Dropping variables in regression due to collinearity

[HeeSung Kim]

Dear Statalisters,

I've encountered an interesting result when I was performing two following regression:

regress y var1 var2, r
regress y var1* var2*, r

where var1* is the growth of var1, and var2* is the growth of var2, defined by var1* = (var1/var1[_n-1]) - 1.

var1 and var2 is related as following: var1 = var3 - var4 and var2 = var3 - var5.

When I run the aforementioned regression, Stata drops var1* in the second regression, but Stata does not drop var1 nor var2 in first regression. I understand that Stata randomly drops a variable that contains the same information because of collinearity, but I don't understand why the variable is dropped only for second regression.

Does anyone have any insights into why Stata is behaving in this way? Thank you so much in advance!

Regards,
Hee Sung

[Nick Cox]

1. var1* is legal Stata syntax for any (all!) variables whose names begin with var1. But you would not be allowed to use the asterisk * in an individual variable name, precisely because of this syntax.

2. "Drop" here is better phrased as "omit".

2. is just a matter of phrasing, but 1. could be part of your problem here. I find it hard to make sense of the question here because it's not clear exactly what you typed, nor is there a data-based example.

[Nick Cox]

Cross-posted at http://stats.stackexchange.com/quest...ticollinearity

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[HeeSung Kim]

Dear Nick,

I'v sorry for the lack of clarity on this question. I've changed the variables names on the example above, just to make it general, and it is not the actual name of the variables in the data.

I agree that I should have used the word "omit" instead of "drop". I couldn't find anyway to edit my previous post, so if you would like it to be edited, let me know how I can do that.

I couldn't post the data example here, nor come up with minimal working example because I couldn't recreate such problem generally.

Let me try to describe the problem in detail here:

I have two models, as following:

regress y x1 x2 x3 x4 ... x13 i.year, r
regress y v1 v2 v3 v4 ... v13 i.year, r

where the y is measured in growth, and v1 is the growth rate of x1.

There are two independent variables, x1 and x2, that are linearly correlated, and their relationship is as following:

x1 = w3 - w4
x2 = w3 - w5

Interestingly, I'd think that first regression will encounter multicollinearity problem, since they are measured in level, and x1 and x2 is linearly related in level, but only second regression omitted variables due to multicollinearity problem. I believe that all x1 ... x13 are correlated, but none are perfectly correlated. Same goes for the relationship between w4 and w5.

What could be the possible reason why Stata will only drop variables in the second regression and not the first?

[HeeSung Kim]

After looking into this issue, I've found another interesting property in this problem. I've tried to see if v1 is a linear combination of all the other variables, and as suspected, it is. However, x1 is ALSO a linear combination of all the other variables, but Stata has not dropped x1. I suspect that it is dependent on how Stata omits variables that are correlated. Any insights as to why Stata is behaving in such a way?