The Effect of Sports Club Vouchers for Primary School Children $(80$ points where $5$ points are extra credit$)$

$($Based on Marcus, Jan, Thomas Siedler, and Nicolas R$.$ Ziebarth. $2022$ "The Long$-$Run Effects of Sports Club Vouchers for Primary School Children." American Economic Journal: Economic Policy, $14(3)$: $128-65.$

Let's explore this topic using data from a randomized experiment. Beginning in $2009,$ the German state of Saxony issued sports club membership vouchers to all $33,000$ third graders within the state. The aim of this policy was to promote a lifelong commitment to exercise. Fast forward to $2018,$ researchers conducted a comprehensive register$-$based survey among several cohorts in Saxony and two adjacent states. This survey was designed to assess the effects of the vouchers on exercise duration and the likelihood of being overweight.

The dataset is in a file called midterm.csv$.$ Table $??$ shows the names and descriptions of the variables in this dataset, where the unit of observation is individuals.

$\backslash$table$[[$variable$,$description$],[\_$id$,$identifying number of each student$],[$treat$,$whether the student received the voucher yes, $0=$ no