Multicollinearity in regression analysis

[Simone Guerriero]

I need to test multicollinearity for my data set. I made the correlation matrix and I notice a correlation between some of my independent variables, but from the analysis of the VIF the result is that there is no multicollinearity (VIF=1.85)
I upload results of the correlation matrix and the Vif.
my interpretation is that there is no multicollinearity, because the correlations and the value of the Vif are low.
are there other tests to identify the presence of multicollinearity on STATA?
I read that eigenvalue analysis and standard error analysis might be useful, but I don't know how to interpret the results of these analyzes.
thank you for your attention and for your help to a STATATALIST neophyte

[Justin Niakamal]

A lot of texts will tell you to ignore multicollinearity, or at least not take it too seriously. You can fish around Statalist for a couple of examples or read this. Even if you were to concern yourself, your low VIFs suggest there isn't much problematic multicollinearity.

[FernandoRios]

Hi Simone
Perhaps there is a misunderstanding of what multicollinearity is. Unless your data is constructed to be completely independent from each other, there is ALWAYS some degree of multicollinearity.
What you need to ask yourself (review of the theoretical material) is "what are the consequences of multicollinearity?"
and second: how severe is multicollinearity in your data?

For most practical purposes, multicollinearity is not a problem you will need to put much attention unless you are facing (almost) perfect multicollinearity. In such cases, you will see that the model as intended cannot be estimated, or that it wont be estimated (some times with MLE models).
Other than that, i dont think there is a formal test of it in stata, but i do recall tests using the ratio between the highest and lowest eigenvalue of the X'X matrix.
Again, i should emphasize, this is not a problem you may need to address or discuss in most cases, and certainly not in your data (from the output you provide)/
HTH
Fernando

[Simone Guerriero]

thanks for your help. from the ratio of the highest eigenvalue (2.8353) and the last (0.1610) the result is 17.610559006211. How should I interpret it?
As for the analysis of standard errors to understand if there is a multicollinearity problem, how do you advise me to proceed? (i I read that I have to check for large standard errors. but in what way?
I attach the eigenvalue table and the standard errors table

[FernandoRios]

Hi Simone
Again, you do not have a problem of severe multicolinearity. I may even say not worth mentioning.

[Phil Bromiley]

I suggest that you search Stata list for some comments by Clyde on collinearity. You might also read Arthur Goldberger's econometrics text which has a chapter making fun of the idea of collinearity as an econometric problem.