Simulate panel data for child-penalty estimation

Generates a balanced panel of annual earnings designed to show the patterns the paper discusses: selection on the timing of first birth that makes parallel trends fail in the paper's direction, effects of parenthood that differ by age at first birth and fade with time since birth, and a gender earnings ratio that falls with age. The true values are attached, so estimates can be compared with them.

Usage

simulate_data(n_individuals = 10000, treatment_groups = 24:28, seed = 42)

Arguments

n_individuals: Whole number $\ge 2$. Number of individuals (default 10 000), half of them women (rounded).
treatment_groups: Whole numbers $\ge 21$: ages at first birth (default 24:28). Ages run from 20 to max(treatment_groups) - 1, so the largest group is never observed treated and serves only as a control.
seed: Whole number or NULL. RNG seed (default 42). The caller's RNG state is saved and restored on exit, so calling this function does not alter the global random stream; set.seed() before the call has no effect unless seed = NULL, which draws from the current RNG state.

Value

A balanced long panel (data.frame), n_individuals x (max(treatment_groups) - 20) rows sorted by id and age, with columns id, female (1 = female), age, D (age at first birth) and Y (earnings, positive). Attribute "truth": the population values for every treatment group d and age a >= d (event_time = a - d): APO_f, APO_m (mean earnings absent children), ATE_f, ATE_m, theta_f, theta_m, gap_theta, rho_cf ($\rho(\infty)$), rho_obs ($\rho(d)$), rho_effect ($\rho(d) - \rho(\infty)$), share_parenthood. Attribute "params": the parameter values.

Details

Earnings of person $i$ with age at first birth $D_i$ at age $a$ are $$\log Y_{i,a} = h_{D_i}(a) + \kappa(a) F_i + \tau_{F_i}(D_i, a - D_i)\,1\{a \ge D_i\} + \alpha_i + \varepsilon_{i,a},$$ with $F_i = 1$ for women and:

Career entry and growth (selection on timing): $h_D(a) = 9.6 + 0.02 (a - 20) + \beta(D) x - 0.0015 x^2$, with experience $x = \max(a - s(D), 0)$, entry age $s(D) = 20 + 0.7 (D - 24)$ and slope $\beta(D) = 0.09 + 0.008 (D - 28)$. Later first births enter the labor market later (more schooling) and then grow faster. Before treatment, distant control groups are not yet working and grow more slowly, so pre-treatment DID estimates grow in magnitude with the distance to the control group and are negative for distant control groups (for the closest ones they are small and can be positive); after treatment, the later control groups grow faster, so parallel trends fails with a negative violation for earlier treatment groups.
Gender gap by age: $\kappa(a) = -0.04 - 0.015 \max(a - 25, 0)$, so the female/male ratio absent children is $e^{\kappa(a)}$: 0.96 up to age 25, then falling.
Effects of parenthood: mothers $\tau_f(D, e) = -0.45 + 0.02 (D - 24) + 0.04 \min(e, 5)$ (smaller for later first births, fading with event time $e$); fathers $\tau_m = -0.02$. In normalized terms $\theta(g) = e^{\tau_g} - 1$.
Noise: $\alpha_i \sim N(0, 0.20^2)$ (permanent), $\varepsilon_{i,a} \sim N(0, 0.15^2)$ (transitory), independent of everything else.
Age at first birth: drawn from treatment_groups with probabilities proportional to a normal density with mean 29 and standard deviation 4, independently of gender.

Under this design DID-PT and TD-PT fail; TD-E-LOGS holds exactly (the gender terms cancel in log means); NTD-PT and TD-PR hold only approximately, because the gender ratio changes with age between the baseline and the target age. The NTD estimator therefore differs slightly from the true effect on the gender earnings ratio (by up to about 0.01 in this design); the attached true values show by how much.

Examples