This looks quite interesting, I look forward to using the improved codes. I have a couple of comments:
Transition path.
In the working paper version, Boar and Midrigan acknowledge that the fixed point iteration (which is the standard method implemented in the VFI toolkit, I think) is “notoriously slow and unreliable” and suggest using a different method.
I think there is another post in this forum where we discussed this algorithm (Type-I Anderson acceleration). I wonder if this “unreliability” is somehow related to the problem I had found solving for the transition after a change in the discount factor in the Aiyagari model (see my older post here)
VFI Infinite horizon
Is the greedyhowards method based on building a large transition matrix P(a',z'|a,z)? I’ve always found this method quite slow compared to the others, and the reason might be that this transition matrix is sparse but not so sparse. It is the same logic of the Tan improvement, just here you should do it in reverse order. First you apply the transition from z to z' and then as a separate step the transition from a to a'. I hope this makes sense. This is the logic I have used in my code howardssparse that you have added to the toolkit (I’m quite proud that my contribution was accepted, by the way:) )