<p>(It appears that the answer was supplied in the original question. The third link was to the time series for the M2 velocity for the United States. This answer is just taking text out of the comments.)</p>

<p>The linked chart <a href="https://fred.stlouisfed.org/series/M2V" rel="nofollow noreferrer">link to FRED website</a> is of the ratio: (nominal GDP at an annual rate) divided by M2 (for the United States).</p>

<p>The units for annualised GDP are \$ per year, and the units for M2 are \$; the \$ cancels and we end up with 1/years as units. (This is tracking units the way that is done in the physical sciences.) If we took non-annualised quarterly GDP, the ratio would be 1/4 as large.</p>

<p>Some economics charts can be confusing from the perspective of physical sciences, because the inverse time units for flows are suppressed. This is a convention that has held for decades; you just have to know what is being done. It probably causes problems because people often look at mixes of stock and flow variables, such as the infamous debt-to-GDP ratio. </p>

CC BY-SA 4.0
2018-05-04T02:32:11.620Z
I HATE it when people quote the debt-to-GDP ratio as if it were a percentage, which is completely nonsensical because it clearly isn't.
tparker
CC BY-SA 4.0
2020-06-25T10:48:55.780Z
It is wrong in so many ways. a purchase and a sale is an interaction, it is something being exchanged. It is much more akin to pressure. Or momentum. M1, M2 on the other hand is counting items in different buckets. It is mass. Or volume. Dem different dollars don't divide. If you say the monetary supply is the mass of money, the gpd is the pressure  - it makes sense. Increasing the mass of money, for a fixed volume ("the economy") increases pressure. If the economy contracts, it is a way to counter that contraction.
Stian
CC BY-SA 4.0
2018-05-03T22:28:37.927Z
2018-05-03T22:28:37.927Z
Brian Romanchuk
<p>All the discussions of the velocity of money that I've come across (e.g. <a href="https://en.wikipedia.org/wiki/Velocity_of_money" rel="nofollow noreferrer">here</a>, <a href="https://fredblog.stlouisfed.org/2014/08/m2-velocity-and-inflation/" rel="nofollow noreferrer">here</a>, and <a href="https://fred.stlouisfed.org/series/M2V" rel="nofollow noreferrer">here</a>) only display relative changes in the velocity of the money (e.g. by normalizing it by an unspecified value). I've never seen any source report an actual numerical value (with the units of inverse time) for a given point in time, for any choice of money supply. Does anyone have a reference for such a value?</p>

CC BY-SA 4.0
2018-05-02T19:41:54.463Z
Which country? I think the St. Louis Fed database (FRED) has a time series.
Brian Romanchuk
CC BY-SA 4.0
2018-05-02T19:44:47.843Z
@BrianRomanchuk Any country, but in particular I'm interested in the US. The second and third links in my question point to FRED, but they don't answer my question.
tparker
CC BY-SA 4.0
2018-05-03T09:20:40.977Z
You can calculate it yourself. Simply divide GDP by the amount of money.
E. Sommer
CC BY-SA 4.0
2018-05-03T21:16:35.117Z
@tparker - I didn’t look at the links, since your description was misleading. The third link shows nominal GDP divided by M2; this is not an unspecified normalisation. The units of GDP are $/year, and the units of M2 is dollars, so the units end up in inverse years, like you asked. The M2 velocity can be thought of as the number of times it turns over as part of GDP transactions in a year.
Brian Romanchuk
CC BY-SA 4.0
2018-05-03T21:29:58.180Z
@BrianRomanchuk I didn't understand the vertical axis of that plot, since it's just labeled "ratio" without any units specified. They describe the numerator as "quarterly nominal GDP" - does that mean income/quarter, or income/year reported quarterly? I.e. are the units of the vertical axis inverse years or inverse quarters? I can never understand economic data plots because economists never use units correctly.
tparker
CC BY-SA 4.0
2018-05-03T22:17:16.827Z
You need to look at the series definitions; the GDP series is a quarterly series, but is quoted at an annual rate. (Which is the amount of GDP transactions in the quarter, multiplied by 4.) So its units are $/year. For whatever reason, economists suppress the inverse time units to the description of flow variables. Even those of us with physical sciences backgrounds are used to that, and would probably view adding in the inverse time as “wrong.”
Brian Romanchuk
CC BY-SA 4.0
2018-05-04T02:29:41.907Z
@BrianRomanchuk (1) Where is the series definition that explains whether the GDP is quoted at an annual rate? The one that I see just says "quarterly nominal GDP", which is ambiguous. (2) Respectfully, people may well view adding the inverse time label as "wrong", but if they do they they are wrong to feel that way. Labeling quantities with the correct units clears up these kind of ambiguities and also provides conceptual intuition for their actual meaning.
tparker
CC BY-SA 4.0
2018-05-04T10:30:25.093Z
@tparker - there’s a link in the description (for the series GDP). As for the convention, it’s a bit late to try and change it...
Brian Romanchuk
<money-supply><money>
What is the actual numerical value of the velocity of money?
tparker
# What is the actual numerical value of the velocity of money?

(Asked by: username_0 on 2018-05-02)

All the discussions of the velocity of money that I've come across (e.g. [here](https://en.wikipedia.org/wiki/Velocity_of_money), [here](https://fredblog.stlouisfed.org/2014/08/m2-velocity-and-inflation/), and [here](https://fred.stlouisfed.org/series/M2V)) only display relative changes in the velocity of the money (e.g. by normalizing it by an unspecified value). I've never seen any source report an actual numerical value (with the units of inverse time) for a given point in time, for any choice of money supply. Does anyone have a reference for such a value?

**Tags:** money-supply, money

> **Comments:**
> **username_1**: Which country? I think the St. Louis Fed database (FRED) has a time series.  
> **username_0**: @username_1 Any country, but in particular I'm interested in the US. The second and third links in my question point to FRED, but they don't answer my question.  
> **username_2**: You can calculate it yourself. Simply divide GDP by the amount of money.  
> **username_1**: @username_0 - I didn’t look at the links, since your description was misleading. The third link shows nominal GDP divided by M2; this is not an unspecified normalisation. The units of GDP are $/year, and the units of M2 is dollars, so the units end up in inverse years, like you asked. The M2 velocity can be thought of as the number of times it turns over as part of GDP transactions in a year.  
> **username_0**: @username_1 I didn't understand the vertical axis of that plot, since it's just labeled "ratio" without any units specified. They describe the numerator as "quarterly nominal GDP" - does that mean income/quarter, or income/year reported quarterly? I.e. are the units of the vertical axis inverse years or inverse quarters? I can never understand economic data plots because economists never use units correctly.  
> **username_1**: You need to look at the series definitions; the GDP series is a quarterly series, but is quoted at an annual rate. (Which is the amount of GDP transactions in the quarter, multiplied by 4.) So its units are $/year. For whatever reason, economists suppress the inverse time units to the description of flow variables. Even those of us with physical sciences backgrounds are used to that, and would probably view adding in the inverse time as “wrong.”  
> **username_0**: @username_1 (1) Where is the series definition that explains whether the GDP is quoted at an annual rate? The one that I see just says "quarterly nominal GDP", which is ambiguous. (2) Respectfully, people may well view adding the inverse time label as "wrong", but if they do they they are wrong to feel that way. Labeling quantities with the correct units clears up these kind of ambiguities and also provides conceptual intuition for their actual meaning.  
> **username_1**: @username_0 - there’s a link in the description (for the series GDP). As for the convention, it’s a bit late to try and change it...  

---

## 1 answers

### Answer by username_1 on 2018-05-03. Score: 0 | Accepted answer

(It appears that the answer was supplied in the original question. The third link was to the time series for the M2 velocity for the United States. This answer is just taking text out of the comments.)

The linked chart [link to FRED website](https://fred.stlouisfed.org/series/M2V) is of the ratio: (nominal GDP at an annual rate) divided by M2 (for the United States).

The units for annualised GDP are \$ per year, and the units for M2 are \$; the \$ cancels and we end up with 1/years as units. (This is tracking units the way that is done in the physical sciences.) If we took non-annualised quarterly GDP, the ratio would be 1/4 as large.

Some economics charts can be confusing from the perspective of physical sciences, because the inverse time units for flows are suppressed. This is a convention that has held for decades; you just have to know what is being done. It probably causes problems because people often look at mixes of stock and flow variables, such as the infamous debt-to-GDP ratio.

> **Comments:**
> **username_0**: I HATE it when people quote the debt-to-GDP ratio as if it were a percentage, which is completely nonsensical because it clearly isn't.  
> **username_3**: It is wrong in so many ways. a purchase and a sale is an interaction, it is something being exchanged. It is much more akin to pressure. Or momentum. M1, M2 on the other hand is counting items in different buckets. It is mass. Or volume. Dem different dollars don't divide. If you say the monetary supply is the mass of money, the gpd is the pressure  - it makes sense. Increasing the mass of money, for a fixed volume ("the economy") increases pressure. If the economy contracts, it is a way to counter that contraction.  

---

