Identification strategy for measuring impact of employee turnover on project quality I am seeking help with identification strategy for figuring out causal direction in the following context:

There is a company where project managers (PM) rotate every 3-7 years across the country/globe. Naturally some PMs leave the company. I would like to measure the impact of PM rotation/turnover on project quality (as measured by time taken for completion ). 

EDIT: I expect the PM rotation to be most likely independent of Project Quality. PM's must rotate between 3 to 7 years, with 7 being a hard limit with rare exceptions. PM's decisions are more likely to be driven by quality of life in a region, schooling, their own career aspirations, the type of opportunities that have opened up within or outside the organization. They cannot be fired (Govt) and don't get too much extra credit for a successful completion of a project and they don't get much flack if things are slow (unless it is a spectacular failure). Sometimes PMs move to a new region which is close to the old region so they are still able to hold on to their portfolio.

I would like help with identification strategy to distinguish between or tease out the separate impacts of the following scenarios:

Scenario 1: PM is rotated/changed --> Project quality suffers --> Project takes longer to complete.

Scenario 2: Project quality is good --> Project completes quickly --> PM didn't have the opportunity/time to leave

and 

Scenario 3: Project quality is bad --> project takes forever --> PM rotates/leaves company due to natural career progression/rotation policy

I've spend the last many hours googling literature studying the impact of  project manager turnover on project quality but I haven't been able to find any good design. Would be grateful for any suggestions for identification.
This looks challenging, and the following would only work in circumstances where:


Reliable estimates can be made of how long each completed project should have taken to complete.
Good records are maintained of the progress of individual projects, enabling assessments to be made of the form "Project A was X% complete after n years".


Suppose two projects that were estimated to require 3 years were actually completed in 5 years, and in both cases a project manager had moved on after 2 years.  One might then focus on how complete each project was at the time when the project manager left.  If one project was 70% complete at that time, and so took a further 3 years on the last 30%, that suggests Scenario 1.  If the other project was only 40% complete after 2 years, and subsequently progressed at the same speed taking a further 3 years on the remaining 60%, that suggests Scenario 3.