After job cuts, do salaries go up for remaining staff?

In the wake of so many companies having significant reductions in their laborforce, I found myself wondering what happens to compensation for the remaining workers?

My basic logic would be that it ought to go up as they assume more responsibility.

But then again, I realize that some job cuts are to remove bloat and redundancy and so has little effect on the actual work that the remaining staff would be doing. i.e the cuts are trimming off 'unnecessary/excess staff'.

How does it all pan out after cuts?