Unemployment and the Frisch-Elasticity 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.
There are a couple of good papers on this that I know of.

Keane, Michael and Richard Rogerson, “Micro and Macro Labor Sup-
ply Elasticities: A Reassessment of Conventional Wisdom,” Journal of
Economic Literature, 2012, 50, 464-476.

"The response of aggregate labor supply to various changes in the economic environment
is central to many economic issues, especially the optimal design of tax policies.
Conventional wisdom based on studies in the 1980s and 1990s has long held that the
analysis of micro data leads one to conclude that aggregate labor supply elasticities
are quite small. In this paper we argue that this conventional wisdom does not hold
up to empirically reasonable and relevant extensions of simple life cycle models that
served as the basis for these conclusions. In particular, we show that several pieces
of conventional wisdom fail in the presence of human capital accumulation or labor
supply decisions that allow for adjustment along both the extensive and intensive
margin. We conclude that previous estimates of small labor supply elasticities based
on micro data are fully consistent with large aggregate labor supply elasticities."

Peterman, William B, “Reconciling Micro and Macro Estimates of the
Frisch Labor Supply Elasticity: A Sensitivity Analysis,” Technical Report,
Federal Reserve Board of Governors 2014.

"Microeconometric estimates of the Frisch labor supply (0 to 0.5) tend to be much lower than the values used by macroeconomists to calibrate general equilibrium models (2-4). This paper explores whether the gap in these ranges can be explained by two restrictions present in the micro Frisch elasticity that are implicitly relaxed in these values of the macro Frisch elasticity. First, the micro estimates focuses only on prime-aged married males who are the head of their household, while the macro values incorporates the whole population. Second, the micro estimates only include fluctuations in hours on the intensive margin, while the macro values also incorporate fluctuations on the extensive margin. Within a consistent microeconometric estimation strategy, this paper estimates a micro Frisch elasticity of 0.2, and, upon relaxing the two restrictions, a macro Frisch elasticity of about 3. The increase in the estimates suggests that these two restrictions can explain the gap. However, given that this paper demonstrates that the estimates of the macro Frisch elasticity are fairly sensitive to the estimation procedure, the sample of agents, and also the margins of fluctuations that are used for estimation one must careful choose the appropriate value for calibration purposes."