There is the long debate on the Frisch-Elasticity being the driver of unemployment over the business cycle.
One argument against the voluntary-unemployment mechanism of RBC models is that if we distinguish two subgroups of the population with different Frisch-elasticities, the one with the higher elasticity should respond stronger to wage fluctuations.
Women have a bigger elasticity than men, yet their employment fluctuates less over the business cycle.
Is there a counterargument to this that salvages the neoclassical model of voluntary unemployment? I'm specifically referring to this argument that builds on heterogeneity in the elasticity, not on the Micro vs Macro estimation discussion.