age-varying transition equations?

[sbenthall]

Continuing from here

But, per our earlier discussion that the "problem" may change, say, at different ages of life, if we can have an architecture can handle that for all the other things that are MORE complicated than the distributions (because, for example, there may be several transition equations or whatever inside a period, but only one draw of exogenous shocks), then we will surely also want to use the same architecture for keeping track of the shocks as for keeping track of everything else about the problem.

The example that's come up for this is:

• A lifecycle model, in which agents face different choices at different ages.
  • For example, there is only a narrow range of ranges at which one decides to attend college.

@llorracc it's clear that you think this is an important case to architect around. But I'm afraid that after our brief discussion of it earlier I'm still not following the logic of this.

A few questions about it:

• Thinking about the example, people pursue education at many stages of life, for different reasons. While it's most common to get certain degrees at certain ages, wouldn't it be more compelling to model those decisions as endogenous, given the incentives around education? Do you have a better example of the kind of problem you have in mind? Or could you make it more concrete in, say, mathematical formalism?
• It's hard to do anything systematic about a problem in which "everything" can change. But it looks like you might be specifically concerned with transition equations varying by age. Is that right?
• I believe that it is in principle possible, given a model where an agent faces different transition equations at each age, to build an equivalent model where the agent faces the same equations at each age, with added age-specific variables which control which transition equations are relevant or viable in that particular period. Do you share this intuition?