An economist this week made the claim that the shocks from the closure of the Straits of Hormuz may result in structural shocks that do not return to normal after some reasonable period of time. Moreover, there may well be many failures that are economically fatal (thus, not only long-term impaired, but long-term non-existent).
What are the basic concepts of modeling the z and e grids and transition matrices so that heterogenous firms can experience a structural shift and/or so that some entities within those firms can be struck off as having failed? I know that the sum of the probabilities of the transition matrices must always sum to 1, but are there other assumptions or constraints to be aware of?
Should the transition matrices have an extra row and an extra column to collect and count the dead? I.e., transitions that can be reached from elsewhere in the matrix, but from which one cannot transition back into the rest of the matrix.
A related question is how to treat estimating firm \beta discounting. In the first equilibrium it can rationally be some number, but as the shocks mount, the seemingly infinite horizon defined in the first period surely must change somewhat as subsequent transitions disrupt expectations. How might that be handled?
I imagine that generally there’s a whole branch of economic modeling looking at stranded assets that could be modeled using the VFIToolkit.
You can model ‘death’ as an absorbing state, and then use simoptions.conditionalrestrictions so that all model stats ignore that ‘dead’ state. E.g.,
In principle you can just ‘delete’ the dead from the model, but this would require you to custom code the agent dist commands (as you then need to renormalize the survivors to mass one).
Note that if ‘death’ is endogenous you need to think about the ‘value’ of death versus ‘life’. If death is exogenous this is not an issue.
Also, you can model endogenous firm entry/exit explictly:
Firm’s are typically modelled as having a discount factor of 1/(1+r), where are r is their cost of borrowing. Note that any firm that aims to maximize present-value of profits will conclude that this is the right discount factor for it (otherwise you can either make more money by borrowing and investing, or by cutting investment so you can lend to others). You could do other things, and people sometimes do, but 1/(1+r) is the basic standard.
Not sure why ‘periodic disasters’ should necessarily change your discount factor (they might, but doesn’t seem necessary). If people with same discount factor expect more disasters they will act in a way that looks more present-biased from the outside (they will give up building houses if they come to expect all houses get destroyed by disasters within the decade; no need for a change in discount factor to get this behaviour).