Is t_age a state?

[sbenthall]

I'm working on updating the old cstwMPC code and it does something that's for me unexpected.
It tries to pull in the agent's t_age data into the Market class as a reap_var.

We've been separating out different kinds of 'model variables' -- states, controls, shocks -- into separate namespaces.

But variables like t_age and t_cycle, which are more about the 'population model' than the structural equations model defined under the SDP framework, have remained part of the core machinery without this treatment.

I can hack around this for the cstwMPC update, but I think it raises an interesting question about how to deal with t_age moving forward.

See related tickets: #95 #669 #837 #847

[mnwhite]

This is sort of a philosophical question. In the "taxonomy of variables" that I preach, the mathematical objects that t_age and t_cycle represent are not "state variables", but rather "time variables". However, "time variables" can be considered a special class of "state variable" because of their trivial dynamics: a time variable is a state variable that evolves monotonically and with no uncertainty. We could write $age' = age + 1$ and define age to be (mathematically) part of the individual's state, but in the Bellman phrasing of problems we use the convenient fact that things happen one after another to break down an intertemporal problem into a sequence of feasible steps. In a continuous time model (not our bag) that includes age, it's just another state variable with trivial dynamics: agents move through the age dimension at a constant positive rate. For cstwMPC, I think I reap t_age because a bunch of the internal statistics collecting and computing is done at the market level. It's gathering that data for application purposes, not model purposes. However, it's entirely possible to write a model where market outcomes actually do depend on the distribution of ages.

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On Mon, Mar 15, 2021 at 4:02 PM Sebastian Benthall ***@***.***> wrote: I'm working on updating the old cstwMPC code and it does something that's for me unexpected. It tries to pull in the agent's t_age data into the Market class as a reap_var. We've been separating out different kinds of 'model variables' -- states, controls, shocks -- into separate namespaces. But variables like t_age and t_cycle, which are more about the 'population model' than the structural equations model defined under the SDP framework, have remained part of the core machinery without this treatment. I can hack around this for the cstwMPC update, but I think it raises an interesting question about how to deal with t_age moving forward. See related tickets: #95 <#95> #669 <#669> #837 <#837> #847 <#847> — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#983>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ADKRAFIXY6F4DNRQOJCAHJLTDZRWVANCNFSM4ZHHHM6Q> .

[mnwhite]

Closing this issue for being stale and not really something to resolve. HARK 1.0 will have a different age-tracking structure anyway.