<p>I have a question regarding the difference between stock and flow variables. </p>

<p>I know that a stock variable is measured at a specific point in time $t$ and the flow of this variable is measured over time, for example from $t-1$ to $t$. </p>

<p>When economists compute the ratio between a stock and a flow variable in some cases they use the geometric mean for the flow variable and the unchanged stock variable. Let's take an example: 
A very popular ratio nowadays is "credit-to-gdp". Nearly all studies compute the credit-to-gdp ratio for year $t$ by using the stock variable of credit at $t$ and the geometric mean of gdp from $t-1$ and $t$ (for example <a href="http://www.nber.org/papers/w14049.pdf" rel="nofollow noreferrer">Mendoza &amp; Terrones, 2008</a> or <a href="https://www.sciencedirect.com/science/article/pii/S1572308913000429" rel="nofollow noreferrer">Dell'Ariccia et al., 2012</a>). But why are they doing this? I know the difference between the two concepts but the question for me still remains "so what?". </p>

<p>Consider a counter example: income per capita. Income is obviously a flow variable while the number of people in an economy is a stock variable. But as far as I know nobody is even considering using the geometric mean or something like this. </p>

<p>Is it just a habit, a practical issue (if we have the data we do it if not we don't) or is there really a logical (mathematical) reason behind this approach? So far I was not able to find a convincing answer and I get the feeling that this is just a method to smooth the data a little bit.   </p>

CC BY-SA 3.0
2018-03-02T09:42:05.523Z
Welcome to the site.  It's a good question, but the title doesn't really summarise what you are asking, and could suggest you are just asking what the difference is between a stock and a flow.  You might consider editing the title to something like "Why use geometric mean of GDP when calculating ratio of credit to GDP?"
Adam Bailey
CC BY-SA 3.0
2018-03-02T09:42:57.867Z
Thank you for your comment. I edited to title of the Question.
PAS
CC BY-SA 3.0
2018-03-04T13:37:58.007Z
This is the sort of thing that is supposed to be explained in academic papers; however, it would probably be a cryptic one sentence comment. I am not familiar with this literature, but GDP is just a scaling factor. Just using one GDP data point probably results in a noisier series. By averaging GDP, changes in the ratio are driven more by the change in credit, which is what the authors are interested in.
Brian Romanchuk
CC BY-SA 3.0
2018-03-05T14:11:55.153Z
Maybe another justification for the geometric mean - besides the smoothing aspect - could be duo to the danger of measurement errors in gdp. Looking at the literature a little bit more the first paper that is using the gdp-to-credit ratio with geometric mean is this one: https://www.researchgate.net/profile/Pierre-Olivier_Gourinchas/publication/4752801_Lending_Booms_Latin_America_and_the_World/links/02bfe51277879ee039000000/Lending-Booms-Latin-America-and-the-World.pdf which quotes a paper on financial crises and economic development/deepening as a source for using the geo mean.
PAS
<macroeconomics><econometrics><mathematical-economics>
Why use geometric mean for GDP when calculating the credit-to-gdp ratio?
PAS
# Why use geometric mean for GDP when calculating the credit-to-gdp ratio?

(Asked by: username_0 on 2018-03-02)

I have a question regarding the difference between stock and flow variables.

I know that a stock variable is measured at a specific point in time $t$ and the flow of this variable is measured over time, for example from $t-1$ to $t$.

When economists compute the ratio between a stock and a flow variable in some cases they use the geometric mean for the flow variable and the unchanged stock variable. Let's take an example:
A very popular ratio nowadays is "credit-to-gdp". Nearly all studies compute the credit-to-gdp ratio for year $t$ by using the stock variable of credit at $t$ and the geometric mean of gdp from $t-1$ and $t$ (for example [Mendoza & Terrones, 2008](http://www.nber.org/papers/w14049.pdf) or [Dell'Ariccia et al., 2012](https://www.sciencedirect.com/science/article/pii/S1572308913000429)). But why are they doing this? I know the difference between the two concepts but the question for me still remains "so what?".

Consider a counter example: income per capita. Income is obviously a flow variable while the number of people in an economy is a stock variable. But as far as I know nobody is even considering using the geometric mean or something like this.

Is it just a habit, a practical issue (if we have the data we do it if not we don't) or is there really a logical (mathematical) reason behind this approach? So far I was not able to find a convincing answer and I get the feeling that this is just a method to smooth the data a little bit.

**Tags:** macroeconomics, econometrics, mathematical-economics
> **Comments:**
> **username_1**: Welcome to the site.  It's a good question, but the title doesn't really summarise what you are asking, and could suggest you are just asking what the difference is between a stock and a flow.  You might consider editing the title to something like "Why use geometric mean of GDP when calculating ratio of credit to GDP?"  
> **username_0**: Thank you for your comment. I edited to title of the Question.  
> **username_2**: This is the sort of thing that is supposed to be explained in academic papers; however, it would probably be a cryptic one sentence comment. I am not familiar with this literature, but GDP is just a scaling factor. Just using one GDP data point probably results in a noisier series. By averaging GDP, changes in the ratio are driven more by the change in credit, which is what the authors are interested in.  
> **username_0**: Maybe another justification for the geometric mean - besides the smoothing aspect - could be duo to the danger of measurement errors in gdp. Looking at the literature a little bit more the first paper that is using the gdp-to-credit ratio with geometric mean is this one: https://www.researchgate.net/profile/Pierre-Olivier_Gourinchas/publication/4752801_Lending_Booms_Latin_America_and_the_World/links/02bfe51277879ee039000000/Lending-Booms-Latin-America-and-the-World.pdf which quotes a paper on financial crises and economic development/deepening as a source for using the geo mean.  

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