Parenting styles, subjective beliefs and skill development

We will read different scenarios to describe a hypothetical family with one child of adolescent age to all study participants. For each respondent, the experimental script will vary three inputs for skill development: (i) child initial skill level (high; low); (ii) parental monetary investments in child’s education during early childhood and early adolescence (high; low); and (iii) the parenting style exerted during the same childhood periods (authoritative vs authoritarian). See below for a complete description.

2026-02-12

2026-07-31

Primary outcome includes respondents' perceived age for a hypothetical child to be able to master two numeracy tasks corresponding to medium and high difficulty levels of numeracy skills under each of the hypothetical situations. We will use the log of this age as our primary outcome.

We aim to compare estimates of the objective process of skill development with those derived from subjective belief data. To do so, we will establish a comparable cardinal metric between outcome that enter our objective process of skill development and those that are based on the subjective beliefs.

When estimating the objective process of skill development, we will leverage a rich panel data. To establish a cardinal metric, we convert our raw test scores into developmental age scores which we will use to estimate a measurement system. We will carefully select a set of observable measures that are salient indicators of skill development. We will use the developmental age of numeracy (mathematics) as an anchor for the other measures of skill development.

In the belief elicitation stage, we will then use the same metric to anchor respondents’ answers to subjective belief questions about the process of skill development and elicit our primary outcome. More specifically, for each situation describing the inputs received, respondents will be asked to estimate the age at which a child would be able to master two numeracy (mathematics) tasks corresponding to medium and high difficulty levels of numeracy skills.

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This study combines a belief elicitation experiment (BEE) with longitudinal data to recover caregivers’ subjective beliefs on returns to investments, and compare them to the objective technology of skill formation. The BEE is designed to elicit caregivers’ beliefs about the returns to key inputs in children’s maths development: educational expenditures, parenting styles, and child skills. In addition, the design allows us to study beliefs about the timing of investments by distinguishing between inputs made in early childhood and early adolescence, as well as to assess whether the perceived returns to investments varies across caregivers.

We will assign respondents to four treatment groups. In each arm, belief scenarios will consist of a short description of a hypothetical adolescent child and her parents, followed by a set of situations that vary along three dimensions: the child’s skills, parental monetary investments, and parenting styles. In two treatment arms, parental monetary investment in the child’s education will be fixed at levels made during early childhood (age 5) and adolescence (age 13) (high or low, depending on the arm), with variations in child initial skills and parenting style (as typically exerted at home during the same periods), one at a time. In the other two treatment arms, parenting style exerted during the different periods of childhood will be fixed (authoritarian or authoritative, depending on the arm), while child initial skill level and parental monetary investments (made during the same childhood periods) will vary, one at a time. For each situation, caregivers will be asked to report the age at which they believe the hypothetical adolescent will be able to correctly master two numeracy questions, an intermediate and a more advanced one, which are our marker of maths skill development in adolescence.

Importantly, we can observe the same maths questions object of the BEE as part of our longitudinal data. Indeed, the two questions were chosen as markers of "intermediate" and "more advanced" maths skills by studying their difficulty levels in previous waves of the longitudinal dataset by using item response theory (IRT). Among a pool of potential maths items in this survey, we then picked item that had the desired level of difficulty and that seemed understandable as "intermediate" and "more advanced" by parents in Ghana. To describe the hypothetical child’s initial skill, we use a similar approach, where we describe "a low skills child " as a child that can only solve easy numeracy items at age 5, and "a high skills child" as one that can solve both easy and medium difficulty items at age 5.

We will use the experimental variation embedded in the scenarios to estimate a subjective skill formation function that summarises parents’ beliefs about how inputs translate into child skill development. The experimental design will identify average perceived returns to each input, as well as differences in perceived returns across the different investment periods. As the sample is embedded in a rich panel data, we will use several available information, including the randomised assignment to both early childhood and adolescence interventions, and socioeconomic characteristics (e.g. parental education level), to explore heterogeneity by these characteristics. We will also explore heterogeneity by sex of the hypothetical child in the scenario.

We also aim to shed light on why parents might differ in their beliefs about the productivity of parental investments and parenting styles made during different child periods. To do so, after the BEE, we will administer survey questions about parental beliefs on the malleability of children’s skills and adaptability of parenting styles across child developmental stages. We will use this information to investigate whether perceived returns vary based on the individual responses.

To compare estimated subjective beliefs against the true skill formation process, we will estimate an objective skill formation technology using multiple waves of longitudinal data. We will use comprehensive information collected over time on actual parenting behaviors (to proxy parenting styles) and parental investments. When recovering the parameters of the objective technology of skill formation, we will address endogeneity of parental investments using an instrumental variable and/or control function method (Attanasio, Meghir & Nix, 2020).

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We will implement the randomization procedure using a Stata do-file to ensure reproducibility

The unit of randomisation will be the individual parent.

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~2,400 parents (no clustering).

~2,400 parents.

The two hypothetical scenarios, each containing two situations will be randomly assigned across four groups of the total sample. This will result in 600 respondents in each treatment arm as follows:

Authoritarian-authoritarian: 600
Authoritative-authoritative: 600
Low-low money investment: 600
High-high money investment: 600

To estimate the minimum detectable effect size, we simulate the specification: ln⁡(devage_ij)= β_0 + β_1 θ_5 + β_2 I_5 + β_3 I_13 + β_4 (θ_5 * I_5) + β_5 (θ_5 * I_13) + β_6 (I_5 * I_13) + μ_i + ε_ij where devage_ij denotes developmental age; θ_5 is the child's initial skill at age 5 and, I_5 and I_13 are parental monetary investments in the child's education at ages 5 and 13, respectively. We standardize the outcome variable: ln(devage). By using the variance structure implied by the field test data (N=120 respondents outside our main sample) and targeting 80% power with a sample size of 2,400 respondents, the simulations indicate that we can detect effects larger than 0.16 standard deviations for all parameters when clustering at the individual level.