The phrase "corresponding shift" is correct and usable in written English.
It is typically used to refer to a change or movement that is related to or has the same characteristics as another change or movement. For example, "The population declined by 10%, corresponding with a shift in economic activity."
But that has sometimes occurred without a corresponding shift in levels of supervision and safety measures.
But while the dialogue on issues like naloxone access may be shifting, a corresponding shift in funding priorities is lagging.
But there is also evidence of a corresponding shift in tax policy debates.
What is not yet widely enough acknowledged is the need for a wholesale cultural and operational change and a corresponding shift in the manner in which a council's sustainability team functions.
These suggest that the change from dimming to brightening is in line with a corresponding shift in the transparency of the atmosphere when it is cloud-free.
This resulted in the disastrous elections of 2006 and 2008, which combined for a total loss of 51 Republicans in the House and 13 in the Senate — with a corresponding shift of the Congressional majority and the White House to the Democrats.
The Taliban member also confirmed the impact, and said the Taliban were dismayed to see the much more concerted offensive by coalition forces, as well as the corresponding shift in the public mood.
Chickens raised with artificial tails showed that as some feathered dinosaurs evolved into modern birds, they shifted from an upright to a more crouched posture, with a corresponding shift from "hip-driven to knee-driven limb movements", said the researchers from the University of Chile.
There could also be a corresponding shift in the common DCB reference.
(b) Turning the eye 10° to the right results in a corresponding shift of the retinal image.
Shifting the revenue stream from the advertisers to the users will have a corresponding shift in how privacy is viewed.
