Modeling inflation with VFIToolkit

A search for the term “inflation” yielded no results from this message board, so here goes.

I have just read Inflation surprises in a New Keynesian economy with a “true” consumption function which lays things out in ways that seem very VFIToolkit friendly.

My question for discussion relates to the pros and cons of attempting to work inflation into just the lifecycle analysis (treating it as basically a wedge in the difference between the real interest rate and the “risk-free rate of return”, with an attacked markov shock model), versus placing it across transition periods.

I am most interested in studying the behavior of fossil fuel cost inflation, which presently influences CPI, but which across the energy transition will both have a stronger effect on CPI (as fossil fuel prices increase) and a weaker effect (as fossil fuel usage decreases across the transition). Heterogeneous agents who can transition will experience that component of inflation differently than those agents who cannot transition. Given that I’m ultimately studying transition, it may be that the inflation question must be studied in the transition paths, but those are manually made and I don’t yet have a good model for how agents discount the future in transition (which they do very elegantly within LCA).

Another question is whether this question is best answered in terms of either/or or both-and (and if so what that means/how it could be done).

You can put deterministic inflation into an OLG model, just doing it with the same ‘renormalization’ tricks used for deterministic productivity growth or deterministic population growth (Life-Cycle Model 22 in Intro to Life-Cycle Models; OLG Model 8 in Intro to OLG Models).

The catch is that inflation won’t do anything in the model, because all the prices are flexible. [“New Keynesian” models all add ‘sticky prices’ of one form or another.] [Partial exemption if some policies in model are inflation indexed and others are not.]

Note, adding stochastic inflation would involve and aggregate shock and so cannot currently be done in VFI Toolkit.