargaining power.
8. Heterogeneity analysis: do mothers and fathers discount the future diﬀerently?
We will look at whether mothers and fathers diﬀer in terms of investments in children on diﬀerent dimensions:
8a. Do mothers plan to invest more in their children in the future? We will test this hypothesis in our baseline sample.
Our sample size allows us to detect a 0.2949 s.d. difference in the share of peanuts mothers and fathers plan to allocate for their child’s t=2 consumption, when making the plan at t=1 (7.70% of the mean outcome variable in the pilot)
8b. Do mothers invest more in the children when the time comes? We will test this hypothesis in our baseline sample. Our sample size allows us to detect a 0.2949 s.d. difference in the share of peanuts mothers and fathers plan to allocate for their child’s t=2 consumption, when making the decisionplan at t=2 (6.1% of the mean outcome variable in the pilot)
8c. Are fathers more time-inconsistent than mothers? We will test this hypothesis in our baseline sample. Our sample size allows us to detect a 0.2949 s.d. difference in the change in the share of peanuts mothers and fathers plan to allocate for their child’s t=2 consumption, when making the decision plan at t=2 and t=1. (316% of the mean outcome variable in the pilot)
8d. Do mothers demand more commitment devices to stick to their within- household allocation plans? We will test this hypothesis in our probabilistic commitment device sample. Our sample size allows us to detect a 0.2084 s.d. difference in the take-up of the probabilistic commitment device between mothers and fathers (4.8% of the mean of the outcome variable, as measured in the pilot).
8e. Do mothers demand to let their children participate in the t = 2 decision more?
We will test this hypothesis in our “Child’s commitment (chosen)” subsample. Our sample size allows us to detect a 0.3243 s.d. difference in the willingness to let the child participate between mothers and fathers. (37% of the mean of the outcome variable, as measured in the pilot).