Compare two coefficients in two different regressions

[Long Hong]

Dear all:

I would like to compare the coefficients generated by two different regressions (in two subsamples).

A simple example of Stata codes looks like the following:

xtreg yvar xvar i.year if age >= 60, fe vce(cluster id)
xtreg yvar xvar i.year if age >= 65, fe vce(cluster id)

Let beta1 and beta2 be the coefficients of xvar in model 1 and model 2, respectively.
I am wondering if there is a simple way to check whether beta1 and beta2 are statistically different.

Thank you very much and I look forward to hearing from you!

Best regards,
Long

[Clyde Schechter]

No, and this sort of thing typically is not done. The problem is that your regressions are based on two subsets of the data which are not complementary. Rather, the second is a subset of the first. Statistical comparisons are usually done between disjoint subsets, not overlapping ones.

It would be better to compare a regression -if age >= 60 & age < 65- with a regression -if age > 65 & !missing(age)-. Those are complementary subsets. The way to do that is illustrated in many threads on this Forum with titles similar to this one.

[Long Hong]

Thank you !

My goal is to see if the coefficients are sensitive to different sample selection.
I am wondering if the best alternative is to simply look at the coefficients and see if they are similar instead of doing any formal test.

Best,
Long

[Clyde Schechter]

I am wondering if the best alternative is to simply look at the coefficients and see if they are similar instead of doing any formal test.

That is what I would do. The concept of significance testing is held in disrepute by the American Statistical Association. See https://www.tandfonline.com/doi/full...5.2019.1583913. But even if you disagree with that reasoning and still favor the use of statistical significance testing in some circumstances, the circumstance you describe is one where it really has no role in any case. First, as I have indicated, there really isn't any way to do a significance test comparing a subset to a superset: you have to compare the subset to the complementary subset. Second, if you could do the subset:superset comparison directly, it would be confounded by the different sample sizes!