<p>Price dispersion refers to how much prices for the same good vary at the <strong>same time</strong>. 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).</p>
<p>Inflation volatility is how much inflation changes <strong>across time</strong>. 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.</p>
<p>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.</p>
<p>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, <a href="https://doi.org/10.17016/FEDS.2024.047" rel="nofollow noreferrer">https://doi.org/10.17016/FEDS.2024.047</a>.</p>

CC BY-SA 4.0
2024-07-26T19:15:32.413Z
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.
Luca Gi
CC BY-SA 4.0
2024-07-26T20:19:08.597Z
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?
Fića
CC BY-SA 4.0
2024-07-26T04:30:03.487Z
2024-07-26T04:30:03.487Z
Fića
<p>In the standard New Keynesian model (e.g. Gali textbook), how are defined &quot;inflation volatility&quot; and &quot;price dispersion?&quot;</p>
<p>Is there a correlation / relation between the two?</p>

CC BY-SA 4.0
2024-07-25T18:24:08.020Z
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
1muflon1
CC BY-SA 4.0
2024-07-26T19:11:26.930Z
It shows up, for example, in welfare calculations. It also shows up when aggregating production functions ("misallocation")
Luca Gi
<inflation><price><new-keynesian-economics>
Relation between price dispersion and inflation volatility in NK model
Luca Gi
# Relation between price dispersion and inflation volatility in NK model

(Asked by: username_0 on 2024-07-25)

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?

**Tags:** inflation, price, new-keynesian-economics
> **Comments:**
> **username_1**: 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  
> **username_0**: It shows up, for example, in welfare calculations. It also shows up when aggregating production functions ("misallocation")  

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## 1 answers

### Answer by username_2 on 2024-07-26. Score: 3 | Accepted answer

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>.

> **Comments:**
> **username_0**: 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.  
> **username_2**: 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?  

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