By Martin Andreasen, Giovanni Caggiano, Efrem Castelnuovo and Giovanni Pellegrino
http://d.repec.org/n?u=RePEc:bof:bofrdp:2021_013&r=dge
This paper uses a nonlinear vector autoregression and a non-recursive identification strategy to show that an equal-sized uncertainty shock generates a larger contraction in real activity when growth is low (as in recessions) than when growth is high (as in expansions). An estimated New Keynesian model with recursive preferences and approximated to third order around its risky steady state replicates these state-dependent responses. The key mechanism behind this result is that firms display a stronger upward nominal pricing bias in recessions than in expansions, because recessions imply higher inflation volatility and higher marginal utility of consumption than expansions.
I would have thought that the higher marginal utility of consumption in recessions was sufficient to explain why risk matters more in those periods. It appears there is more to it on the firm side. Firms like to set (nominally rigid) prices a bit higher in the face on uncertainty, and there is more uncertainty in recessions.
NEP-DGE Blog 
Thanks for your comment, Christian! Yes, our paper is on the structural reasons behind the larger real activity response to an uncertainty shock we observe in recessions. After documenting this fact with a VAR analysis in which we use a state-of-the-art identification strategy, we match the VAR impulse responses with those produced with a micro-founded DSGE framework featuring several transmission channels. Technical note: Our nonlinear model is approximated at a third-order around the stochastic steady state – this choice, which is a novelty per se in the literature, enables us to have policy functions that acknowledge the role of initial conditions when it comes to understanding the role played by uncertainty shocks in booms vs. busts.
As you pointed out, simulations conducted with our estimated nonlinear models suggest that the key channel behind the model’s ability to replicate our VAR facts is the stronger upward nominal pricing bias in recessions. Why do firms bias their prices upward more in recessions? Recessions imply higher inflation volatility, against which firms insure by setting prices higher than in a world without uncertainty. But not only that. A higher marginal utility of consumption in recessions influences the stochastic discount factor, giving firms an extra reason to upward bias their prices. So, your hunch is correct – a higher marginal utility of consumption does play a role in our framework, but it is a subtle one – it works via the stochastic discount factor, and eventually via the pricing channel.