Anticipated Child Sex and Prospective Parents' Labour Supply and Childcare Intentions

Respondents are recruited via Prolific and complete a single online survey in Qualtrics (median completion time approximately 7 minutes). After a block of pre-treatment demographic and labour market questions, each respondent is randomly assigned with equal probability to one of two conditions by an embedded randomiser, stratified by respondent sex (both measured before assignment).

In both conditions respondents are asked to imagine that they and their partner are expecting their first child. The conditions differ only in the sex of the imagined child: the daughter condition asks respondents to imagine a girl, the son condition a boy. The screen displays the sentence "This is your future child" alongside a stick figure of the assigned sex. An accompanying adult figure is set by the respondent's own reported sex and is not randomised. The two conditions are otherwise identical in wording, layout and length. Assignment and receipt coincide, since every respondent reaching the vignette screen is exposed to the assigned condition; only intention-to-treat effects are estimated.

Immediately after the vignette, all respondents complete an identical outcome block: open-ended responses on their main apprehensions and on what they are excited about; expected own and partner weekly working hours when the child is aged 1 to 5; the expected division of childcare and household work; and desired own hours, partner hours and division over the same period. A subsequent block elicits preference over the child's sex and desired number of children, beliefs about whether daughters or sons are harder to raise and about maternal and paternal effort by child sex, and a five-item gender role attitudes battery. A manipulation check asks respondents to recall the sex of the imagined child.

A second, subsidiary randomisation determines whether two questions about the respondent's surprise at findings from a companion observational study appear before or after the gender role attitudes battery, since those questions reveal a research finding that could otherwise contaminate attitudes responses. The order indicator is recorded and tested.

There is no intervention outside the survey instrument; respondents receive no treatment beyond exposure to the assigned vignette.

2026-08-26

2026-10-31

1. Labour supply reduction intention (binary): respondent expects to work fewer weekly hours when the child is aged 1 to 5 than they currently work.
2. Expectation-preference gap in own weekly working hours (continuous, hours per week): desired hours minus expected hours over the same period.
3. Expected own hours

All outcomes are measured post-randomisation, in a block presented immediately after the vignette, and refer to the period when the first child is aged 1 to 5. Respondents are told in advance that this reference period excludes the immediate post-birth months and that "work" means paid work at a job, not housework.

Working hours are elicited in ten bands (none; 1–9; 10–15; 16–20; 21–24; 25–30; 31–35; 36–40; 41–45; 46 or more) for the respondent's current hours, expected hours, and desired hours, and separately for the partner on each. Bands are converted to midpoints of 0, 5, 12.5, 18, 22.5, 27.5, 33, 38, 43 and 48 hours per week. An ordinal 1–10 coding is retained as a pre-specified robustness check. Write current, expected and desired own hours as h, e and d respectively.

Outcome 1 is an indicator equal to one if e < h. Outcome 2 is d − e, in hours per week, so that a negative value indicates a respondent who expects to work fewer hours than they would choose. Outcome 3 is equal to e.

Two estimands are reported for each outcome. The first is the pooled average treatment effect of the daughter condition. The second, and the quantity the study is powered on, is the difference between the effect among women and the effect among men: the survey analogue of the mother-minus-father differential in the companion observational study, where maternal employment falls by roughly 20 percentage points after a daughter against 6 after a son. Every table reports the pooled effect, the effect among men, the effect among women, and the differential side by side.

Estimation is by OLS with covariates centred at their means and interacted with treatment (Lin 2013), always including the stratification indicators, with HC1 standard errors. Only pre-treatment covariates are used; the gender attitudes battery, being measured after the vignette, is never a control. These three outcomes as well as two secondary confirmatory outcomes listed below constitute the confirmatory family and are corrected jointly by the Romano-Wolf stepdown procedure with 1,000 bootstrap replications, for both the pooled effect and the differential. Unadjusted and adjusted p-values are reported.

Confirmatory Outcomes
1. Childcare allocation (binary): respondent expects to do most of the childcare and household work.
2. Couple specialisation (binary): respondent's expected hours fall relative to current hours while the partner's hold or rise.

Additional Outcomes
1. Expected own weekly hours in levels conditional on working; an indicator for expecting no paid work at all; the change in expected hours relative to current hours; partner expected hours, partner desired hours, and the partner expectation-preference gap; expected and desired division of childcare and household work in levels.
2. Standardised index of gender role attitudes (five items). Belief that daughters are harder to raise than sons; belief that mothers invest more effort in daughters than sons; the same for fathers; and the mother-minus-father effort gap, each on a signed scale from +1 (daughter) through 0 to -1 (son). Stated preference for a daughter, a son, or neither. Desired number of children, and desired number of girls and boys.
3. Text measures from the two open-ended questions asked after assignment, all expressed as counts per 100 words: first-person singular and first-person plural use and the plural share of first-person references; fear, sadness, joy, trust and anticipation categories from the NRC Word-Emotion Association Lexicon; mean valence and mean arousal from the Warriner, Kuperman and Brysbaert norms; care and harm language from Moral Foundations Dictionary 2.0; and masculine- and feminine-typed trait and activity language from word lists adapted from the item content of published gender role instruments, together with their difference.
4. Total words and total characters written across the open-ended questions, and total survey duration, estimated by median regression with OLS reported alongside.

Outcome 1 is an indicator taken from a single item on the expected division of childcare and household work. Outcome 4 is an indicator equal to one if e < h and the partner's expected hours are greater than or equal to the partner's current hours.

Full details on each outcome as well as whether they are confirmatory is provided in the accompanying pre-analysis plan.

A single-vignette survey experiment, fielded online through Qualtrics with respondents recruited from Prolific. Eligible respondents are aged 22 to 35, cohabiting with a partner, and have no children; eligibility is enforced through platform prescreeners rather than in-survey screening. A recruitment quota targets approximately half female and half male respondents.

Respondents first complete a pre-treatment block covering sex, age, education, ethnicity, religion, occupation, own and partner current weekly working hours, and own and partner gross annual earnings. They are then randomly assigned with equal probability to imagine that their expected first child is a daughter or a son, and immediately complete an identical outcome block: open-ended text on apprehensions and on sources of excitement; expected own and partner weekly hours for the period when the child is aged 1 to 5; the expected division of childcare and household work; and desired own hours, partner hours and division over the same period. A later block collects preferences over child sex, beliefs about raising sons and daughters, and gender role attitudes. A manipulation check asks respondents to recall the sex of the imagined child.

Estimation is intention-to-treat throughout, by OLS with mean-centred covariates interacted with treatment (Lin 2013) and stratification indicators always included, with HC1 standard errors. Covariates measured after the vignette are never used as controls. Heterogeneity by respondent sex is confirmatory and is estimated separately within men and within women, with the male-female differential and its standard error obtained from a single fully interacted pooled regression. Heterogeneity by education is designated exploratory in advance, because the design cannot detect plausible differentials on that margin.

Data collection proceeds in two stages. Stage 1 collects 200 complete responses and is assessed against four pre-specified feasibility criteria: at least 5 per cent of respondents reporting zero expected paid hours; Stage 1 filling within seven days at the offered reward; median length across the open-ended questions of at least 60 words; and at least 80 per cent passing the attention check with median completion time between 4 and 15 minutes. Continuation is conditioned on these criteria only. No treatment effect on any outcome is examined at the end of Stage 1, and continuation is not conditioned on the sign or magnitude of any estimate. Stage 1 observations are retained in the final pooled analysis in all cases. If the extensive-margin criterion fails, the study will be reported as a descriptive exercise on stated intentions and will not be presented as a test of the employment-margin result in the companion observational study.

Not available

Randomization done by computer. Assignment is carried out by an embedded randomiser in the Qualtrics survey instrument at the point the respondent reaches the vignette screen, with equal probability to each of the two conditions. Randomization is stratified by respondent sex, collected before assignment, implemented as a separate balanced randomiser within each of the two strata. The realised assignment is written to a stored data field for every respondent, and the stratum indicator is included in all estimation.

A second, independent computer randomisation within the same instrument sets the order of two question blocks in the post-outcome section; the realised order is likewise stored and tested.

Individual

No

Not clustered. Randomization is at the level of the individual respondent, so the number of clusters equals the number of observations: 2,510 individual respondents recruited.

2,510 individual respondents recruited, from a target analysis sample of 2,180 individual respondents with over-recruitment of 15 per cent to allow for attrition and pre-specified exclusions. Collected in two stages: 200 respondents in Stage 1 and the remainder in Stage 2.

1,255 respondents assigned to the daughter condition and 1,255 to the son condition as recruited; 1,090 per arm in the target analysis sample. Assignment is stratified by respondent sex, so each arm is designed to contain approximately 1,090 individuals in the analysis sample.

No clustering, equal allocation across two arms, 80 per cent power, 5 per cent two-sided size. Figures below are for the unadjusted difference in means and are therefore conservative: stratification and the covariate-adjusted specification will both improve precision. At the target analysis sample of N = 2,180 (1,090 per arm): Expectation-preference gap in own weekly hours (continuous): pooled effect 1.25 hours per week, or 0.12 standard deviations, using a standard deviation of 10.4 hours per week. Female-minus-male differential 2.49 hours per week, or 0.24 standard deviations. Binary outcomes -- labour supply reduction intention, childcare allocation, couple specialisation: pooled effect 6.0 percentage points, or 0.12 standard deviations at the variance-maximising proportion of 0.5. Female-minus-male differential 12.0 percentage points, or 0.24 standard deviations. The differential is a difference in differences across four cells and its minimum detectable effect is exactly twice the pooled figure. The design is powered on the differential rather than the pooled effect. The benchmark is the 14.6 percentage point mother-minus-father employment differential in the companion observational study; detecting an effect of that size on a binary outcome at 80 per cent power requires approximately 1,470 respondents, and the target sample of 2,180 detects 12.0 percentage points. At the Stage 1 sample of N = 200 the detectable differential is approximately 39.6 percentage points, which is why no interim assessment of treatment effects is made. The standard deviation of 10.4 hours per week is taken from a ten-response pilot and is imprecisely estimated; a standard deviation from a sample that size carries a wide confidence interval. It is also the dispersion of expected hours in levels rather than of the expectation-preference gap, which is a difference between two banded variables and will have a substantial mass point at zero. We therefore pre-specify that outcome standard deviations will be recomputed from the Stage 1 sample of 200 respondents and the minimum detectable effects in this table updated by registry amendment before Stage 2 collection begins. This is a blinded re-estimation of a nuisance parameter: the standard deviations will be computed on the Stage 1 sample pooled across treatment arms, without reference to the treatment indicator and without estimating any treatment effect, which is why it does not constitute an interim look and does not compromise the stopping rule in the experimental design field. The target sample size of N = 2,180 is fixed and will not be revised in light of the recomputed standard deviations; the recomputation updates the reported minimum detectable effects only. Full details can be found in the accompanying pre-analysis plan.