I am not sure if it affects all babies. My lo has always been bottle fed, and was getting hungry earlier and earlier everyday, so I switched him to the hungry baby formula. This I found constipated him. I kept him on the formula for amonth hoping that things would change however they did not. When I switched back to stage 1 he seemed fine. When we introduced solids it did start again, but that is a whole other story.
What formula are you using? We use Cow and Gate.