Low estrogen does not cause depression, but yes birth control pills can cause extreme mood swings and depression !!!!
You see you are adding hormones to a womans already hormonal cycle, some women are not bothered by this, others become depressed.
She may need a lower dose pill..
I cannot tolerate hormonal birth control at all, so I use an iud , or as it is most commonly reffered to where you are a 'coil'....
These coils are hormone free and do cause the side effects that birth control does, I reccommend them to everyone who has depression issues on birth control.
Of course anti depressant medications can work very well too.