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note: some errors have been corrected since initial post
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Ok, let's sandbag right away. I don't know if I got this in the right groove but let's roll anyway.
Using a life consumption utility model, and a simple model for auto-regressive inflation based on historical data, I ran a few new models today:
1. a baseline with deterministic inflation set to the mean of the random distribution I'll use for #2
2. a simulation using stochastic inflation that is bootstrapped from history (1914-2018) with a coefficient of auto-regression over 1 period of .64. (see the link above on inflation)
3. This scenario is the same as #2 except that the initial wealth is stepped up a bit (+25%) to get the life consumption utility up back towards #1 levels (not done analytically. Pretty much just eyeballed it). This is more or less like evaluating "certainty equivalent wealth" but I'm not totally sure about that so I won't precisely make that claim.
The goal was to determine how much extra wealth might be necessary at retirement-start to make the life consumption utility roughly the same as the baseline i.e., that is, either: a) we implicitly spend less...I realize that I have not really shown that here, or b) we have some amount of "redundant" (higher) wealth (vs the baseline) that is held in reserve in a way. Either way, same thing. I might have to expand on this because I know it's a little fuzzy.