In the comments to this post, Matt writes:
Let's ignore non-labor sources of income for a moment. Then, in a very simple static model of labor supply, unless substitution effects are much stronger than income effects (which would imply a counterfactual secular rise in labor hours), a fall in the level of real wages does not imply a decline in labor hours. If we adopt cancellation between substitution and income effects as a baseline, then hours should be constant regardless of the real wage. Not clear why a fall in productivity, say, should translate into a decline in hours.
Dynamically, there is a similar invariance of labor hours to shifts in the long-run level of productivity, but there may be some intertemporal substitution of labor depending on the (1) real interest rate vs. the (2) rate of expected real wage growth. Specifically, labor supply today is increasing in (1) - (2), though the actual amount of intertemporal substitution is determined by the Frisch elasticity, which does not seem to be that high in practice. The recent recession involved declines in both (1) and (2), maybe with an overall decrease in (1) - (2), but (I don't think) quantitatively enough to get a large decline in labor supply. Intertemporal substitution is pretty problematic as a mechanism in general, since the people whose employment fell the most tended to be the ones who don't have much ability to smooth wages over time and thus can't engage in much intertemporal substitution. . . .
Anyway, I could go on and on about the ways in which a classical labor supply model is not a good description of reality, and we'd probably agree there. My point is to emphasize that since it's hard to justify the decline in employment in a frictionless model, there are probably some substantial labor market imperfections at work here. And a lot of the most plausible imperfections suggest that we should pursue policies to boost aggregate demand, if only as an application of the theory of the second best.
To be clear, when I hint at the idea that trends in firm dynamics could be affecting the business cycle, I'm not really thinking about a productivity channel. I'm thinking in very rough partial equilibrium terms about the simple fact that high firm growth rates are increasingly rare, so I'm left wondering where we'll get the labor demand "needed" to accommodate growth in the labor force (and also, as a side issue, wondering whether we need the high rates of excess reallocation that we used to see). That's all pretty non-rigorous, basically lump-of-labor reasoning, so it's a long way from being ready for prime time. I don't know how to build a model of this yet, because we still are mostly ignorant about what's driving the trends. But my view is this: either these trends in firm dynamics matter for the cycle or they don't. If they don't, I'm very curious about why they don't. If they do, they may complicate the AD/AS story.