I want to introduce single men, single women and married couple households into the model. Everyone has experience assets, so it is necessary to decide their working hours separately in the married couple households subject to decide their experience assets (human capital). But I don’t seem to see this design in the handbook. I want to ask if this kind of situation is allowed in VFITOOKIT.
Thanks a lot!
For a model with single men, single women and married households you may find this example based on a paper by Borella, De Nardi and Yang useful:
Moreover, there is an example with experience asset here:
I know this example. But I read the reference books and source codes that experienceasset needs to be placed in the second place of endogenous states. For example, in the source code, it says "n_d2=n_d(end-1); % n _ d2 is the decision variable that influences the experienceasset " and “n_a=[201,21]; % Endogenous asset holdings, female-labor-force-participation“, which seems to mean that two experience assets cannot be set because there is only one second position.
Unfortunately currently not possible to do two experienceassets. This is obviously something that should be possible, but has not yet been implemented.
PS. Many papers with models along these lines compromise and just model the female human capital, so your single male is just savings, the single female is savings and human capital, and the married couple is savings and female human capital. [This is not a suggestion, just a comment.]
PPS. You can kind of trick it because an expericeneasset sets aprime(d,a), which you can invert to get d(aprime,a) which is now just a standard endogenous state (the aprime and a) and then inside the ReturnFn you can calculate d(aprime,a). But this is rather rough and not nearly as fast nor as smooth as using the experienceasset.
@LeonChen I take it you want savings alongside the two human capitals?
Thanks for your help! What I originally wanted to do was for a couple to have a common savings and two separate human capitals, to decide their respective working hours and whether their wives should have children, and finally to compare the human capital gap between their wives and husbands. But since you said that two human capitals can’t be set at the same time, I think I should remove the male human capital or set it as a constant that changes with time.
Empirically men’s earnings don’t change much around the birth of a child, which suggests their human capital doesn’t react much, and as a result most models in the literature take this as a reason not to model men’s human capital and instead just use somethings simpler for mens earnings (just make it an age-dependent parameter, maybe some markov shocks, even some iid if you wanted). [Not claiming this is good or bad, just what most papers do.]
The early generation of models like Attanasio, Low & Sanchez-Marcos (2008) has female human capital and makes children exogenous (age dependent parameter). VFI Toolkit does this using a ‘experienceasset’ for the human capital. [toolkit code for ALS2008]
Then models of endogenous fertility came along, like Sommer (2016). VFI Toolkit does this using a ‘semi-exogenous state’, semiz, for the fertility choice/number of children. [toolkit code for Sommer2016]
The more recent generation of models combines these. You model the female human capital together with endogenous fertility, you can use permanent types for ‘single male’, ‘married couple’, etc. For example, Guner, Kaya & Sanchez-Marcos (2024); they also have stuff about employment contracts but that doesn’t much change the model setup. VFI Toolkit can do, e.g., a model with savings (standard endogenous state), female human capital (experienceasset), and endogenous fertility (semi-exogenous state).
If you do want to use experienceasset together with semi-exogenous state I don’t think the combination is publicly documented anywhere, but it is all coded. Most of it is likely easy enough to infer how to do. The ‘last’ decision variable controls the semi-exogenous state, and the ‘second last’ decision variable controls the experienceasset.
Actually, by default it sets vfoptions.l_dsemiz=1, and if you make this =2 then it is the ‘second last and the last’ decision variables that control the semi-exogenous state. And by default vfoptions.l_dexperienceasset=1, and if you also make this =2 then it would be the ‘fourth last and third last’ decision variables that control the experienceasset.
Thinking aloud while my model cranks through its latest tests…
I’ve been somewhat successful using PTypes to build models loosely using the paradigm of “split, apply, combine”. In my case, firms and households make a set of decisions that jointly feed into an energy supplier, and then we solve the GE and/or transition path for the lot of them. The obvious advantage of splitting the problem apart is that we can solve equilibria that span both finite and infinite horizon models. But a second advantage is that by splitting the problem into parts, our rate-limiting step becomes solving the largest sub-model, not the exponentially larger dimensional expansion of everything.
I wonder whether it makes sense to model single, married, divorced, and widowed males and females as individuals who can then form households (including MM and FF) where the equations of the household PType can (re)use calculations from the individuals (or individual). We know for example that individual survival is correlated with individual history of being single, marrier, divorced, widowed, etc., for example.
I’m not saying this is THE answer, but depending on how the experience assets play into the decisions, it might be possible to factor the problem in a way that provides extraordinary modeling power without requiring extraordinary computing power. Just ordinarily powerful GPU processing…