---
title: "Notation"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{notation}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

Symbols used throughout the package vignettes (see [Leventer 2025, §2–3](https://arxiv.org/abs/2602.07486) 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 |