# Why use geometric mean for GDP when calculating the credit-to-gdp ratio?

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 or Dell'Ariccia et al., 2012). 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.

• 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?" Mar 2, 2018 at 9:42
• Thank you for your comment. I edited to title of the Question.
– PAS
Mar 2, 2018 at 9:42
• 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. Mar 4, 2018 at 13:37
• 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: researchgate.net/profile/Pierre-Olivier_Gourinchas/publication/… which quotes a paper on financial crises and economic development/deepening as a source for using the geo mean.
– PAS
Mar 5, 2018 at 14:11