Collinearity between edu and edu square

[Kusha Verma]

Hello,
I am trying to run a modified version of the Mincer equation that includes education square as an independent variable. The variable 'education' is defined as a categorical variable that divides the dataset into 7 educational categories.

When I run a basic OLS regression, stata drops edu square due to collinearity.
According to me, centering does not seem a solution to the problem as it will alter the values of the 'education' variable, that have a unique interpretation.

Following is the equation:

reg logincph i.edu edu_sq exp exp2 if sex == 0
reg logincph i.edu edu_sq exp exp2 if sex == 1

Any help on possible solutions is greatly appreciated,

Thanks,

Kusha

[daniel klein]

I think this is more a theoretical problem than a technical one. How would you interpret a squared term of a categorical variable of nominal type?

Best
Daniel

[Richard Williams]

It is questionable to square education if it is categorical. But if you are going to treat it as continuous, be consistent and don't use i.edu.

reg logincph edu c.edu#c.edu exp c.exp#c.exp if sex == 0

Or, leave it as categorical and forget about the squared term

[Richard Williams]

This handout offers ideas on what to do with ordinal independent variables:

https://www3.nd.edu/~rwilliam/stats3...ndependent.pdf

[Bruce Weaver]

I'm not an economist, and had never heard of the Mincer equation. But Googling it took me to this Wikipedia page. Judging from what I see there, I don't understand why you are treating education as categorical, or why you are squaring it. The Wikipedia page shows that only years of experience ought to be squared. It looks like you've also omitted the log of I think you want code more like this:

regress logincph edu exp##exp if sex == 0
regress logincph edu exp##exp if sex == 1

And you may wish to include sex and its interaction with the other variables in a single model, like this:

regress logincph sex##(edu exp##exp)

This allows you to compare the male & female values of the other coefficients.

HTH.

[Richard Williams]

When using # or ##, don't forget to use c. If you want the var treated as continuous, e.g. c.exp##c.exp

[Bruce Weaver]

Good catch, Richard. Correction to the code I suggested in #5:

regress logincph edu c.exp##c.exp if sex == 0
regress logincph edu c.exp##c.exp if sex == 1
regress logincph sex##(c.edu c.exp##c.exp)

[Richard Williams]

As a sidelight, if I ruled the world the default for all variables would be c. (Continuous) and i. Would be used as necessary. Then c. Wouldn't even be necessary. But I suspect there are some sort of historical reasons Stata did it the way it did.