It's Linnaea amabilis (aka Kolkwitzia amabilis), beauty bush:
A spectacular shrub when in full bloom and good condition:
It struggles a bit with the winters here in Zone 4, I envy you having enough for a hedge!
One thing I notice is that you have another plant there mixed in with it, it looks like buckthorn, Rhamnus cathartica. Now that one is a weed if that's what it is.
You can rejuvenate the still living beauty bushes by cutting them almost to the ground.