My experience has been that if it lags far enough, output starts dropping to realign with it.

Especially in cases where people are being underpaid by quite a bit, it can be a hugely demotivational factor. It's not even about the money as such, but rather about the signal how much all your hard work and effort is appreciated: apparently not all that much if you're not being paid what you know you're worth.

I really don't care all that much about how I'm being paid, I'm pretty easy about it. But it nonetheless played a direct factor in quitting two jobs because I felt I was being woefully underpaid (which I objectively was; although I guess you'll have to my word for it) and efforts to bring it up to a more standard level were being frustrated to such a degree I felt that a lot of "extra effort" I had put in to the job just wasn't being appreciated at all.

But pay determines whether I have a future at a company and if I have no future, my objective goes from getting a good performance review to avoiding termination.