Lifecycle models with health

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In the macro literature on lifecycle choices and health, the survival probability depends not only on age but also on health. Health is often modelled as a Markov shock, either exogenous or somehow affected by health effort. Some relevant papers:

In any case, in all these models the survival probability and hence the effective discount factor does depend on z, if we interpret z as health.

How costly would be to allow this feature in the toolkit? I know there is a trick (transition to dead state, explanation in older post here), but the code is not very clean. In particular, when doing model moments, you have to use conditional restrictions and it becomes complicated

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I’m assuming: Costly=how much work to code. Conceptually, easy to code. In practice, I could do the value fn easy enough, the stationary dist commands would need some work as there is currently no concept of being eliminated before you reach next period, but in practice this is just pi_z where some rows do not sum to 1. Of course I would need to go and implement it for a whole variety of different cases (with and without e, with and without d, etc.).

From my perspective: the trick (transition to dead state) is only a very minor computational loss, coding it explicitly would be easy enough but a fair bit of work.

Summary: I don’t plan to do it currently, but if convinced there would be a number of users for it I would be happy to implement. It is not hard, would just take some time (a few days).

PS. One cool thing the toolkit does and none of those articles do, is that you can do ‘double epstein-zin prefences’ where people treat the risk of death differently to the financial risks (which a paper or two claim is realistic). [Doesn’t allow death probability do depend on z, only on age.]

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Thanks for your answer! Maybe it would help to have a short appendix somewhere that explains how to implement a health-dependent survival rate by adding an extra state.

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Alessandro,

I have forked your Endogenous_survival repo to study. Yesterday I was at a presentation of the Cancer Society and their ambitious plans and goals. They presented the fact that 1 in 3 people will be affected by cancer (either directly or as care-taker/support person for a cancer patient). Somehow that got me thinking about cancer as an effect in Life Cycle Analysis.

Cancer takes many forms, and its progression (or resolution to remission) happens over a variety of pathways and timeframes. There are genetic, environmental, and behavioral predictors of cancer, and there are therapeutic, medical, and behavioral mitigations that can prevent specific cancers (HPV vaccine) and/or put them into remission (CAR-T for one).

It got me thinking about how a model using anonymized community data and stochastic markov processes could help people understand better the risks and returns on investment of various behaviors and interventions. Particularly the ability to look at a sample of agents who all start in the same place and whose fates are spread out by probability transitions. It would help people understand “yes, this one in a hundred did keep smoking and lived until he was hit by a car” but also “wow, I see that 70 in one hundred died from lung cancer, even after quitting later in life”. Or whatever.

You have already listed some papers, and I’ve found a few others (using LLMs to model risk over time based on behavior changes over time), but if you come across anything relevant (especially models), please chime in!

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There are several papers in the macro-health literature that can hopefully give a hint on how to model these patterns. I will come back to this and write a longer post when I have a bit of time (I write this as a memo to myself).

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