By Which

[Volcano1985]

We provide a statistical criterion by which to choose the most appropriate specification of our empirical model, in terms of whether additional variables enter the cost function itself or the set of efficiency determinants.

What does by which mean here?

[David L.]

'which' refers back to 'statistical criterion. '

So, 'by which' = and with this statistical criterion, we are able to compare it with something else
/ we are able to 'measure/compare something else against it'/

We can "choose the most appropriate specification for our empirical model" because we have "a statistical criterion" for comparison.