Understanding Demand for Children: A Discrete Choice Experiment

There is no real-world intervention. This is a hypothetical discrete choice experiment: the
"treatment" is the randomized variation of attributes within the survey instrument (the number of
additional children, household income, and time allocation shown in each choice task). No
respondent receives any real-world treatment, payment tied to choices, or change in circumstances.

2026-07-21

2026-08-04

1. The choice probability of the larger-family option as a function of its money price (household
income cost) and its time price (non-leisure hours cost).
2. The dependence of the money-price/income relationship on household income level (the
income-interaction parameter of the demand model).
3. Willingness to pay for additional children, expressed in money and in time.

Further specification of these outcomes -- estimation equations, the confidence-interval framing
for the income-interaction parameter, the willingness-to-pay construction, and the education-
stratum breakdowns -- is provided in the hidden fields and the attached pre-analysis plan.

Outcome 1: choice probability of the larger-family option, estimated via a linear probability model
with respondent fixed effects (and via a scaled/heteroscedastic logit as the structural
counterpart), on the reduced-form contrasts in money price (log income ratio) and time price
(non-leisure hours).

Outcome 2 -- the normal-good test: the registered output is the confidence interval on the
income-interaction parameter (mu) from the reduced-form specification, not a reject/fail-to-reject
verdict. Because the reduced-form model is a linear probability model, its coefficients measure
changes in choice probability, not utility; we report mu, its confidence interval, and the implied
change in the predicted probability of choosing the larger-family scenario across the displayed
income range (p25 to p90), with a confidence interval obtained by propagating coefficient
uncertainty. A tight interval bounding mu near zero is the substantive finding that the value of
children is flat as a share of income (normal in dollars but not in share). The structural
interaction is reported as a corroborating cross-check.

Outcome 3 -- willingness to pay: reported in dollars and in leisure/sleep hours for one and for two
additional children, by education stratum, from the structural model (which supplies the utility
metric; WTP is not derived from the reduced-form probability coefficients). WTP for each child
contrast is defined as the compensating change in income that equates utility between child levels
under the full structural utility function, including the income interaction, holding time fixed;
reported at each displayed income level with the p50 value as the headline within-stratum quantity.
We also report the parity-zero, one-versus-none willingness to pay as the first-birth extensive-
margin value.

Confirmatory tests (hidden until unlock): H1, demand slopes down in the money price; H3, demand
slopes down in the time price (both one-sided at 5%); H2, the income-interaction (normal-good)
test, reported as the confidence interval on mu. H1-H3 are treated as three distinct hypotheses
with no family-wise multiplicity correction.

An exploratory analysis, identified during piloting, of the asymmetry between a respondent's stated
ideal family size and her revealed choices.

H4 (exploratory): among women without children, whether revealed choices track a respondent's own
stated ideal family size asymmetrically above versus below that ideal. Estimated on the parity-zero
subsample via the between-group log-odds contrast described in the pre-analysis plan; reported with
full sample-sensitivity. Additional deferred analyses (heterogeneity, a bridge to stated ideal
fertility, external calibration, and a childcare-cost robustness exercise) will be added in a later
timestamped registry update.

A discrete choice experiment. Each respondent completes ten binary choice tasks; in each, she
compares two hypothetical descriptions of her life ten years hence and selects the one she prefers.
The two descriptions independently and exogenously vary three attributes: the number of additional
children over the next ten years, combined pre-tax household income, and a typical weekday's
allocation of hours across paid work, care/household tasks, and leisure/sleep. Because the income
and time attributes are randomized independently of the children attribute and of each other, the
design separately identifies the money price and the time price of an additional child. The exact
attribute levels, the randomization procedure, the estimation specifications, and the power
analysis are provided in the hidden experimental-design field and in the attached pre-analysis
plan, which will be released on completion.

Not available

Randomization done by computer. Attribute combinations for the ten choice tasks are drawn
independently and uniformly (rejecting fully identical option pairs) from pre-generated task sets,
assigned sequentially to respondents within education stratum. The generation seed and version
counts are recorded with the study materials.

The scenario profile within a respondent's choice task. Within each education stratum, question
sets (each of ten choice tasks) are pre-generated by drawing both scenarios' attribute profiles
independently and uniformly from the 108 possible profiles (rejecting identical pairs), and are
then assigned to respondents sequentially -- not at random -- within stratum. There is no
respondent-level random assignment and no treatment arms; the randomization is in the drawing of
the attribute profiles that populate each choice task.

No

Not applicable (no clustered treatment). Randomization is at the individual-respondent and
choice-task level.

2,000 women (20,000 choice tasks: 2,000 respondents x 10 tasks each).

Not applicable. The design has no fixed treatment arms; all 2,000 respondents complete ten choice
tasks with independently randomized attributes. Soft recruitment targets are approximately 45%
college graduates (about 900) and 55% non-college (about 1,100), subject to realized composition.

Power was assessed from pilot variance components scaled to the target sample of 2,000. On the choice-probability scale, the design is well powered for the money-price and time-price responses; precision on the income-interaction parameter is the binding constraint and is reported as a confidence interval rather than a reject/fail-to-reject test. Minimum-detectable-effect figures, the pilot standard errors, and the scaling are given in the attached pre-analysis plan. These are approximate planning benchmarks rather than exact operating characteristics of the final design.