Test with weighted regression

[Ann Jun]

I am running a simple weighted regression as follows:

reghdfe y i.treatment [weight=size], noa vce(robust)

My treatment variable has 4 categories, and I would like to test if the pairwise mean differences in y are different for each of the pairs (1 vs. 4, 2 vs. 4, etc.). Normally, I would do something like this:

test 1.treatment = 2.treatment

I am wondering if this command is still valid with weighted least squares. If not, is there another way to do this test?

[Clyde Schechter]

Yes, it is still valid with a weighted regression. The test is calculated by calculating the difference 1.treatment-2.treatment and its standard error from linear transforms of the coefficients and their covariance matrix. The coefficients and covariance matrix were estimated in a weigh that accounts for the weighting, so this carries through to everything calculated from them.

[Joro Kolev]

Clyde answered your question regarding the weighting.

Regarding your tests, note that you can do them pairwise, or you can do a joint test whether all treatments are the same. Both of these tests make sense in your set up.