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“Have we paid sufficient attention to the natural or the neutral rate of inflation—“the level that would be ground out by the Walrasian system of general equilibrium equations… [accounting for] structural characteristics… including market imperfections, stochastic variability… cost of gathering information… [and] of mobility, and so on…”? I guess that the natural rate of inflation will be higher in times when there is a good deal of reallocation to be done—at times when the economy is not in a stable configuration with respect to sectors and industries, but is instead hunting for a new and different cross-sector and cross-industry relative allocation of effort. Is that how to read 1947 and 1951?”

By “natural” do you mean maximally market-clearing/real income maximizing inflation? Since there is always reallocation to be done, isn’t a sensible way to model this to have an average target rate for normal amounts of reallocations to be done [relative price changed to be made] and a temporarily higher, "flexible" over-target rate when there is more re-allocation to be done [relative price changes to be made] -- financial crisis/OPEC/COVID down shock/COVID up shock.

FAIT QED

But why would this schema be valuable only for 1947 and 1951? A significant change in the budget deficit would be just one more kind of shock that could call for an over-target rate.

“Still, I put forward the thesis that FOMC policy since the start of 2020 has been very close to perfect both ex ante and ex post.”

I fully agree, but even a “little” rubber on the road is an IMperfection. At least with hindsight [but TIPS signaled it] starting to tighten in September 2021 might have prevented having to raise ST rates as high and for as long as it has and the risk of rescission to be as high as it still is. Also, I guess the Fed was as surprised as anyone else at how MUCH the public hates rubber on its roads and blames Biden not Powell for the "dammed spot."

“This is, at its base, a strongly right-wing market-fundamentalist argument: the market has its logic that we need to respect, and for it to work prices need to do what they need to do—and to keep them from doing so by artificially pushing demand down diminishes the market’s power to do its proper job properly.”

Right wing? The Right-winger respects the market "logic" only when it transfers income and power up the SE scale. The neoliberal respects the “logic” of the market but not its resource allocations (externalities, information asymmetries, public goods) nor its distributional consequences.

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I like "luck-of-the-epsilons". But, not being an economist, I usually work in continuous time. My version would have to be something like "that's the way the Wiener process wiggles".

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