Dear all,
I am interested in modeling the effects of housing on the demand for risky assets. I am looking for code that replicates models similar to Cocco (2005). In this paper, consumption within the utility function is divided into nondurable goods consumption, denoted as Ct, and housing consumption, denoted as Ht, as follows:
Is it possible to handle such problem by combining available VFI Toolkit life-cycle models? Could you please assist me with your suggestions?
Thank you.
I leafed over the paper. Unless there is a trick I am missing this model has two endogenous states: assets and housing. In principle the toolkit can do this but in practice it will be too slow to be of any real use 
He makes each model period 5 years, so doesn’t have to solve many periods. This helps.
Housing has a dual meaning here. Homeowners receive utility from its consumption services and also return from its investment if the house were to be sold. I plan to introduce only 5 periods, similar to Hu (2005) in 'Portfolio Choices for Homeowners’ published in the Journal of Urban Economics:
I intend to focus solely on solving the model for homeowners (Hu additionally introduces the renting and owning problem).
Do you think it makes sense to delve into modeling this problem with the toolkit? Could you please provide me with some advice? Thank you very much.
In Cocco paper there are two (but read below) endogenous states: asset holdings a and housing h but in practice the second state (housing) is discretized using few grid points. However an extra complexity is the choice of renting vs owning, so in principle you have three endo states: (a,h,o) where o is a dummy for housing tenure.
I think the code would work just fine for 5-10 periods, portfolio-choice plus housing, and in my head I can see how to implement it. If I can find some spare time in the next 1-3 months I will put it together. Hopefully, but no promises 
[Is just a matter of combining the risky endogenous state, which is currently Case3, with a standard endogenous state. Easy given that each is already done seperately, just will take a few days to code and debug.]
You can typically avoid having a whole state for own/rent. The trick is to have one of the points on the housing grid be zero, and simply assume that everyone who does not own any housing rents. You can then assume that housing and consumption are joined together by a CES function, and so the split can be analytically derived, thereby avoiding computing renting altogether (it is modelled, but it does not meaningfully complicate any of the computations). [I’ve solved a model with housing before, hence why I know this trick 
]
Portfolio-Choice with Housing
Hmm, 1-3 months turns out to be a pretty good call 
I went and read Cocco (2005) in detail. VFI Toolkit will easily do everything but one piece of the model. Specifically, Cocco (2005) has the risky asset returns shock (i.i.d. between period shock) correlating with the innovations to the earning shock (markov shock).
VFI Toolkit allows two shocks of the same type to be correlated, but it does not permit shocks of different kinds —here a u shock and a z shock— to be correlated.
You could do a workaround and model both as z shocks, and then do two endogenous states instead of the riskyasset, and this would work in the toolkit but would be rather wasteful. In some sense, the issue is that the is a ‘missing’ aggregate shock, which is the motive Cocco (2005) gives for the shocks being correlated.
So everything else in Cocco (2005) will be easy with VFI Toolkit, but a full replication is not possible because you cannot correlate the u and z shocks (the between period i.i.d. shock and the markov shock).
