In many ways, Robert Lucas' famous estimate of the welfare costs of the business cycle is a restatement of the equity premium puzzle. If you take a standard model in which consumer preferences are time-separable, iso-elastic and have 'plausible' levels of risk aversion, then the fluctuations in marginal utility associated with unanticipated movements in consumption generate welfare losses that are much too small to justify either a high risk premium for stocks or the degree to which macroeconomic policy analysts have been preoccupied with the business cycle.
So if you were able to come up with a model that can explain the equity premium, there's a pretty good chance that it'll generate estimates for the welfare costs of the business cycle that are much larger than what Lucas calculates. And there are at least two theoretical approaches that reach just that conclusion.
One approach is pursued by Robert Barro, who makes use of a model that incorporates a small probability of a catastrophic loss. The implications for the equity premium are discussed here, and he now has a paper that applies the model to the costs of the business cycle (thanks to Mark Thoma for the link). Sure enough, he concludes that the welfare costs of consumption uncertainty are much larger than the Lucas estimate.
But there's another approach which is, sadly, not as well-known. In a couple of papers (here and here; working paper versions available here and here), Pascal St-Amour and I explored the implications for what we call 'state-dependent risk aversion.' The idea is pretty simple: peoples' attitudes towards risk are not not likely to be constant over time, and particularly not over the business cycle. We find that we can replicate the equity premium for very low levels of (atemporal) risk aversion, and that consumption risk plays a small role in determining the size of the risk premium.
While we were working on these papers, I had in mind the idea of trying to revisit the Lucas estimate, but we never got around to it. Happily, Angelo Melino has done the job for me. He has his own state-dependent model (working paper version available here) - fittingly entitled 'State-dependent preferences can explain the equity premium puzzle' - and has applied it to the question of the welfare cost of the business cycle. As does Barro, Angelo finds that
a model consistent with observed data on asset prices leads to very different conclusions [than the Lucas estimate]. Calibrating preferences to observed asset market data raises the estimated welfare gains from completely eliminating the business cycle by approximately two orders of magnitude. Most of the gains, however, come from the elimination of low frequency contributions.
So maybe all those articles on how to attenuate the business cycle weren't a waste of time after all.
Okay, okay: not entirely a waste of time.