Two-Sample KS test

[Ulla Andersen]

Good day,

I have a sample of European countries and I'm analyzing bank profitability for EU banks with panel data. However, Italy is heavily overweighted in my sample, as it constitutes more than half of all observations. I suspect it's because there are many small Italian banks in the sample that are not very representative of the overall EU banking sector, but I was wondering if I can test this with a two-sample KS test? I have split the sample with a dummy into Italian banks and the rest of the EU banks and so if I test for difference in distributions, would this be indicative that I should drop some smallest banks in Italy? I have already performed ttests, but I was wondering if I can also supplement these with a two-sample KS test?

I apologize if this is a very basic question, but I would greatly appreciate your help!

[Joro Kolev]

I presume you mean the Kolmogorov-Smirnoff test... I always wondered whether the person from the Kolmogorov-Smirnoff test is the same Smirnoff as the Smirnoff after whom the famous Russian vodka Smirnoff was named...

In any case, I do not think that this is a good way to go. The KS test is for (unconditional) comparison of distributions.

You are fitting some model there, studying how bank profitability is explained by other factors, that is, you study the conditional distribution of profitability.

What you want to do is broadly called outlier detection, you want to know whether Italian banks are outliers in your regression.

The easiest way to do this, is to run your regressions with, and then without the Italian banks, and see whether your results dramatically change.

[Ulla Andersen]

Dear Joro,

Thanks for your response and your insightful comment! I was just worried about the representativeness of the sample as with the current composition it does not seem very representative of the whole Europe... Do you think I could possibly just exclude a percentage of the smallest Italian banks to make it more representative or is this unreasonable?
Thank you again!!

[Carlo Lazzaro]

Ulla:
a limited number of big banks actually owes smaller banks in Italy.
Perhaps, you can group them together according to the bigger player that owes them before regressing.

[Joro Kolev]

Carlo has a good proposal, maybe you could "consolidate" your small banks into the bigger entities owning them? Somehow aggregate the data of small bank by the entity owning them?

Otherwise you can do whatever you want, it is your research, it is reasonable enough to exclude small banks if you are not interested in small banks.

But you should definitely compare the full sample results, with the results where Italian or small banks are excluded. Even just looking at the coefficients of interest, and how their significance changes after you exclude small/Italian banks will tell you a lot.

There are many other things that you can do and are reasonable, depends on what the literature to which you are contributing does.

1. You can control for bank size, e.g., by putting size and size^2, or by breaking the banks in categories by size (say small, medium, big) and then include dummies for the categories.

2. You can weight by bank size, thereby placing larger weight on bigger banks than on the smaller ones.

Dear Joro,

Thanks for your response and your insightful comment! I was just worried about the representativeness of the sample as with the current composition it does not seem very representative of the whole Europe... Do you think I could possibly just exclude a percentage of the smallest Italian banks to make it more representative or is this unreasonable?
Thank you again!!

[Ulla Andersen]

Dear Joro and Carlo,

Thanks for all the great proposals, I will definitely take a look at all the options! Thanks again, I appreciate your help!