The Stata command cic implements the estimator suggested in the paper "The changes-in-changes model with covariates" (with Giulia Santangelo); the slides are available.
You can install the command by typing
net install cic, from("https://raw.githubusercontent.com/bmelly/Stata/main/")
in Stata.
Note that you must also install qrprocess if you have not yet installed this command:
net install qrprocess, from("https://raw.githubusercontent.com/bmelly/Stata/main/")