# Notation

Symbols used throughout the package vignettes (see Leventer 2025, §2–3 for formal definitions):

Symbol | Definition
--- | ---
\(G \in \{f,m\}\) | Gender (female, male)
\(D\) | Age at first childbirth (treatment timing)
\(Y_{i,a}(d)\) | Potential earnings of individual \(i\) at age \(a\) if first birth occurs at age \(d\)
\(Y_{i,a}(\infty)\) | Potential earnings under never having a child
\(\text{APO}(g,d,a) = \mathbb{E}[Y_a(\infty) \mid G=g, D=d]\) | Average counterfactual earnings
\(\text{ATE}(g,d,a) = \mathbb{E}[Y_a(d) - Y_a(\infty) \mid G=g, D=d]\) | Average treatment effect of parenthood
\(\theta(g,d,a) = \text{ATE}/\text{APO}\) | Normalised effect (proportional earnings change)
\(\rho(d,a) = \text{APO}(f,d,a) / \text{APO}(m,d,a)\) | Gender earnings ratio (counterfactual)
\(\Delta\rho(d,a)\) | Effect of parenthood on the gender earnings ratio