Educational Inequality in the Household

We conduct a lab-in-the-field experiment with children and parents to test how parents allocate resources between their children. In an allocation task, parents are given nine tokens which they can allocate between their children. In combination with the children's performance on a Raven's test, these are to determine the payoffs received by each child. These payoffs are non-transferable, and should be highly valued by parents and children. The allocation task is repeated six times. Across these six distinct scenarios, one of which is drawn at random and implemented after the experiment, we vary the relative cost of compensating existing performance differences between the children.

We conduct a lab-in-the-field experiment with children and parents, in which we first ask children to solve a 12-item Raven’s test. At this stage, children are informed that the test is incentivized, but that there will be a lottery element involved in determining their ‘gift’ and that the gift can only be revealed at the end of the data collection. Parents are interviewed thereafter. During the interview, we show them a series of scenarios in which we ask them to allocate nine tokens between their children. Together with the performance of the children in the Raven’s test, these tokes are to determine the payoffs received by each child. The payoffs are sessions of an innovative AI course each child is entitled to participate in free of charge.

In a within-person design, we vary across six distinct scenarios, the convexity of the payoff function, as well as the degree of complementarity between child performance and parental inputs. The order of scenarios is randomized at the individual level. The scenarios will be shown to parents graphically, and from each scenario the parent chooses his or her preferred allocation (nine tokens are split between the children by means of moving a slider on a tablet). Because we worry about parental backlash concerning each individual child’s performance in a high-stakes environment, we do not disclose the identities of each child during the allocation task. Instead, we show two color-coded outcomes, one for “child orange” and one for “child green”.

2025-11-10

2025-12-15

The number of tokens allocated to the relatively better performing child.

Parents can either reinforce or compensate the differences in child performance. The number of tokens allocated to the better performing child per scenario is a clear indication of how parents handle these trade-offs.

3x2 factorial design that varies across six scenarios (randomly ordered within person) the i. complementarity in child performance and parental investment, and ii. the convexity in the payoff function. We will compare allocations to the high performing child for the three levels of complementarity (low complementarity, medium complementarity, high complementarity) and allocations to the high performing child for the two levels of convexity in payoffs (no convexity, high convexity).

The order of scenarios is randomized at the individual level (computer-based).

The order of scenarios is randomized within individual.

No

No clusters

240 individuals (parents)

When considering only the choice in the first scenario shown to households, the effective sample size by treatment arm is 80 (three levels of complementarity in payoffs), or 120 (two levels of convexity in payoffs). When considering all choices (all scenarios per individual), the effective sample by arm is 2*240= 480 (three levels of complementarity), and 3*240=720 (two levels of convexity).

We use two-sided tests for power calculation to test directional hypotheses on token allocations. Our analysis returns a sample of 240 individuals in order to estimate the effect of convexities changing reinforcement behavior with 92.2 power, 100 power for the effect of changing the complementarity on allocation behavior, and 100 on the effect of convexities on payoff maximizing behavior. These at cohen's d = 0.2, d = 0.2, and d = 0.3 respectively.