The Mortensen-Pissarides (MP) framework of search labor is the thing in analyzing (equilibrium) unemployment over the business cycle. Shimer showed that the lack of hires is the big margin that affects the volatility of labor. Since then people tried to analyze potential wage rigidity for new hires.
Is it safe to conclude that - in this context - wage rigidity of old matches does not matter anymore? Is this somewhat depending on the framework (As in: old wages don't matter for hires in MP because of XYZ, but this is a strong assumption)?
Is wage rigidity, conditional on the match being new, the only relevant metric onwards?