In the standard New Keynesian model (e.g. Gali textbook), how are defined "inflation volatility" and "price dispersion?"
Is there a correlation / relation between the two?
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$\begingroup$ Price dispersion is not really macro concept, where did you find it in Gali? I know lot of places that have definition of it but it’s possible Gali has some own definition $\endgroup$– 1muflon1 ♦Commented Jul 25 at 18:24
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$\begingroup$ It shows up, for example, in welfare calculations. It also shows up when aggregating production functions ("misallocation") $\endgroup$– Luca GiCommented Jul 26 at 19:11
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Price dispersion refers to how much prices for the same good vary at the same time. For example, you may see different prices for bread at different supermarkets on the same day. The standard deviation of prices is one measure of dispersion. The difficulty comes in when looking at the 'aggregate price dispersion' - that is, a measure of how dispersed prices are in the whole economy. A paper by Alvarez, Beraja, Gonzalez-Rozada, and Neumeyer (2019) in the QJE measures aggregate price dispersion as the residual variance in a regression of prices on a large set of fixed effects (to control for which goods are really the same).
Inflation volatility is how much inflation changes across time. For example, one month inflation might be 5% and the next 20% (this would be quite volatile). A natural measure is the standard deviation of monthly inflation.
A recent working paper by Francisca Sara-Zaror explores this link. She finds that the relationship between inflation and price dispersion is V shaped (high dispersion when inflation is low and high but not moderate) and shows this is consistent writes down a menu-cost model to rationalize this fact.
Sara-Zaror, Francisca (2024). “Inflation, Price Dispersion, and Welfare: The Role of Consumer Search,” Finance and Economics Discussion Series 2024-047. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2024.047.
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1$\begingroup$ Thanks. I believe in the NK model the two quantities are related mathematically. See for example the welfare calculations in the appendix of chapter 4, which uses results from Woodford's book. I cannot fully wrap my head around it though. $\endgroup$– Luca GiCommented Jul 26 at 19:15
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1$\begingroup$ In the NK model, price dispersion comes about because some firms can't adjust their prices. So you can solve for the distribution of prices as a function of the shocks and the aggregate state. I'm not really sure what specific confusion you have though! Maybe if you post a question related to how a specific equation is derived? $\endgroup$– FićaCommented Jul 26 at 20:19