@Charlie_9839, I looked at Catherine (2022). Because it needs to do correlation of u (shocks to the risky asset return) with z (idiosyncratic markov on earnings) the toolkit is going to have the same issue as described in:
Replication: Cocco (2005) - #7 by robertdkirkby
[and the same workaround of doing the ‘riskyasset’ as two endogenous states]
I hope to put aggregate shocks into the toolkit at some point. But remains just a hope for now.