I was wondering if the toolkit is able to replicate models with uncertainty shocks like Bloom (2009). These are highly non-linear models where sometimes value function iteration is the only feasible method, so the toolkit should in principle be great at this. Note that Bloom (2009) is a partial equilibrium model
The key point is how to discretize the stochastic process for uncertainty shocks…
Partially unrelated: I think it would be nice to add to the toolkit a command to generate impulse response functions, for example in the replication of the famous Hansen (1985) paper. IRFs are commonly used in RBC models and the toolkit can handle RBC models with non-linearities that make other packages like Dynare not ideal.
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I will take a look at the Bloom (2009) model. At first glance the only complication is those random walks are going to mean a subtle renormalization is needed before you can solve [from the looks of things, you likely take logs (to turn ‘geometric’/multiplication into standard/addition random-walks), renormalize, and then all you are left with is three normally distributed shocks]. If you know of any existing codes for solving Bloom (2009) model I can look at please let me know (will make it much easier for me to get a grip on the model). Because it is partial eqm, VFI should work fine (nothing obvious that will be a problem).
For IRFs. In some sense there already is an IRF command, namely the transition path command. This —solving a transition and treating the result as an IRF— is exactly what Kaplan, Moll & Violante (2018) do; of course this only works under the assumption of ‘certainty equivalent’ (an assumption that the model is linear in the aggregates; see Boppart, Krussell & Mitman (2018) for discussion). For a full IRF in a general eqm model with aggregate uncertainty, you would need the full model solution, which for now is not something VFI Toolkit can do. [Loosely related, Guerrieri & Lorenzoni (2017) is not an IRF, but it is a ‘path that plays out in response to an unexpected shock’, and you solve it as a transition path, it is general eqm and you treat shock as a zero-probability shock (aka MIT-shock).]
This transition path as way to compute an IRF is also generally going to work fine for partial eqm models, it is the general eqm models where it doesn’t work (without assumption of linearity in aggregates/certainty equivalance).
PS. I am not about to get into the non-linear Rep Agent DSGE model field, it is not really the strength of VFI (projection methods are much better for that; nor is it my personal interest). I’ve not used it but there is also https://www.gdsge.com/
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The code for Bloom (2009) are publicly available and they are written in Matlab. I looked at them years ago 
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