cd "/Users/bernardofanfani/Desktop/teaching/research_topics_labor/lab_4/fourth_lab/"

log using example_late.log, replace

*********
* ESTIMATING LATE WITH AN RCT

use "rapporti_lavoro_2001.dta", clear

su retrib03

* define a treatment that gives a positive shock on income of approximately 10%, and which has a given variability across individuals (10% of the income standard deviation)
ge treatment=rnormal(`r(mean)'/10, `r(sd)'/10)

* there is a lottery that gives access to the treatment with 50% probability
ge lottery=runiform()<.5
* however, only 50% of the lottery winners actually get the treatment (the compliers)
ge compliers=runiform()<.5 & lottery==1

* thus, only compliers have non-zero treatment effect
replace treatment = 0 if compliers!=1

* let's add the treatment effect to the income variable
replace retrib03=retrib03+treatment

* expected LATE
su treatment if compliers
* expected Intent to Treat
su treatment if lottery

* let's check if the ITT and LATE models estimate the correct parameter
reg retrib03 lottery
ivregress 2sls retrib03 (compliers=lottery)

log close