Is stoppage time representative of the true time that was lost?

As far as I know, stoppage time is at the discretion of the referee. When the half time is full, they decide the time that is to be added by themselves, at their discretion, and then after that amount of minutes is passed, the referee can call the half finished at any time (but they usually wait for a moment where there is not a probable scoring play ongoing).

But I wonder, was there any statistical study, ever, if that stoppage time is usually about right on how long the ball was really in a ‘dead-ball’ state? Or does usually the referees under/over estimate the amount of time the ball was dead?

(By a dead ball state I mean moments where there is no play, like when the players reset after a goal, or substitutions, injuries, etc.)

I would guess such a study has been done at some point, I just have no clue where to look.