---
title: "Value of educational time lost"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Value of educational time lost}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

This vignette explains how the value of lost educational time is calculated in _daedalus_.

In _daedalus_, educational time is assumed to be lost due to pandemic-mitigation restrictions on education, such as **school closures**.

We also assume that education shifts to a remote format that has a reduced efficacy compared to in-person schooling.

## Value of a school year

The value of a school year in a country ($\text{VSY}_c$) is the product of the country-specific gross national income ($\text{GNI}_c$) per capita, the rate of return on education ($R$), and the present value of expected future earnings (which we denote as $V$).

$$\text{VSY}_c = \text{GNI}_c \times V \times R$$

### Valuation constants

The following constants are assumed when calculating the value of a school year:

- $r = 0.03$: the discount rate for future earnings;

- $m_Y = 45$: the expected future years of work;

- $a = 12.5$: the mean age of school-going individuals. **Note that** the mean age of school-goers is a simple mean of the age-bin `[5, 20)`.

- $R = 0.08$: the rate of return on one year of education.

### Country GNI

Country GNI values are for the most recent year available, and are taken from the [World Bank's World Development Indicators](https://databank.worldbank.org/source/world-development-indicators).

### Present value of future earnings

A constant scaling factor for the present value of future (lost) earnings ($V$) is calculated using the valuation constants defined above.

$$\frac{1 - (1 + r)^{-(m_Y + 20 - a)}}{r} - \frac{1 - (1 + r)^{-(20 - a)}}{r}$$

## Value of education lost

The value of lost education is the product of:

- The number of school days lost due to pandemic-mitigation measures (in DAEDALUS, these are school closures); this is explained more below;

- $1 - E_{\text{remote}}$: the loss in educational efficacy due to remote education during closures;

- $\text{VSD}_c$: the value of a school day, which is the value of a school year divided by 365 ($\text{VSY}_c / 365$); and

- $N$: the number of school age children.

$$\text{VSD}_c \times N \times (1 - O_{\text{edu}}) \times T \times (1 - E_{\text{remote}})$$

The **number of school days lost** is calculated as the product of the closure coefficient for the educational sector ($1 - O_{\text{edu}}$) and the number of days a pandemic-mitigation measure is active $T$.
The closure coefficient indicates the stringency of measures applied to schooling, and can take a value in the range $[0, 1]$.

## Future developments

Future development on the valuation of education lost is planned, and includes:

- Accounting for the numbers of children in each age-bin in demographic data and correctly calculating the present value of future earnings ($V$) by accounting for differences in expected remaining years of work;

- Including the effect of education missed due to student absences caused by illness or isolation.