0
$\begingroup$

I have a question regarding my regression model and would be grateful for any help.

I have a dataset that contains every tranche of a Deal (a Deal may contain multiple Tranches) and its Variables like Poolsize, Rating etc. The Tranches are included into the dataset at the time the Deal is launched and are from all Deals of the last 10 years, so each observation is a different tranche that is part of a deal. Every Tranche is just collected once, that means Tranches collected 5 years later are Tranches from different Deals. That is the reason why I believe my dataset is pooled cross sectional data and not panel data.

With this in mind, I ran a Regression in R using the lm package:

MR1111 <- lm(Credit_Spread ~ log_Poolgroesse + Anzahl_Tranchen_Deal + 
             Zwei_Ratingagenturen + Anzahl_Finanzinstitute + 
             Anzahl_Arten_Gewerbeimmobilien + Regel_144A_SEC + 
             Pool_LTV + Uneinigkeit_Ratingagenturen + WAL + 
             Waehrungsrisiko + log_Tranchevolumen + Arbeitslosenquote,
             data = Datensatz_neu6)

I then checked for Multicollinearity using the VIF command. Everything was good, no Value was above 5, mostly between 1 to 1.5.

Then I ran the same Regression as above, but with fixed effects for the quarter in which the deal was launched and the Country the deal was launched in (Land_der_Sicherheiten):

MR1111 <- lm(Credit_Spread ~ log_Poolgroesse + (...) + 
              as.factor(FE_Quartal) + 
              as.factor(Land_der_Sicherheiten), data = Datensatz_neu6)

While testing for Multicollinearity, all Variables are still under 5 except for as.factor(FE_Quartal) with a value of 51367.27 and as.factor(Land_der_Sicherheiten) 320.326.

How can I deal with this?

An information which might be important: There are several observations that were launched in the same quarter. The same goes for the country the deal was launched in.

$\endgroup$
3
  • $\begingroup$ What are tranches and deals? $\endgroup$
    – Peter Flom
    Commented Nov 12, 2023 at 15:31
  • $\begingroup$ @Peter Flom: In the context of asset-backed securities (ABS), a "tranche" refers to a specific portion or slice of the overall pool of assets that backs the security. When an ABS is created, the underlying assets, such as mortgages, auto loans are pooled together. These assets generate cash flows from interest payments and principal repayments. A "deal" in the context of ABS refers to the issuance or creation of an asset-backed security $\endgroup$ Commented Nov 12, 2023 at 16:14
  • $\begingroup$ Could you please elaborate on your question: what do you mean by "deal with it"? Why is there a problem? What is the objective of your new, modified regression model? $\endgroup$
    – whuber
    Commented Nov 12, 2023 at 17:33

1 Answer 1

0
$\begingroup$

Multicollinearity means that the contribution of a variable (or a combination of variables) cannot be identified because it could be emulated by another variable (or a combination of them). Looking at two fixed effects, you have the simplest case of collinearity if for all observations one level of one fixed effect (say level A) always goes with the same level of the other fixed effect (say level I) and vice versa, because then any contribution of level A could well be added to the coefficient of level I were the first fixed effect left out. It would be enough to have such a correspondence between one level of the first fixed effect and a group of levels of the second fixed effect, or the other way round. The more levels the fixed effects have, the more likely is it to find some levels for which this happens. As your VIF is high for the fixed effects but not for the other variables, I'd expect that something like this is going on. The problem should go away if you only use one fixed effect, but you may not want to do that. Merging levels may also help but try to know which levels cause the problem first.

The interplay between your fixed effects and a numerical variable (or a linear combination of them) may also cause collinearity if the numerical variable is approximately constant within all levels of a fixed effect or if any deviation from this can be caught somehow by the other fixed effect. I wouldn't expect your VIF pattern in such a case but I can't rule it out with certainty.

Generally fixed effects with too many levels give the regression very flexible possibilities to model the data, and this is not good as it may easily lead to identifiability/collinearity issues.

In any case look at a crosstable of your fixed effects and see what happens if you run your regression with one fixed effect only to see whether the problem is what I think it is (and for having a clue about how to make the issue go away).

$\endgroup$
4
  • $\begingroup$ Hey Christian, thank you for your answer! I'll try it as soon as possible and come back to you! Thanks again. $\endgroup$ Commented Nov 17, 2023 at 12:27
  • $\begingroup$ Hey Christian, I removed a fixed effect like u told me and tested for Multicollinearity again while using the VIF command. All variable values are still under 5, a few increased while other decreased. The value for as.factor(FE_Quartal) is high with 879.034. When i remove the fixed effect as.factor(FE_Quartal) and keep the fixed effect as.factor(Land_der_Sicherheiten) instead and then test for multicollinearity all variables have values <2. Only the fixed effect as.factor(Land_der_Sicherheiten) has a value of 5.48. How do i deal with this now? $\endgroup$ Commented Dec 1, 2023 at 9:50
  • $\begingroup$ I guess the multicollinearity is caused by the fixed effect FE_Quartal (the quarter in which the deal was launched) because in my dataset i have approximately 40 Quarter, while only 7 Countries i hold fixed effects for. Can I use the regression with the two fixed effects, or do I have to remove the fixed effects for quarter so the assumption of Multicollinearity is not violated to have accurate results? $\endgroup$ Commented Dec 1, 2023 at 9:55
  • $\begingroup$ @NasimEl-Issa Sorry, I can't tell you how to analyse your data; whatever I personally would do depends on how exactly the data look like and all background information. It seems FE_Quartal causes the problem and the analysis using it looks suspicious, but I don't know enough of data and background to say what to do. You may be better off looking for professional advice. $\endgroup$ Commented Dec 1, 2023 at 10:49

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.